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Soil & Water Management & Conservation

Numerical Modeling of Wheat Irrigation using Coupled HYDRUS and WOFOST Models Jian Zhou Guodong Cheng Xin Li Cold and Arid Regions Environmental and Engineering Research Institute Chinese Academy of Sciences Lanzhou 730000, China

Bill X. Hu* China Univ. of Geosciences Beijing 100083, China and Dep. of Geological Sciences Florida State Univ. Tallahassee, FL 32306

Genxu Wang Institute of Mountain Hazards and Environment Chinese Academy of Sciences Chengdu 610041, China

To efficiently manage water resources in agriculture, the hydrologic model HYDRUS-1D and the crop growth model WOFOST were coupled to improve crop production prediction through accurate simulations of actual transpiration with a root water uptake method and soil moisture profile with the Richards equation during crop growth. An inverse modeling method, the shuffled complex evolution algorithm, was used to identify soil hydraulic parameters for simulating the soil moisture profile. The coupled model was validated by experimental study on irrigated wheat (Triticum aestivum L.) in the middle reaches of the Heihe River, northwest China, in a semiarid and arid region. Good agreement was achieved between the simulated actual evapotranspiration, soil moisture, and crop production and their respective field measurements under a realistic irrigation scheme. A water stress factor, actual root uptake with potential transpiration, is proposed as an indicator to guide irrigation. Numerical results indicated that the irrigation scheme guided by the water stress factor can save 27% of irrigation water compared with the current irrigation scheme. Based on the calibrated model, uncertainty and sensitivity analysis methods were used to predict the risk of wheat production loss with decreasing irrigation and to study the effects of coupled model parameters and environmental factors on wheat production. The analysis revealed that the most suitable groundwater depth for wheat growth is 1.5 m. These results indicate that the coupled model can be used for analysis of schemes for saving water and study of the interaction between crop growth and the hydrologic cycle. Abbreviations: LAI, leaf area index; NSE, Nash–Sutcliffe coefficient; SCE, shuffled complex evolution; WOFOST, World Food Studies.

I

n semiarid and arid regions, there is increasing competition for water resources between agricultural irrigation and other ecological water uses due to a growing population (Molden, 1997; Seckler et al., 1998). Efficient management of water resources in agriculture is needed to balance water supply and demand (Tuong and Bhuiyan, 1999; Ines et al., 2002). In the last 20 yr, irrigation planning methods have switched from the allocation approach, e.g., based on socio-political considerations, to quantitative management (Paudyal and Das Gupta, 1990; Raman et al., 1992). The development of mathematical models is a fundamental step to guide quantitative irrigation. The accurate estimation of temporal and spatial variations in soil moisture, evaporation, and transpiration is crucial to determine the availability of water resources (Aggarwal, 1995; Addiscott et al.,1995; Scanlon et al., 2002) and sustainable management of limited water resources in arid and semiarid regions (e.g., Garatuza-Payan et al., 1998). Simulation models of crop physiological growth are widely accepted tools for field study of efficient and sustainable water use in agricultural production in various

Soil Sci. Soc. Am. J. 76:648–662 Posted online 21 Dec. 2011 doi:10.2136/sssaj 2010.0467 Received 29 Dec. 2010 *Corresponding author ([email protected]) © Soil Science Society of America, 5585 Guilford Rd., Madison WI 53711 USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.

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agro-ecological zones. Such models can aid in understanding the interactions between crops and environments (Kropff and Goudriaan, 1994; Yin et al., 2004) and provide optimal agricultural management strategies under uncertain weather conditions and climatic change (Meinke et al., 2001; Booltink et al., 2001; Munch et al., 2001; Kersebaum et al., 2002). Several crop physiological growth models (e.g., Simple and Universal Crop Growth Simulator [SUCROS] and ORYZA [Goudriaan and van Laar, 1994]; World Food Studies [WOFOST; Boogaard et al., 1998]; Genotype by Environment Interaction on Crop Growth Simulator [GECROS; Yin and van Laar 2005]; Decision Support System for Agrotechnology Transfer [DSSAT; Jones et al., 2003]) have been developed from photosynthesis modeling based on the complex biochemical approach (Farquhar et al., 1980), the constant lightuse efficiency approach, or the C assimilation approach (Arora and Boer, 2005). In crop growth modeling schemes, the various components of the water balance in an agro-ecological system are the most important physical and physiological factors for calculations (Aggarwal, 1995; Addiscott et al., 1995). Spatial and temporal variation of soil moisture is one of the main causes of crop production variation (Shepherd et al., 2002; Anwar et al., 2003; Patil and Sheelavantar, 2004). Meanwhile, actual evaporation and transpiration, which determine the soil moisture profile, are the main processes for water loss in a soil–plant system (Burman and Pochop, 1994; Monteith and Unsworth, 1990). Crops can only absorb the soil moisture present within reach of their roots. These processes could be represented in hydrologic models. Therefore, the coupling of hydrologic and crop growth models connects hydrology and agronomy quantitatively and provides a bridge across the boundaries of the two subjects. In the last several years, numerous studies have been conducted to understand the complex interactions between ecological systems and the hydrologic cycle, resulting in the development of ecohydrologic models and soil–plant–atmosphere models (Smettem, 2008). Simulation modeling can be used to understand the relationships among crop production, groundwater recharge, soil evaporation, and crop transpiration (de Willigen, 1991; Engel and Priesack, 1993; Diekkrüger et al., 1995; Smith et al., 1997; Shaffer et al., 2001; van Ittersum and Donatelli, 2003). Kendy et al. (2003) used a numerical model to evaluate groundwater recharge in an irrigated cropland. By coupling hydrologic and crop growth models, Eitzinger et al. (2004) studied soil water movement during crop growth stages and concluded that the coupled modeling approach was better than a single-model method. A few studies have been conducted to investigate the effects of the soil moisture distribution along a vertical soil profile during crop transpiration (e.g., Varado et al., 2006). The model coupling studies have generally focused on the effect of crop growth on soil moisture, and much less attention has been paid to improving crop growth models by properly modeling the root growth algorithm and root water uptake. In this study, we developed a modeling approach to simultaneously estimate crop production, soil moisture dynamics, evaporation, and transpiration by coupling HYDRUS with WOFOST. The soil moisture dynamic movements are simulated through the Richards


equation (in the HYDRUS model), while root water uptake and transpiration are calculated according to the method of Feddes et al. (1978, p. 9–30). The parameters of soil hydraulic properties are identified with the shuffled complex evolution (SCE) algorithm. The CO2 assimilation (photosynthesis) and respiration of the crop are simulated by the WOFOST model. The ratio of the crop actual transpiration and potential transpiration is used to represent the influence of soil water stress on crop production. Based on the coupled model, we conducted sensitivity and uncertainty analyses to verify the coupled model approach. Then, the coupled model was used to optimize water use for farmland irrigation and predict crop production variability due to variations in uncertain parameters and driving variables.

FIELD EXPERIMENT AND NUMERICAL MODELING Study Region and Experimental Station Description The Heihe River basin, located in a semiarid and arid region, is the second largest inland river basin in China. The region has a typical continental climate, with the mean annual precipitation and evaporation ranging from 60 to 280 and 1000 to 2000 mm, respectively. In this region, the main crops are wheat and maize (Zea mays L.), and irrigation water use efficiency is low. The key to solving water scarcity and ecological problems is through effective management of water resources and optimization of irrigation. An agricultural experimental station, located at 39°20.9′ N, 100°7.8′ E, altitude 1382 m, was established in the middle reach of the Heihe River, in the northwest of China (Fig. 1). The experimental station is operated by the Chinese Academy of Science to study the impact of quantitative irrigation on wheat growth. The station is managed according to agricultural practices in the Heihe River basin region, including crop rotations (spring wheat and maize) and flood irrigation.

Characterization of Soil Properties The experimental station was established on a sandy soil (USDA classification system). To characterize the soil physical properties, five soil samples were extracted from the ground surface to a depth of 1.5 m at 30-cm intervals. The samples were analyzed in the laboratory to determine the soil bulk density (Grossman and Reinsch, 2002), water retention properties (soil water contents at 0–1000-kPa matric potentials; Equi-pf, Streat Instruments, Christchurch, New Zealand) and the percentages of sand, silt, and clay (Gee and Or, 2002). Saturated conductivity was measured from the ground surface to a depth of 1.5 m at 30-cm intervals in the field (2800K1 Guelph permeameter, Soilmoisture Equipment Corp., Santa Barbara, CA). The analysis results are shown in Table 1 and Fig. 2. The soil nutrient status was analyzed in the laboratory (TPY-6PC Soil Nutrient Tester, Zhejiang Top Instrument Co., Hangzhou, China). The total N, total P, available N, available K, and available P contents of the surface soil (0–30 cm) were 0.74, 1.03, 0.028, 0.126, and 0.03 g kg−1, respectively.

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Fig. 1. Location of the experimental station.

Field Experiment

Table 1. The soil properties derived in the laboratory. Textural fractions

Bulk

Saturated

Depth As shown in Fig. 3, the experimental field was cultivated 2–0.05 mm 0.05–0.002 mm h1

where h1, h2, h3, and h4 are threshold parameters. The uptake is at the potential rate when the pressure head is between h2 and h3. It decreases linearly when h > h2 or h < h3. The uptake rate becomes zero when h < h4 or h > h1. Crop-specific values for these parameters were chosen from the database in HYDRUS1D (Šimůnek, 2005). An atmospheric boundary condition was implemented at the soil surface. The atmospheric boundary condition required daily irrigation, precipitation rate, potential evaporation, and transpiration rate as inputs. A detailed description about how to calculate the potential evaporation and transpiration can be found in HYDRUS-1D (Šimůnek, 2005). A deep drainage condition was used at the bottom. The condition required the initial reference groundwater depth to be given (Šimůnek, 2005). The soil hydraulic properties were modeled using the van Genuchten–Mualem constitutive relationships (Mualem, 1976; van Genuchten, 1980): θs + θ r ⎧ h 2 and up to 3 m, wheat production will decrease with decreasing irrigation. The critical irrigation for guaranteeing wheat production is 15 mm each time for a 2-m groundwater depth and 20 mm each time for a 2.5- to 3-m groundwater depth.

Sensitivity Analysis The guided irrigation scheme, eight irrigations with 40 mm of irrigated water each time, was studied. Figure 10 displays graphically the average strength (μ*) and spread Fig. 5. Comparison between observed and fitted soil moisture by the shuffled complex evolution (σ) of the simulation results for changes (SCE) algorithm: (a) 30-cm soil moisture; (b) 60-cm soil moisture; (c) 100-cm soil moisture. in production due to variations in the parameters according to their various functions of crop growth included AMAXTB, ZIT, TSUMEM, TSUM1, TSUM2, (phenology, assimilation, respiration, conversion, and so forth) EFFTB, CVO, HYDRUS parameters, SLATB, and DSOW. and environmental factors (sowing date, groundwater depth, Furthermore, the study results showed σ values close to the μ* soil hydraulic parameters, and so forth). The parameters were values for the majority of parameters, which indicates that inranked in descending order of the μ* values, which are shown in teractions, correlation, and nonlinearity are relevant for the Table 7. Through the screening study performed with the Morris coupled model. method, eight out of 30 parameters (26.7%) were identified as irWe also analyzed the distribution of simulated production relevant factors because the variation in each factor changed the with Monte Carlo methods to study the effects of variations in production only slightly, 500 kg ha , which times. The uncertainty analysis was performed and the results 656


each other in the coupled model, which indicates that the coupled model is balanced. Summation values of the totalorder indices were mainly between 2.8 and 3.94, which suggests that the simulated production was generally affected by several parameters acting in conjunction with each other. Table 8 further reveals that when each irrigation decreased from 40 to10 mm for a total of eight irrigations, the total of first-order effects for the environment parameters (including sowing date, groundwater depth, and soil hydraulic characteristics) on output increased from 0.323 to 0.676. The total of total-order effects for the environmental parameters increased from 0.709 to 1.162. Especially, the effect of groundwater depth (single factor) on output increased from 0.08 Fig. 6. Comparison between simulated and observed weight of total aboveground biomass (TADRW) to 0.347, and the total effect of groundand weight of storage organs (WSO). water depth (including interactions are shown in Fig. 11, which reveals the risk of crop production with other factors) on output increased loss with decreases in irrigation. The average crop production from 0.26 to 0.65 for the study region. The analysis results indiincreased from 2960 kg ha−1 in the case where each irrigation cate that the groundwater depth is the main environmental con−1 was 10 mm to 4410 kg ha where each irrigation was 40 mm. trol factor for wheat harvest under arid conditions. The effects When each irrigation was >30 mm, the distribution of simulated of most physiological parameters on output decreased as irriproduction was mainly between 3500 and 5500 kg ha−1, which gation decreased. The total of first-order effects for crop physiaccounts for 90% of the realizations. ological parameters on output decreased from 0.645 to 0.365. The Soboľ method was used to improve our understanding The total of total-order effects for crop physiological parameters of the effect of parameter groups on crop production under varion output decreased from 3.236 to 1.664. These results can be ous irrigation schemes. The results are shown in Table 8. In the explained as the shortage of water uptake from the soil causes above-mentioned irrigation scenarios, summations of first-order stoma closure and reduces assimilation and respiration of crops. indices of parameters were always close to 1, which suggests that the coupled model was not overparameterized. Total-order inSUMMARY AND CONCLUSIONS dices of the parameters were not significantly different from The objective of this study was to develop a fully coupled hydrology–crop growth model to optimize an irrigation scheme under various environmental conditions. A crop growth model (WOFOST) was coupled to a hydrologic model (HYDRUS) as a calculation tool for this purpose. The coupled models take account of the wheat physiological processes and the water balance during the wheat growth process. Inverse modeling methods (the SCE algorithm) were used to identify the parameters of soil hydraulic properties to improve simulation accuracy of the soil moisture profile. The coupled model was applied to a wheat field experiment in the middle reach of Northwest China’s Heihe River, located in a semiarid and arid region. The results show that good agreement was achieved Fig. 7. Comparison between simulated and observed leaf area index (LAI). SSSAJ: Volume 76: Number 2 • March–April 2012

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Fig. 8. Comparison between simulated and observed actual evapotranspiration.

between the coupled model simulations and field measurements under water-limited conditions. A factor, actual root uptake–potential transpiration, is proposed as an indicator to guide irrigation. The numerical modeling results reveal that the simulated irrigation scheme guided by this factor can save 131.9 mm of irrigation water over current irrigation schemes with a guarantee of crop production. The total water savings accounts for 27.27% of the irrigation water. Based on the coupled model, the scenario analysis results indicate that the most suitable groundwater depth for wheat growth is 1.5 m, at which the wheat roots can take up water from the groundwater. The study results indicate that the coupled model can be used for analysis of a water-saving approach and also for study of interactions between crop growth and the hydrologic cycle. Uncertainty and sensitivity analysis methods were used to evaluate the coupled model, to predict wheat production, and to study the effects of the crop parameters and environmental factors on wheat production. The study results indicate that the

uncertainty analysis using a Monte Carlo method could reveal the risk of a possible loss of crop production with a decrease in irrigation and provide the probability of crop production in the uncertainty range of crop and environmental parameters. The sensitivity analysis revealed the effects of the coupled model parameters and environmental scenarios on wheat production. This method could be used for crop production estimation in a region with limited available data. In summary, integrating the coupled hydrologic and crop growth model with an optimization method and sensitivity–uncertainty analysis can be used to guide agricultural irrigation, saving water resources, and predicting agricultural production and to evaluate the effects of environmental changes on agricultural production.

Table 5. The simulated water balance under actual (realistic) and guided irrigation schemes. Irrigation scheme

Realistic Guided Difference

Irrigation + precipitation

Transpiration

Evaporation

Deep percolation

Change in soil moisture storage

———————————————————————————————— mm ———————————————————————————————— 483.6 264 119 173 72 351.7 270 111 49.4 78.7 −131.9 6 −8 123.6 6.7

Table 6. The simulated water balance and crop output under various irrigation schemes. Weight of storage organs

Aboveground dry matter

————————— g m−2 ———————— 530 1207.9 422.64 1068.6 340.28 911.26 270.8 761.95 206.8 613.05 144.7 459.19 93.7 319.38

658

Irrigation + precipitation

Evaporation

Transpiration

Deep percolation

Change in soil moisture storage

——————————————————————————— mm ——————————————————————————— 311.7 102 266 43.4 98 271.7 94.9 242.6 40.7 108.71 231.7 88.9 211 39.5 113.4 191.7 82.7 181.2 38.9 116.8 151.7 76 151.85 38.7 119.7 111.7 68.4 122.77 38.58 121.9 71.7 59.3 96.15 38.56 123.1


Fig. 9. Simulated weight of storage organs (WSO) under various amounts of irrigation with groundwater at (a) 0.5 m, (b) 1 m, (c) 1.5 m, (d) 2 m, (e) 2.5 m, and (f) 3 m.

Fig. 10. Morris sensitivity study results of the strength, μ*, vs. the spread, σ, for 13 groups of parameters. SSSAJ: Volume 76: Number 2 • March–April 2012

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Table 7. The Morris sensitivity study results of the strength, μ*, and spread, σ, of 30 parameters used in the coupled model. Parameter Max. leaf CO2 assimilation at development stage of crop growth (AMAXTB) Initial depth of groundwater table (ZIT) Thermal time from anthesis to maturity (TSUM2) Thermal time from emergence to anthesis (TSUM1) Thermal time from sowing to emergence (TSUMEM) Initial light-use efficiency of leaf assimilation as a function of daily temperature (EFFTB) Conversion efficiency of assimilates into storage organ (CVO) Soil hydraulic parameters in HYDRUS Specific leaf area as a function of development stage (SLATB) Sowing date (IDSOW) Correction factor transpiration rate (CFET) RDMCR Extinction coefficient for diffuse visible light as a function of development stage (KDIFTB) Conversion efficiency of assimilates into root (CVR) Life span of leaves growing at 35°C (SPAN) Initial rooting depth (RDI) Conversion efficiency of assimilates into leaf (CVL) Conversion efficiency of assimilates into stem (CVS) Max. leaf CO2 assimilation rate at crop maturity (AMAXTB1) Max. relative increase in leaf area index (RGRLAI) Relative maintenance respiration rate, storage organs (RMO) Relative change in respiration rate per 10°C temperature change (Q10) Relative maintenance respiration rate, leaves (RML) Max. relative death rate of leaves due to water stress (PERDL) Max. daily increase in rooting depth (RRI) Relative maintenance respiration rate, stems (RMS) Relative maintenance respiration rate, roots (RMR) Lower threshold temperature for emergence (TBASEM) Leaf area index at emergence (LAIEM) Max. effective temperature for emergence (TEFFMX)

μ* 1848 1192.6 956.6 886.6 851.2 829.8 724.2 715.2 700.35 640.2 487.6 477.6 398.67 347.6 318.6 298.6 182.4 169.8 160 159.6 157 126.6 92.4 85.8 84.8 58.4 43.6 0 0 0

σ 1280.2222 993.6 422.9736 322.9736 355.9813 155.9813 87.7163 402.263 518.9661 702.263 516.9559 529.2696 432.56 329.2696 173.395 308.24 55.2078 107.0055 121.4636 225.7194 84.0601 48.1207 30.3357 14.4052 69.0173 36.9793 26.8933 0 0 0

Fig. 11. The distributions of the weight of storage organs (WSO) at harvest time after eight irrigation times of (a) 10 mm each, (b) 20 mm each, (c) 30 mm each, and (d) 40 mm each. 660


Table 8. First effect and total effect indices of 13 parameter groups. Group of parameters

1. Sowing date 2. Groundwater depth 3. Soil hydraulic parameters (HYDRUS) Total of environmental parameters 4. Emergence 5. Phenology 6. Initial 7. Green leaf 8. Assimilation 9. Conversion of assimilates into biomass 10. Maintenance respiration 11. Death rates due to water stress 12. Correction factor transpiration rate 13. Root parameters Total of crop physiological parameters Total parameters

Each irrigation 40 mm First

Each irrigation 30 mm

Total

First

Total


Environmental parameters 0.1057 0.2686 0.0982 0.2228 0.10017 0.0817 0.2601 0.1257 0.3466 0.2588 0.1355 0.1805 0.1446 0.1997 0.1846 0.3229 0.7092 0.3685 0.7691 0.54357 Crop physiological parameters 0.0785 0.3383 0.0945 0.3843 0.1085 0.0535 0.303 0.0476 0.3171 0.0195 0.0332 0.1609 0.0398 0.1541 0.0173 0.0565 0.3596 0.0466 0.263 0.0247 0.1574 0.5965 0.1446 0.6634 0.0958 0.103 0.36 0.1023 0.3113 0.06402 0.0441 0.3123 0.0407 0.306 0.0277 0.0112 0.3429 0.0042 0.2882 0.0048 0.0707 0.2563 0.0764 0.2858 0.088 0.0369 0.2057 0.0382 0.1615 0.0293 0.645 3.2355 0.6349 3.1347 0.47962 Environmental + crop physiological parameters 0.9679 3.9447 1.0034 3.9038 1.02319

ACKNOWLEDGMENTS This work is supported by the Chinese Academy of Sciences knowledge innovation project (Grant no. KZCX2-YW-Q10-1) and the NSFC (National Science Foundation of China) project (Grant no. 40901020). Gratitude is expressed to Linze experimental plot for collecting data and working.

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Total 0.18872 0.4384 0.2927 0.91982


Total

0.07316 0.13765 0.3469 0.651 0.2561 0.3734 0.67616 1.16205

0.3956 0.2224 0.1161 0.1691 0.3577 0.2049 0.266 0.1632 0.3538 0.1885 2.4373

0.1507 0.0056 0.007 0.0054 0.0416 0.0144 0.0193 0.0083 0.096 0.0164 0.3647

0.3246 0.1136 0.0809 0.0913 0.1421 0.1556 0.1618 0.0924 0.404 0.0981 1.6644

3.35712

1.04086

2.82645

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