Modeling NPP and NDVI time series in different bioclimatic regions of Iran

Modeling NPP and NDVI time series in different bioclimatic regions of Iran | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Modeling NPP and NDVI time series in different bioclimatic regions of Iran Fahimeh Sayedzadeh, Saied Soltani, reza modarres This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4600410/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Nov, 2024 Read the published version in Environmental Monitoring and Assessment → Version 1 posted 9 You are reading this latest preprint version Abstract Vegetation is one of the important components of ecosystems that usually changes seasonally. An accurate parameterization of vegetation cover dynamics by developing time series models can strengthen our understanding of vegetation change. This research is aims to investigate and model the temporal changes of Net Primary Production (NPP) and Normalized Difference Vegetation Index (NDVI) across bioclimatic regions of Iran, including the Khazari, Baluchi, semi-desert, steppe, semi-steppe and Arid forests. We used Moderate Resolution Imaging Spectroradiometer (MODIS) sensor products for NPP and NDVI time series (MOD17A2 and MOD13Q1, respectively). The SARIMA (Seasonal Autoregressive Integrated Moving Average) time series model is developed for NPP and NDVI time series. The investigation of Auto Correlation Functions (ACF) showed a strong seasonality in NPP and NDVI at the 12-month lag time. Comparing the lag times from 1 to 24 month for different regions shows that the NPP variable has a stronger seasonality. The evaluation of error criteria showed NPP time series models based on RMSE, R 2 , MRE, and CE criteria was better, while based on the ME criteria, the models performs better for NDVI time series (For example, in Khazari region for NPP and NDVI time series respectively, ME = 3.67, 0.05, RMSE = 0.12, 0.18, R2 = 0.87, 0.63, MRE = 0.02, 0.12, and CE = 0.84, 0.12). The selected models provided a short-term forecasting of the NPP and NDVI index for study regions at 24-month time, that useful for the planning and management to reduce vegetation degradation and preserve ecosystem and biodiversity. Autocorrelation function vegetation cover seasonal change SARIMA models forecast Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction The atmosphere, soil, and water are linked by vegetation, in turn facilitate flow of energy and materials cycling by photosynthesis (Han and Song, 2022 ). Vegetation alteration serves substantial index for climate change of region and anthropogenic functions due to the integrated impacts of biological and non-biological pathways (Bégué et al., 2011 ). From aforementioned point of view, tracking dynamism of vegetation serves vital to figure out biological and chemical pathways and their intrinsic interaction on the climatic system (Arneth et al., 2010 ), can enhance potential for forecast, reduce as well as coping with further weather variations (Sitch et al., 2008 ; Zhang et al., 2017 ; Zhao et al., 2017 ; Bai, 2021 ). The limitation and low accuracy of field data can lead to problems in vegetation monitoring and prediction, thus, the use of remote sensing indicators can be useful for monitoring ecological processes. The Normalized Difference Vegetation Index (NDVI) is a remote sensing method to assess plant greenness which is related to structural properties and vegetation productivity. (Forkel et al., 2013 ). This index was developed for studying vegetation characteristic and has the ability to determine vegetation and vegetative stress (Huang et. al., 2021 ). Analysis of NDVI are widely used to monitor temporal and spatial dynamics of vegetation (Busetto et. al., 2008 ). Net Primary Production (NPP) is level of organic matters generated via photosynthesis in absence of autotroph respiration being considered as the net rate of organically matters consolidated through vegetation by photosynthesis (Sun et al., 2021 ). NPP supports a wide range of ecosystem services, including forage production and soil carbon sequestration (Frank et al., 2012; Penner and Frank, 2021 ). NPP depends on different factors such as temperature, humidity, the amount of nutrients in the soil, etc., and is significantly affected by climate change. It is a measurement of ecosystem performance as well as a key indicator of ecosystem health (Wilcox et al., 2020). Monitoring and predicting NPP changes is essential to assess ecosystem performance. Xing et al ( 2010 ) simulated the net primary production of meadows in Asian north east by data of MODIS since 2000 to 2005 and improved CASA model. They showed that grasslands NPP closely correlated to rainfall and heat indicating climate change affects the grassland NPP (Xing et al., 2010 ). Liu et al ( 2015 ) investigated the variations of NPP and their association with climatic parameters given the converting various scaling within Gansu in China. The result expressed that the NPP values have been decreasing. The forestlands and grasslands ecosystems were affected majorly through heat, whereas rainfall considered the primary determinant parameters in the deserts and farmlands biomes annually. In comparison to the forests and deserts ecosystems, the grasslands and farmland biomes indicated time-lag as well as incremental associations with rainfall and temperatures, respectively (Liu et al., 2015 ). Hao et al ( 2022 ) indicated that NPP has a limiting function on marine ecosystems services within the alpines ecosystems of Qinghai, China. They concluded that a suitable adaptations of aerial vegetation exposing to climate change can deteriorate the limiting impact of NPP on the marine ecosystems services together with achieving interaction of various ecosystems services, hence conserving marine ecosystem services as well as enhancing sustainable development in the alpines ecosystems (Hao et al., 2022 ). The data of time series offer a strong method to acquire from last occurrences, track present situations, and prepare for future change (van Leeuwen et al., 2006 ). Contrasting present vegetation information along with past long-run means have been utilized to enhance ecosystems tracking (Orr et al., 2004 ). There are many time series models that have different applications. Hipel and McLeod (1994) considered ARMA class models to be suitable for describing hydrological and environmental datasets and showed that ARMA models have the ability to predict environmental time series and perform better than other models (Piwowar and Ledrew, 2002 ). Recently, models of times series including Autoregressive-moving average (ARMA) time series were considered to track ecological and environmental variables. ARMA models have been used by many researchers. Fernandez Monso et al. (2011) used ARIMA analysis and regional scale climate data to predict NDVI (Normalized Differential Vegetation Index) in areas with conifers species. They used the time series of NDVI index extracted from NOVA AVHRR in the period from 1993 to 1997 as well as SARIMA (Seasonally Auto Regressive Integrate Moving Averages) model. They showed the relationship between NDVI and rainfall in some conifer species using climate time series and dynamic model analysis and predicted NDVI values for the near future in Castile and Leon, Spain and they concluded that time series models could be used for vegetation monitoring at regional level (Fernandez Monso et al., 2011). Muti et al (2019) conducted a study for NDVI predicting using MODIS MOD13A2 product and concluded that the predictions for a future seasonally periods considered acceptable showing the model is a tool to monitor short-term vegetation conditions. Salaberria et al ( 2019 ) modeled the aboveground primary net productions (ANPP) of an Atlantics mountainous meadow in terms of the times series method. They modeled the monthly data of ANPP in the period from 2006 to 2008 using the models of incremental smoothing approach and ARIMA model. They result showed two approaches can generate insufficient predictions given the existence of pronounced locally characters (new outliers) in our relative low time-series data. Nevertheless, advantageous data to an initiative grazing management was indicated (for example the existence of yearly changes in ANPP, as well as discrepancies between the graze and exclusions treatment) (Salaberria et al., 2019 ). Said Ommar and Kawamukai (2021). predicted NDVI by used the Holt- Winter and SARIMA models in an dry area within Kenya, and concluded that Holt-Winter model has better predictions than SARIMA models for 600 ✕ 600 pixels (Said and Kawamukai. 2021). Tian et al. ( 2016 ) using ARIMA models, forecasted drought based on Vegetation’s Temperatures Conditions indicator in the plain of Guanzhong and they showed that models of ARIMA can be predict class and extend of dry seasons as well as they may be used to predict dry seasons in plains (Tian. et al. 2016). Based on literature review, no study has been carried out to investigate the changes in vegetation cover over time in various ecosystems in Iran. Considering that Iran has different bioclimatic areas with diverse vegetation, it seems necessary to implement a research to investigate the changes of vegetation over time in Iran. Therefore, the current research was performed with the aim of modeling the variation in Net Primary Production (NPP) and NDVI time series across Iran's bioclimatic regions and also to compare the stochastic behavior of them in these bioclimatic regions. 2. Materials and Methods 2.1. Study area Iran is placed in the semi-tropical high-pressured spot of the north hemisphere in coordinates of 24° and 40° N, and44° and 64° E (Ghadamii et al. 2020). The estimated areas of Iran are 1,873,959 km 2 characterized by a topographical limits of − 26 to 5610 m AMSL. Whereas large part of Iran is plain, two big mountainous belts are located in the northern (Alborz Mountains) and western (Zagrus Mountains) areas. As such both mountain areas prelude humidity to arrive Iran centers, both big and locally atmospherically systems influence Iran’s weather (Fathian et al. 2022). Around 75 percent of Iran placed in dry and semi-dry areas. The annually rainfall is 2000 mm/year in the southern coastal areas of the Caspian Sea and lower than 50 mm/year in the central desert, southern and eastern points of the Iran (Fathian et al. 2020). This research considers the classification of Iran's bio climatically areas introduced by Pabot ( 1967 ). Pabot classified Iran into 3 main floras, namely the Baluchi, Khazari and Iran-Turani floras. Flora of Iran-Turani was also divided in 5 semi-regions including semi-desert, steppe, semi-steppe, dry forest and elevated mountain. In this research, bioclimatic regions of Baluchi, Khazari, Semi-desert, Steppe, Semi-steppe, and Dry forests was selected (Fig. 1). These regions were chosen in the climatic regions due to the appropriate distribution across the country. In the following, we describe the bioclimatic characteristics of each region in more details. 2.1.1. Khazari flora The average annual rainfall is 600–2000 mm in this region, where the minimum rainfall is observed in June while the maximum rainfall happens in autumn. There is no significant dry period, and the relative humidity is generally more than 80%. This flora includes many species of the temperate region of Europe, basically a forest where trees and shrubs species are dominant in this region. The main tree species of this flora are Quercus castanefolia , Buxus sempervirens and etc . 2.1.2. Baluchi flora This region is similar to the sandy and subtropical desert climates. Amount of yearly rainfall is lower than 300 mm and the winter season is the wet period while dry spell lasts for 6 to 8 months. However, its relative humidity is high (60 to 80 percent). The most important trees and shrubs in this climatic region are Acasia Arabica , Prospis spisigera , Ziziphus spina-christi , and Phoenix dactylifera . The annual species which are observed in this area are mainy growing in winter. All perennial grasses are specific to warm regions, especially Paniaceae and Andropogonacea . There are plenty of permanent and perennial legumes and most of them are specific to subtropical regions such as Taverniera, Indigofera, Tefrosia, Cassia, Crotalaria, Caragana and Rhynchosia. 2.1.3. Semi-desert flora This is the driest part of Iran being located in the central plateau of Iran where the annual rainfall is less than 100 mm. In the central desert of Iran, it is possible to find a series of scattered vegetation, but many areas are devoid of any vegetation cover due to human interventions and the accumulation of large amounts of saline soils and the development of sand dunes. Most of the species in this area are salt-resistant spinach such as Halocnemum strobilaceum , Salicornia herbacea , Seidlitzia rosmarinus and Salsola varieties. 2.1.4. Steppe In this flora, the annual rainfall varies 100 to 200 millimeter on southern point to 230 millimeters in the northern direction. Annual plant is abundant in this area and Artemisia harba-alba is the typical species of this flora. Aristida plumose is also an important grass in the steppe region. 2.1.5. Semi-Steppe The annual rainfall in this region varies between 200 to o 450 mm depending on the region. The herbaceous flora is much richer than the steppe region and the families such as Labiatae , Compositae , Cruciferae , Caryophyllaceae, Papilionaceae , Umbelliferae , Graminaceae and Borraginaceae are commonly observed. In this region, two species of Amygdalus (A. scoparia, A. horrida) are found on rocks and hill slopes. The pastures of the semi-steppe region are considered to be among the most valuable pastures in Iran (Pabot 1967 ). 2.1.6. Arid forests This region is located along the Zagros mountain range covering the slopes of south and east Alborz and areas into highlands in the northwest. The average height of this area is between 800 and 2600 meters with the annual rainfall more than 400 mm. Zagros forests are mainly composed of Quercus persica . Hordeum bulbosum and Poa bulbosa and are among the most far-reaching perennial grasses while there are different species of Stipa or Agropyron and a few legume species. Labiatae and Compositae family plants often make the majority of vegetation species (Pabot 1967 ). 2.2. Data 2.2.1. NDVI and NPP time series The NDVI time series based on the products of Moderates Resolutions Image Spectroradiometers (MODIS) sensor (MOD13Q1) attained of the NASA Lands Process Distribute Actives Archives Centers (LP DAAC), USGS/Earth Resource Observations and Sciences (EROS) Centers ( www.lpdaac.usgs.gov ). This dataset consists of 16-Daily images at a spatial resolution of 250 m and HDF format. Totally, 1055 pictures utilized for a duration of eighteen years, from Feb 2000 to Sep 2018. In order to build monthly time series of NDVI from the 16-day products of the 13Q1 data series, we carried out the following steps. The images were cut based on the polygons specified in the studied bioclimatic areas in the ArcMap. After that, the average NDVI values were calculated for each region. Finally, the average of the two images was placed as monthly NDVI values. The NPP data was obtained from products of MODIS sensor (MOD17A2). These data had monthly temporal resolution, spatial resolution of 1.1 km, and HDF format. The MOD17A2 products are available from the https://neo.gsfc.nasa.govwebsite . MOD17A2 series has monthly products and in order to obtain NPP time series the images were cut based on the polygons of the studied areas in the ArcMap and finally the monthly NPP time series from 2000 to 2016 were extracted. 2.3. Time series modeling A times series is defined as group of quantitative observation arranged within chronological order (Kirchgässner et al., 2013). Times-series predicting has great contributions in scientific contexts. (Aggrawal et al. 2020). In this study, Autoregressive-moving averages times series models (Box-Jenkins ,1970) are developed to model NDVI and NPP time series. These models include Autoregressive (AR) or Moving averages (MA) models or an integration of the both, i.e. ARMA. ARMA models are used once processes lies in equilibriums around consistent average levels that at the same time called stationaries. Some of times series show non-stationaries manner and are constant around a constant average, in these cases ARIMA and SARIMA models were considered (Tian et al. 2016 ). In addition, some of the time series such as vegetation or rainfall, having the characteristic of seasonality which allows to include seasonal differences in a SARIMA (Seasonal ARIMA) model. SARIMA models are displayed as SARIMA(p,d,q)(P,D,Q)S, so that p and q are the magnitude of AR and MA parameters, respectively; d is the magnitude of non-seasonal difference applied in series in order to attain constancy. P, D and Q are, respectively, the orders of SAR and SMA seasoned parameters and seasonal variations used according to the seasonal duration S. The simple relation for the SARIMA model serves as follows: $${\varphi }_{\rho }\left(B\right){{\Phi }}_{P}\left({B}^{S}\right){\nabla }^{d}{\nabla }_{S}^{D}{Y}_{t}={\theta }_{q}\left(B\right){{\Theta }}_{Q}\left({B}^{S}\right){\epsilon }_{t}$$ 1 so that Y t is the seen times series in a specific duration t with seasonal duration S, ε t is the residuals of the model at time step t. B is a non-seasonal backward operator and B s is the seasonal backward operator. The ϕ p and ϴ q are non-seasonal autoregressive and moving average parameters, respectively, Ф P and Θ Q are seasonal autoregressive and moving average parameters, respectively. The Box-Jenkins time series modeling has three steps including model identification, parameter estimation, diagnosis and model validation. The first step in time series modeling is to identify the order of the model based on the characteristics and behavior of the time series which involves choosing the difference parameters d and/or D to achieve data stationary, and model ranks comprising p, q, P and Q through the analysis of autocorrelations function (ACF) and partial autocorrelations function (PACF) of differential series. Autocorrelation function is one of the characteristics of time series that shows the degree of linear correlation among components of times series. The autocorrelation coefficient between Z t and Z t+k is in the form of the following equation: $${p}_{k}=\frac{{Y}_{k}}{{Y}_{O}}=\frac{Cov({Z}_{t}. {Z}_{t+k})}{\sqrt{Var({Z}_{t}})\sqrt{Var\left({Z}_{t+k}\right)}}$$ 2 The partial autocorrelation function is also an important characteristic of time series and is calculated from the following equation: $${\phi }_{kk}= Corr\left({Z}_{t}. {Z}_{t+k}/{Z}_{t+1}\dots . {Z}_{t+k-1}\right)$$ 3 In parameter evaluation stage, magnitude of model parameters is specified and then estimated. The second step of time series modeling is parameter estimation. When model was experimentally recognized, variable should effectively evaluated, as well as fitting measured, majorly through an analyses of residual, for assessing if it may be considered as a good approximation of the series (Anderrson 1977). The third step in modeling is the model validation. Ultimate part of the Boxes-Jenkins cycles is expose the recognized and evaluated models for "diagnostics check" of its sufficiency. Here, the residuals of the model should have a normal distribution and do not show significant autocorrelation structure (Anderson 1977 ). At this stage, the independence of residuals is checked by drawing the ACF diagram and the normality of the residuals is checked by the Kolmogorov-Smirnov normality test or the quantile-quantile plot of the residuals. 2.4. Out-of-sample forecasting Time series models are capable of forecasting a variable in n-step ahead lead time. Here, to show the capacity of the selected models for forecasting NPP and NDVI, we keep two years monthly NPP time series (from January 2014 to December 2016) and NDVI time series (from January 2016 to December 2018) for evaluating outlirers samples predicting performance. The outlier sample forecasting times series Z t of the whole ARIMA ( p, d, q ) process is calculate from the following equation: $${\phi }_{p }\left(B\right){\left(1-B\right)}^{d}{Z}_{t}= {\theta }_{o}+{\theta }_{q}\left(B\right){a}_{t}$$ 4 Wherein θ is naturally 0 in case d ≠ 0 as well as associated to average µ of the series once d = 0, φ p , ( B ) = (1 – φ 1 B - ⋯ -φ p B p ), θ q ( B ) = (1 - θ q ( B ) = 0 has different root which placed out of the united circles, and series a t is a Gaussians N(0, \({\sigma }_{a}^{2})\) whites noises processes (Wei 2013 ). 2.5. Model evaluations For evaluating the efficiency time series model, different performance criteria such as Means Relatives Errors (MRE), Root Mean Squared Error (RMSE), Mean Error (ME), Coefficients of Efficiency (CE), and R-squared (R 2 ) are applied. The equations of these relationships are given follow. ME indicates alignment among estimated and modeled dataset. The values of ME are unlimited as well as for a complete models finding is 0. ME= \(\frac{1}{n}\sum _{i=1}^{n}({Q}_{i}-\widehat{{Q}_{i}})\) (5) The RMSE values were calculated using the following equation: RMSE = \(\sqrt{\frac{\sum _{i=1}^{n}{\left({Q}_{i}-\widehat{{Q}_{i}}\right)}^{2}}{n}}\) (6) The model obtained from this relationship is non-negative having no higher bound, and given complete models, findings is 0. MRE includes average of errors generated than the estimated one. The values obtained from this metric are unlimited, and given perfected model, findings are 0. It is susceptible to prediction error which occurs in the low(er) magnitude of every dataset. The MRE values computed by below equation: MRE = \(\frac{1}{n}\sum _{i=1}^{n}\left(\frac{{Q}_{i}-\widehat{{Q}_{i}}}{{Q}_{i}}\right)\) (7) CE allows errors and differences to be weighted more appropriately through the use of absolute values. CE values are variable from zero to one, and the most positive value indicates the best model. The CE values were calculated using the following equation: CE = 1- \(\frac{\sum _{i=1}^{n}{\left({Q}_{i}-\widehat{{Q}_{i}}\right)}^{2}}{\sum _{i=1}^{n}{\left({Q}_{i}-\stackrel{-}{{Q}_{i}}\right)}^{2}}\) (8) R 2 shows ratio of totally variances in the estimated data series which may be assessed through the models. Its values are variable from zero (poor model) to one (perfect model). The R 2 values were calculated using the following equation: R 2 = \({\left[\frac{{\sum }_{i=1}^{n}\left({Q}_{i}-\stackrel{-}{Q}\right)\left(\widehat{Q}-\stackrel{\sim}{Q}\right)}{\sqrt{\sum _{i=1}^{n}{\left({Q}_{i}-\stackrel{-}{Q}\right)}^{2}}\sum _{i=1}^{n}{\left({\widehat{Q}}_{i}-\stackrel{\sim}{Q}\right)}^{2}}\right]}^{2}\) (9) In these equations, \({Q}_{i}\) is the observation value, \(\widehat{{Q}_{i}}\) is the model estimation \(\stackrel{-}{\text{Q}}\) is the average of the observations, and \(\stackrel{\sim}{Q}\) is the average model estimation and n considered numbers of observation and model estimation (Dawson et al. 2005). The same performance criteria are also calculated for the forecasting period to check the accuracy of the selected models in forecasting NDVI and NPP. 3. Results and Discussion 3.1. Exploratory Data Analyses According to NPP time series (Fig. 2 ) for different regions, it can be seen that the NPP has monthly fluctuation. In addition, the time series looks stationary during the data record as they do not show a significant increasing or decreasing trend. The NDVI times series are also shown in Fig. 3 for different bioclimatic regions. Almost all time series have no significant change, except for the Khazari (in Jan 2008) and Semi-Steppe (in Jan 2008) regions which indicate a breakpoint in the time series structure. To show the seasonal characteristics of NPP and NDVI, boxes plot of monthly NPP and NDVI shown in Figs. 4 as well as 5, respectively. Each box plot contains annual data for each month during record period. We can observe in the NPP time series that the seasonal patterns in Semi-Desert, Arid Forest, Steppe, and Semi-Steppe regions are similar, while Baluchi and Khazari regions show different seasonal patterns which due to the different climate of these areas. The box plot of the NDVI index shows that the seasonal patterns in the Arid forest, Steppe, and Semi-Steppe regions were similar. Again, the Baluchi and Khazari regions have different seasonal patterns. Semi-Desert region did not have distinct seasonal patterns (Fig. 5 ). The seasonal average NPP and NDVI time series are also provided in Tables 1 as well as 2, respectively. As it is shown the average NPP in Khazari region is highest in May. This amount is observed for the Baluchi region in February, for the semi-desert region in March, for the steppe region in April, for the semi-steppe region in February, and for the Arid forest region in April (Table 1 ). In cold regions, the maximum NPP is observed in spring, and in warm regions the maximum NPP is observed in winter which is due to the presence of suitable conditions for plant growth in these seasons. The minimum amount of NPP is observed in Iran's Turani flora regions (semi-deserts, steppe, semi-steppes, and dry forests) in early summer as well as July that related to summers hydrated deficits duration, that leds to dry in farmlands vegetation biomasses (zoffuli et al., 2008)., in the Khazari region in winter and February related to vegetation inaction, and within Baluchi region in late spring and May due to dryness and high temperature in this month (Table 1 ). Table 1 Monthly average NPP (kg/ha) during 2000 to 2016 for different bioclimatic regions (Bold values show maximum and italics are the lowest NPP (kg/ha) for each region) Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec Khazari 45.43 51.98 70.81 106.98 135.2 126.09 102.74 76.80 95.50 84.33 61.65 45.57 Baluchi 39.30 40.42 32.84 22.82 16.60 16.21 17.24 18.87 20.55 23.87 31.55 34.94 Semi-desert 6.59 7.05 7.65 7.23 5.71 4.32 3.92 4.42 5.53 6.68 6.97 6.50 Steppe 20.32 22.16 25.93 28.37 23.68 18.04 15.64 17.18 20.78 23.00 22.46 20.37 Semi-Steppe 43.40 48.03 47.96 44.84 39.37 31.14 26.73 27.51 31.46 35.46 40.17 39.87 Arid forest 39.63 44.80 59.45 76.20 64.18 34.25 22.35 24.93 37.34 43.04 44.30 39.42 The average NDVI from 2000 to 2018 for different months Table (2) showed that the Khazari regions, Semi-Steppe and Arid Forests have a distinct seasonal pattern. This attributed to the great variations in rainfall as well as heat among the seasons in these areas. In the semi-desert region, there is no difference in the amount of NDVI in different months, may be due to the limited moisture of plant growth throughout the year. The seasonal pattern in Baluchi and Steppe regions are not significant either because the rainfall in the wet season is very low and does not create a big difference between different seasons. Table 2 Monthly average NDVI during 2000 to 2018 for different bioclimatic regions (Bold values show maximum and italics are the lowest NDVI) Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec Khazari 0.25 0.25 0.31 0.41 0.46 0.45 0.45 0.43 0.43 0.43 0.35 0.30 Baluchi 0.08 0.08 0.09 0.07 0.07 0.07 0.06 0.07 0.07 0.07 0.07 0.08 Semi-desert 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.08 stepp 0.10 0.10 0.11 0.12 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 Semi-Stepp 0.14 0.16 0.18 0.18 0.16 0.14 0.13 0.13 0.13 0.13 0.13 0.14 Arid forest 0.16 0.18 0.25 0.32 0.28 0.21 0.18 0.18 0.17 0.18 0.19 0.18 3.2. Time Series Modeling 3.2.1. Autocorrelation Structure Examining the ACF and PACF functions makes it possible to understand how the time series behaves in stationarity and seasonality. If ACF decreases gradually, the time series is non-stationary; if ACF decreases suddenly, the times series is constant. Before developing times series models, the behavior of ACF of NPP and NDVI time series are examined to compare the different stationary and non-stationary characteristics of them. For NPP times series, in lag-1autocorrelation, the autocorrelation value has high in all regions (0.6 to 0.8). That high lag-1autocorrelation for the Khazari and Semi-Steppe regions is most probably due to relatively continuous seasonal rainfall throughout the year and, despite the low annual rainfall (around 100 mm) in Baluchi, Semi desert and Steppe regions, they have high autocorrelation (about 0.7). In Baluchi region it is probably due to the presence of rich annual species and in Steppe region it is due to the existence of irrigated agricultural plains in some regions, such as Khuzestan province. In Semi desert region it can be due to the uniform environment, permanent lack of water, and vegetation adapted to these conditions. The yearly precipitation of Arid Forest area is high (around 600 mm) and it has suitable conditions for the growth of plants, but it has a lower autocorrelation value compared to drier regions which this can be due to large differences in temperature and precipitation between seasons (Fig. 6 a, b, c, d, e, f). Considering that the autocorrelation value has suddenly decreased in all regions, it indicates the stability of NPP time series in all studied regions. All study regions have a 12-month periods regular seasonal patterns (Fig. 6 a, b, c, d, e, f). In the semi-steppe and Bauchi regions, there is also a strong autocorrelation in 6-month periods, that is due to the growth conditions of plants due to suitable temperature and autumn rains (Fig. 6 b, e). The Arid Forest region has the different autocorrelation pattern. Many changes in this region can be due to climatic variations and the destruction of forest trees by humans and diseases such as Loranthus (Javanmiri pour et al. 2022) (Fig. 6 f). For the NDVI time series, in 1-month lag the ACF was 0.55 to 0.83. The Khazari regions has maximum autocorrelation (0.83) and Semi steppe region has minimum autocorrelation (about 0.55). In the Semi-Desert region, despite the inadequate environmental conditions for plant growth, ACF is higher (about 0.8) than the Semi-Steppe and Arid forests regions, which can be due to the presence of plant species adapted to dry environments (Fig. 7 a, c, e, f). Since the ACF has suddenly decreased in Steppe, Semi steppe and Arid forest regions, it shows the stability of NDVI time series in this regions, and the ACF decreases gradually in Khazari, Baluchi and Semi desert was indicating non- stability (Fig. 7 a, B, C, D, E, F). Time series of the Khazari, Baluchi, steppe, Semi-Steppe and Arid forests regions had periodic changes of 12 months. This is indicating that the annual cycle of vegetation phenology affects the NDVI. The semi-desert region had weak seasonal behavior which can be due to the very low vegetation cover in this area (Fig. 7 a, b, c, d, e, f). Comparing the lag times from 1 to 24 month for different regions shows that the NPP variable has a stronger seasonality than the NDVI (Fig. 8 ). In NPP, the maximum value of ACF is observed at the 12-month lag time while for NDVI it is observed at the 1-month lag. However, the ACF value at lag12 is also high for NDVI time series indicating significant seasonality. Figure 8 also indicates that the range of autocorrelation coefficients is higher for NDVI time series comparing NPP time series which shows a distinct diversity between bioclimatic regions. 3.2.2. SARIMA Models As the ACFs of NPP and NDVI show significant seasonality, the Seasonal ARIMA model seem to be appropriate. To fit the SARIMA model to the NPP and NDVI time series, regarding the seasonal non-stationary behavior of the time series, seasonal differentiation (D = 12) is considered. For the all-time series, different models with different magnitudes of non-seasonally and seasonally autoregressive as well as moving averages are investigated with and without non-seasonal differentiation. Finally, the best model was selected regarding minimum AIC criteria and no autocorrelation in the residuals the time independence of the residuals is checked using the ACF diagram in residuals. Normality of residual is also controlled through Q-Q plot diagram for NPP (Fig. 9 ) and NDVI (Fig. 10 ). Given model adequacy, the best SRIMA models for NPP and NDVI in each region is selected (Table 3 ). Table 3 The selected SARIMA models for NPP and NDVI time series in all regions NDVI series NPP series Khazari SARIMA(0,1,1)(0,1,1) 12 SARIMA(1,1,1)(1,1,1) 12 Baluchi SARIMA(1,1,1)(0,1,1) 12 SARIMA (1,1,1)(0,1,1) 12 Semi-Desert SARIMA(0,1,1)(1,1,1) 6 SARIMA (1,1,1)(0,1,1) 12 Steppe SARIMA(1,1,1)(0,1,1) 12 SARIMA (1,1,1)(0,1,1) 12 Semi-Steppe SARIMA(0,1,0)(0,1,1) 12 SARIMA (1,1,1)(0,1,1) 12 Arid forest SARIMA(0,1,0)(0,1,1) 12 SARIMA (1,1,1)(0,1,1) 12 In order to check the efficiency of NPP and NDVI time series perdition, the error criteria are calculated (Table 4 ). These criteria show that the models for the NPP time series have more accuracy than NDVI time series based on RMSE, R 2 , MRE, and CE criteria, while based on the ME criteria, the models perform better for NDVI time series. Given that the difference between the minimum and maximum values in the variable NPP is greater and the ME criterion cannot weight the minimum and maximum values, this criterion is not suitable for the NPP time series models. The selected models for Baluchi and Steppe regions which have less climate variability, have higher accuracy than the more humid regions (Khazari, Semi-Steppe, and arid forest). For Semi desert region, the selected model for NPP time series have more accuracy than the NDVI time series (Table 4 ). Table 4 Errors criteria for selected models in all region ME RMSE R 2 MRE CE NPP NDVI NPP NDVI NPP NDVI NPP NDVI NPP NDVI Khazari 3.67 0.05 0.12 0.18 0.87 0.63 0.02 0.13 0.84 0.12 Baluchi -1.23 0.01 0.13 0.23 0.91 0.99 -0.10 0.04 0.85 0.15 Semi-Desert -0.11 0.003 0.12 0.38 0.95 0.46 -0.02 0.04 0.93 -2.03 Steppe -0.55 0.01 0.17 0.005 0.93 0.82 -0.02 -0.03 0.95 0.66 Semi-Steppe 0.62 0.01 0.14 0.08 0.87 0.54 -0.01 0.09 0.90 0.31 Arid forest 0.61 0.04 0.12 0.22 0.89 0.46 -0.04 0.18 0.84 0.15 3.2.3. Out of-sample Forecasting Following specifying model as well as evaluating variables, next step is to evaluate the model's capability in out-of-sample forecasting between 2015 to 2016 for NPP and between for 2017 to 2018 for NDVI. For the NPP variable, the data from 2015 to 2016 were used to evaluate the model's forecasting. In the Khazari region, the model is able to forecast the changes both in trend and quantity well, and only in May 2015, there is a significant difference in the forecasted trend and value, which may be due to the indiscriminate harvesting of wood and other unpredicted environmental factors. The proposed model in the Balochi region also forecasts the changes well, and only in June 2016, both in terms of trend and value, there is a significant difference between observations and forecasting. In the semi-desert region, the model is able to forecast the changes well regarding trends and values, and all points are within the 95% significance range. In the steppe, Semi-steppe, and Arid forest regions, the models have forecasted the NPP values and trends very well, and all points are within the 95% confidence range. Generally, the selected NPP time series models can correctly forecast the NPP changes in all regions (Fig. 11 ). We show the monthly observed and forecasted NDVI time series from January 2017 to December 2018 in Fig. 12 . This figure shows which elected models to NDVI times series in the Khazari region performs very well in forecasting NDVI and its tendency, as forecasts are within the 95% confidence interval. In the Baluchi region, only in September 2017, the observed value was outside the 95% confidence interval of the model. The proposed models in Semi-Deserts, Steppes, Semi-Steppes, and dry forest regions have predicted the tendency and data values very well, and the observed data were completely within the range of 95% predicted by the model. Muti et al. (2019) also stated that SARIMA modeling performed better in predicting dry seasons, where the variability of climate is less, and predicts variable values in wet seasons, where annual changes are higher (Muti et al. 2019). Fernández Manso et al. )2011(also and stated that the prediction of the selected models for the NDVI data series using SARIMA was acceptable. The performance criteria of the models in forecasting NPP and NDVI are presented in Table (5). The results of these criteria showed that for the NPP variable, the selected models for the semi-desert region performs better than other regions (R 2 = 0.94, RMSE = 0.12, ME = 0.05, MRE = 0.01, and CE = 0.91) and other regions also have acceptable accuracy. For the NDVI index, the selected models for the Arid forest region performs the best (R 2 = 0.87, RMSE = 0.22, ME = 0.044, MRE= -0.04, and CE = 0.86), and Khazari, Baluchi, and Steppe have acceptable accuracy, but the selected models for semi-desert and semi-steppe regions do not show high accuracy. In general, the results showed that time series modeling has a suitable capability for forecasting NDVI and NPP, and in all regions, the forecasted values are within 95% confidence. Table 5 Errors criteria for forecast models in all regions ME RMSE R 2 MRE CE NPP NDVI NPP NDVI NPP NDVI NPP NDVI NPP NDVI Khazari 3.67 0.05 0.13 0.19 0.86 0.62 0.02 0.14 0.85 0.11 Baluchi -3.23 0.01 0.12 0.19 0.91 0.57 -0.16 0.04 0.83 0.15 Semi-Desert 0.05 0.003 0.12 0.38 0.94 0.43 0.01 0.04 0.91 -2.03 Steppe -0.67 -0.01 0.17 0.004 0.92 0.80 -0.03 -0.03 0.93 0.60 Semi-Steppe 0.62 0.013 0.14 0.02 0.85 0.38 -0.01 0.08 0.87 0.24 Arid forest 0.61 0.044 0.11 0.22 0.89 0.87 -0.04 0.18 0.85 0.86 4. Summary and Conclusions Time series modeling is considered as promising method to predicting naturally hazards including as dry seasons, wildfire risks, forests diseases, etc. ( Fernández Manso et al. 2011). Such models can be applied as a foundation for vegetation tracking systems, range management, livestock grazing management, etc. (Guan et al. 2014 ). The present research evaluated the behavior of net primary production (NPP) as well as NDVI time series, and it also developed SARIMA models for modeling and prediction NPP and NDVI in different bioclimatic regions of Iran. It was found that in all regions for two-time series had a 12-month periods regular seasonal patterns. The NPP time series in the studied regions showed seasonal changes better than the NDVI time series. In both time series, the Arid forest area had heterogeneity, which shows that in the future, they will be more affected by changes, including climate changes, and the ecosystems are weaker in front of these changes and human interventions. The results of checking the error criteria for all the selected NPP time series models in all the studied regions showed that the models have good accuracy. In general, the models selected for the NPP time series are more suitable than the NDVI time series models. This is due to regular seasonal variations and stationary NPP time series. Overall, the selected models provided a short-term forecasting of the NPP and NDVI index for study regions at 24-month time, that may be useful for the planning and management to reduce vegetation degradation and preserve ecosystem and biodiversity. Thus, temporal analysis using historical databases of long-term vegetation characteristics could help describe vegetation condition and the implications humans have on it at regional scale. 5. Recommendation for Future studies Vegetation is influenced by other factors such as rainfall, temperature, soil moisture, etc. In this research, we monitored and forecasted the state of vegetation in regions bioclimatic regions of Iran using only vegetation data, so we suggested to use environmental variables as predictor variables in other different regions of the world. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4600410","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":334464834,"identity":"a73e2af2-092f-4b6c-80ad-a9505deea81a","order_by":0,"name":"Fahimeh Sayedzadeh","email":"","orcid":"","institution":"Isfahan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"Fahimeh","middleName":"","lastName":"Sayedzadeh","suffix":""},{"id":334464835,"identity":"5f301e44-aea6-40ab-a1e0-a0d52cd2d228","order_by":1,"name":"Saied Soltani","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyElEQVRIiWNgGAWjYHACxgNAgoefGcplI0bPAaAeHslmBsYGkrQwGByAaiEI5PsPHzj8oeaOjPFxHvMHDDV2DHzSB/BrMbiRlnDgwLFnPGaHeQwbGI4lM7DxJRDQIsFjcOAA22GoFrYDDGw8BB12Bqjl32Ee42aQln9EaGE4kGNw4GDbYR4DZqAWxjYitID9crbvMI/EYbbCGYl9yTxEOOzwwQcV3w7b8/cf3vDhwzc7OfkeQg5DAQnAOCVJwygYBaNgFIwC7AAAFVlAAZ+/+QcAAAAASUVORK5CYII=","orcid":"","institution":"Isfahan University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Saied","middleName":"","lastName":"Soltani","suffix":""},{"id":334464836,"identity":"c8504e28-0696-4c58-997a-b794e0ddb87f","order_by":2,"name":"reza modarres","email":"","orcid":"","institution":"Isfahan University of Technology","correspondingAuthor":false,"prefix":"","firstName":"reza","middleName":"","lastName":"modarres","suffix":""}],"badges":[],"createdAt":"2024-06-18 13:42:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4600410/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4600410/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10661-024-13238-1","type":"published","date":"2024-11-01T16:20:20+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62154709,"identity":"4e0c057c-58ab-4c39-8e93-3724257cf1b5","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":359292,"visible":true,"origin":"","legend":"\u003cp\u003eSelected regions in bioclimatic flora in Iran\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/ea54a04c2b00d0a7ae1fe0d7.png"},{"id":62156235,"identity":"7e1da3ac-ae6b-4915-ba91-f9ea0fa618c4","added_by":"auto","created_at":"2024-08-09 21:08:18","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":551301,"visible":true,"origin":"","legend":"\u003cp\u003eMonthly NPP time series (kgh\u003csup\u003e-1\u003c/sup\u003em\u003csup\u003e-1\u003c/sup\u003e) in different vegetation regions of Iran during 2000 to 2016\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/f9ec1f81e0b897181a3630a1.png"},{"id":62157270,"identity":"1353dd50-0e7a-4425-b850-967ec664e4cf","added_by":"auto","created_at":"2024-08-09 21:16:18","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":332329,"visible":true,"origin":"","legend":"\u003cp\u003eMonthly NDVI Time series in different vegetation regions of Iran in the period from 2000 to 2018\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/f9ad5c759849c36302273afa.png"},{"id":62154715,"identity":"ea3c6fdc-9f6a-4d42-86ec-81075a75e6b0","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":301656,"visible":true,"origin":"","legend":"\u003cp\u003eNPP box plot for different Iran׳s bioclimatic regions during. 2000 to 2016. Each box plot consists of 16 NPP values for each month\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/c6ee45e1c706d0fc6e4ed02d.png"},{"id":62156229,"identity":"008c7f4f-299f-4878-b164-b3f860cf9717","added_by":"auto","created_at":"2024-08-09 21:08:18","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":304121,"visible":true,"origin":"","legend":"\u003cp\u003eNDVI box plot for different Iran׳s bioclimatic regions during. 2000 to 2018. Each box plot consists of 18 NDVI values for each month\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/70eca2ad86bb90b816ed4b5b.png"},{"id":62156227,"identity":"69a97e7a-acaf-4d15-9ab9-4f385847de50","added_by":"auto","created_at":"2024-08-09 21:08:18","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":373149,"visible":true,"origin":"","legend":"\u003cp\u003eACF diagrams of NPP time series for Iran's bioclimatic regions, a) Khazari b) Baluchi c) Semi-desert d) Steppe e) Semi-steppe f) Arid forests\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/838a3a2a4b75539cbfb504a3.png"},{"id":62154720,"identity":"c7e81911-456f-4406-85c1-eba4589ab20b","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":376274,"visible":true,"origin":"","legend":"\u003cp\u003eACF and PACF diagrams of NDVI in Iran's bioclimatic regions, a) Khazari b) Baluchi c) Semi-desert d) Steppe e) Semi-steppe f) Arid forests\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/4002c916a2c0697840323c35.png"},{"id":62154713,"identity":"487127e2-4199-4ea3-a1c8-990726d54a66","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":97524,"visible":true,"origin":"","legend":"\u003cp\u003eBox-plots of monthly ACF in lag times from 1 to 24 of all regions. Each box-plot consists of 6 value (a: NPP values and b: NDVI values)\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/00ee5a7fa82491c9f2478d78.png"},{"id":62154719,"identity":"76b0dba8-c64f-4d1b-a8dd-76fca9cc2a92","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":519582,"visible":true,"origin":"","legend":"\u003cp\u003eThe ACF and QQ-Plot of residuals for NPP time series in different regions, a) Khazari b) Baluchi c) Semi-desert d) Steppe e) Semi-steppe f) Arid forests\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/363ae15d28de6e23d4a84a6b.png"},{"id":62154710,"identity":"7d8847e6-70f5-4e72-b134-9cd84b102517","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":478028,"visible":true,"origin":"","legend":"\u003cp\u003eThe ACF and QQ-Plot of residuals for NDVI time series in different regions, a) Khazari b) Baluchi c) Semi-desert d) Steppe e) Semi-steppe f) Arid forests\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/aba8984762167d7a41dbe68f.png"},{"id":62154718,"identity":"95412721-f5c5-4832-985f-2499e5634e17","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":262000,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and forecasted NPP time series between January 2015 to December 2016 for a) Khazari b) Baluchi c) Semi-desert d) Steppe e) Semi-steppe f) Arid forests, dotted line: upper and lower bounds at 95% confidence level. The red line shows forecast and the blue line shows observations\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/d3f400c909b0687e9c40e4c4.png"},{"id":62154711,"identity":"88124427-2320-4966-ac80-a76daf49b2ab","added_by":"auto","created_at":"2024-08-09 21:00:18","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":251337,"visible":true,"origin":"","legend":"\u003cp\u003eObserved and forecasted NDVI time series between January 2017 to December 2018 for a) Khazari b) Baluchi c) Semi-desert d) Steppe e) Semi-steppe f) Arid forests, dotted line: upper and lower bounds at 95% confidence level. The red line shows forecast and the blue line shows observations\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/3c711711f0b3a42101343890.png"},{"id":68207142,"identity":"22dc644e-30fe-4866-9d1e-d2361bbc81d0","added_by":"auto","created_at":"2024-11-04 16:35:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4823700,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4600410/v1/b6743ad2-04f1-4097-b3e5-fb2d34730caa.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modeling NPP and NDVI time series in different bioclimatic regions of Iran","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe atmosphere, soil, and water are linked by vegetation, in turn facilitate flow of energy and materials cycling by photosynthesis (Han and Song, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Vegetation alteration serves substantial index for climate change of region and anthropogenic functions due to the integrated impacts of biological and non-biological pathways (B\u0026eacute;gu\u0026eacute; et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). From aforementioned point of view, tracking dynamism of vegetation serves vital to figure out biological and chemical pathways and their intrinsic interaction on the climatic system (Arneth et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), can enhance potential for forecast, reduce as well as coping with further weather variations (Sitch et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Zhao et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Bai, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The limitation and low accuracy of field data can lead to problems in vegetation monitoring and prediction, thus, the use of remote sensing indicators can be useful for monitoring ecological processes. The Normalized Difference Vegetation Index (NDVI) is a remote sensing method to assess plant greenness which is related to structural properties and vegetation productivity. (Forkel et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). This index was developed for studying vegetation characteristic and has the ability to determine vegetation and vegetative stress (Huang et. al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Analysis of NDVI are widely used to monitor temporal and spatial dynamics of vegetation (Busetto et. al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Net Primary Production (NPP) is level of organic matters generated via photosynthesis in absence of autotroph respiration being considered as the net rate of organically matters consolidated through vegetation by photosynthesis (Sun et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). NPP supports a wide range of ecosystem services, including forage production and soil carbon sequestration (Frank et al., 2012; Penner and Frank, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). NPP depends on different factors such as temperature, humidity, the amount of nutrients in the soil, etc., and is significantly affected by climate change. It is a measurement of ecosystem performance as well as a key indicator of ecosystem health (Wilcox et al., 2020).\u003c/p\u003e \u003cp\u003eMonitoring and predicting NPP changes is essential to assess ecosystem performance. Xing et al (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) simulated the net primary production of meadows in Asian north east by data of MODIS since 2000 to 2005 and improved CASA model. They showed that grasslands NPP closely correlated to rainfall and heat indicating climate change affects the grassland NPP (Xing et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Liu et al (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) investigated the variations of NPP and their association with climatic parameters given the converting various scaling within Gansu in China. The result expressed that the NPP values have been decreasing. The forestlands and grasslands ecosystems were affected majorly through heat, whereas rainfall considered the primary determinant parameters in the deserts and farmlands biomes annually. In comparison to the forests and deserts ecosystems, the grasslands and farmland biomes indicated time-lag as well as incremental associations with rainfall and temperatures, respectively (Liu et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Hao et al (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) indicated that NPP has a limiting function on marine ecosystems services within the alpines ecosystems of Qinghai, China. They concluded that a suitable adaptations of aerial vegetation exposing to climate change can deteriorate the limiting impact of NPP on the marine ecosystems services together with achieving interaction of various ecosystems services, hence conserving marine ecosystem services as well as enhancing sustainable development in the alpines ecosystems (Hao et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe data of time series offer a strong method to acquire from last occurrences, track present situations, and prepare for future change (van Leeuwen et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Contrasting present vegetation information along with past long-run means have been utilized to enhance ecosystems tracking (Orr et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). There are many time series models that have different applications. Hipel and McLeod (1994) considered ARMA class models to be suitable for describing hydrological and environmental datasets and showed that ARMA models have the ability to predict environmental time series and perform better than other models (Piwowar and Ledrew, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Recently, models of times series including Autoregressive-moving average (ARMA) time series were considered to track ecological and environmental variables. ARMA models have been used by many researchers. Fernandez Monso et al. (2011) used ARIMA analysis and regional scale climate data to predict NDVI (Normalized Differential Vegetation Index) in areas with conifers species. They used the time series of NDVI index extracted from NOVA AVHRR in the period from 1993 to 1997 as well as SARIMA (Seasonally Auto Regressive Integrate Moving Averages) model. They showed the relationship between NDVI and rainfall in some conifer species using climate time series and dynamic model analysis and predicted NDVI values for the near future in Castile and Leon, Spain and they concluded that time series models could be used for vegetation monitoring at regional level (Fernandez Monso et al., 2011). Muti et al (2019) conducted a study for NDVI predicting using MODIS MOD13A2 product and concluded that the predictions for a future seasonally periods considered acceptable showing the model is a tool to monitor short-term vegetation conditions. Salaberria et al (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) modeled the aboveground primary net productions (ANPP) of an Atlantics mountainous meadow in terms of the times series method. They modeled the monthly data of ANPP in the period from 2006 to 2008 using the models of incremental smoothing approach and ARIMA model. They result showed two approaches can generate insufficient predictions given the existence of pronounced locally characters (new outliers) in our relative low time-series data. Nevertheless, advantageous data to an initiative grazing management was indicated (for example the existence of yearly changes in ANPP, as well as discrepancies between the graze and exclusions treatment) (Salaberria et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Said Ommar and Kawamukai (2021). predicted NDVI by used the Holt- Winter and SARIMA models in an dry area within Kenya, and concluded that Holt-Winter model has better predictions than SARIMA models for 600 \u003cem\u003e✕\u003c/em\u003e 600 pixels (Said and Kawamukai. 2021). Tian et al. (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) using ARIMA models, forecasted drought based on Vegetation\u0026rsquo;s Temperatures Conditions indicator in the plain of Guanzhong and they showed that models of ARIMA can be predict class and extend of dry seasons as well as they may be used to predict dry seasons in plains (Tian. et al. 2016). Based on literature review, no study has been carried out to investigate the changes in vegetation cover over time in various ecosystems in Iran. Considering that Iran has different bioclimatic areas with diverse vegetation, it seems necessary to implement a research to investigate the changes of vegetation over time in Iran. Therefore, the current research was performed with the aim of modeling the variation in Net Primary Production (NPP) and NDVI time series across Iran's bioclimatic regions and also to compare the stochastic behavior of them in these bioclimatic regions.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1. Study area\u003c/h2\u003e\n \u003cp\u003eIran is placed in the semi-tropical high-pressured spot of the north hemisphere in coordinates of 24\u0026deg; and 40\u0026deg; N, and44\u0026deg; and 64\u0026deg; E (Ghadamii et al. 2020). The estimated areas of Iran are 1,873,959 km\u003csup\u003e2\u003c/sup\u003e characterized by a topographical limits of \u0026minus;\u0026thinsp;26 to 5610 m AMSL. Whereas large part of Iran is plain, two big mountainous belts are located in the northern (Alborz Mountains) and western (Zagrus Mountains) areas. As such both mountain areas prelude humidity to arrive Iran centers, both big and locally atmospherically systems influence Iran\u0026rsquo;s weather (Fathian et al. 2022). Around 75 percent of Iran placed in dry and semi-dry areas. The annually rainfall is 2000 mm/year in the southern coastal areas of the Caspian Sea and lower than 50 mm/year in the central desert, southern and eastern points of the Iran (Fathian et al. 2020). This research considers the classification of Iran\u0026apos;s bio climatically areas introduced by Pabot (\u003cspan class=\"CitationRef\"\u003e1967\u003c/span\u003e). Pabot classified Iran into 3 main floras, namely the Baluchi, Khazari and Iran-Turani floras. Flora of Iran-Turani was also divided in 5 semi-regions including semi-desert, steppe, semi-steppe, dry forest and elevated mountain. In this research, bioclimatic regions of Baluchi, Khazari, Semi-desert, Steppe, Semi-steppe, and Dry forests was selected (Fig. 1). These regions were chosen in the climatic regions due to the appropriate distribution across the country. In the following, we describe the bioclimatic characteristics of each region in more details.\u003c/p\u003e\n \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.1. Khazari flora\u003c/h2\u003e\n \u003cp\u003eThe average annual rainfall is 600\u0026ndash;2000 mm in this region, where the minimum rainfall is observed in June while the maximum rainfall happens in autumn. There is no significant dry period, and the relative humidity is generally more than 80%. This flora includes many species of the temperate region of Europe, basically a forest where trees and shrubs species are dominant in this region. The main tree species of this flora are \u003cem\u003eQuercus castanefolia\u003c/em\u003e, \u003cem\u003eBuxus sempervirens and etc\u003c/em\u003e.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.2. Baluchi flora\u003c/h2\u003e\n \u003cp\u003eThis region is similar to the sandy and subtropical desert climates. Amount of yearly rainfall is lower than 300 mm and the winter season is the wet period while dry spell lasts for 6 to 8 months. However, its relative humidity is high (60 to 80 percent). The most important trees and shrubs in this climatic region are \u003cem\u003eAcasia Arabica\u003c/em\u003e, \u003cem\u003eProspis spisigera\u003c/em\u003e, \u003cem\u003eZiziphus spina-christi\u003c/em\u003e, and \u003cem\u003ePhoenix dactylifera\u003c/em\u003e. The annual species which are observed in this area are mainy growing in winter. All perennial grasses are specific to warm regions, especially \u003cem\u003ePaniaceae\u003c/em\u003e and \u003cem\u003eAndropogonacea\u003c/em\u003e. There are plenty of permanent and perennial legumes and most of them are specific to subtropical regions such as Taverniera, Indigofera, Tefrosia, Cassia, Crotalaria, Caragana and Rhynchosia.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.3. Semi-desert flora\u003c/h2\u003e\n \u003cp\u003eThis is the driest part of Iran being located in the central plateau of Iran where the annual rainfall is less than 100 mm. In the central desert of Iran, it is possible to find a series of scattered vegetation, but many areas are devoid of any vegetation cover due to human interventions and the accumulation of large amounts of saline soils and the development of sand dunes. Most of the species in this area are salt-resistant spinach such as \u003cem\u003eHalocnemum strobilaceum\u003c/em\u003e, \u003cem\u003eSalicornia herbacea\u003c/em\u003e, \u003cem\u003eSeidlitzia rosmarinus\u003c/em\u003e and Salsola varieties.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.4. Steppe\u003c/h2\u003e\n \u003cp\u003eIn this flora, the annual rainfall varies 100 to 200 millimeter on southern point to 230 millimeters in the northern direction. Annual plant is abundant in this area and \u003cem\u003eArtemisia harba-alba\u003c/em\u003e is the typical species of this flora. \u003cem\u003eAristida plumose\u003c/em\u003e is also an important grass in the steppe region.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.5. Semi-Steppe\u003c/h2\u003e\n \u003cp\u003eThe annual rainfall in this region varies between 200 to o 450 mm depending on the region. The herbaceous flora is much richer than the steppe region and the families such as \u003cem\u003eLabiatae\u003c/em\u003e, \u003cem\u003eCompositae\u003c/em\u003e, \u003cem\u003eCruciferae\u003c/em\u003e, \u003cem\u003eCaryophyllaceae, Papilionaceae\u003c/em\u003e, \u003cem\u003eUmbelliferae\u003c/em\u003e, \u003cem\u003eGraminaceae\u003c/em\u003e and \u003cem\u003eBorraginaceae\u003c/em\u003e are commonly observed. In this region, two species of Amygdalus (A. scoparia, A. horrida) are found on rocks and hill slopes. The pastures of the semi-steppe region are considered to be among the most valuable pastures in Iran (Pabot \u003cspan class=\"CitationRef\"\u003e1967\u003c/span\u003e).\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.6. Arid forests\u003c/h2\u003e\n \u003cp\u003eThis region is located along the Zagros mountain range covering the slopes of south and east Alborz and areas into highlands in the northwest. The average height of this area is between 800 and 2600 meters with the annual rainfall more than 400 mm. Zagros forests are mainly composed of \u003cem\u003eQuercus persica\u003c/em\u003e. \u003cem\u003eHordeum bulbosum\u003c/em\u003e and \u003cem\u003ePoa bulbosa\u003c/em\u003e and are among the most far-reaching perennial grasses while there are different species of \u003cem\u003eStipa\u003c/em\u003e or \u003cem\u003eAgropyron\u003c/em\u003e and a few legume species. \u003cem\u003eLabiatae\u003c/em\u003e and \u003cem\u003eCompositae\u003c/em\u003e family plants often make the majority of vegetation species (Pabot \u003cspan class=\"CitationRef\"\u003e1967\u003c/span\u003e).\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e2.2. Data\u003c/h2\u003e\n \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.1. NDVI and NPP time series\u003c/h2\u003e\n \u003cp\u003eThe NDVI time series based on the products of Moderates Resolutions Image Spectroradiometers (MODIS) sensor (MOD13Q1) attained of the NASA Lands Process Distribute Actives Archives Centers (LP DAAC), USGS/Earth Resource Observations and Sciences (EROS) Centers (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ewww.lpdaac.usgs.gov\u003c/span\u003e\u003c/span\u003e). This dataset consists of 16-Daily images at a spatial resolution of 250 m and HDF format. Totally, 1055 pictures utilized for a duration of eighteen years, from Feb 2000 to Sep 2018. In order to build monthly time series of NDVI from the 16-day products of the 13Q1 data series, we carried out the following steps. The images were cut based on the polygons specified in the studied bioclimatic areas in the ArcMap. After that, the average NDVI values were calculated for each region. Finally, the average of the two images was placed as monthly NDVI values.\u003c/p\u003e\n \u003cp\u003eThe NPP data was obtained from products of MODIS sensor (MOD17A2). These data had monthly temporal resolution, spatial resolution of 1.1 km, and HDF format. The MOD17A2 products are available from the \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://neo.gsfc.nasa.govwebsite\u003c/span\u003e\u003c/span\u003e. MOD17A2 series has monthly products and in order to obtain NPP time series the images were cut based on the polygons of the studied areas in the ArcMap and finally the monthly NPP time series from 2000 to 2016 were extracted.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e2.3. Time series modeling\u003c/h2\u003e\n \u003cp\u003eA times series is defined as group of quantitative observation arranged within chronological order (Kirchg\u0026auml;ssner et al., 2013). Times-series predicting has great contributions in scientific contexts. (Aggrawal et al. 2020). In this study, Autoregressive-moving averages times series models (Box-Jenkins ,1970) are developed to model NDVI and NPP time series. These models include Autoregressive (AR) or Moving averages (MA) models or an integration of the both, i.e. ARMA. ARMA models are used once processes lies in equilibriums around consistent average levels that at the same time called stationaries. Some of times series show non-stationaries manner and are constant around a constant average, in these cases ARIMA and SARIMA models were considered (Tian et al. \u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e). In addition, some of the time series such as vegetation or rainfall, having the characteristic of seasonality which allows to include seasonal differences in a SARIMA (Seasonal ARIMA) model. SARIMA models are displayed as SARIMA(p,d,q)(P,D,Q)S, so that p and q are the magnitude of AR and MA parameters, respectively; d is the magnitude of non-seasonal difference applied in series in order to attain constancy. P, D and Q are, respectively, the orders of SAR and SMA seasoned parameters and seasonal variations used according to the seasonal duration S. The simple relation for the SARIMA model serves as follows:\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$${\\varphi }_{\\rho }\\left(B\\right){{\\Phi }}_{P}\\left({B}^{S}\\right){\\nabla }^{d}{\\nabla }_{S}^{D}{Y}_{t}={\\theta }_{q}\\left(B\\right){{\\Theta }}_{Q}\\left({B}^{S}\\right){\\epsilon }_{t}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eso that Y\u003csub\u003et\u003c/sub\u003e is the seen times series in a specific duration \u003cem\u003et\u003c/em\u003e with seasonal duration S, \u0026epsilon;\u003csub\u003et\u003c/sub\u003e is the residuals of the model at time step t. B is a non-seasonal backward operator and B\u003csup\u003es\u003c/sup\u003e is the seasonal backward operator. The ϕ\u003csub\u003ep\u003c/sub\u003e and ϴ\u003csub\u003eq\u003c/sub\u003e are non-seasonal autoregressive and moving average parameters, respectively, Ф\u003csub\u003eP\u003c/sub\u003e and \u0026Theta;\u003csub\u003eQ\u003c/sub\u003e are seasonal autoregressive and moving average parameters, respectively. The Box-Jenkins time series modeling has three steps including model identification, parameter estimation, diagnosis and model validation. The first step in time series modeling is to identify the order of the model based on the characteristics and behavior of the time series which involves choosing the difference parameters d and/or D to achieve data stationary, and model ranks comprising p, q, P and Q through the analysis of autocorrelations function (ACF) and partial autocorrelations function (PACF) of differential series. Autocorrelation function is one of the characteristics of time series that shows the degree of linear correlation among components of times series. The autocorrelation coefficient between Z\u003csub\u003et\u003c/sub\u003e and Z\u003csub\u003et+k\u003c/sub\u003e is in the form of the following equation:\u003c/p\u003e\n \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$${p}_{k}=\\frac{{Y}_{k}}{{Y}_{O}}=\\frac{Cov({Z}_{t}. {Z}_{t+k})}{\\sqrt{Var({Z}_{t}})\\sqrt{Var\\left({Z}_{t+k}\\right)}}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe partial autocorrelation function is also an important characteristic of time series and is calculated from the following equation:\u003c/p\u003e\n \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e$${\\phi }_{kk}= Corr\\left({Z}_{t}. {Z}_{t+k}/{Z}_{t+1}\\dots . {Z}_{t+k-1}\\right)$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn parameter evaluation stage, magnitude of model parameters is specified and then estimated.\u003c/p\u003e\n \u003cp\u003eThe second step of time series modeling is parameter estimation. When model was experimentally recognized, variable should effectively evaluated, as well as fitting measured, majorly through an analyses of residual, for assessing if it may be considered as a good approximation of the series (Anderrson 1977). The third step in modeling is the model validation. Ultimate part of the Boxes-Jenkins cycles is expose the recognized and evaluated models for \u0026quot;diagnostics check\u0026quot; of its sufficiency. Here, the residuals of the model should have a normal distribution and do not show significant autocorrelation structure (Anderson \u003cspan class=\"CitationRef\"\u003e1977\u003c/span\u003e). At this stage, the independence of residuals is checked by drawing the ACF diagram and the normality of the residuals is checked by the Kolmogorov-Smirnov normality test or the quantile-quantile plot of the residuals.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e2.4. Out-of-sample forecasting\u003c/h2\u003e\n \u003cp\u003eTime series models are capable of forecasting a variable in n-step ahead lead time. Here, to show the capacity of the selected models for forecasting NPP and NDVI, we keep two years monthly NPP time series (from January 2014 to December 2016) and NDVI time series (from January 2016 to December 2018) for evaluating outlirers samples predicting performance. The outlier sample forecasting times series \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e of the whole \u003cem\u003eARIMA\u003c/em\u003e (\u003cem\u003ep, d, q\u003c/em\u003e) process is calculate from the following equation:\u003c/p\u003e\n \u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e$${\\phi }_{p }\\left(B\\right){\\left(1-B\\right)}^{d}{Z}_{t}= {\\theta }_{o}+{\\theta }_{q}\\left(B\\right){a}_{t}$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eWherein \u0026theta; is naturally 0 in case \u003cem\u003ed\u003c/em\u003e\u0026thinsp;\u0026ne;\u0026thinsp;0 as well as associated to average \u0026micro; of the series once \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0, \u0026phi;\u003csub\u003ep\u003c/sub\u003e, (\u003cem\u003eB\u003c/em\u003e) = (1 \u0026ndash; \u0026phi;\u003csub\u003e1\u003c/sub\u003e \u003cem\u003eB\u003c/em\u003e-\u003cem\u003e⋯\u003c/em\u003e-\u0026phi;\u003csub\u003ep\u003c/sub\u003e \u003cem\u003eB\u003c/em\u003e\u003csup\u003ep\u003c/sup\u003e ), \u0026theta;\u003csub\u003eq\u003c/sub\u003e (\u003cem\u003eB\u003c/em\u003e) = (1 - \u0026theta;\u003csub\u003eq\u003c/sub\u003e (\u003cem\u003eB\u003c/em\u003e)\u0026thinsp;=\u0026thinsp;0 has different root which placed out of the united circles, and series \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e is a Gaussians N(0, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\sigma }_{a}^{2})\\)\u003c/span\u003e\u003c/span\u003e whites noises processes (Wei \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003e2.5. Model evaluations\u003c/h2\u003e\n \u003cp\u003eFor evaluating the efficiency time series model, different performance criteria such as Means Relatives Errors (MRE), Root Mean Squared Error (RMSE), Mean Error (ME), Coefficients of Efficiency (CE), and R-squared (R\u003csup\u003e2\u003c/sup\u003e) are applied. The equations of these relationships are given follow. ME indicates alignment among estimated and modeled dataset. The values of ME are unlimited as well as for a complete models finding is 0.\u003c/p\u003e\n \u003cp\u003eME= \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{1}{n}\\sum _{i=1}^{n}({Q}_{i}-\\widehat{{Q}_{i}})\\)\u003c/span\u003e\u003c/span\u003e (5)\u003c/p\u003e\n \u003cp\u003eThe RMSE values were calculated using the following equation:\u003c/p\u003e\n \u003cp\u003eRMSE = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sqrt{\\frac{\\sum _{i=1}^{n}{\\left({Q}_{i}-\\widehat{{Q}_{i}}\\right)}^{2}}{n}}\\)\u003c/span\u003e\u003c/span\u003e (6)\u003c/p\u003e\n \u003cp\u003eThe model obtained from this relationship is non-negative having no higher bound, and given complete models, findings is 0.\u003c/p\u003e\n \u003cp\u003eMRE includes average of errors generated than the estimated one. The values obtained from this metric are unlimited, and given perfected model, findings are 0. It is susceptible to prediction error which occurs in the low(er) magnitude of every dataset. The MRE values computed by below equation:\u003c/p\u003e\n \u003cp\u003eMRE = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{1}{n}\\sum _{i=1}^{n}\\left(\\frac{{Q}_{i}-\\widehat{{Q}_{i}}}{{Q}_{i}}\\right)\\)\u003c/span\u003e\u003c/span\u003e (7)\u003c/p\u003e\n \u003cp\u003eCE allows errors and differences to be weighted more appropriately through the use of absolute values. CE values are variable from zero to one, and the most positive value indicates the best model. The CE values were calculated using the following equation:\u003c/p\u003e\n \u003cp\u003eCE\u0026thinsp;=\u0026thinsp;1-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{\\sum _{i=1}^{n}{\\left({Q}_{i}-\\widehat{{Q}_{i}}\\right)}^{2}}{\\sum _{i=1}^{n}{\\left({Q}_{i}-\\stackrel{-}{{Q}_{i}}\\right)}^{2}}\\)\u003c/span\u003e\u003c/span\u003e (8)\u003c/p\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e shows ratio of totally variances in the estimated data series which may be assessed through the models. Its values are variable from zero (poor model) to one (perfect model). The R\u003csup\u003e2\u003c/sup\u003e values were calculated using the following equation:\u003c/p\u003e\n \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left[\\frac{{\\sum }_{i=1}^{n}\\left({Q}_{i}-\\stackrel{-}{Q}\\right)\\left(\\widehat{Q}-\\stackrel{\\sim}{Q}\\right)}{\\sqrt{\\sum _{i=1}^{n}{\\left({Q}_{i}-\\stackrel{-}{Q}\\right)}^{2}}\\sum _{i=1}^{n}{\\left({\\widehat{Q}}_{i}-\\stackrel{\\sim}{Q}\\right)}^{2}}\\right]}^{2}\\)\u003c/span\u003e\u003c/span\u003e (9)\u003c/p\u003e\n \u003cp\u003eIn these equations,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the observation value, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\widehat{{Q}_{i}}\\)\u003c/span\u003e\u003c/span\u003e is the model estimation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{-}{\\text{Q}}\\)\u003c/span\u003e\u003c/span\u003e is the average of the observations, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\stackrel{\\sim}{Q}\\)\u003c/span\u003e\u003c/span\u003e is the average model estimation and n considered numbers of observation and model estimation (Dawson et al. 2005). The same performance criteria are also calculated for the forecasting period to check the accuracy of the selected models in forecasting NDVI and NPP.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Exploratory Data Analyses\u003c/h2\u003e \u003cp\u003eAccording to NPP time series (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e2\u003c/span\u003e) for different regions, it can be seen that the NPP has monthly fluctuation. In addition, the time series looks stationary during the data record as they do not show a significant increasing or decreasing trend.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe NDVI times series are also shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e for different bioclimatic regions. Almost all time series have no significant change, except for the Khazari (in Jan 2008) and Semi-Steppe (in Jan 2008) regions which indicate a breakpoint in the time series structure.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo show the seasonal characteristics of NPP and NDVI, boxes plot of monthly NPP and NDVI shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e as well as 5, respectively. Each box plot contains annual data for each month during record period. We can observe in the NPP time series that the seasonal patterns in Semi-Desert, Arid Forest, Steppe, and Semi-Steppe regions are similar, while Baluchi and Khazari regions show different seasonal patterns which due to the different climate of these areas.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe box plot of the NDVI index shows that the seasonal patterns in the Arid forest, Steppe, and Semi-Steppe regions were similar. Again, the Baluchi and Khazari regions have different seasonal patterns. Semi-Desert region did not have distinct seasonal patterns (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e). The seasonal average NPP and NDVI time series are also provided in Tables\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e as well as 2, respectively.\u003c/p\u003e \u003cp\u003eAs it is shown the average NPP in Khazari region is highest in May. This amount is observed for the Baluchi region in February, for the semi-desert region in March, for the steppe region in April, for the semi-steppe region in February, and for the Arid forest region in April (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In cold regions, the maximum NPP is observed in spring, and in warm regions the maximum NPP is observed in winter which is due to the presence of suitable conditions for plant growth in these seasons.\u003c/p\u003e \u003cp\u003eThe minimum amount of NPP is observed in Iran's Turani flora regions (semi-deserts, steppe, semi-steppes, and dry forests) in early summer as well as July that related to summers hydrated deficits duration, that leds to dry in farmlands vegetation biomasses (zoffuli et al., 2008)., in the Khazari region in winter and February related to vegetation inaction, and within Baluchi region in late spring and May due to dryness and high temperature in this month (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMonthly average NPP (kg/ha) during 2000 to 2016 for different bioclimatic regions (Bold values show maximum and italics are the lowest NPP (kg/ha) for each region)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eJan\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFeb\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMar\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eApr\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMay\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eJun\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eJuly\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAug\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eSep\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eOct\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eNov\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eDec\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKhazari\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e45.43\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e106.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e135.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e126.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e102.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e76.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e95.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e84.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e61.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e45.57\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaluchi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e39.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e40.42\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e32.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e22.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e16.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e16.21\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e17.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e18.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e20.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e23.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e31.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e34.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSemi-desert\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e7.65\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e3.92\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e4.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e5.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e6.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e6.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e6.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSteppe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e28.37\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e23.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e18.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e15.64\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e17.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e20.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e23.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e22.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e20.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSemi-Steppe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e43.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e48.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e47.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e44.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e39.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e31.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e26.73\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e27.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e31.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e35.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e40.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e39.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArid forest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e39.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e44.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e59.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e76.20\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e64.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e34.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e22.35\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e24.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e37.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e43.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e44.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e39.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe average NDVI from 2000 to 2018 for different months Table\u0026nbsp;(2) showed that the Khazari regions, Semi-Steppe and Arid Forests have a distinct seasonal pattern. This attributed to the great variations in rainfall as well as heat among the seasons in these areas. In the semi-desert region, there is no difference in the amount of NDVI in different months, may be due to the limited moisture of plant growth throughout the year. The seasonal pattern in Baluchi and Steppe regions are not significant either because the rainfall in the wet season is very low and does not create a big difference between different seasons.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMonthly average NDVI during 2000 to 2018 for different bioclimatic regions (Bold values show maximum and italics are the lowest NDVI)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eJan\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFeb\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMar\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eApr\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMay\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eJun\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eJuly\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAug\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eSep\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eOct\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eNov\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eDec\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKhazari\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e0.25\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e0.25\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.46\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaluchi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003e0.06\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSemi-desert\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003estepp\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSemi-Stepp\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArid forest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c12\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Time Series Modeling\u003c/h2\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1. Autocorrelation Structure\u003c/h2\u003e \u003cp\u003eExamining the ACF and PACF functions makes it possible to understand how the time series behaves in stationarity and seasonality. If ACF decreases gradually, the time series is non-stationary; if ACF decreases suddenly, the times series is constant. Before developing times series models, the behavior of ACF of NPP and NDVI time series are examined to compare the different stationary and non-stationary characteristics of them.\u003c/p\u003e \u003cp\u003eFor NPP times series, in lag-1autocorrelation, the autocorrelation value has high in all regions (0.6 to 0.8). That high lag-1autocorrelation for the Khazari and Semi-Steppe regions is most probably due to relatively continuous seasonal rainfall throughout the year and, despite the low annual rainfall (around 100 mm) in Baluchi, Semi desert and Steppe regions, they have high autocorrelation (about 0.7). In Baluchi region it is probably due to the presence of rich annual species and in Steppe region it is due to the existence of irrigated agricultural plains in some regions, such as Khuzestan province. In Semi desert region it can be due to the uniform environment, permanent lack of water, and vegetation adapted to these conditions. The yearly precipitation of Arid Forest area is high (around 600 mm) and it has suitable conditions for the growth of plants, but it has a lower autocorrelation value compared to drier regions which this can be due to large differences in temperature and precipitation between seasons (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003ea, b, c, d, e, f). Considering that the autocorrelation value has suddenly decreased in all regions, it indicates the stability of NPP time series in all studied regions. All study regions have a 12-month periods regular seasonal patterns (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003ea, b, c, d, e, f). In the semi-steppe and Bauchi regions, there is also a strong autocorrelation in 6-month periods, that is due to the growth conditions of plants due to suitable temperature and autumn rains (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003eb, e).\u003c/p\u003e \u003cp\u003eThe Arid Forest region has the different autocorrelation pattern. Many changes in this region can be due to climatic variations and the destruction of forest trees by humans and diseases such as Loranthus (Javanmiri pour et al. 2022) (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003ef).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor the NDVI time series, in 1-month lag the ACF was 0.55 to 0.83. The Khazari regions has maximum autocorrelation (0.83) and Semi steppe region has minimum autocorrelation (about 0.55). In the Semi-Desert region, despite the inadequate environmental conditions for plant growth, ACF is higher (about 0.8) than the Semi-Steppe and Arid forests regions, which can be due to the presence of plant species adapted to dry environments (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003ea, c, e, f). Since the ACF has suddenly decreased in Steppe, Semi steppe and Arid forest regions, it shows the stability of NDVI time series in this regions, and the ACF decreases gradually in Khazari, Baluchi and Semi desert was indicating non- stability (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003ea, B, C, D, E, F). Time series of the Khazari, Baluchi, steppe, Semi-Steppe and Arid forests regions had periodic changes of 12 months. This is indicating that the annual cycle of vegetation phenology affects the NDVI. The semi-desert region had weak seasonal behavior which can be due to the very low vegetation cover in this area (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003ea, b, c, d, e, f).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eComparing the lag times from 1 to 24 month for different regions shows that the NPP variable has a stronger seasonality than the NDVI (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e). In NPP, the maximum value of ACF is observed at the 12-month lag time while for NDVI it is observed at the 1-month lag. However, the ACF value at lag12 is also high for NDVI time series indicating significant seasonality.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e also indicates that the range of autocorrelation coefficients is higher for NDVI time series comparing NPP time series which shows a distinct diversity between bioclimatic regions.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2. SARIMA Models\u003c/h2\u003e \u003cp\u003eAs the ACFs of NPP and NDVI show significant seasonality, the Seasonal ARIMA model seem to be appropriate. To fit the SARIMA model to the NPP and NDVI time series, regarding the seasonal non-stationary behavior of the time series, seasonal differentiation (D\u0026thinsp;=\u0026thinsp;12) is considered. For the all-time series, different models with different magnitudes of non-seasonally and seasonally autoregressive as well as moving averages are investigated with and without non-seasonal differentiation. Finally, the best model was selected regarding minimum AIC criteria and no autocorrelation in the residuals the time independence of the residuals is checked using the ACF diagram in residuals. Normality of residual is also controlled through Q-Q plot diagram for NPP (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e) and NDVI (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e). Given model adequacy, the best SRIMA models for NPP and NDVI in each region is selected (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe selected SARIMA models for NPP and NDVI time series in all regions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNDVI series\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNPP series\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eKhazari\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMA(0,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSARIMA(1,1,1)(1,1,1)\u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBaluchi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMA(1,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSARIMA (1,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSemi-Desert\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMA(0,1,1)(1,1,1) \u003csub\u003e6\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSARIMA (1,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSteppe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMA(1,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSARIMA (1,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSemi-Steppe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMA(0,1,0)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSARIMA (1,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArid forest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSARIMA(0,1,0)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSARIMA (1,1,1)(0,1,1) \u003csub\u003e12\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eIn order to check the efficiency of NPP and NDVI time series perdition, the error criteria are calculated (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). These criteria show that the models for the NPP time series have more accuracy than NDVI time series based on RMSE, R\u003csup\u003e2\u003c/sup\u003e, MRE, and CE criteria, while based on the ME criteria, the models perform better for NDVI time series. Given that the difference between the minimum and maximum values in the variable NPP is greater and the ME criterion cannot weight the minimum and maximum values, this criterion is not suitable for the NPP time series models. The selected models for Baluchi and Steppe regions which have less climate variability, have higher accuracy than the more humid regions (Khazari, Semi-Steppe, and arid forest). For Semi desert region, the selected model for NPP time series have more accuracy than the NDVI time series (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eErrors criteria for selected models in all region\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eME\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eMRE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003eCE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eKhazari\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBaluchi\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-1.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSemi-Desert\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e-2.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSteppe\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.66\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSemi-Steppe\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eArid forest\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section3\"\u003e \u003ch2\u003e3.2.3. Out of-sample Forecasting\u003c/h2\u003e \u003cp\u003eFollowing specifying model as well as evaluating variables, next step is to evaluate the model's capability in out-of-sample forecasting between 2015 to 2016 for NPP and between for 2017 to 2018 for NDVI. For the NPP variable, the data from 2015 to 2016 were used to evaluate the model's forecasting. In the Khazari region, the model is able to forecast the changes both in trend and quantity well, and only in May 2015, there is a significant difference in the forecasted trend and value, which may be due to the indiscriminate harvesting of wood and other unpredicted environmental factors. The proposed model in the Balochi region also forecasts the changes well, and only in June 2016, both in terms of trend and value, there is a significant difference between observations and forecasting. In the semi-desert region, the model is able to forecast the changes well regarding trends and values, and all points are within the 95% significance range. In the steppe, Semi-steppe, and Arid forest regions, the models have forecasted the NPP values and trends very well, and all points are within the 95% confidence range. Generally, the selected NPP time series models can correctly forecast the NPP changes in all regions (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe show the monthly observed and forecasted NDVI time series from January 2017 to December 2018 in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e12\u003c/span\u003e. This figure shows which elected models to NDVI times series in the Khazari region performs very well in forecasting NDVI and its tendency, as forecasts are within the 95% confidence interval. In the Baluchi region, only in September 2017, the observed value was outside the 95% confidence interval of the model. The proposed models in Semi-Deserts, Steppes, Semi-Steppes, and dry forest regions have predicted the tendency and data values very well, and the observed data were completely within the range of 95% predicted by the model. Muti et al. (2019) also stated that SARIMA modeling performed better in predicting dry seasons, where the variability of climate is less, and predicts variable values in wet seasons, where annual changes are higher (Muti et al. 2019). Fern\u0026aacute;ndez Manso et al. )2011(also and stated that the prediction of the selected models for the NDVI data series using SARIMA was acceptable.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe performance criteria of the models in forecasting NPP and NDVI are presented in Table\u0026nbsp;(5). The results of these criteria showed that for the NPP variable, the selected models for the semi-desert region performs better than other regions (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.94, RMSE\u0026thinsp;=\u0026thinsp;0.12, ME\u0026thinsp;=\u0026thinsp;0.05, MRE\u0026thinsp;=\u0026thinsp;0.01, and CE\u0026thinsp;=\u0026thinsp;0.91) and other regions also have acceptable accuracy. For the NDVI index, the selected models for the Arid forest region performs the best (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.87, RMSE\u0026thinsp;=\u0026thinsp;0.22, ME\u0026thinsp;=\u0026thinsp;0.044, MRE= -0.04, and CE\u0026thinsp;=\u0026thinsp;0.86), and Khazari, Baluchi, and Steppe have acceptable accuracy, but the selected models for semi-desert and semi-steppe regions do not show high accuracy. In general, the results showed that time series modeling has a suitable capability for forecasting NDVI and NPP, and in all regions, the forecasted values are within 95% confidence.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eErrors criteria for forecast models in all regions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eME\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eMRE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003eCE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eNPP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eNDVI\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eKhazari\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eBaluchi\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-3.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSemi-Desert\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e-2.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSteppe\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e-0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSemi-Steppe\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.013\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eArid forest\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.044\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e-0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c10\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c11\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Summary and Conclusions","content":"\u003cp\u003eTime series modeling is considered as promising method to predicting naturally hazards including as dry seasons, wildfire risks, forests diseases, etc. \u003cem\u003e(\u003c/em\u003eFern\u0026aacute;ndez Manso et al. 2011). Such models can be applied as a foundation for vegetation tracking systems, range management, livestock grazing management, etc. (Guan et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). The present research evaluated the behavior of net primary production (NPP) as well as NDVI time series, and it also developed SARIMA models for modeling and prediction NPP and NDVI in different bioclimatic regions of Iran. It was found that in all regions for two-time series had a 12-month periods regular seasonal patterns. The NPP time series in the studied regions showed seasonal changes better than the NDVI time series. In both time series, the Arid forest area had heterogeneity, which shows that in the future, they will be more affected by changes, including climate changes, and the ecosystems are weaker in front of these changes and human interventions. The results of checking the error criteria for all the selected NPP time series models in all the studied regions showed that the models have good accuracy. In general, the models selected for the NPP time series are more suitable than the NDVI time series models. This is due to regular seasonal variations and stationary NPP time series.\u003c/p\u003e \u003cp\u003eOverall, the selected models provided a short-term forecasting of the NPP and NDVI index for study regions at 24-month time, that may be useful for the planning and management to reduce vegetation degradation and preserve ecosystem and biodiversity. Thus, temporal analysis using historical databases of long-term vegetation characteristics could help describe vegetation condition and the implications humans have on it at regional scale.\u003c/p\u003e"},{"header":"5. Recommendation for Future studies","content":"\u003cp\u003eVegetation is influenced by other factors such as rainfall, temperature, soil moisture, etc. In this research, we monitored and forecasted the state of vegetation in regions bioclimatic regions of Iran using only vegetation data, so we suggested to use environmental variables as predictor variables in other different regions of the world. It is also suggested that time series models be compared with various other models such as multivariate models.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eDeclaration: There was no Funding\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eCompeting Interest\u003c/strong\u003e \u003cp\u003edeclaration: The authors have no conflict of interest\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eF.S. and S.S. and R.M. conceptualize; F.S. Modeling, and write the manuscript; S.S. and R.M. provided editorial advice.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAggarwal, A., Alshehri, M., Kumar, M., Alfarraj, O., Sharma, P., \u0026amp; Pardasani, K. R. (2020). 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Seasonal and interannual analysis of wetlands in South America using NOAA-AVHRR NDVI time series: the case of the Parana Delta Region. \u003cem\u003eLandscape Ecology\u003c/em\u003e, 23, 833\u0026ndash;848.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"environmental-monitoring-and-assessment","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"emas","sideBox":"Learn more about [Environmental Monitoring and Assessment](http://link.springer.com/journal/10661)","snPcode":"10661","submissionUrl":"https://submission.nature.com/new-submission/10661/3","title":"Environmental Monitoring and Assessment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Autocorrelation function, vegetation cover, seasonal change, SARIMA models, forecast","lastPublishedDoi":"10.21203/rs.3.rs-4600410/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4600410/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eVegetation is one of the important components of ecosystems that usually changes seasonally. An accurate parameterization of vegetation cover dynamics by developing time series models can strengthen our understanding of vegetation change. This research is aims to investigate and model the temporal changes of Net Primary Production (NPP) and Normalized Difference Vegetation Index (NDVI) across bioclimatic regions of Iran, including the Khazari, Baluchi, semi-desert, steppe, semi-steppe and Arid forests. We used Moderate Resolution Imaging Spectroradiometer (MODIS) sensor products for NPP and NDVI time series (MOD17A2 and MOD13Q1, respectively). The SARIMA (Seasonal Autoregressive Integrated Moving Average) time series model is developed for NPP and NDVI time series. The investigation of Auto Correlation Functions (ACF) showed a strong seasonality in NPP and NDVI at the 12-month lag time. Comparing the lag times from 1 to 24 month for different regions shows that the NPP variable has a stronger seasonality. The evaluation of error criteria showed NPP time series models based on RMSE, R\u003csup\u003e2\u003c/sup\u003e, MRE, and CE criteria was better, while based on the ME criteria, the models performs better for NDVI time series (For example, in Khazari region for NPP and NDVI time series respectively, ME\u0026thinsp;=\u0026thinsp;3.67, 0.05, RMSE\u0026thinsp;=\u0026thinsp;0.12, 0.18, R2\u0026thinsp;=\u0026thinsp;0.87, 0.63, MRE\u0026thinsp;=\u0026thinsp;0.02, 0.12, and CE\u0026thinsp;=\u0026thinsp;0.84, 0.12). The selected models provided a short-term forecasting of the NPP and NDVI index for study regions at 24-month time, that useful for the planning and management to reduce vegetation degradation and preserve ecosystem and biodiversity.\u003c/p\u003e","manuscriptTitle":"Modeling NPP and NDVI time series in different bioclimatic regions of Iran","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-09 21:00:13","doi":"10.21203/rs.3.rs-4600410/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-08-28T23:48:27+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-28T13:14:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"3261693308130714820668200200148371849","date":"2024-08-28T03:12:15+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-27T15:33:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"287022293075090627377712448382150842582","date":"2024-08-13T05:14:30+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-07-11T22:34:51+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-09T12:29:58+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-09T12:29:27+00:00","index":"","fulltext":""},{"type":"submitted","content":"Environmental Monitoring and Assessment","date":"2024-06-18T13:41:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"environmental-monitoring-and-assessment","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"emas","sideBox":"Learn more about [Environmental Monitoring and Assessment](http://link.springer.com/journal/10661)","snPcode":"10661","submissionUrl":"https://submission.nature.com/new-submission/10661/3","title":"Environmental Monitoring and Assessment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d212a8b6-3fbe-4f9c-b83f-e4ab0c9aabac","owner":[],"postedDate":"August 9th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-11-04T16:27:12+00:00","versionOfRecord":{"articleIdentity":"rs-4600410","link":"https://doi.org/10.1007/s10661-024-13238-1","journal":{"identity":"environmental-monitoring-and-assessment","isVorOnly":false,"title":"Environmental Monitoring and Assessment"},"publishedOn":"2024-11-01 16:20:20","publishedOnDateReadable":"November 1st, 2024"},"versionCreatedAt":"2024-08-09 21:00:13","video":"","vorDoi":"10.1007/s10661-024-13238-1","vorDoiUrl":"https://doi.org/10.1007/s10661-024-13238-1","workflowStages":[]},"version":"v1","identity":"rs-4600410","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4600410","identity":"rs-4600410","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}