Sensitivity Analysis of Modeled Soil Water Dynamics within Variable Rate Irrigation Zones for Winter Wheat

Sensitivity Analysis of Modeled Soil Water Dynamics within Variable Rate Irrigation Zones for Winter Wheat | 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 Sensitivity Analysis of Modeled Soil Water Dynamics within Variable Rate Irrigation Zones for Winter Wheat Elisa A. Flint, Jeffrey D. Svedin, Austin P. Hopkins, Ruth Kerry, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9420591/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Understanding within-field and within-season variability of soil water supply and crop water stress is critical for successful variable-rate irrigation (VRI) management. The objectives of this study were to 1) assess within-field variability of field capacity (FC), wilting point (WP), total available water (TAW), and initial soil volumetric water content (VWC init ); 2) validate a water balance model based on the American Society of Civil Engineers (ASCE) standardized Penman-Monteith estimation of reference evapotranspiration (ET 0 ) using measured within-field VWC; and 3) evaluate the model sensitivity to FC, WP, VWC init , and crop coefficients. A 22-ha field of winter wheat ( Triticum aestivum L.) near Grace, Idaho, United Sates of America was delineated into five zones and managed with VRI. There was observable spatial variability of soil water characteristics among 102 measured sites in the field: FC (355–488 mm), WP (103–153 mm), TAW (230–361 mm), and VWC init (325–464 mm) in the 1.2 m soil profile. Model validation against measured VWC resulted in root mean square error (RMSE) values of 23.2–61.3 mm for the different sampling dates. These RMSE values showed the ability to model within-field spatially variable soil water dynamics and crop water stress at the 102 locations. The model showed high sensitivity of predicted output values, such as ET and soil water depletion to FC and VWC init inputs. The sensitivity analysis suggested that using spatially variable crop coefficients could improve prediction of spatially variable ET rates. Model sensitivity to soil water characteristics present opportunities for a spatially variable modelling approach to assist in scheduling VRI. STATEMENTS AND DECLARATIONS Competing Interests : The authors declare no competing interests. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results. Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION Conserving water is a vital societal goal in agricultural (Svedin et al., 2021 ) and urban (Burgin et al., 2021 ) environments. Variable-rate irrigation (VRI) is a tool with potential to improve the efficiency of crop water use by spatially matching irrigation rates to variable properties such as crop water demand and soil properties (King et al., 1995 ; Zhu et al., 2018 ). There are many published observations of within-field spatial variability in soil and crop characteristics that support the potential of VRI (Baroni et al., 2013 ; Daccache et al., 2015 ; Flint et al., 2023; Hawley et al., 1983 ; Longchamps et al., 2015 ; Sadler et al., 2005 ; Smith et al., 2021 ; Svedin et al., 2019 , 2021 ; Woolley et al., 2021 ). King et al. ( 2006 ) observed greater water productivity under VRI in potato ( Solanum tuberosum L.). Lo et al. ( 2016 ) described potential water application savings of 25 mm yr -1 on 13% of Nebraska, USA center pivots through VRI. Hedley and Yule ( 2009a ) demonstrated the ability of VRI to conserve up to 26% of applied irrigation compared to uniform irrigation when using a water balance approach in VRI zones delineated using soil apparent electrical conductivity (ECa). Flint et al. (2023) observed an average of 12% applied water reduction when utilizing VRI compared to a grower’s standard practice rate in Idaho, USA. While VRI systems are commercially available, decision support systems (such as zone delineation) need further scientific development. Spatial variation of yield and crop water use have been linked to the variability of topography and soil properties, such as soil: texture, depth, water holding capacity, and ECa (Haghverdi et al., 2015 ; Longchamps et al., 2015 ; Sadler et al., 2005 ). As such, these factors are commonly used to delineate VRI zones (et al. 2017a; Hedley et al. 2009a; Hedley and Yule 2009b ; Messick et al. 2017 ). One irrigation scheduling approach commonly used at the field scale is the reference ET (ET 0 ) and crop coefficient (K c ) approach, coupled with a soil water balance. Specifically, ET 0 from the American Society of Civil Engineers (ASCE) Standard Penman-Monteith ET model (Allen et al., 1998 ) is used within the following equation to estimate adjusted crop ET: $$\:\begin{array}{c}{ET}_{c\:adj}={K}_{s}\times\:{K}_{c}\times\:{ET}_{o}\:\#\left(1\right)\end{array}$$ where ET c adj is the adjusted crop ET, K s is the transpiration reduction factor reflecting conditions where soil water availability limits the rate of ET, K c is the crop coefficient that reflects the crop type and development stage, and ET o is the reference crop ET. Previous studies have shown the ability to schedule irrigation at the field scale with this approach, but few have evaluated it in a VRI setting with spatially variable model inputs (Al-Kufaishi et al., 2006 ). In a study under uniform irrigation management, Svedin et al. ( 2019 , 2021 ) modelled within-field variation of ET using measured variation of VWC init and soil water characteristics and documented correlation with measured, within-field variation of ET. While this is promising, collecting spatially dense soil water characteristics for model inputs can be time and cost prohibitive. Further, modelling based on spatially uniform K c values is uncertain for a VRI application. Within-field variation of crop height and leaf area index (LAI) values and their interactions with K c and soil VWC have been documented (Baroni et al., 2013 ; Hawley et al., 1983 ). Svedin et al. ( 2019 , 2021 ) proposed the utilization of spatially variable K c when modelling ET for VRI. For this approach to be effective, understanding the within-field variation of and model sensitivity to input parameters is necessary (Crick and Hill, 1987 ). The objectives of the study were to (1) assess the within-field variability of FC, WP, total available water (TAW) and VWC init , (2) to validate the ASCE Penman-Monteith ET o water balance model using measured, within-field spatially variable VWC, and (3) to evaluate the model sensitivity to FC, WP, and VWC init , and K c . We hypothesized that VWC init would have a greater effect on the average stress coefficient, (K s ), average soil water depletion within the root zone, and average ET c adj within the model than soil properties and the crop coefficient. MATERIALS AND METHODS Site Description This study was conducted near Grace, ID, USA (elevation 1687 m above sea level; 42.60904 latitude, -111.78833 longitude) on a winter wheat ( Triticum aestivum L) production field (22 ha) with a wheat-wheat-potato ( Solanum tuberosum L.) rotation. The field is in a semi-arid region with about 80 to 110 frost-free days. Average annual precipitation is 390 mm with much of the precipitation occurring during winter as snow, which often blows and accumulates variably based on topography and surface conditions. The historical precipitation from May-August is 148 mm (National Water and Climate Center, NRCS-USDA, 2021). For this study duration precipitation was low, with 99, 90, and 92 mm in 2016, 2017 and 2019, respectively. Irrigation water was applied using a 380-m long center pivot equipped with a VRI system (GrowSmart Precision VRI, Lindsay Zimmatic, Omaha, NE, USA) and rotator nozzles spaced 5 m apart with 103 kPa pressure regulators (Nelson Irrigation, Walla Walla, WA, USA). Irrigation events occurred every 5–7 d in the spring and every 3–5 d during the summer at peak ET demand. The field has some areas of shallow soil and basalt bedrock at the surface that are not farmed (0.3 ha total). The soils are a Rexburg-Ririe complex, with a silty clay loam texture and 1 to 4% slopes. Rexburg and Ririe soils are coarse-silty, mixed, superactive, frigid Calcic Haploxerolls (Soil Survey Staff, 2021). There was little observed spatial variation in soil textural class. A texture analysis at 42 randomly selected locations sampled at 0.3 m depth increments down to 0.9 m within the field confirmed the texture to be a silty clay loam. The field has a relatively uniform topography, with a 6 m difference between lowest and highest elevation (Fig. 1 ). Conventional best management practices for nutrient, soil, pest, and crop management were used by the grower. Soil Sampling Grid soil sample size was determined by computing a variogram of the normalized difference vegetation index (NDVI) from bare soil imagery. The variogram had a range of ~ 140 m. Following the guideline developed by Kerry & Oliver ( 2003 ) of a sampling interval approximately half the variogram range, the interval of 70 m was used for the main sampling grid with 46 samples. An additional 56 sample points were located at random points along the grids to improve the geostatistical predictions. This sampling scheme was used to calculate spatial and temporal variation of soil VWC and soil water depletion at the specific dates mentioned below. Spring green-up and post-harvest soil samples were collected on 23 April and on 5 September 2019, and two mid-season sampling dates occurred on 30 May and 25 June 2019. Samples for VWC determination were collected at four depths 0-0.3 m, 0.3–0.6 m, 0.6–0.9 m, and 0.9–1.2 m with a soil probe driven into the profile with a modified gas-powered post driver (AMS, Inc. American Falls, ID, USA). Samples were placed in plastic bags and sealed for transport to the laboratory where gravimetric soil water was determined by drying in a forced air oven at 105 ° C until consistent weights were reached. Soil gravimetric water content was converted to volumetric water content using soil bulk density values determined in 2016 from previous samples (Svedin et al., 2019 , 2021 ). Bulk density values ranged from 1.13–1.69 g cm − 3 with an average bulk density value of 1.46 g cm − 3 (Svedin et al., 2019 , 2021 ). VRI Zone Delineation and Sensor-based Irrigation Scheduling The VRI zones were created from yield and ET data collected from the 2016 and 2017 crops (Flint et al., 2023). The yield and ET data from these two years were used in a regression with the response variable being yield and the explanatory variable being ET. A k-means clustering algorithm was then used from the slope of the regression to determine the five zones (Flint et al., 2023). Once these zones were created in 2019, soil VWC (TEROS 12, Meter, Pullman, WA, USA) and matric potential sensors (TEROS 21, Meter, Pullman, WA, USA) with data loggers (ZL6, Meter, Pullman, WA, USA) were placed at depths of 15, 45, and 75 cm in one location within each zone. The location of each sensor set was established based on the combination of the following; grower knowledge of the water variability across the field, historical yield variability between and within zones, and average values of soil VWC within the specified zone (Flint et al., 2023; Woolley, 2020 ). One of each type of sensor was installed at every depth for all of the five locations (Fig. 1 ). The amounts of irrigation applied to each zone were derived from a combination of the VWC data provided by these soil sensors and the zone-specific averaged field capacities. Rates were determined to maintain VWC between FC and the RAW value. Modeling Water Dynamics Modeling the spatial and temporal changes in ET for the 2019 season followed Allen et al. ( 1998 ) and the FAO Penman-Monteith estimation of reference ET to predict daily soil water levels individually for each of the 102 sampling locations. The model was initiated using measured VWC init , the VWC measured as the winter wheat emerged from dormancy in the spring (Svedin et al., 2019 , 2021 ). Depletion of soil water within the root zone was modeled with a daily time step from spring sampling (23 April) to post-harvest sampling (5 September). Spatially uniform ET o and K c were used to estimate ET c for wheat. When depth of soil water fell below a site-specific RAW threshold, ET c was adjusted with a site-specific crop stress coefficient (K s ) to estimate the adjusted crop ET (ET c−adj ) (Svedin et al., 2019 , 2021 ). Weather data were collected from a station ~ 2 km from the field site (42.51496 N, -111.73606 W; Cooperative Agricultural Weather Network AgriMet). The weather data were used to calculate daily ET (ET c adj ) using ET o from the ASCE Standard Penman-Monteith ET model (Allen et al., 1998 ). The crop coefficient approach was used to calculate daily ET c−adj using Eq. 1, where K s was calculated daily for each sample point and the K c curve was estimated from tabular values from a similar environment (Allen et al., 1998 ) and validated with field observations. The K s was calculated as: $$\:\begin{array}{c}{K}_{s}=\left(SWHC-{D}_{r}\right)÷\left[\left(1-p\right)\times\:SWHC\right]\: \left(2\right)\end{array}$$ where SWHC is the soil water holding capacity in the 1.2 m deep soil profile, p is the table value 0.55 from (Allen et al., 1998 ) that represents the average fraction of SWHC that can be depleted before crop stress occurs in winter wheat, and D r is the current root zone water depletion (Allen et al., 1998 ). Soil water holding capacity and RAW were calculated from Allen et al. ( 1998 ) as follows: $$\:\begin{array}{c}SWHC={\theta\:}_{FC}-{\theta\:}_{WP}\: \left(3\right)\end{array}$$ $$\:\begin{array}{c}RAW=p\times\:SWHC\: \left(4\right)\end{array}$$ where \(\:\theta\:\) FC is the VWC (mm) at FC, \(\:\theta\:\) WP is the VWC at WP (mm), and the estimated rooting depth of the crop and was assumed to be 1200 mm for this study. The RAW value is the readily available soil water content in the root zone (mm), and p is defined above. At this site, winter snowfall and spring thaw act as the wetting event and FC was estimated for each sampling point as the greatest observed depth of soil water for each depth increment as measured at that site over a four-year observation period (2016–2019) (Flint et al., 2023; Svedin et al., 2019 , 2021 ). This approach for estimating FC assumed the soil was saturated from melting snow and spring precipitation but had at least three days for drainage with minimal ET losses (Martin, et al., 1990 ). It was assumed that post-harvest soil samples were at WP because the soils had been dried down for harvest in the wheat crop years with 15, 7.1, and 5 mm of rain since the last irrigation event 18, 16, and 5 d prior to harvest in 2016, 2017, and 2019, respectively. The WP was then determined by using the minimum observed VWC value at each location over these study years. Field measurements of WP values were validated with lab analysis utilizing a Dewpoint Potentiometer (WP4C, Meter Group Inc., Pullman, WA, USA). Volumetric soil water content was measured at -1500 kPa with satisfactory field and lab measurement error ( n = 39, RMSE = 11mm) (Svedin et al., 2019 , 2021 ). These ranges set the upper and lower boundaries for the changes in these input values within the model. Daily soil water depletion within the root zone was estimated using the following equation: $$\:\begin{array}{c}{D}_{r,i}={D}_{r,i-1}-{P}_{i}-{I}_{i}+{ET}_{c\:adj\:i}+{DP}_{i}\: \left(5\right)\end{array}$$ where D r,i is the soil water depletion at the end of a specified day (d i ), D r,i-1 is the soil water depletion at the end of the previous day, P i is the precipitation on d i , I i is the irrigation depth on d i , ET c-adj,i is the crop ET on d i , and DP i is deep percolation out of the root zone on d i (Allen et al., 1998 ). Deep percolation was calculated from any amount of water that exceeded site-specific FC values for the 1.2 m deep profiles from the ET model. Model Validation The 2019 model output was validated following the procedures from Svedin et al. ( 2019 , 2021 ) by comparing the calculated VWC to the measured VWC at two in-season sampling dates (30 May, 25 June), and at the end of the growing season (5 September)(Svedin et al., 2019 , 2021 ). Statistical measures of model performance followed Miner et al. ( 2013 ) including: (1) relative error (RE), (2) normalized objective function (NOF) (3) root mean square error (RMSE), and (4) r-squared, where RE represents model bias, NOF indicates the fit of the model (where NOF < 1 is less than one standard deviation from the mean), and RMSE is the difference between predicted and measured values. Desirables values of RE, NOF, RMSE are close to zero, and desirable r-squared values are above 0.50. Sensitivity Analysis A “one-at-a-time” sensitivity analysis was performed on the soil water depletion model (Downing et al., 1985 ; Hamby, 1994 ). The input variables FC, WP, VWC init , and K c were individually altered one-at-a-time to evaluate the change that would occur in output variables including K s , ET c adj , and soil water depletion from the root zone. For the sensitivity analysis, the standard condition was modelled using input values averaged over the 102 sample locations. Then, one at a time changes were made for FC, WP, and VWC init values by adjusting the input from one to four observed standard deviations (SDs) above and below their respective mean values (Downing et al., 1985 ; Hamby, 1994 ). When either the FC or WP values were adjusted individually, each sampling point’s TAW values were adjusted. The K c value was adjusted by first calculating the spatially variable K c from LAI data measured on 25 June at each sampling location using an AccuPAR ceptometer (LP-80 PAR/LAI, Meter, Pullman, WA, USA) (Hopkins, 2021 ; Johnson & Trout, 2012 ; Trout et al., 2008 ) and then averaged over the 102 sample locations. A SD was calculated from this data and the K c value was adjusted from negative four to positive four SDs away from the average K c value from 25 June. RESULTS Spatial Variation of Soil Properties The soil water characteristics varied in their ranges of distribution across the 22-ha wheat field. Soil water at FC ranged from 355 to 488 mm in the 1200 mm profile, averaging 412 mm (Table 1, Fig. 2 ). Soil water at WP ranged from 103–153 mm, averaging 125 mm (Table 1, Fig. 2 ). The TAW ranged from 230 to 361 mm, averaging 286 mm (Table 1, Fig. 2 ). The VWC init ranged from 325–464 mm, averaging 388 mm (Table 1, Fig. 2 ). Variability in VWC continued throughout the season, ranging from 321–450, 249–417, and 142–334 mm and averaging 393, 330, and 213 mm on 30 May, 25 June, and 5 September, respectively (Table 1). Table 1 Water retention properties and volumetric water content (VWC) values within a 1200 mm depth profile for the 2019 growing season (mm) Location FC WP April VWC May VWC June VWC Sept VWC - - - - - - - - - - - - - - - - - - - - - - - mm - - - - - - - - - - - - - - - - - - - - - - - - - Average Field 412 125 388 393 330 213 Zone 1 418 132 398 394 348 209 Zone 2 412 126 389 391 328 209 Zone 3 411 123 387 393 320 218 Zone 4 408 124 382 392 331 211 Zone 5 421 116 400 401 327 230 Max Field 488 153 463 450 417 334 Zone 1 465 153 463 419 385 284 Zone 2 450 145 433 447 380 281 Zone 3 450 142 430 432 364 334 Zone 4 488 148 451 446 417 272 Zone 5 475 126 444 450 383 249 Min Field 355 103 325 321 249 142 Zone 1 390 103 365 338 305 178 Zone 2 379 106 348 321 288 171 Zone 3 355 108 325 325 267 142 Zone 4 360 104 332 350 281 144 Zone 5 375 108 346 358 249 203 Standard Deviation Field 24 11 27 26 33 31 Zone 1 25 15 31 22 25 28 Zone 2 19 8 22 26 28 28 Zone 3 23 10 30 29 27 43 Zone 4 25 11 27 25 38 27 Zone 5 39 6 33 35 49 15 The observations of FC, WP, TAW and VWC init served as the parameter ranges used in the sensitivity analysis. The variograms for each soil property reported similar ranges of 340, 350, and 370 m for spring VWC, FC and TAW, respectively, and WP had a range of 60 m (Table 2). The spatial random variation of each soil water retention property characterized by the nugget:sill ratio of variograms was high and similar for each variable with 80%, 62%, 73% and 72% for spring VWC, FC, TAW, and WP, respectively (Table 2). Large random variation ranges of similar percentages for soil water retention properties could mean that changing the model will have similar effects on the ET calculation for each sampling point. However, it could also account for the differences in outputs of the model. Table 2 Variogram range and random variation of soil water retention properties from 102 sample locations in 2019 Soil Property Range Nugget Sill Random Variation - - - - - - - - - - - - m - - - - - - - - - - - % FC 350 3.80 2.30 62.3 WP 61.0 0.78 0.30 72.4 TAW 370 4.00 1.50 72.7 VWC init 338 6.19 1.54 80.1 FC = field capacity WP = wilting point TAW = total available water VWC init = initial soil volumetric water content Model Validation The model validation approach compared predicted VWC with measured values for two in-season sampling dates. Modelled VWC also showed good agreement with measured data (Fig. 3 ). The relative error was − 3.7% for 30 May and 0.84% for 25 June. For both sampling dates, model predictions of VWC were within one standard deviation of the mean (NOF < 1). The model fit of VWC was excellent for the two mid-season dates (Fig. 3 ). Model Sensitivity Analysis The sensitivity analysis on the soil water depletion model was performed by varying key input factors one at a time and evaluating output changes of 1) field average stress coefficient (K s ); 2) field average ET c adj ; and 3) field average soil water depletion from the root zone. The key input factors included the static soil water retention properties FC and WP, and the dynamic properties VWC init and crop coefficient values. Model Sensitivity to Static Soil Water Retention Properties: Field Capacity (FC) and Wilting Point (WP) The depletion model outputs were sensitive to changes in soil water retention properties such as FC and WP (Fig. 4 ). Most output values showed significant differences between the original output values ( p < 0.05). The exceptions were when the output values K s at FC + 1 SD and + 2 SDs had p -values of 0.334 and 0.065, respectively, and ET c adj at FC + 1 SD had a p -value of 0.722. Changes in FC between + 1 and + 4 SDs caused the most change in soil VWC values (Fig. 4 c). Model Sensitivity to VWC init When VWC init values were adjusted to either positive or negative changes away from their cumulative mean value, all output values were significantly different than the original output values ( p < 0.05) (Fig. 4 c). The VWC init expressed variable ranking of sensitivity on the output variables, depending on the output variable and the direction of change within the VWC init values (Fig. 4 ). The outputs K s and ET c adj showed they were less sensitive towards VWC init when the input value was changed in the negative direction (less VWC) compared to the K c input value (Fig. 4 a, b). Model Sensitivity to K c All changes in K c led to significant changes in the output values ( p < 0.05). K c values were adjusted from − 1 to -4 SDs and had the greatest impact on model outputs. All outputs, except for soil water depletion, were most sensitive to + 1 to + 4 SD changes from the average K c values (Fig. 4 ). Crop coefficient values were ranked as the second most sensitive for soil water depletion, with FC being ranked most sensitive when values were adjusted above their mean values. However, K c had the greatest impact on all outputs (Fig. 4 ). DISCUSSION Soil Water Characteristics and Irrigation Management Many have documented similar substantial within-field variation of soil water retention properties and theorized on using this variation to improve VRI management and crop production through zone delineation and irrigation scheduling (Daccache et al., 2015 ; de Lara et al., 2017 ; Haghverdi et al., 2015 ; Lo et al., 2017 ; Longchamps et al., 2015 ). In the present study, the degrees of within-field variation of FC, WP, and VWC were similar to the variation found by Lo et al. ( 2017 ) who demonstrated the benefit of using zone irrigation to match VWC measured from sensors and zone-specific FC values. It can be assumed similar improvements could occur at this location but would require further research to demonstrate this approach. Model Validation The validation approach supports that the used water balance model was able to predict within-field variation of soil water dynamics, crop water stress, and evapotranspiration rates over time. In general, the results of the modelling approach within this current study show that with spatially dense soil water characteristics, a water balance modelling approach may be a good way to schedule variable irrigation rates (Fig. 3 ), but the practical limitation is that spatially dense soil water retention properties and VWC init are not easily obtained. The sensitivity analysis was performed to shed light on how critical specific inputs are for the model. Model Sensitivity Substantial changes occurred within the soil VWC output levels when soil water retention properties (FC and WP) were averaged and adjusted one-at-a-time by the prescribed SDs from the mean. These changes would either suggest the need to add more or less water at each irrigation event, or have more or less frequent irrigations, depending on the values of FC, WP, and TAW. These changes in water needs from the adjusted model might be correct for some areas of the field, but incorrect for other areas, thus causing either over- or under-watering and eventually leading to early onset of crop water stress or excess drainage without recognition from the model. As these outputs affect the irrigation management of the field, model predictions are highly dependent upon spatially variable soil water retention properties. Spatial variability of VWC init has been observed to be a predicting factor of the spatial variability of onset of crop water stress (Svedin et al., 2019 , 2021 ). Uniform above average spring VWC values resulted in little change to K s , ET c adj , and soil water depletion within the root zone during the 2019 season. When VWC init model inputs were below the field average, predicted K s and ET c adj both decreased, while soil water depletion increased, signifying more stress within the field throughout the season. This suggests that if model input values for VWC init are above the field average, the predicted irrigation recommendations would be low in parts of the field, and the model would not accurately describe crop water stress. The opposite would occur if VWC init was uniformly low throughout the field. The model would indicate the field needed to be irrigated, when parts of it may not need irrigation, and thus drainage and runoff would occur without the model. This suggests the need for spatially accurate input of VWC init . However, this dependency is challenging for commercial VRI implementation, because obtaining spatially dense VWC init data is not practical for most growers. This issue could be solved if large amounts of cost-effective soil sensors could be placed throughout a field to read the spatial and temporal variation in soil moisture. The adjusted K c values were created by taking the mean value and standard deviation of LAI data from the field on 25 June and calculating the standard deviation values in K c . These standard deviation values were then added or subtracted from the original canopy K c value. All outputs from the adjusted K c were more sensitive to the negative change in K c values than to positive changes. K c standard deviation adjustments were changed to values that were generally not within a normal range of a K c during that particular time of the growing season, especially for a winter wheat crop. The extreme changes in the K c values could explain their large impact on outputs. Changes in the outputs could also be affected by the K c values due to the different irrigation rates that were applied to sections of the field, suggesting that multiple factors or inputs can affect each other in how they impact the outputs of the model. An approach that may improve this model would be the measurement of the variation of crop canopy conditions to inform the model (Svedin et al., 2019 , 2021 ). This approach is consistent with other studies noted in the review by O’Shaughnessy et al. ( 2015 ) that show improvement in irrigation management when dynamic crop conditions are assessed. As Svedin et al. ( 2019 , 2021 ) suggested, having a variable K c could improve the original model based on the ASCE method within this study by addressing the different growth rates of the crop due to the different irrigation rates that affect the rate of growth for each zone. Also, looking into how the interaction of these inputs affect the outputs of the model will assist in understanding the need for accuracy of each input. CONCLUSIONS Field observations and assessment of model sensitivity were combined to evaluate the roles of soil water retention properties and dynamic factors on soil and crop water dynamics. The influence of crop coefficients on irrigated winter wheat within a soil water depletion model based on the standards of Allen et al. ( 1998 ) and the FAO ET equation was also considered. Outputs (average K s , average ET c adj and average soil water depletion within the root zone) from the original model based on spatially variable values of soil properties (VWC init , FC, WP and TAW) with a uniform crop coefficient for winter wheat were compared to the same model with different values (1 to 4 SDs of mean values) of soil properties and crop coefficient values. Variable FC, WP, spring VWC, and K c values were all important factors in predicting accurate temporal and spatial K s , soil water depletion, and ET to accurately make VRI recommendations. All assessed input variables also played a role in the accuracy of the soil water depletion model. This model, based on the ASCE method, used with spatially variable inputs, can improve water conservation within irrigation management when coupled with VRI. Further research is required to understand the necessary level of accuracy for input variables to create the most practical and reliable models for irrigation recommendations, as well as understanding if other adjustments need to be made to the model for improved accuracy. Additionally, improvements to this work could advance significantly if large amounts of affordable sensors could be used to estimate soil moisture properties for input into the Penman Monteith equation rather than relying on expensive and time-consuming sampling and lab analysis. Declarations ACKNOWLEDGMENTS AND FUNDING INFORMATION We would like to acknowledge BKR farms for providing the field site equipped with the variable rate irrigation system for this project’s fulfillment. We would also like to thank the many students from Brigham Young University research labs not listed as authors who assisted in the field work related with data from this paper. This research was funded by United States-Israel Binational Agricultural Research and Development Fund, grant number IS-5218-10, and the United States Department of Agriculture Western Sustainable Agricultural Research and Education Program, grant number SW19-909. The APC was funded by Brigham Young University. Author Contribution E.A.F., J.D.S., A.B., M.A.Y., B.G.H., and N.C.H. provided substantial contributions to the design of the work.E.A.F., A.P.H., J.D.S., R.K., B.G.H., and N.C.H. provided substantial contributions to the acquisition of the data. E.A.F., A.P.H., J.D.S., R.K., A.B., R.J., B.G.H., and N.C.H. provided substantial contributions to the analysis, and interpretation of the data. E.A.F., B.G.H., and N.C.H. wrote the main manuscript text. E.A.F. prepared the figures and tables. All authors reviewed and revised the manuscript critically for important intellectual content.All authors approved the version to be published.All authors agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. Acknowledgement We would like to acknowledge BKR farms for providing the field site equipped with the variable rate irrigation system for this project’s fulfillment. We would also like to thank the many students from Brigham Young University research labs not listed as authors who assisted in the field work related with data from this paper. References Al-Kufaishi SA, Blackmore BS, Sourell H (2006) The feasibility of using variable rate water application under a central pivot irrigation system. Irrigat Drain Syst 20(2–3):317–327. https://doi.org/10.1007/s10795-006-9010-2 Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration - Guidelines for computing crop water requirements - FAO irrigation and drainage paper 56. Food and Agriculture Organization of the United Nations. https://www.fao.org/3/x0490e/x0490e00.htm Baroni G, Ortuani B, Facchi A, Gandolfi C (2013) The role of vegetation and soil properties on the spatio-temporal variability of the surface soil moisture in a maize-cropped field. J Hydrol 489:148–159. https://doi.org/10.1016/j.jhydrol.2013.03.007 Burgin HR, Wear GA, Hansen NC, Hopkins BG (2021) Variable impacts on growth of deficit irrigation on Cynodon dactylon (L.) Pers. × Cynodon transvaalensis Burtt Davy and Poa pratensis L. Int Turfgrass Soc Res J 14(1):152–156. https://doi.org/10.1002/its2.71 Crick MJ, Hill MD (1987) The role of sensitivity analysis in assessing uncertainty . https://inis.iaea.org/records/acbtg-hc646 Daccache A, Knox JW, Weatherhead EK, Daneshkhah A, Hess TM (2015) Implementing precision irrigation in a humid climate - Recent experiences and on-going challenges. Agric Water Manage 147:135–143. https://doi.org/10.1016/j.agwat.2014.05.018 de Lara A, Khosla R, Longchamps L (2017) Characterizing spatial variability in soil water content for precision irrigation management. Adv Anim Biosci 8(2):418–422. https://doi.org/10.1017/s2040470017000279 Downing DJ, Gardner RH, Hoffman FO (1985) An examination of response-surface methodologies for uncertainty analysis in assessment models. Technometrics 27(2):151–163. https://doi.org/10.2307/1268763 Flint EA, Hopkins BG, Svedin JD, Kerry R, Heaton MJ, Jensen RR, Campbell CS, Yost MA, Hansen NC Irrigation zone delineation and management with a field-scale variable rate irrigation system in winter wheat. Agronomy 2023 13 (4), 1125–1138. https://doi.org/10.3390/agronomy13041125 Haghverdi A, Leib BG, Washington-Allen RA, Ayers PD, Buschermohle MJ (2015) High-resolution prediction of soil available water content within the crop root zone. J Hydrol 530:167–179. https://doi.org/10.1016/j.jhydrol.2015.09.061 Hamby DM (1994) A review of techniques for parameter sensitivity analysis of environmental models. Environ Monit Assess 32:135–154. https://doi.org/10.1007/BF00547132 Hawley ME, Jackson TJ, McCuen RH (1983) Surface soil moisture variation on small agricultural watersheds. J Hydrol 62(1–4):179–200. https://doi.org/10.1016/0022-1694(83)90102-6 Hedley CB, Yule IJ (2009a) A method for spatial prediction of daily soil water status for precise irrigation scheduling. Agric Water Manage 96(12):1737–1745. https://doi.org/10.1016/j.agwat.2009.07.009 Hedley CB, Yule IJ (2009b) Soil water status mapping and two variable-rate irrigation scenarios. Precision Agric 10(4):342–355. https://doi.org/10.1007/s11119-009-9119-z Hopkins AP (2021) Remote sensing and spatial variability of leaf area index of irrigated wheat fields [Master’s thesis, Brigham Young University]. https://scholarsarchive.byu.edu/etd/9523 Johnson LF, Trout TJ (2012) Satellite NDVI assisted monitoring of vegetable crop evapotranspiration in California’s San Joaquin Valley. Remote Sens 4(2):439–455. https://doi.org/10.3390/rs4020439 Kerry R, Oliver MA (2003) Variograms of ancillary data to aid sampling for soil surveys. Precision Agric 4:261–278. https://doi.org/10.1023/A:1024952406744 King BA, Brady RA, McCann IR, Stark JC (1995) Variable rate water application through sprinkler irrigation. In Site-Specific Management for Agricultural Systems (pp. 485–493). https://doi.org/10.2134/1995.site-specificmanagement.c33 King BA, Stark JC, Wall RW (2006) Comparison of site-specific and conventional uniform irrigation management for potatoes. Appl Eng Agric 22(5):677–688. https://doi.org/10.13031/2013.22000 Lo TH, Heeren DM, Martin DL, Mateos L, Luck JD, Eisenhauer DE (2016) Pumpage reduction by using variable rate irrigation to mine undepleted soil water. Trans Am Soc Agricultural Biol Eng 59(5):1285–1298. https://doi.org/10.13031/trans.59.11773 Lo T, Heeren DM, Mateos L, Luck JD, Martin DL, Miller KA, Barker JB, Shaver TM (2017) Field characterization of field capacity and root zone available water capacity for variable rate irrigation. Appl Eng Agric 33(4):559–572. https://doi.org/10.13031/aea.11963 Longchamps L, Khosla R, Reich R, Gui DW (2015) Spatial and temporal variability of soil water content in leveled fields. Soil Sci Soc Am J 79(5):1446–1454. https://doi.org/10.2136/sssaj2015.03.0098 Martin DL, Stegman EC, Freres E (1990) Irrigation scheduling principles. In: Hoffman GJ, Howell TA,Solomon K. H. (eds) Management of Farm Irrigation Systems. American Society of Agricultural Engineers, St. Joseph, MI, USA, pp 155–206 Messick RM, Heaton MJ, Hansen N (2017) Multivariate spatial mapping of soil water holding capacity with spatially varying cross-correlations. Annals Appl Stat 11(1):69–92. https://doi.org/10.1214/16-AOAS991 Miner GL, Hansen NC, Inman D, Sherrod LA, Peterson GA (2013) Constraints of no-till dryland agroecosystems as bioenergy production systems. Agron J 105(2):364–367. https://doi.org/10.2134/agronj2012.0243 O’Shaughnessy SA, Evett SR, Colaizzi PD (2015) Dynamic prescription maps for site-specific variable rate irrigation of cotton. Agric Water Manage 159:123–138. https://doi.org/10.1016/j.agwat.2015.06.001 Sadler EJ, Evans RG, Stone KC, Camp CR (2005) Opportunities for conservation with precision irrigation. J Soil Water Conserv 60(6):371–379. https://doi.org/10.1080/00224561.2005.12435829 Smith R, Oyler L, Campbell C, Woolley EA, Hopkins BG, Kerry R, Hansen NC (2021) A new approach for estimating and delineating within-field crop water stress zones with satellite imagery. Int J Remote Sens 42(16):6005–6024. https://doi.org/10.1080/01431161.2021.1931536 Svedin JD, Hansen NC, Kerry R, Hopkins BG (2019) Modeling spatio-temporal variations in crop water stress for variable-rate irrigation. Precision Agriculture ’19 - Papers Presented at the 12th European Conference on Precision Agriculture , 687–693. https://doi.org/10.3920/978-90-8686-888-9_85 Svedin JD, Kerry R, Hansen NC, Hopkins BG (2021) Identifying within-field spatial and temporal crop water stress to conserve irrigation resources with variable-rate irrigation. Agronomy 11(7):1377–1390. https://doi.org/10.3390/agronomy11071377 Trout TJ, Johnson LF, Gartung J (2008) Remote Sensing of Canopy Cover in Horticultural Crops. HortScience 43(2):333–337. https://doi.org/10.21273/HORTSCI.43.2.333 Woolley EA (2020) Soil water dynamics within variable rate irrigation zones of winter wheat [Master’s thesis, Brigham Young University]. https://scholarsarchive.byu.edu/etd/9302 Woolley EA, Kerry R, Hansen NC, Hopkins BG (2021) Variable rate irrigation: investigating within-zone variability. Precision Agriculture ’21, Proceedings of the 13th European Conference on Precision Agriculture , 635–641 https://doi.org/10.3920/978-90-8686-916-9_76 Zhu XY, Chikangaise P, Shi WD, Chen WH, Yuan SQ (2018) Review of intelligent sprinkler irrigation technologies for remote autonomous system. Int J Agricultural Biol Eng 11(1):23–30. https://doi.org/10.25165/j.ijabe.20181101.3557 Additional Declarations No competing interests reported. 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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-9420591","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627629233,"identity":"bca06275-422a-4bb2-a1b2-0dbffcd75869","order_by":0,"name":"Elisa A. Flint","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYDACdsYGICknw8bAwPgAIpRAQAszWIsxDxsDM7MBkVrApDEPkMUmQZQWfmbm5g8/GAx4+KT7j1Xz/DnMwM+eY4BXi2QzY5tkD1ALm8xhttu8bYcZJHve4NdicJixjYGH4Q8Pm0QyUEvDYQaDGwRssT/M2PzxD8gWoJZikMPsCWkxAIaYNA9UCzMPG9AWCQJaJIAOk5YxAGsxlpzbls4jceZZAV4t/O3tjz++qTCQk5+R+PDDmz/WcvztyRvwaoE6D8HkIUL5KBgFo2AUjAJCAAA2fjb4Zqb9hgAAAABJRU5ErkJggg==","orcid":"","institution":"Utah State University","correspondingAuthor":true,"prefix":"","firstName":"Elisa","middleName":"A.","lastName":"Flint","suffix":""},{"id":627629234,"identity":"7716875b-1c05-4f04-a42e-6475957365f4","order_by":1,"name":"Jeffrey D. Svedin","email":"","orcid":"","institution":"AgriNorthWest","correspondingAuthor":false,"prefix":"","firstName":"Jeffrey","middleName":"D.","lastName":"Svedin","suffix":""},{"id":627629235,"identity":"d546e2a1-7aa1-4863-86d5-7abd54d01a80","order_by":2,"name":"Austin P. 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Hansen","email":"","orcid":"","institution":"Brigham Young University","correspondingAuthor":false,"prefix":"","firstName":"Neil","middleName":"C.","lastName":"Hansen","suffix":""}],"badges":[],"createdAt":"2026-04-15 02:08:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9420591/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9420591/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108128884,"identity":"cfba2aed-29fa-4955-bd11-effdf2bfc1ce","added_by":"auto","created_at":"2026-04-29 15:52:56","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":199329,"visible":true,"origin":"","legend":"\u003cp\u003eField site near Grace, ID, USA with elevation contour lines (m), soil sample points (diamonds), sensor locations (red circles), and five irrigation management zones delineated based on winter wheat results from 2016 and 2017 and evaluated on winter wheat for 2019.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-9420591/v1/9129e458691b2005c8af521d.png"},{"id":108182681,"identity":"a1fc58c1-c1bd-4700-a68a-f2100af3d440","added_by":"auto","created_at":"2026-04-30 08:59:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":249074,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial variation of (a) field capacity (FC), (b) wilting point (WP), (c) total available water (TAW) and (d) initial volumetric water content (VWC\u003csub\u003einit\u003c/sub\u003e) within a 1200 mm depth soil profile for the study for field site near Grace, ID, USA\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-9420591/v1/d36ff41d797439950672743b.png"},{"id":108128886,"identity":"2eb0ff28-7f69-45ae-b12a-fbfa394ace35","added_by":"auto","created_at":"2026-04-29 15:52:56","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":132443,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between measured and modelled volumetric water content (VWC), with model fit statistics verifying agreement of the model with the measured data at two sampling dates within the 2019 season\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-9420591/v1/1383aca258f5cfd8b80f669e.png"},{"id":108128887,"identity":"0b141a19-aa46-42b3-a76f-ddb9c57e50bf","added_by":"auto","created_at":"2026-04-29 15:52:56","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":114901,"visible":true,"origin":"","legend":"\u003cp\u003eModel sensitivity of ± 4 standard deviations (SDs) for the input change for field capacity (FC), wilting point (WP), early spring volumetric water content (VWC\u003csub\u003einit\u003c/sub\u003e) and the crop coefficient (K\u003csub\u003ec\u003c/sub\u003e) value compared to the output change for SD changes in: Ks (a), ETc Adj (b), and soil water depletion within the root zone (c)\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-9420591/v1/8f22cd57190a6cf494d0c5d2.png"},{"id":108183833,"identity":"58a19600-e41f-480d-b2c3-9c06f9a525d6","added_by":"auto","created_at":"2026-04-30 09:02:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1052251,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9420591/v1/afddbb30-b70d-4438-b57d-ba442392ad1e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Sensitivity Analysis of Modeled Soil Water Dynamics within Variable Rate Irrigation Zones for Winter Wheat","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eConserving water is a vital societal goal in agricultural (Svedin et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) and urban (Burgin et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) environments. Variable-rate irrigation (VRI) is a tool with potential to improve the efficiency of crop water use by spatially matching irrigation rates to variable properties such as crop water demand and soil properties (King et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Zhu et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). There are many published observations of within-field spatial variability in soil and crop characteristics that support the potential of VRI (Baroni et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Daccache et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Flint et al., 2023; Hawley et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1983\u003c/span\u003e; Longchamps et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Sadler et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Smith et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Svedin et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Woolley et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). King et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) observed greater water productivity under VRI in potato (\u003cem\u003eSolanum tuberosum\u003c/em\u003e L.). Lo et al. (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) described potential water application savings of 25 mm yr\u003csup\u003e-1\u003c/sup\u003e on 13% of Nebraska, USA center pivots through VRI. Hedley and Yule (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2009a\u003c/span\u003e) demonstrated the ability of VRI to conserve up to 26% of applied irrigation compared to uniform irrigation when using a water balance approach in VRI zones delineated using soil apparent electrical conductivity (ECa). Flint et al. (2023) observed an average of 12% applied water reduction when utilizing VRI compared to a grower\u0026rsquo;s standard practice rate in Idaho, USA.\u003c/p\u003e \u003cp\u003eWhile VRI systems are commercially available, decision support systems (such as zone delineation) need further scientific development. Spatial variation of yield and crop water use have been linked to the variability of topography and soil properties, such as soil: texture, depth, water holding capacity, and ECa (Haghverdi et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Longchamps et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Sadler et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). As such, these factors are commonly used to delineate VRI zones (et al. 2017a; Hedley et al. 2009a; Hedley and Yule \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2009b\u003c/span\u003e; Messick et al. \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOne irrigation scheduling approach commonly used at the field scale is the reference ET (ET\u003csub\u003e0\u003c/sub\u003e) and crop coefficient (K\u003csub\u003ec\u003c/sub\u003e) approach, coupled with a soil water balance. Specifically, ET\u003csub\u003e0\u003c/sub\u003e from the American Society of Civil Engineers (ASCE) Standard Penman-Monteith ET model (Allen et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) is used within the following equation to estimate adjusted crop ET:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{ET}_{c\\:adj}={K}_{s}\\times\\:{K}_{c}\\times\\:{ET}_{o}\\:\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere ET\u003csub\u003ec adj\u003c/sub\u003e is the adjusted crop ET, K\u003csub\u003es\u003c/sub\u003e is the transpiration reduction factor reflecting conditions where soil water availability limits the rate of ET, K\u003csub\u003ec\u003c/sub\u003e is the crop coefficient that reflects the crop type and development stage, and ET\u003csub\u003eo\u003c/sub\u003e is the reference crop ET. Previous studies have shown the ability to schedule irrigation at the field scale with this approach, but few have evaluated it in a VRI setting with spatially variable model inputs (Al-Kufaishi et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). In a study under uniform irrigation management, Svedin et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) modelled within-field variation of ET using measured variation of VWC\u003csub\u003einit\u003c/sub\u003e and soil water characteristics and documented correlation with measured, within-field variation of ET. While this is promising, collecting spatially dense soil water characteristics for model inputs can be time and cost prohibitive. Further, modelling based on spatially uniform K\u003csub\u003ec\u003c/sub\u003e values is uncertain for a VRI application. Within-field variation of crop height and leaf area index (LAI) values and their interactions with K\u003csub\u003ec\u003c/sub\u003e and soil VWC have been documented (Baroni et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Hawley et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1983\u003c/span\u003e). Svedin et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) proposed the utilization of spatially variable K\u003csub\u003ec\u003c/sub\u003e when modelling ET for VRI. For this approach to be effective, understanding the within-field variation of and model sensitivity to input parameters is necessary (Crick and Hill, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1987\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe objectives of the study were to (1) assess the within-field variability of FC, WP, total available water (TAW) and VWC\u003csub\u003einit\u003c/sub\u003e, (2) to validate the ASCE Penman-Monteith ET\u003csub\u003eo\u003c/sub\u003e water balance model using measured, within-field spatially variable VWC, and (3) to evaluate the model sensitivity to FC, WP, and VWC\u003csub\u003einit\u003c/sub\u003e, and K\u003csub\u003ec\u003c/sub\u003e. We hypothesized that VWC\u003csub\u003einit\u003c/sub\u003e would have a greater effect on the average stress coefficient, (K\u003csub\u003es\u003c/sub\u003e), average soil water depletion within the root zone, and average ET\u003csub\u003ec adj\u003c/sub\u003e within the model than soil properties and the crop coefficient.\u003c/p\u003e"},{"header":"MATERIALS AND METHODS","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n\u003ch2\u003eSite Description\u003c/h2\u003e\n\u003cp\u003eThis study was conducted near Grace, ID, USA (elevation 1687 m above sea level; 42.60904 latitude, -111.78833 longitude) on a winter wheat (\u003cem\u003eTriticum aestivum\u003c/em\u003e L) production field (22 ha) with a wheat-wheat-potato (\u003cem\u003eSolanum tuberosum\u003c/em\u003e L.) rotation. The field is in a semi-arid region with about 80 to 110 frost-free days. Average annual precipitation is 390 mm with much of the precipitation occurring during winter as snow, which often blows and accumulates variably based on topography and surface conditions. The historical precipitation from May-August is 148 mm (National Water and Climate Center, NRCS-USDA, 2021). For this study duration precipitation was low, with 99, 90, and 92 mm in 2016, 2017 and 2019, respectively. Irrigation water was applied using a 380-m long center pivot equipped with a VRI system (GrowSmart Precision VRI, Lindsay Zimmatic, Omaha, NE, USA) and rotator nozzles spaced 5 m apart with 103 kPa pressure regulators (Nelson Irrigation, Walla Walla, WA, USA). Irrigation events occurred every 5\u0026ndash;7 d in the spring and every 3\u0026ndash;5 d during the summer at peak ET demand. The field has some areas of shallow soil and basalt bedrock at the surface that are not farmed (0.3 ha total).\u003c/p\u003e\n\u003cp\u003eThe soils are a Rexburg-Ririe complex, with a silty clay loam texture and 1 to 4% slopes. Rexburg and Ririe soils are coarse-silty, mixed, superactive, frigid Calcic Haploxerolls (Soil Survey Staff, 2021). There was little observed spatial variation in soil textural class. A texture analysis at 42 randomly selected locations sampled at 0.3 m depth increments down to 0.9 m within the field confirmed the texture to be a silty clay loam. The field has a relatively uniform topography, with a 6 m difference between lowest and highest elevation (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Conventional best management practices for nutrient, soil, pest, and crop management were used by the grower.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eSoil Sampling\u003c/h3\u003e\n\u003cp\u003eGrid soil sample size was determined by computing a variogram of the normalized difference vegetation index (NDVI) from bare soil imagery. The variogram had a range of ~\u0026thinsp;140 m. Following the guideline developed by Kerry \u0026amp; Oliver (\u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e) of a sampling interval approximately half the variogram range, the interval of 70 m was used for the main sampling grid with 46 samples. An additional 56 sample points were located at random points along the grids to improve the geostatistical predictions. This sampling scheme was used to calculate spatial and temporal variation of soil VWC and soil water depletion at the specific dates mentioned below.\u003c/p\u003e\n\u003cp\u003eSpring green-up and post-harvest soil samples were collected on 23 April and on 5 September 2019, and two mid-season sampling dates occurred on 30 May and 25 June 2019. Samples for VWC determination were collected at four depths 0-0.3 m, 0.3\u0026ndash;0.6 m, 0.6\u0026ndash;0.9 m, and 0.9\u0026ndash;1.2 m with a soil probe driven into the profile with a modified gas-powered post driver (AMS, Inc. American Falls, ID, USA). Samples were placed in plastic bags and sealed for transport to the laboratory where gravimetric soil water was determined by drying in a forced air oven at 105\u003csup\u003e\u0026deg;\u003c/sup\u003eC until consistent weights were reached. Soil gravimetric water content was converted to volumetric water content using soil bulk density values determined in 2016 from previous samples (Svedin et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Bulk density values ranged from 1.13\u0026ndash;1.69 g cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e with an average bulk density value of 1.46 g cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e (Svedin et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003ch3\u003eVRI Zone Delineation and Sensor-based Irrigation Scheduling\u003c/h3\u003e\n\u003cp\u003eThe VRI zones were created from yield and ET data collected from the 2016 and 2017 crops (Flint et al., 2023). The yield and ET data from these two years were used in a regression with the response variable being yield and the explanatory variable being ET. A k-means clustering algorithm was then used from the slope of the regression to determine the five zones (Flint et al., 2023). Once these zones were created in 2019, soil VWC (TEROS 12, Meter, Pullman, WA, USA) and matric potential sensors (TEROS 21, Meter, Pullman, WA, USA) with data loggers (ZL6, Meter, Pullman, WA, USA) were placed at depths of 15, 45, and 75 cm in one location within each zone. The location of each sensor set was established based on the combination of the following; grower knowledge of the water variability across the field, historical yield variability between and within zones, and average values of soil VWC within the specified zone (Flint et al., 2023; Woolley, \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e). One of each type of sensor was installed at every depth for all of the five locations (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). The amounts of irrigation applied to each zone were derived from a combination of the VWC data provided by these soil sensors and the zone-specific averaged field capacities. Rates were determined to maintain VWC between FC and the RAW value.\u003c/p\u003e\n\u003ch3\u003eModeling Water Dynamics\u003c/h3\u003e\n\u003cp\u003eModeling the spatial and temporal changes in ET for the 2019 season followed Allen et al. (\u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e) and the FAO Penman-Monteith estimation of reference ET to predict daily soil water levels individually for each of the 102 sampling locations. The model was initiated using measured VWC\u003csub\u003einit\u003c/sub\u003e, the VWC measured as the winter wheat emerged from dormancy in the spring (Svedin et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Depletion of soil water within the root zone was modeled with a daily time step from spring sampling (23 April) to post-harvest sampling (5 September). Spatially uniform ET\u003csub\u003eo\u003c/sub\u003e and K\u003csub\u003ec\u003c/sub\u003e were used to estimate ET\u003csub\u003ec\u003c/sub\u003e for wheat. When depth of soil water fell below a site-specific RAW threshold, ET\u003csub\u003ec\u003c/sub\u003e was adjusted with a site-specific crop stress coefficient (K\u003csub\u003es\u003c/sub\u003e) to estimate the adjusted crop ET (ET\u003csub\u003ec\u0026minus;adj\u003c/sub\u003e) (Svedin et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eWeather data were collected from a station\u0026thinsp;~\u0026thinsp;2 km from the field site (42.51496 N, -111.73606 W; Cooperative Agricultural Weather Network AgriMet). The weather data were used to calculate daily ET (ET\u003csub\u003ec adj\u003c/sub\u003e) using ET\u003csub\u003eo\u003c/sub\u003e from the ASCE Standard Penman-Monteith ET model (Allen et al., \u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e). The crop coefficient approach was used to calculate daily ET\u003csub\u003ec\u0026minus;adj\u003c/sub\u003e using Eq.\u0026nbsp;1, where K\u003csub\u003es\u003c/sub\u003e was calculated daily for each sample point and the K\u003csub\u003ec\u003c/sub\u003e curve was estimated from tabular values from a similar environment (Allen et al., \u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e) and validated with field observations. The K\u003csub\u003es\u003c/sub\u003e was calculated as:\u003c/p\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{K}_{s}=\\left(SWHC-{D}_{r}\\right)\u0026divide;\\left[\\left(1-p\\right)\\times\\:SWHC\\right]\\: \\left(2\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere SWHC is the soil water holding capacity in the 1.2 m deep soil profile, \u003cem\u003ep\u003c/em\u003e is the table value 0.55 from (Allen et al., \u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e) that represents the average fraction of SWHC that can be depleted before crop stress occurs in winter wheat, and D\u003csub\u003er\u003c/sub\u003e is the current root zone water depletion (Allen et al., \u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e). Soil water holding capacity and RAW were calculated from Allen et al. (\u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e) as follows:\u003c/p\u003e\n\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equc\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}SWHC={\\theta\\:}_{FC}-{\\theta\\:}_{WP}\\: \\left(3\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equd\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}RAW=p\\times\\:SWHC\\: \\left(4\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:\\)\u003c/span\u003e\u003c/span\u003e\u003csub\u003eFC\u003c/sub\u003e is the VWC (mm) at FC, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\theta\\:\\)\u003c/span\u003e\u003c/span\u003e\u003csub\u003eWP\u003c/sub\u003e is the VWC at WP (mm), and the estimated rooting depth of the crop and was assumed to be 1200 mm for this study. The RAW value is the readily available soil water content in the root zone (mm), and \u003cem\u003ep\u003c/em\u003e is defined above. At this site, winter snowfall and spring thaw act as the wetting event and FC was estimated for each sampling point as the greatest observed depth of soil water for each depth increment as measured at that site over a four-year observation period (2016\u0026ndash;2019) (Flint et al., 2023; Svedin et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). This approach for estimating FC assumed the soil was saturated from melting snow and spring precipitation but had at least three days for drainage with minimal ET losses (Martin, et al., \u003cspan class=\"CitationRef\"\u003e1990\u003c/span\u003e). It was assumed that post-harvest soil samples were at WP because the soils had been dried down for harvest in the wheat crop years with 15, 7.1, and 5 mm of rain since the last irrigation event 18, 16, and 5 d prior to harvest in 2016, 2017, and 2019, respectively. The WP was then determined by using the minimum observed VWC value at each location over these study years. Field measurements of WP values were validated with lab analysis utilizing a Dewpoint Potentiometer (WP4C, Meter Group Inc., Pullman, WA, USA). Volumetric soil water content was measured at -1500 kPa with satisfactory field and lab measurement error (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;39, \u003cem\u003eRMSE\u003c/em\u003e\u0026thinsp;=\u0026thinsp;11mm) (Svedin et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). These ranges set the upper and lower boundaries for the changes in these input values within the model. Daily soil water depletion within the root zone was estimated using the following equation:\u003c/p\u003e\n\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Eque\" class=\"mathdisplay\"\u003e$$\\:\\begin{array}{c}{D}_{r,i}={D}_{r,i-1}-{P}_{i}-{I}_{i}+{ET}_{c\\:adj\\:i}+{DP}_{i}\\: \\left(5\\right)\\end{array}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere D\u003csub\u003er,i\u003c/sub\u003e is the soil water depletion at the end of a specified day (d\u003csub\u003ei\u003c/sub\u003e), D\u003csub\u003er,i-1\u003c/sub\u003e is the soil water depletion at the end of the previous day, P\u003csub\u003ei\u003c/sub\u003e is the precipitation on d\u003csub\u003ei\u003c/sub\u003e, I\u003csub\u003ei\u003c/sub\u003e is the irrigation depth on d\u003csub\u003ei\u003c/sub\u003e, ET\u003csub\u003ec-adj,i\u003c/sub\u003e is the crop ET on d\u003csub\u003ei\u003c/sub\u003e, and DP\u003csub\u003ei\u003c/sub\u003e is deep percolation out of the root zone on d\u003csub\u003ei\u003c/sub\u003e (Allen et al., \u003cspan class=\"CitationRef\"\u003e1998\u003c/span\u003e). Deep percolation was calculated from any amount of water that exceeded site-specific FC values for the 1.2 m deep profiles from the ET model.\u003c/p\u003e\n\u003ch3\u003eModel Validation\u003c/h3\u003e\n\u003cp\u003eThe 2019 model output was validated following the procedures from Svedin et al. (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e) by comparing the calculated VWC to the measured VWC at two in-season sampling dates (30 May, 25 June), and at the end of the growing season (5 September)(Svedin et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). Statistical measures of model performance followed Miner et al. (\u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e) including: (1) relative error (RE), (2) normalized objective function (NOF) (3) root mean square error (RMSE), and (4) r-squared, where RE represents model bias, NOF indicates the fit of the model (where NOF\u0026thinsp;\u0026lt;\u0026thinsp;1 is less than one standard deviation from the mean), and RMSE is the difference between predicted and measured values. Desirables values of RE, NOF, RMSE are close to zero, and desirable r-squared values are above 0.50.\u003c/p\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n\u003ch2\u003eSensitivity Analysis\u003c/h2\u003e\n\u003cp\u003eA \u0026ldquo;one-at-a-time\u0026rdquo; sensitivity analysis was performed on the soil water depletion model (Downing et al., \u003cspan class=\"CitationRef\"\u003e1985\u003c/span\u003e; Hamby, \u003cspan class=\"CitationRef\"\u003e1994\u003c/span\u003e). The input variables FC, WP, VWC\u003csub\u003einit\u003c/sub\u003e, and K\u003csub\u003ec\u003c/sub\u003e were individually altered one-at-a-time to evaluate the change that would occur in output variables including K\u003csub\u003es\u003c/sub\u003e, ET\u003csub\u003ec adj\u003c/sub\u003e, and soil water depletion from the root zone. For the sensitivity analysis, the standard condition was modelled using input values averaged over the 102 sample locations. Then, one at a time changes were made for FC, WP, and VWC\u003csub\u003einit\u003c/sub\u003e values by adjusting the input from one to four observed standard deviations (SDs) above and below their respective mean values (Downing et al., \u003cspan class=\"CitationRef\"\u003e1985\u003c/span\u003e; Hamby, \u003cspan class=\"CitationRef\"\u003e1994\u003c/span\u003e). When either the FC or WP values were adjusted individually, each sampling point\u0026rsquo;s TAW values were adjusted. The K\u003csub\u003ec\u003c/sub\u003e value was adjusted by first calculating the spatially variable K\u003csub\u003ec\u003c/sub\u003e from LAI data measured on 25 June at each sampling location using an AccuPAR ceptometer (LP-80 PAR/LAI, Meter, Pullman, WA, USA) (Hopkins, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e; Johnson \u0026amp; Trout, \u003cspan class=\"CitationRef\"\u003e2012\u003c/span\u003e; Trout et al., \u003cspan class=\"CitationRef\"\u003e2008\u003c/span\u003e) and then averaged over the 102 sample locations. A SD was calculated from this data and the K\u003csub\u003ec\u003c/sub\u003e value was adjusted from negative four to positive four SDs away from the average K\u003csub\u003ec\u003c/sub\u003e value from 25 June.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"RESULTS","content":"\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eSpatial Variation of Soil Properties\u003c/h2\u003e \u003cp\u003eThe soil water characteristics varied in their ranges of distribution across the 22-ha wheat field. Soil water at FC ranged from 355 to 488 mm in the 1200 mm profile, averaging 412 mm (Table\u0026nbsp;1, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Soil water at WP ranged from 103\u0026ndash;153 mm, averaging 125 mm (Table\u0026nbsp;1, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The TAW ranged from 230 to 361 mm, averaging 286 mm (Table\u0026nbsp;1, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The VWC\u003csub\u003einit\u003c/sub\u003e ranged from 325\u0026ndash;464 mm, averaging 388 mm (Table\u0026nbsp;1, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Variability in VWC continued throughout the season, ranging from 321\u0026ndash;450, 249\u0026ndash;417, and 142\u0026ndash;334 mm and averaging 393, 330, and 213 mm on 30 May, 25 June, and 5 September, respectively (Table\u0026nbsp;1).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"9\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"8\" nameend=\"c8\" namest=\"c1\"\u003e \u003cp\u003eTable\u0026nbsp;1 Water retention properties and volumetric water content (VWC) values within a 1200 mm depth profile for the 2019 growing season (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"1\" nameend=\"c9\" namest=\"c9\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eLocation\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eFC\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003eWP\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eApril VWC\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003eMay VWC\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eJune VWC\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003eSept VWC\u003c/b\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c8\" namest=\"c3\"\u003e \u003cp\u003e- - - - - - - - - - - - - - - - - - - - - - - mm - - - - - - - - - - - - - - - - - - - - - - - - -\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003e\u003cb\u003eAverage\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eField\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e388\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e393\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e418\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e132\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e398\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e394\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e348\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e389\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e391\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e328\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e411\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e123\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e387\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e393\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e218\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e408\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e124\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e382\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e392\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e331\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e211\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e421\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e327\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e230\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003e\u003cb\u003eMax\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eField\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e488\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e463\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e334\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e465\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e153\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e463\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e385\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e433\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e447\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e281\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e142\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e430\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e432\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e334\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e488\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e451\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e446\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e272\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e475\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e444\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e450\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e383\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003e\u003cb\u003eMin\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eField\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e142\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e365\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e305\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e178\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e379\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e106\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e348\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e288\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e171\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e355\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e108\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e142\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e104\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e332\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e281\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e108\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e358\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e249\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e203\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003e\u003cb\u003eStandard Deviation\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eField\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eZone 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\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\u003eThe observations of FC, WP, TAW and VWC\u003csub\u003einit\u003c/sub\u003e served as the parameter ranges used in the sensitivity analysis. The variograms for each soil property reported similar ranges of 340, 350, and 370 m for spring VWC, FC and TAW, respectively, and WP had a range of 60 m (Table\u0026nbsp;2). The spatial random variation of each soil water retention property characterized by the nugget:sill ratio of variograms was high and similar for each variable with 80%, 62%, 73% and 72% for spring VWC, FC, TAW, and WP, respectively (Table\u0026nbsp;2). Large random variation ranges of similar percentages for soil water retention properties could mean that changing the model will have similar effects on the ET calculation for each sampling point. However, it could also account for the differences in outputs of the model.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"6\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c5\" namest=\"c1\"\u003e \u003cp\u003eTable\u0026nbsp;2 Variogram range and random variation of soil water retention properties from 102 sample locations in 2019\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"1\" nameend=\"c6\" namest=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSoil Property\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eRange\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003eNugget\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003eSill\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eRandom Variation\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003e- - - - - - - - - - - - m - - - - - - - - - - -\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e62.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e61.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e72.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTAW\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e370\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e72.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVWC\u003csub\u003einit\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e80.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eFC\u0026thinsp;=\u0026thinsp;field capacity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eWP\u0026thinsp;=\u0026thinsp;wilting point\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eTAW\u0026thinsp;=\u0026thinsp;total available water\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eVWC\u003csub\u003einit\u003c/sub\u003e = initial soil volumetric water content\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\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=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eModel Validation\u003c/h2\u003e \u003cp\u003eThe model validation approach compared predicted VWC with measured values for two in-season sampling dates. Modelled VWC also showed good agreement with measured data (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The relative error was \u0026minus;\u0026thinsp;3.7% for 30 May and 0.84% for 25 June. For both sampling dates, model predictions of VWC were within one standard deviation of the mean (NOF\u0026thinsp;\u0026lt;\u0026thinsp;1). The model fit of VWC was excellent for the two mid-season dates (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eModel Sensitivity Analysis\u003c/h2\u003e \u003cp\u003eThe sensitivity analysis on the soil water depletion model was performed by varying key input factors one at a time and evaluating output changes of 1) field average stress coefficient (K\u003csub\u003es\u003c/sub\u003e); 2) field average ET\u003csub\u003ec adj\u003c/sub\u003e; and 3) field average soil water depletion from the root zone. The key input factors included the static soil water retention properties FC and WP, and the dynamic properties VWC\u003csub\u003einit\u003c/sub\u003e and crop coefficient values.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eModel Sensitivity to Static Soil Water Retention Properties: Field Capacity (FC) and Wilting Point (WP)\u003c/h2\u003e \u003cp\u003eThe depletion model outputs were sensitive to changes in soil water retention properties such as FC and WP (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Most output values showed significant differences between the original output values (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). The exceptions were when the output values K\u003csub\u003es\u003c/sub\u003e at FC\u0026thinsp;+\u0026thinsp;1 SD and +\u0026thinsp;2 SDs had \u003cem\u003ep\u003c/em\u003e-values of 0.334 and 0.065, respectively, and ET\u003csub\u003ec adj\u003c/sub\u003e at FC\u0026thinsp;+\u0026thinsp;1 SD had a \u003cem\u003ep\u003c/em\u003e-value of 0.722. Changes in FC between +\u0026thinsp;1 and +\u0026thinsp;4 SDs caused the most change in soil VWC values (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eModel Sensitivity to VWC\u003csub\u003einit\u003c/sub\u003e\u003c/h2\u003e \u003cp\u003eWhen VWC\u003csub\u003einit\u003c/sub\u003e values were adjusted to either positive or negative changes away from their cumulative mean value, all output values were significantly different than the original output values (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). The VWC\u003csub\u003einit\u003c/sub\u003e expressed variable ranking of sensitivity on the output variables, depending on the output variable and the direction of change within the VWC\u003csub\u003einit\u003c/sub\u003e values (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The outputs K\u003csub\u003es\u003c/sub\u003e and ET\u003csub\u003ec adj\u003c/sub\u003e showed they were less sensitive towards VWC\u003csub\u003einit\u003c/sub\u003e when the input value was changed in the negative direction (less VWC) compared to the K\u003csub\u003ec\u003c/sub\u003e input value (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea, b).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eModel Sensitivity to K\u003csub\u003ec\u003c/sub\u003e\u003c/h2\u003e \u003cp\u003eAll changes in K\u003csub\u003ec\u003c/sub\u003e led to significant changes in the output values (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). K\u003csub\u003ec\u003c/sub\u003e values were adjusted from \u0026minus;\u0026thinsp;1 to -4 SDs and had the greatest impact on model outputs. All outputs, except for soil water depletion, were most sensitive to +\u0026thinsp;1 to +\u0026thinsp;4 SD changes from the average K\u003csub\u003ec\u003c/sub\u003e values (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Crop coefficient values were ranked as the second most sensitive for soil water depletion, with FC being ranked most sensitive when values were adjusted above their mean values. However, K\u003csub\u003ec\u003c/sub\u003e had the greatest impact on all outputs (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"DISCUSSION","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eSoil Water Characteristics and Irrigation Management\u003c/h2\u003e \u003cp\u003eMany have documented similar substantial within-field variation of soil water retention properties and theorized on using this variation to improve VRI management and crop production through zone delineation and irrigation scheduling (Daccache et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; de Lara et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Haghverdi et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Lo et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Longchamps et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). In the present study, the degrees of within-field variation of FC, WP, and VWC were similar to the variation found by Lo et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) who demonstrated the benefit of using zone irrigation to match VWC measured from sensors and zone-specific FC values. It can be assumed similar improvements could occur at this location but would require further research to demonstrate this approach.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eModel Validation\u003c/h2\u003e \u003cp\u003eThe validation approach supports that the used water balance model was able to predict within-field variation of soil water dynamics, crop water stress, and evapotranspiration rates over time. In general, the results of the modelling approach within this current study show that with spatially dense soil water characteristics, a water balance modelling approach may be a good way to schedule variable irrigation rates (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), but the practical limitation is that spatially dense soil water retention properties and VWC\u003csub\u003einit\u003c/sub\u003e are not easily obtained. The sensitivity analysis was performed to shed light on how critical specific inputs are for the model.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section2\"\u003e \u003ch2\u003eModel Sensitivity\u003c/h2\u003e \u003cp\u003eSubstantial changes occurred within the soil VWC output levels when soil water retention properties (FC and WP) were averaged and adjusted one-at-a-time by the prescribed SDs from the mean. These changes would either suggest the need to add more or less water at each irrigation event, or have more or less frequent irrigations, depending on the values of FC, WP, and TAW. These changes in water needs from the adjusted model might be correct for some areas of the field, but incorrect for other areas, thus causing either over- or under-watering and eventually leading to early onset of crop water stress or excess drainage without recognition from the model. As these outputs affect the irrigation management of the field, model predictions are highly dependent upon spatially variable soil water retention properties.\u003c/p\u003e \u003cp\u003eSpatial variability of VWC\u003csub\u003einit\u003c/sub\u003e has been observed to be a predicting factor of the spatial variability of onset of crop water stress (Svedin et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Uniform above average spring VWC values resulted in little change to K\u003csub\u003es\u003c/sub\u003e, ET\u003csub\u003ec adj\u003c/sub\u003e, and soil water depletion within the root zone during the 2019 season. When VWC\u003csub\u003einit\u003c/sub\u003e model inputs were below the field average, predicted K\u003csub\u003es\u003c/sub\u003e and ET\u003csub\u003ec adj\u003c/sub\u003e both decreased, while soil water depletion increased, signifying more stress within the field throughout the season. This suggests that if model input values for VWC\u003csub\u003einit\u003c/sub\u003e are above the field average, the predicted irrigation recommendations would be low in parts of the field, and the model would not accurately describe crop water stress. The opposite would occur if VWC\u003csub\u003einit\u003c/sub\u003e was uniformly low throughout the field. The model would indicate the field needed to be irrigated, when parts of it may not need irrigation, and thus drainage and runoff would occur without the model. This suggests the need for spatially accurate input of VWC\u003csub\u003einit\u003c/sub\u003e. However, this dependency is challenging for commercial VRI implementation, because obtaining spatially dense VWC\u003csub\u003einit\u003c/sub\u003e data is not practical for most growers. This issue could be solved if large amounts of cost-effective soil sensors could be placed throughout a field to read the spatial and temporal variation in soil moisture.\u003c/p\u003e \u003cp\u003eThe adjusted K\u003csub\u003ec\u003c/sub\u003e values were created by taking the mean value and standard deviation of LAI data from the field on 25 June and calculating the standard deviation values in K\u003csub\u003ec\u003c/sub\u003e. These standard deviation values were then added or subtracted from the original canopy K\u003csub\u003ec\u003c/sub\u003e value. All outputs from the adjusted K\u003csub\u003ec\u003c/sub\u003e were more sensitive to the negative change in K\u003csub\u003ec\u003c/sub\u003e values than to positive changes. K\u003csub\u003ec\u003c/sub\u003e standard deviation adjustments were changed to values that were generally not within a normal range of a K\u003csub\u003ec\u003c/sub\u003e during that particular time of the growing season, especially for a winter wheat crop. The extreme changes in the K\u003csub\u003ec\u003c/sub\u003e values could explain their large impact on outputs. Changes in the outputs could also be affected by the K\u003csub\u003ec\u003c/sub\u003e values due to the different irrigation rates that were applied to sections of the field, suggesting that multiple factors or inputs can affect each other in how they impact the outputs of the model. An approach that may improve this model would be the measurement of the variation of crop canopy conditions to inform the model (Svedin et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This approach is consistent with other studies noted in the review by O\u0026rsquo;Shaughnessy et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) that show improvement in irrigation management when dynamic crop conditions are assessed. As Svedin et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) suggested, having a variable K\u003csub\u003ec\u003c/sub\u003e could improve the original model based on the ASCE method within this study by addressing the different growth rates of the crop due to the different irrigation rates that affect the rate of growth for each zone. Also, looking into how the interaction of these inputs affect the outputs of the model will assist in understanding the need for accuracy of each input.\u003c/p\u003e \u003c/div\u003e"},{"header":"CONCLUSIONS","content":"\u003cp\u003eField observations and assessment of model sensitivity were combined to evaluate the roles of soil water retention properties and dynamic factors on soil and crop water dynamics. The influence of crop coefficients on irrigated winter wheat within a soil water depletion model based on the standards of Allen et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) and the FAO ET equation was also considered. Outputs (average K\u003csub\u003es\u003c/sub\u003e, average ET\u003csub\u003ec adj\u003c/sub\u003e and average soil water depletion within the root zone) from the original model based on spatially variable values of soil properties (VWC\u003csub\u003einit\u003c/sub\u003e, FC, WP and TAW) with a uniform crop coefficient for winter wheat were compared to the same model with different values (1 to 4 SDs of mean values) of soil properties and crop coefficient values. Variable FC, WP, spring VWC, and K\u003csub\u003ec\u003c/sub\u003e values were all important factors in predicting accurate temporal and spatial K\u003csub\u003es\u003c/sub\u003e, soil water depletion, and ET to accurately make VRI recommendations. All assessed input variables also played a role in the accuracy of the soil water depletion model. This model, based on the ASCE method, used with spatially variable inputs, can improve water conservation within irrigation management when coupled with VRI. Further research is required to understand the necessary level of accuracy for input variables to create the most practical and reliable models for irrigation recommendations, as well as understanding if other adjustments need to be made to the model for improved accuracy. Additionally, improvements to this work could advance significantly if large amounts of affordable sensors could be used to estimate soil moisture properties for input into the Penman Monteith equation rather than relying on expensive and time-consuming sampling and lab analysis.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eACKNOWLEDGMENTS AND FUNDING INFORMATION\u003c/p\u003e\n\u003cp\u003eWe would like to acknowledge BKR farms for providing the field site equipped with the variable rate irrigation system for this project’s fulfillment. We would also like to thank the many students from Brigham Young University research labs not listed as authors who assisted in the field work related with data from this paper. This research was funded by United States-Israel Binational Agricultural Research and Development Fund, grant number IS-5218-10, and the United States Department of Agriculture Western Sustainable Agricultural Research and Education Program, grant number SW19-909. The APC was funded by Brigham Young University.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eE.A.F., J.D.S., A.B., M.A.Y., B.G.H., and N.C.H. provided substantial contributions to the design of the work.E.A.F., A.P.H., J.D.S., R.K., B.G.H., and N.C.H. provided substantial contributions to the acquisition of the data. E.A.F., A.P.H., J.D.S., R.K., A.B., R.J., B.G.H., and N.C.H. provided substantial contributions to the analysis, and interpretation of the data. E.A.F., B.G.H., and N.C.H. wrote the main manuscript text. E.A.F. prepared the figures and tables. All authors reviewed and revised the manuscript critically for important intellectual content.All authors approved the version to be published.All authors agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eWe would like to acknowledge BKR farms for providing the field site equipped with the variable rate irrigation system for this project\u0026rsquo;s fulfillment. We would also like to thank the many students from Brigham Young University research labs not listed as authors who assisted in the field work related with data from this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAl-Kufaishi SA, Blackmore BS, Sourell H (2006) The feasibility of using variable rate water application under a central pivot irrigation system. Irrigat Drain Syst 20(2\u0026ndash;3):317\u0026ndash;327. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s10795-006-9010-2\u003c/span\u003e\u003cspan address=\"10.1007/s10795-006-9010-2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAllen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration - Guidelines for computing crop water requirements - FAO irrigation and drainage paper 56. 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Int J Agricultural Biol Eng 11(1):23\u0026ndash;30. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.25165/j.ijabe.20181101.3557\u003c/span\u003e\u003cspan address=\"10.25165/j.ijabe.20181101.3557\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"irrigation-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"irsc","sideBox":"Learn more about [Irrigation Science](http://link.springer.com/journal/271)","snPcode":"271","submissionUrl":"https://submission.nature.com/new-submission/271/3","title":"Irrigation Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-9420591/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9420591/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eUnderstanding within-field and within-season variability of soil water supply and crop water stress is critical for successful variable-rate irrigation (VRI) management. The objectives of this study were to 1) assess within-field variability of field capacity (FC), wilting point (WP), total available water (TAW), and initial soil volumetric water content (VWC\u003csub\u003einit\u003c/sub\u003e); 2) validate a water balance model based on the American Society of Civil Engineers (ASCE) standardized Penman-Monteith estimation of reference evapotranspiration (ET\u003csub\u003e0\u003c/sub\u003e) using measured within-field VWC; and 3) evaluate the model sensitivity to FC, WP, VWC\u003csub\u003einit\u003c/sub\u003e, and crop coefficients. A 22-ha field of winter wheat (\u003cem\u003eTriticum aestivum\u003c/em\u003e L.) near Grace, Idaho, United Sates of America was delineated into five zones and managed with VRI. There was observable spatial variability of soil water characteristics among 102 measured sites in the field: FC (355\u0026ndash;488 mm), WP (103\u0026ndash;153 mm), TAW (230\u0026ndash;361 mm), and VWC\u003csub\u003einit\u003c/sub\u003e (325\u0026ndash;464 mm) in the 1.2 m soil profile. Model validation against measured VWC resulted in root mean square error (RMSE) values of 23.2\u0026ndash;61.3 mm for the different sampling dates. These RMSE values showed the ability to model within-field spatially variable soil water dynamics and crop water stress at the 102 locations. The model showed high sensitivity of predicted output values, such as ET and soil water depletion to FC and VWC\u003csub\u003einit\u003c/sub\u003e inputs. The sensitivity analysis suggested that using spatially variable crop coefficients could improve prediction of spatially variable ET rates. Model sensitivity to soil water characteristics present opportunities for a spatially variable modelling approach to assist in scheduling VRI.\u003c/p\u003e \u003cp\u003eSTATEMENTS AND DECLARATIONS\u003c/p\u003e \u003cp\u003e \u003cb\u003eCompeting Interests\u003c/b\u003e: The authors declare no competing interests. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.\u003c/p\u003e","manuscriptTitle":"Sensitivity Analysis of Modeled Soil Water Dynamics within Variable Rate Irrigation Zones for Winter Wheat","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-29 15:52:52","doi":"10.21203/rs.3.rs-9420591/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"18764282826882436998687396955247890682","date":"2026-04-22T09:35:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"7908115833270324554458393775803454115","date":"2026-04-22T07:42:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"101342223213974121592569464965871924186","date":"2026-04-21T20:25:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"157300347766180321080815356902252080980","date":"2026-04-21T11:52:51+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-21T08:53:40+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-15T13:31:44+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-15T13:30:52+00:00","index":"","fulltext":""},{"type":"submitted","content":"Irrigation Science","date":"2026-04-15T02:01:13+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"irrigation-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"irsc","sideBox":"Learn more about [Irrigation Science](http://link.springer.com/journal/271)","snPcode":"271","submissionUrl":"https://submission.nature.com/new-submission/271/3","title":"Irrigation Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"441c7214-74b8-47ab-b430-0ea98953eb67","owner":[],"postedDate":"April 29th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-29T15:52:53+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-29 15:52:52","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9420591","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9420591","identity":"rs-9420591","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}