Forecasting Soil Moisture In The Soil Under The Caragana Shrubland Using Wavelet Analysis And NARX Neural Network

Forecasting Soil Moisture In The Soil Under The Caragana Shrubland Using Wavelet Analysis And NARX Neural Network | 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 Forecasting Soil Moisture In The Soil Under The Caragana Shrubland Using Wavelet Analysis And NARX Neural Network Dong-Mei Bai, Zhong-Sheng Guo, Man-Cai Guo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-977050/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Purpose: It is important for sustainable use of soil water resources to forecast soil moisture in forestland of water-limited regions. There are some soil moisture models. However, there is not a better method to forecast soil moisture. Methods: The change of soil moisture with time were investigated and the data of soil moisture were divided into a low frequency and a high frequency component using wavelet analysis, and then NARX neural network was used to build model I and model II. For model I, low frequency component was the input variable, and for model II, low frequency component and high frequency component were predicted. Results: the average relative error for model I is 3.5% and for model II is 0.3%. The average relative error of predicted soil moisture in100cm layer using model II is 0.8%, then soil water content in 40 cm and 200 cm soil depth is selected and the forecast errors are 4.9 % and 0.4 %.Using model II to predict soil water is well． Conclusion: Predicting soil water will be important for sustainable use of soil water resource and controlling soil degradation, vegetation decline and crop failure in water limited regions. Agricultural Engineering semi-arid loess hilly region plant growth soil moisture wavelet analysis NARX recurrent neural network forecast Figures Figure 1 Figure 2 Figure 3 Introduction Soil moisture is one of the most basic elements of the soil fertility, and the foundation for the crop fertility (li ,1962). Soil water is the most important factors influencing plant growth in the loess plateau. Because rain is shortage, soil drought often happens, which cause soil degradation, vegetation decline and crop failure in the loess plateau (Guo and Shao, 2013 ,2021a,2021b). The soil water resources are the soil water storage in a root soil, and soil water resources use limit by plant refers to the amount of water stored within the maximum infiltration depth, in which the soil moisture content at each layer is equal to the withering coefficient (Guo, 2010, 2021a and b ). When soil water resources in the maximum infiltration depth reduce to the soil water resources use limit by plant, the plant water relation enters the critical period of plant-water relationship regulation. At this time, soil drought serious influence plant growth, which cause serious soil degradation, vegetation decline and crop failure because the limit of soil water resources and soil water carrying capacity for vegetation. At this stage, the plant water relationship has to be regulated according to the soil water carrying capacity for vegetation in the critical period of plant-water relationship regulation (Guo, 2021a and b ). So, soil moisture has been highly considered because predicting the dynamics of soil moisture is the foundation for sustainable use of soil water resources, drought assessment and maximum yield. There are some soil moisture models such as water balance model, the SPAC water transport model, the SPAC water heat transport model, the mathematical statistics model, the random water balance model and the stochastic soil water dynamics model and so on (Shang, 2004 ). Because meteorology, soil and crops have some random features in time and space, it is difficult to predict soil water (Liu, et al, 2003 ). Artificial neural network (ANN) is an analysis method dealing with global and nonlinear mapping relationship between inputs and outputs. Because of self-organizing, self-learning and redundant fault-tolerant properties of the input data, ANN has a great advantage in the data fitting and function approximation and have widely been applied (Pisoni, et al. 2009; Cai, et al. 2009), such as the predication of soil moisture (Pisoni, et al . 2009; Liu et al ,2008; Guo ,2012; Kseneman et al ,2012). As a kind of LAN transformation of time and frequency, Wavelet analysis can extract the information effectively in the signal, and proceeds multi-scale refinement analysis of signal through scaling and translation to realize the high-resolution local positioning of the time domain and frequency domain. Combining with the artificial neural network and wavelet analysis method, wavelet neural network method has two sides of advantages and widely applied in the hydrological forecasting (Xu et al, 2012 ), water quality prediction (Lu et al. 2008 ) and so on. However, there are a few reports of the application of wavelet neural network method in soil moisture forecast, especially the predict accuracy of soil water content in forest land. In this paper, authors try to use wavelet and neural network model to forecast the soil moisture in caragana shrubland and then estimate soil water resources use limit by plant. The results will provide a powerful basis for regulating the relationship between plant growth and soil water and promoting the vegetation restoration in loess hilly region. Material And Methods Site description This study was carried out at the Shanghuang Eco-experiment Station, located in the semiarid region of the Loess Plateau (35°59′- 36°02′ N, 106°26′- 106°30′E) in Guyuan, Ningxia Hui Autonomous Region, China. The altitude ranges from 1,534 to 1,824 m above the sea level. Precipitation is scarce in the period from January to March, and the rainfall from June to September accounts for more than 70% of the annual precipitation. Mean rainfall measured between 1983 and 2001 was 415.6 mm with a maximum of 635 mm in 1984 and a minimum of 260 mm in 1991. The frost-free period is 152 days. The soil is mainly loamy loess (FAO/UNESCO. 1988), which is porous and widely distributed in the semiarid region of the Loess Plateau. There is a little change of soil texture with the depth in the soil profile (Yang and Shao ,2000). The experimental field was located in the Caragana bushland in the middle of Heici Mountain with a slope gradient of 3°, facing southeast at the station. The study object is 16-year-old Caragana ( Caragana korshinskii ) Plantation, under which the main plant species are Stipa bungeana , Heteropappus altaicus , Artemisia giraldii and Thymus mongolicus (Guo and Shao,2013; Guo 2021a and 2021b ). Measurement The investigation of the existing Caragana shrubs was made at the study site in April of 2002. There are five 100 m 2 (5×20m) standard runoff plots. The sowing amounts of Caragana were 2.0 kg, 1.5 kg, 1.0 kg, 0.5 kg and 0 kg/100m 2 (wasteland, control), respectively. A neutron probe, CNC503A (Beijing Nuclear Instrument Company, Beijing), was used to measure soil moisture in the soil layers from 5 cm to 780 cm and measurement was made at every 20cm interval. The soil water content obtained for each measuring depth was taken to be representative for the soil layer that included the measuring point ±10 cm depth, apart from that for the 5 cm depth, which was taken to represent the upper 10 cm of soil. Neutron counts were made for 16 seconds. The growing season of Caragana was in the period from April to October every year. Plant growth of height and basal diameter) and Measurement was made at 15 days interval in growing season and one time per month in the period of dormancy. This paper selects the soil water contents measured in the experimental plot with the sowing amount of 1.5 kg /100m 2 as the research object to analysis and predict the dynamics of soil moisture in Caragana brushland. Data Process The MATLAB software was used to process the data. The data measured in this study basically reflect the soil moisture dynamic change trend, but it is short for neural network training and wavelet analysis, so cubic spline interpolation method was used to enlarge the measure frequency to one time a week and then got 113 sets of data. Wavelet analysis Wavelet analysis, a kind of mathematical method based on Fourier analysis, can show the subtle structure and characteristics of measured data using wavelet transform through selecting proper scale and window functions. Wavelet transformation needs to choose suitable wavelet function such as Haar、Daubechies、Symlets、Coiflets and so on. The Daubechies wavelet function can be used to better analyze the problems of time series reported by Zhou Gui and & Gui (Zhou et al ,2006). Narx Recursive Neural Network Nonlinear Auto-regressive with Exogenous Inputs Model (NARX network) (Shi et al ,2009) was a kind of recursive neural networks with delay unit and was referred to the nonlinear auto-regressive models with external input. The input layer of the network receives two kinds of signals. The inputs from the outside the network can be expressed as u(k), u(k-1), ..., u(k-p+1), and the outputs of feedback signals from the network can be expressed as y(k), y(k-1),..., y(k-p+1), and the nonlinear system of network dynamic can be expressed as y(k+1) = F(y(k), ..., y(k-p+1), u(k), ..., u(k-p+1)). The NARX network training algorithm adopted LM algorithm of BP network. Model Soil water data were divided and reconstruct based on the wavelet analysis method, and then authors got the general picture of the low-frequency components and high -frequency details. In model I, authors selected the low frequency component and the soil water content in a soil layer which is highly correlated with that in the predicted soil layers as input variables to build NARX recursive neural network prediction model I according to wavelet analysis. In Model II: NARX neural network was used to predict the general picture of low-frequency components and high frequency detail respectively, and then we have got the soil moisture forecast results by summing the network outputs. Results And Analyse Selection of target layers The soil moisture contents in 5 to 300 cm soil layers were selected as the research target. The variation coefficient of soil moisture content in each soil layer were estimated. The variation coefficient of soil moisture content in 5 cm soil layer, CV 5, is more than 30%, that is to say, CV 5 > 30%, 20% < CV 20−80 < 30%, 5% < CV 100−180 < 20%, CV 200−300 < 5%, respectively, so the 5 to 300 cm soil layers can be classified into four groups, 0 to 5 cm, 20 to 80 cm, 80 to 180 cm and 200 to 300 cm soil layer. Because soil moisture content in the 5 cm soil layer is surface soil and interfered by outside factors and the change trend of soil water in the soil layer was uncertainty in Caragana brushland, it was not be selected as the research target. Finally, the soil water contents in the rest three soil layers such as 40 cm, 100 cm and 200 cm soil layers were chosen respectively as the analysis object. Wavelet Analysis Of Soil Moisture First, the soil water content in the 100 cm layer were selected as the research objects, and the interpolated 113 sets of data in 100 cm layer were selected as the original wavelet sequence s 1 , then db 2 was selected to do single scaling wavelet decomposition and reconstruction (Jiang and Liu, 2004 ; Zhang ,2012), as shown in figure 1. In figure 1, s 1 is time series trend diagram of soil moisture data measured in 100 cm soil layer, a 1 is the general picture part of low frequency and its variation trend is consistent with the original signal. The high frequency detail part is d 1 after soil water data were decomposed using single scale wavelet, which reflects the change of the original signal frequency. s 1 , s 1 = a 1 +d 1 , is the synthesized reconstruction signal of decomposed by single scaling wavelet. The Selection Of Input Variable This article selected the soil moisture content in the soil layers that highly correlated with s 1 as the inputs, the correlation results at each soil layer are shown in Table1. Besides, a 1 can be used as an model inputs because it has the similar dynamic change trend with s 1 , so input variables of model I were as follows: 60cm, 80cm, 120cm, 140cm, a 1 and output variables was s 1 . Table 1. The Correlation analysis among soil water contents in 40cm to 160cm soil lavers Soil layer (cm) 40 60 80 100 120 140 160 40 1 0.893 0.717 0.423 0.375 0.32 0.177 60 0.893 1 0.889 0.616 0.525 0.416 0.228 80 0.717 0.889 1 0.683 0.62 0.51 0.323 100 0.423 0.616 0.683 1 0.892 0.711 0.229 120 0.375 0.525 0.62 0.892 1 0.923 0.431 140 0.32 0.416 0.51 0.711 0.923 1 0.598 160 0.177 0.228 0.323 0.229 0.431 0.598 1 The selection of input variables in model II: (1) when predicting a 1 , the soil water contents in 60cm, 80cm, 100cm, 120 cm and 140cm soil layers were inputs, a 1 was outputs; (2) when predicting d1, s 1 is only related to s 1 , d 1 was output variable. Comparison Between Model I And Model Ii The range of soil moisture content was volatile due to much affecting factors, so this article was only used for short-term prediction. The input variables of week N and output variables of week N + 1 form a sample set, and there was a total of No.112 samples sets. Data sets was divided as follows: the data from 1 to 90 groups was taken as the training set, which used for fitting model; the data from No.91 to No.101 sets was taken as the validation set, which used for the prediction of error estimation in the selected model; the remaining data in II sets be used as a test set to ultimately evaluate the generalization error of selected model. Figure 2 showed the simulation correlation analysis in training set s 1 for model I and model II. of d 1 is only related to s 1 , d 1 was output variable. It can be seen from Figure 2 that model II was better than model I in the overlap of the simulated values predicting d 1 , s 1 was input variable for the change and the measured values and in the correlation analysis, showing that the NARX recursive neural network has the better learning ability than BP neural network. Table 2 Comparison of predicted error of validation set No. 92 to No.98 at 40 cm and 200 cm soil layers Items Relative error (%) Items Relative error % 92 6.99 99 -3.27 93 5.98 100 -4.75 94 6.27 101 2.68 95 10.90 102 4.77 96 5.56 Average relative error(%) 3.52 97 -0.08 98 3.66 Table 2 is the validation set of forecast error analysis for the model I and model II. It can be seen from the Table 2 that average relative error of model I was 3.5% and that of model II was 0.3%, showing that the prediction accuracy using the model II is higher than that using model I. The Applicant Of Model Ii In order to study the feasibility of actual operation of model II, in the paper soil water content from 103 to 113 weeks in the 100cm soil layer were forecasted, as shown in table 3. Based on wavelet analysis, the model II was more suitable than model I for forecasting soil water content in the Caragana shrubland by comparing the results of correlation analysis of simulated and measured values and the prediction error analysis of validation set. The average relative error of predicted soil water from 103 to 113 weeks is 0.8%, and absolute values of relative error of soil water in the 11 weeks’were lower than 10%, showing that modelⅡ is feasible in prediction of soil water content in the woodland. The model after training (learning) right reflects the samples that did not occurred in training set. Learning is not simply to memorize the studied inputs, but to learn the inner regularity of environment itself embedded in the sample through the study of a finite number of training samples16. In order to further test the model generalization ability, moisture contents from 103 to 113 weeks in 40 cm and 200 cm soil layer were predicted. The correlation analysis of the predicted values and the measured values were shown in figure 3. The error analysis of prediction values was shown in table 4. The figure 3 and table 4 showed that the curves of predicted values were consistent with the measured values in 40 cm and 200 cm soil layer. The correlation coefficients of the linear regression equation were 0.981, 0.984 respectively, and p< 0.05. The average relative errors were less than 5%, suggesting that the wavelet neural network model II has good generalization performance. Discussion Table 3 Comparison of predicted error and observed values from No.103 to No.113 week in 100 cm soil layer Week Observed predicted relative error (%) 103 6.8622 6.8836 0.31 104 6.8289 6.8951 0.97 105 6.6937 6.7091 0.23 106 6.4809 6.4841 0.05 107 7.1149 7.1138 -0.02 108 9.2415 9.2373 -0.05 109 11.4952 11.5012 0.05 110 12.4359 12.4043 -0.25 111 12.3375 12.2879 -0.40 112 11.9021 11.3647 -4.52 113 11.8320 12.0770 2.07 Average relative error(%) 0.81 Table 4 Error analysis of the predicted values from 103 to 113 week at 40 cm and 200 cm soil layers Items 40cm 200cm Week Actual data predicted Actual data predicted Actual data relative error (%) 103 6.862 6.4253 -6.37 6.314 6.2957 -0.30 104 6.123 5.9140 -3.41 6.327 6.2908 -0.57 105 6.704 6.2114 -7.35 6.357 6.3538 -0.05 106 13.05 12.66 -3.02 6.358 6.3704 0.20 107 16.73 16.518 -1.26 6.399 6.3696 -0.46 108 17.48 17.353 -0.74 6.537 6.5047 -0.49 109 13.78 12.784 -7.23 6.652 6.6998 0.72 110 13.43 15.053 12.06 6.627 6.6682 0.63 111 11.96 12.717 6.35 6.525 6.5400 0.23 112 11.05 10.554 -4.45 6.455 6.4755 0.31 113 9.389 9.7211 3.53 6.525 6.4913 -0.52 Average error (%) 4.94 Average error (%) 0.41 After the original signal were divided into low-frequency components and high-frequency components, wavelet analysis was used to analyse the data, and fully highlighted the trend and frequency fluctuations of signals changing with time, and avoided bad learning problems of some high-frequency mutation data when directly using neural network to predict the original data. The low-frequency component of the soil water content after wavelet analysis in the soil layers largely correlated with that were selected as the input variables in Model I to predict soil general picture of the low-frequency water content in target soil layer. Model II used NARX recursive neural network to predict the component and high frequency detail component, then combined the outputs. Because of higher fitting precision and smaller error compared with the model I after training analysis and error analysis of verification set. Model II can better predict soil moisture content in the Caragana brushland of loess hilly-gully region. There were different change degrees of soil moisture in each soil layer. The changes of soil moisture content with soil depth gradually tend to be steady. The soil moisture in 100 cm soil layer was selected to forecast soil water content in other soil layers, and the soil moisture in 40 cm and 200 cm soil layer were chose to generalize the model. All of obtained results were ideal. If we obtain the maximum infiltration depth and the change of withering coefficient with soil depth and soil water resources use limit by plant, the amount of water stored within the maximum infiltration depth, in which the soil moisture content in each layer is equal to the withering coefficient before forecasting soil water content in the the maximum infiltration depth in advance, we can estimate soil water resources within the maximum infiltration depth and then compare the soil water resources and soil water resources use limit by plant. If the soil water resources equal to soil water resources use limit by plant, soil drought is serious. At this stage of plant water relation, the soil water seriously influences plant growth. The serious soil drought will cause soil degradation, plant death, crop failure, and waste land resource. In order to control the serious soil drought and obtain high production, we have to predict soil moisture content in the the maximum infiltration depth and estimate soil water resources, and soil water resources use limit by plant and soil water carrying capacity for vegetation in the key period of plant water relation regulation, and then regulate the relationship between soil water and plant growth and improve the soil water condition by reducing plant density to increase the soil water supply from rainfall and reduce the soil water consumption if the soil water resources is more than soil water resources use limit by plant because soil water resources are renewable resources and only come from rainfall, there is not enough water resource to irrigation, and ground water is deep and cannot be used by plant.When regulate the relationship between soil water and plant growth, the amount of regulation equal the difference between present density minus soil water carrying capacity for vegetation to realize sustainable use of soil water resources and high quality sustainable development of forest vegetation (Guo, 2021a and b ). Conclusions According to the wavelet analysis, NARX recursive neural network model has higher prediction accuracy of soil water content, and can well predict soil moisture content at a given soil layers with various fluctuating frequency, and has better generalization performance. This is a good model to predict soil moisture in the soil under caragana brushland. If we measured the change of soil water with time and the change of withering coefficient with soil depth, and then we can estimate the maximum infiltration depth, soil water resources, soil water resources use limit by plant in advance before predicting soil moisture content at a given soil layers, then we can take effective measure to control the soil degradation and vegetation decline by regulating the relationship between soil moisture and plant growth and realizing the sustainable use of soil water resources in the water-limited regions. The research needs to continue. Declarations Acknowledge This study was supported by the National Science Fund of China (Project No. 42077079, 41271539, 41071193) and National key R & D plan（Project No. 2016YFC0501702）and Study on high quality sustainable development of soil and water conservation (A2180021002). Funding (information that explains whether and by whom the research was supported) This study was supported by the National Science Fund of China (Project No. 42077079, 41271539, 41071193) and Study on high quality sustainable development of soil and water conservation (A2180021002). Conflicts of interest/Competing interests There is not Competing Financial and non-financial interests Availability of data and material (data transparency) Data available on request due to privacy/ethical restrictions Code availability (software application or custom code):exel. Authors' contributions (optional: please review the submission guidelines from the journal whether statements are mandatory) Dong-Mei Bai wrote the paper and Zhong-Sheng Guo investigate the soil water and review and edit the paper References Cai L et al (2009) Prediction of SYM-H index by NARX neural network from IMF and solar wind data. Science in China (Series E: Technological Sciences) 10:2877–2885 FAO/UNESCO (1988) Soil map of the world, revised legend. FAO/UNESCO, Rome Guo Z (2010b) Soil water resource use limit in semi-arid loess hilly area. Chin J App Eco 21:3029–3035. http://connection.ebscohost.com /c/articles/63484494/soil-water-resource-use-limit-semi-arid-loess-hilly-area Guo Z-S (2021a) Soil water carrying capacity for vegetation. Land Degradation & Development 32(14):3801–3811. https://doi.org/10.1002/ldr.3950 Guo Z (2021b) Soil hydrology process and Sustainable Use of Soil Water Resources in Desert Regions. 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Mechanical Industry Press. Beijing. China Zhou W, Gui L, Zhou L (2006) High-level technology of MATLAB Wavelet Analysis. Xidian University Press, Xi’an, pp 51–63 Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-977050","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":64326144,"identity":"64f749fb-0807-4b15-b311-55c2bdb009e2","order_by":0,"name":"Dong-Mei Bai","email":"","orcid":"","institution":"Northwest A \u0026 F University","correspondingAuthor":false,"prefix":"","firstName":"Dong-Mei","middleName":"","lastName":"Bai","suffix":""},{"id":64326143,"identity":"b8145e09-c47d-4159-b9c6-a160197448ad","order_by":1,"name":"Zhong-Sheng Guo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYNCCCiBmJk3LGZK1MLaRolo+Ivnwx5/zttkzsLM/k/jBYCfPwH72AF4thjfSEox5t91ObGDmMZPsYUg2bODJS8CvZUaOQTLjttsJDMw8bLeBPkpgkOAxIKjl4M85t+0ZmNmfAbXUE9YiL5Fj2MDbcJuxgZnBDKjlMGEtBjzPkpl5jt1ObGPmMf/ZY3DcsI0nh4At7cAQ+1Fz256f//hjgx8V1fL87GcI2HIAymCDcGEMfLY0EFIxCkbBKBgFowAAc605neHETzcAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-5461-8530","institution":"Northwest A \u0026 F University","correspondingAuthor":true,"prefix":"","firstName":"Zhong-Sheng","middleName":"","lastName":"Guo","suffix":""},{"id":64326145,"identity":"1bec5912-4e6f-4358-acba-4cef5cb2a638","order_by":2,"name":"Man-Cai Guo","email":"","orcid":"","institution":"Northwest A \u0026 F University","correspondingAuthor":false,"prefix":"","firstName":"Man-Cai","middleName":"","lastName":"Guo","suffix":""}],"badges":[],"createdAt":"2021-10-16 03:26:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-977050/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-977050/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":16296249,"identity":"4b2ecdbe-bc66-444f-94a4-30c5ab3e22b1","added_by":"auto","created_at":"2021-12-08 22:16:53","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":45388,"visible":true,"origin":"","legend":"Wavelet analysis of soil water content in 100cm soil layer.","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-977050/v1/34eaa5f1666a9d0687e51b4d.png"},{"id":16296298,"identity":"4582f23a-553c-46ac-9917-2f88164c7f72","added_by":"auto","created_at":"2021-12-08 22:19:53","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":69887,"visible":true,"origin":"","legend":"Correlation analysis of simulated values in 100cm soil layer.","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-977050/v1/107ced81c3fc738f365f8bf8.png"},{"id":16296247,"identity":"e1c520e6-ab96-4bbe-846f-56de54596d3d","added_by":"auto","created_at":"2021-12-08 22:16:53","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":4493,"visible":true,"origin":"","legend":"This image is not available with this version.","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-977050/v1/14fc0245423daeb543aa0ebd.png"},{"id":17964157,"identity":"97319a0c-1515-4c5f-bada-7413222d43fb","added_by":"auto","created_at":"2022-02-05 21:53:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":491390,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-977050/v1/0908fd33-9fa6-4344-afcb-873551a78672.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eForecasting Soil Moisture In The Soil Under The Caragana Shrubland Using Wavelet Analysis And NARX Neural Network \u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSoil moisture is one of the most basic elements of the soil fertility, and the foundation for the crop fertility (li ,1962). Soil water is the most important factors influencing plant growth in the loess plateau. Because rain is shortage, soil drought often happens, which cause soil degradation, vegetation decline and crop failure in the loess plateau (Guo and Shao, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2013\u003c/span\u003e,2021a,2021b). The soil water resources are the soil water storage in a root soil, and soil water resources use limit by plant refers to the amount of water stored within the maximum infiltration depth, in which the soil moisture content at each layer is equal to the withering coefficient (Guo, 2010,\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e and \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003eb\u003c/span\u003e). When soil water resources in the maximum infiltration depth reduce to the soil water resources use limit by plant, the plant water relation enters the critical period of plant-water relationship regulation. At this time, soil drought serious influence plant growth, which cause serious soil degradation, vegetation decline and crop failure because the limit of soil water resources and soil water carrying capacity for vegetation. At this stage, the plant water relationship has to be regulated according to the soil water carrying capacity for vegetation in the critical period of plant-water relationship regulation (Guo, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e and \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003eb\u003c/span\u003e). So, soil moisture has been highly considered because predicting the dynamics of soil moisture is the foundation for sustainable use of soil water resources, drought assessment and maximum yield.\u003c/p\u003e \u003cp\u003eThere are some soil moisture models such as water balance model, the SPAC water transport model, the SPAC water heat transport model, the mathematical statistics model, the random water balance model and the stochastic soil water dynamics model and so on (Shang, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). Because meteorology, soil and crops have some random features in time and space, it is difficult to predict soil water (Liu, et al, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eArtificial neural network (ANN) is an analysis method dealing with global and nonlinear mapping relationship between inputs and outputs. Because of self-organizing, self-learning and redundant fault-tolerant properties of the input data, ANN has a great advantage in the data fitting and function approximation and have widely been applied (Pisoni, et al. 2009; Cai, et al. 2009), such as the predication of soil moisture (Pisoni, \u003cem\u003eet al\u003c/em\u003e. 2009; Liu \u003cem\u003eet al\u003c/em\u003e ,2008; Guo ,2012; Kseneman \u003cem\u003eet al\u003c/em\u003e,2012).\u003c/p\u003e \u003cp\u003eAs a kind of LAN transformation of time and frequency, Wavelet analysis can extract the information effectively in the signal, and proceeds multi-scale refinement analysis of signal through scaling and translation to realize the high-resolution local positioning of the time domain and frequency domain. Combining with the artificial neural network and wavelet analysis method, wavelet neural network method has two sides of advantages and widely applied in the hydrological forecasting (Xu et al, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), water quality prediction (Lu et al. \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) and so on. However, there are a few reports of the application of wavelet neural network method in soil moisture forecast, especially the predict accuracy of soil water content in forest land. In this paper, authors try to use wavelet and neural network model to forecast the soil moisture in caragana shrubland and then estimate soil water resources use limit by plant. The results will provide a powerful basis for regulating the relationship between plant growth and soil water and promoting the vegetation restoration in loess hilly region.\u003c/p\u003e"},{"header":"Material And Methods","content":"\u003cp\u003e \u003cb\u003eSite description\u003c/b\u003e This study was carried out at the Shanghuang Eco-experiment Station, located in the semiarid region of the Loess Plateau (35\u0026deg;59\u0026prime;- 36\u0026deg;02\u0026prime; N, 106\u0026deg;26\u0026prime;- 106\u0026deg;30\u0026prime;E) in Guyuan, Ningxia Hui Autonomous Region, China. The altitude ranges from 1,534 to 1,824 m above the sea level. Precipitation is scarce in the period from January to March, and the rainfall from June to September accounts for more than 70% of the annual precipitation. Mean rainfall measured between 1983 and 2001 was 415.6 mm with a maximum of 635 mm in 1984 and a minimum of 260 mm in 1991. The frost-free period is 152 days. The soil is mainly loamy loess (FAO/UNESCO. 1988), which is porous and widely distributed in the semiarid region of the Loess Plateau. There is a little change of soil texture with the depth in the soil profile (Yang and Shao ,2000). The experimental field was located in the Caragana bushland in the middle of Heici Mountain with a slope gradient of 3\u0026deg;, facing southeast at the station. The study object is 16-year-old Caragana (\u003cem\u003eCaragana korshinskii\u003c/em\u003e) Plantation, under which the main plant species are \u003cem\u003eStipa bungeana\u003c/em\u003e, \u003cem\u003eHeteropappus altaicus\u003c/em\u003e, \u003cem\u003eArtemisia giraldii\u003c/em\u003e and \u003cem\u003eThymus mongolicus\u003c/em\u003e (Guo and Shao,2013; Guo \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e and \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2021b\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cb\u003eMeasurement\u003c/b\u003e The investigation of the existing Caragana shrubs was made at the study site in April of 2002. There are five 100 m\u003csup\u003e2\u003c/sup\u003e (5\u0026times;20m) standard runoff plots. The sowing amounts of Caragana were 2.0 kg, 1.5 kg, 1.0 kg, 0.5 kg and 0 kg/100m\u003csup\u003e2\u003c/sup\u003e (wasteland, control), respectively. A neutron probe, CNC503A (Beijing Nuclear Instrument Company, Beijing), was used to measure soil moisture in the soil layers from 5 cm to 780 cm and measurement was made at every 20cm interval. The soil water content obtained for each measuring depth was taken to be representative for the soil layer that included the measuring point \u0026plusmn;10 cm depth, apart from that for the 5 cm depth, which was taken to represent the upper 10 cm of soil. Neutron counts were made for 16 seconds. The growing season of Caragana was in the period from April to October every year. Plant growth of height and basal diameter) and Measurement was made at 15 days interval in growing season and one time per month in the period of dormancy. This paper selects the soil water contents measured in the experimental plot with the sowing amount of 1.5 kg /100m\u003csup\u003e2\u003c/sup\u003e as the research object to analysis and predict the dynamics of soil moisture in Caragana brushland.\u003c/p\u003e\n\u003ch2\u003eData Process\u003c/h2\u003e\n\u003cp\u003eThe MATLAB software was used to process the data. The data measured in this study basically reflect the soil moisture dynamic change trend, but it is short for neural network training and wavelet analysis, so cubic spline interpolation method was used to enlarge the measure frequency to one time a week and then got 113 sets of data.\u003c/p\u003e \u003cp\u003eWavelet analysis\u003c/p\u003e \u003cp\u003eWavelet analysis, a kind of mathematical method based on Fourier analysis, can show the subtle structure and characteristics of measured data using wavelet transform through selecting proper scale and window functions. Wavelet transformation needs to choose suitable wavelet function such as Haar、Daubechies、Symlets、Coiflets and so on. The Daubechies wavelet function can be used to better analyze the problems of time series reported by Zhou Gui and \u0026amp; Gui (Zhou \u003cem\u003eet al\u003c/em\u003e ,2006).\u003c/p\u003e\n\u003ch2\u003eNarx Recursive Neural Network\u003c/h2\u003e\n\u003cp\u003eNonlinear Auto-regressive with Exogenous Inputs Model (NARX network) (Shi et al ,2009) was a kind of recursive neural networks with delay unit and was referred to the nonlinear auto-regressive models with external input. The input layer of the network receives two kinds of signals. The inputs from the outside the network can be expressed as u(k), u(k-1), ..., u(k-p+1), and the outputs of feedback signals from the network can be expressed as y(k), y(k-1),..., y(k-p+1), and the nonlinear system of network dynamic can be expressed as y(k+1) = F(y(k), ..., y(k-p+1), u(k), ..., u(k-p+1)). The NARX network training algorithm adopted LM algorithm of BP network.\u003c/p\u003e\n\u003ch2\u003eModel\u003c/h2\u003e\n\u003cp\u003eSoil water data were divided and reconstruct based on the wavelet analysis method, and then authors got the general picture of the low-frequency components and high -frequency details. In model I, authors selected the low frequency component and the soil water content in a soil layer which is highly correlated with that in the predicted soil layers as input variables to build NARX recursive neural network prediction model I according to wavelet analysis. In Model II: NARX neural network was used to predict the general picture of low-frequency components and high frequency detail respectively, and then we have got the soil moisture forecast results by summing the network outputs.\u003c/p\u003e"},{"header":"Results And Analyse","content":"\u003cdiv class=\"Section2\" id=\"Sec7\"\u003e\n \u003ch2\u003eSelection of target layers\u003c/h2\u003e\n \u003cp\u003eThe soil moisture contents in 5 to 300 cm soil layers were selected as the research target. The variation coefficient of soil moisture content in each soil layer were estimated. The variation coefficient of soil moisture content in 5 cm soil layer, CV\u003csub\u003e5,\u003c/sub\u003e is more than 30%, that is to say, CV\u003csub\u003e5\u003c/sub\u003e \u0026gt; 30%, 20% \u0026lt; CV\u003csub\u003e20\u0026minus;80\u003c/sub\u003e \u0026lt; 30%, 5% \u0026lt; CV\u003csub\u003e100\u0026minus;180\u003c/sub\u003e \u0026lt; 20%, CV\u003csub\u003e200\u0026minus;300\u003c/sub\u003e \u0026lt; 5%, respectively, so the 5 to 300 cm soil layers can be classified into four groups, 0 to 5 cm, 20 to 80 cm, 80 to 180 cm and 200 to 300 cm soil layer. Because soil moisture content in the 5 cm soil layer is surface soil and interfered by outside factors and the change trend of soil water in the soil layer was uncertainty in Caragana brushland, it was not be selected as the research target. Finally, the soil water contents in the rest three soil layers such as 40 cm, 100 cm and 200 cm soil layers were chosen respectively as the analysis object.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch2\u003eWavelet Analysis Of Soil Moisture\u003c/h2\u003e\n\u003cp\u003eFirst, the soil water content in the 100 cm layer were selected as the research objects, and the interpolated 113 sets of data in 100 cm layer were selected as the original wavelet sequence s\u003csub\u003e1\u003c/sub\u003e, then db\u003csub\u003e2\u003c/sub\u003e was selected to do single scaling wavelet decomposition and reconstruction (Jiang and Liu, \u003cspan class=\"CitationRef\"\u003e2004\u003c/span\u003e; Zhang ,2012), as shown in figure 1.\u003c/p\u003e\n\u003cp\u003eIn figure 1, s\u003csub\u003e1\u003c/sub\u003e is time series trend diagram of soil moisture data measured in 100 cm soil layer, a\u003csub\u003e1\u003c/sub\u003e is the general picture part of low frequency and its variation trend is consistent with the original signal. The high frequency detail part is d\u003csub\u003e1\u003c/sub\u003e after soil water data were decomposed using single scale wavelet, which reflects the change of the original signal frequency. s\u003csub\u003e1\u003c/sub\u003e, s\u003csub\u003e1\u003c/sub\u003e= a\u003csub\u003e1\u003c/sub\u003e+d\u003csub\u003e1\u003c/sub\u003e, is the synthesized reconstruction signal of decomposed by single scaling wavelet.\u003c/p\u003e\n\u003ch2\u003eThe Selection Of Input Variable\u003c/h2\u003e\n\u003cp\u003eThis article selected the soil moisture content in the soil layers that highly correlated with s\u003csub\u003e1\u003c/sub\u003e as the inputs, the correlation results at each soil layer are shown in Table1. Besides, a\u003csub\u003e1\u003c/sub\u003e can be used as an model inputs because it has the similar dynamic change trend with s\u003csub\u003e1\u003c/sub\u003e, so input variables of model I were as follows: 60cm, 80cm, 120cm, 140cm, a\u003csub\u003e1\u003c/sub\u003e and output variables was s\u003csub\u003e1\u003c/sub\u003e.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003eTable 1. The Correlation analysis among soil water contents in 40cm to 160cm soil lavers\u003cbr\u003e\u003cbr\u003e\n \u003ctable border=\"1\" id=\"Taba\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoil layer (cm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e140\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.717\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.423\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.375\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.177\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.893\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.616\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.416\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.228\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.717\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.683\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.323\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.423\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.616\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.683\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.892\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.711\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.229\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.375\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.892\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.923\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.431\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.416\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.711\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.923\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.598\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.177\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.228\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.323\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.229\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.431\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.598\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe selection of input variables in model II: (1) when predicting a\u003csub\u003e1\u003c/sub\u003e, the soil water contents in 60cm, 80cm, 100cm, 120 cm and 140cm soil layers were inputs, a\u003csub\u003e1\u003c/sub\u003e was outputs; (2) when predicting d1, s\u003csub\u003e1\u003c/sub\u003e is only related to s\u003csub\u003e1\u003c/sub\u003e, d\u003csub\u003e1\u003c/sub\u003e was output variable.\u003c/p\u003e\n\u003ch2\u003eComparison Between Model I And Model Ii\u003c/h2\u003e\n\u003cp\u003eThe range of soil moisture content was volatile due to much affecting factors, so this article was only used for short-term prediction. The input variables of week N and output variables of week N + 1 form a sample set, and there was a total of No.112 samples sets. Data sets was divided as follows: the data from 1 to 90 groups was taken as the training set, which used for fitting model; the data from No.91 to No.101 sets was taken as the validation set, which used for the prediction of error estimation in the selected model; the remaining data in II sets be used as a test set to ultimately evaluate the generalization error of selected model.\u003c/p\u003e\n\u003cp\u003eFigure 2 showed the simulation correlation analysis in training set s\u003csub\u003e1\u003c/sub\u003e for model I and model II. of d\u003csub\u003e1\u003c/sub\u003e is only related to s\u003csub\u003e1\u003c/sub\u003e, d\u003csub\u003e1\u003c/sub\u003e was output variable. It can be seen from Figure 2 that model II was better than model I in the overlap of the simulated values predicting d\u003csub\u003e1\u003c/sub\u003e, s\u003csub\u003e1\u003c/sub\u003e was input variable for the change and the measured values and in the correlation analysis, showing that the NARX recursive neural network has the better learning ability than BP neural network.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u0026nbsp;\u003ctable border=\"1\" id=\"Tab1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eComparison of predicted error of validation set \u0026nbsp;No. 92 to \u0026nbsp;No.98 at 40 cm and 200 cm soil layers\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eItems\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRelative error (%)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eItems\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRelative error %\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-3.27\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-4.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6.27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.68\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e10.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e102\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4.77\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eAverage relative error(%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" rowspan=\"3\"\u003e\n \u003cp\u003e3.52\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e-0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3.66\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable 2 is the validation set of forecast error analysis for the model I and model II. It can be seen from the Table 2 that average relative error of model I was 3.5% and that of model II was 0.3%, showing that the prediction accuracy using the model II is higher than that using model I.\u003c/p\u003e\n\u003ch2\u003eThe Applicant Of Model Ii\u003c/h2\u003e\n\u003cp\u003eIn order to study the feasibility of actual operation of model II, in the paper soil water content from 103 to 113 weeks in the 100cm soil layer were forecasted, as shown in table 3.\u003c/p\u003e\n\u003cp\u003eBased on wavelet analysis, the model II was more suitable than model I for forecasting soil water content in the Caragana shrubland by comparing the results of correlation analysis of simulated and measured values and the prediction error analysis of validation set.\u003c/p\u003e\n\u003cp\u003eThe average relative error of predicted soil water from 103 to 113 weeks is 0.8%, and absolute values of relative error of soil water in the 11 weeks\u0026rsquo;were lower than 10%, showing that modelⅡ is feasible in prediction of soil water content in the woodland.\u003c/p\u003e\n\u003cp\u003eThe model after training (learning) right reflects the samples that did not occurred in training set. Learning is not simply to memorize the studied inputs, but to learn the inner regularity of environment itself embedded in the sample through the study of a finite number of training samples16. In order to further test the model generalization ability, moisture contents from 103 to 113 weeks in 40 cm and 200 cm soil layer were predicted. The correlation analysis of the predicted values and the measured values were shown in figure 3. The error analysis of prediction values was shown in table 4.\u003c/p\u003e\n\u003cp\u003eThe figure 3 and table 4 showed that the curves of predicted values were consistent with the measured values in 40 cm and 200 cm soil layer. The correlation coefficients of the linear regression equation were 0.981, 0.984 respectively, and p\u0026lt; 0.05. The average relative errors were less than 5%, suggesting that the wavelet neural network model II has good generalization performance.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eTable 3 Comparison of predicted error and observed values from No.103 to No.113 week in 100 cm soil layer\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tabb\"\u003e\n \u003ccolgroup cols=\"4\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWeek\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eObserved\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003epredicted\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003erelative error\u003c/p\u003e\n \u003cp\u003e(%)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e103\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.8622\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.8836\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e104\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.8289\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.8951\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e105\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.6937\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.7091\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.4809\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.4841\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e107\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.1149\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.1138\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.2415\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.2373\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e109\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.4952\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.5012\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e110\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.4359\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.4043\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.3375\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.2879\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.9021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.3647\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-4.52\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e113\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.8320\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.0770\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.07\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eAverage relative error(%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eTable 4 Error analysis of the predicted values from 103 to 113 \u0026nbsp;week at 40 cm and 200 cm soil layers\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Tabc\"\u003e\n \u003ccolgroup cols=\"7\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eItems\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e40cm\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003e200cm\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eWeek\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eActual data\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epredicted\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eActual data\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003epredicted\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eActual data\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003erelative error\u003c/p\u003e\n \u003cp\u003e(%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e103\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.862\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.4253\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-6.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.314\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.2957\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e104\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.123\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.9140\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-3.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.327\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.2908\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.57\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e105\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.704\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.2114\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-7.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.357\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.3538\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e106\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-3.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.358\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.3704\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e107\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e16.518\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-1.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.399\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.3696\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.353\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.537\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.5047\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.49\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e109\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.784\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-7.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.652\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.6998\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e110\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e13.43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15.053\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.627\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.6682\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.63\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.717\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.5400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e112\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e11.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.554\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-4.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.455\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.4755\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e113\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.389\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.7211\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.525\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.4913\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e-0.52\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eAverage error (%) 4.94\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colspan=\"3\"\u003e\n \u003cp\u003eAverage error (%) 0.41\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAfter the original signal were divided into low-frequency components and high-frequency components, wavelet analysis was used to analyse the data, and fully highlighted the trend and frequency fluctuations of signals changing with time, and avoided bad learning problems of some high-frequency mutation data when directly using neural network to predict the original data.\u003c/p\u003e\n\u003cp\u003eThe low-frequency component of the soil water content after wavelet analysis in the soil layers largely correlated with that were selected as the input variables in Model I to predict soil general picture of the low-frequency water content in target soil layer. Model II used NARX recursive neural network to predict the component and high frequency detail component, then combined the outputs. Because of higher fitting precision and smaller error compared with the model I after training analysis and error analysis of verification set. Model II can better predict soil moisture content in the Caragana brushland of loess hilly-gully region.\u003c/p\u003e\n\u003cp\u003eThere were different change degrees of soil moisture in each soil layer. The changes of soil moisture content with soil depth gradually tend to be steady. The soil moisture in 100 cm soil layer was selected to forecast soil water content in other soil layers, and the soil moisture in 40 cm and 200 cm soil layer were chose to generalize the model. All of obtained results were ideal.\u003c/p\u003e\n\u003cp\u003eIf we obtain the maximum infiltration depth and the change of withering coefficient with soil depth and soil water resources use limit by plant, the amount of water stored within the maximum infiltration depth, in which the soil moisture content in each layer is equal to the withering coefficient before forecasting soil water content in the the maximum infiltration depth in advance, we can estimate soil water resources within the maximum infiltration depth and then compare the soil water resources and soil water resources use limit by plant. If the soil water resources equal to soil water resources use limit by plant, soil drought is serious. At this stage of plant water relation, the soil water seriously influences plant growth. The serious soil drought will cause soil degradation, plant death, crop failure, and waste land resource. In order to control the serious soil drought and obtain high production, we have to predict soil moisture content in the the maximum infiltration depth and estimate soil water resources, and soil water resources use limit by plant and soil water carrying capacity for vegetation in the key period of plant water relation regulation, and then regulate the relationship between soil water and plant growth and improve the soil water condition by reducing plant density to increase the soil water supply from rainfall and reduce the soil water consumption if the soil water resources is more than soil water resources use limit by plant because soil water resources are renewable resources and only come from rainfall, there is not enough water resource to irrigation, and ground water is deep and cannot be used by plant.When regulate the relationship between soil water and plant growth, the amount of regulation equal the difference between present density minus soil water carrying capacity for vegetation to realize sustainable use of soil water resources and high quality sustainable development of forest vegetation (Guo, \u003cspan class=\"CitationRef\"\u003e2021a\u003c/span\u003e and \u003cspan class=\"CitationRef\"\u003eb\u003c/span\u003e).\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eAccording to the wavelet analysis, NARX recursive neural network model has higher prediction accuracy of soil water content, and can well predict soil moisture content at a given soil layers with various fluctuating frequency, and has better generalization performance. This is a good model to predict soil moisture in the soil under caragana brushland.\u003c/p\u003e \u003cp\u003eIf we measured the change of soil water with time and the change of withering coefficient with soil depth, and then we can estimate the maximum infiltration depth, soil water resources, soil water resources use limit by plant in advance before predicting soil moisture content at a given soil layers, then we can take effective measure to control the soil degradation and vegetation decline by regulating the relationship between soil moisture and plant growth and realizing the sustainable use of soil water resources in the water-limited regions. The research needs to continue.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledge\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by the National Science Fund of China (Project No. 42077079, 41271539, 41071193) and National key R \u0026amp; D plan（Project No. 2016YFC0501702）and Study on high quality sustainable development of soil and water conservation (A2180021002).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding (information that explains whether and by whom the research was supported)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study was supported by the National Science Fund of China (Project No. 42077079, 41271539, 41071193) and Study on high quality sustainable development of soil and water conservation (A2180021002).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThere is not Competing Financial and non-financial interests\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and material (data transparency)\u003c/strong\u003e\u0026nbsp;\u003cbr\u003eData available on request due to privacy/ethical restrictions\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability (software application or custom code):exel.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions (optional: please review the submission guidelines from the journal whether statements are mandatory)\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDong-Mei Bai wrote the paper and \u0026nbsp;Zhong-Sheng Guo investigate the soil water and review and edit the paper\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eCai L et al (2009) Prediction of SYM-H index by NARX neural network from IMF and solar wind data. Science in China (Series E: Technological Sciences) 10:2877\u0026ndash;2885\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFAO/UNESCO (1988) Soil map of the world, revised legend. FAO/UNESCO, Rome\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuo Z (2010b) Soil water resource use limit in semi-arid loess hilly area. Chin J App Eco 21:3029\u0026ndash;3035. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://connection.ebscohost.com /c/articles/63484494/soil-water-resource-use-limit-semi-arid-loess-hilly-area\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuo Z-S (2021a) Soil water carrying capacity for vegetation. Land Degradation \u0026amp; Development 32(14):3801\u0026ndash;3811. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/ldr.3950\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuo Z (2021b) Soil hydrology process and Sustainable Use of Soil Water Resources in Desert Regions. Water,2021,13(17): 2377. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://doi.org/10.3390/w13172377\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuo Z, Shao M (2013) Impact of afforestation density on soil and water conservation of the semiarid Loess Plateau, China. J Soil Water Conserv 68:401\u0026ndash;410\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGuo QC, He ZF (2012) Forecast Model of Soil Water Content Based on Artificial Neural Network. Journal of Shanxi Agricultural Sciences 40:892\u0026ndash;895\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJiang X, Liu H (2004) Radial Basis Function Networks Based on Wavelet Analysis for the Annual Flow Forecast. Journal of Applied Sciences 22:411\u0026ndash;414\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKseneman M, Gleich D, Božidar P (2012) Soil-moisture estimation from TerraSAR-X data using neural networks. Machine Vision and Applications 23:937\u0026ndash;952\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLi YS (1962) Soil Moisture and Crop Growth Condition of LOU Soil. Acta Pedol Sin 10:289\u0026ndash;304\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu HB, Wu W, Wei CF (2003) Study of Soil Water Forecast with Neural Network. J Soil Water Conserv 17:59\u0026ndash;62\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu HB, Xie DT, Wu W 2008.Soil water content forecasting by ANN and SVM hybrid architecture. Environ Monit Assess. 143;187-193\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLu ZJ, Zhu L, Pei HP et al (2008) The model of chlorophy II-a concentration forecast in the West Lake based on wavelet analysis and BP neural networks. Acta Ecologica Sinica. 28;4965-4973\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePisoni E, Farina M, Carnevale C et al 2009.Forecasting peak air pollution levels using NARX models. Engineering Applications of Artificial Intelligence. 22;593-602\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShi Y, Han LQ, Lian XQ .2009.Neural Network Design and Instance Analysis.Beijing University of Posts and Telecommunications Press. Beijing. China\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShang SH (2004) .Advances in Soil Moisture Simulation and Forecasting Models. Journal of Shenyang Agricultural University 35:455\u0026ndash;458\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXu TB et al (2012) BP network prediction model and its application in annual runoff forecasting based on wavelet analysis. Water Resources and Power 30:17\u0026ndash;19\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYang WZ, Shao MA 2000.Study on soil moisture in the Loess Plateau. Science Press. Beijing.China. 23-24\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang DF (2012) MATLAB Wavelet Analysis(The Second Edition). Mechanical Industry Press. Beijing. China\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou W, Gui L, Zhou L (2006) High-level technology of MATLAB Wavelet Analysis. Xidian University Press, Xi\u0026rsquo;an, pp 51\u0026ndash;63\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"semi-arid loess hilly region, plant growth, soil moisture, wavelet analysis, NARX recurrent neural network, forecast","lastPublishedDoi":"10.21203/rs.3.rs-977050/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-977050/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003ePurpose:\u003c/strong\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003eIt is important for sustainable use of soil water resources to forecast soil moisture in forestland of water-limited regions. There are some soil moisture models. However, there is not a better method to forecast soil moisture.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eMethods:\u003c/strong\u003e The change of soil moisture with time were investigated and the data of soil moisture were divided into a low frequency and a high frequency component using wavelet analysis, and then NARX neural network was used to build model I and model II. For model I, low frequency component was the input variable, and for model II, low frequency component and high frequency component were predicted.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eResults:\u003c/strong\u003e the average relative error for model I is 3.5% and for model II is 0.3%. The average relative error of predicted soil moisture in100cm layer using model II is 0.8%, then soil water content in\u0026nbsp;40 cm and 200 cm soil depth is selected and the forecast errors are 4.9 % and 0.4 %.Using model \u0026nbsp;II to predict soil water is well．\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eConclusion:\u003c/strong\u003e Predicting soil water will be important for sustainable use of soil water resource and controlling soil degradation, vegetation decline and crop failure in water limited regions.\u003c/p\u003e","manuscriptTitle":"Forecasting Soil Moisture In The Soil Under The Caragana Shrubland Using Wavelet Analysis And NARX Neural Network","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2021-12-08 22:16:51","doi":"10.21203/rs.3.rs-977050/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f2cd4d42-1063-42fa-89c1-c1fcd90c3098","owner":[],"postedDate":"December 8th, 2021","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":8986830,"name":"Agricultural Engineering"}],"tags":[],"updatedAt":"2022-02-05T21:53:07+00:00","versionOfRecord":[],"versionCreatedAt":"2021-12-08 22:16:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-977050","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-977050","identity":"rs-977050","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}