Modeling Regional Soil Water Balance in Farmland of the Middle Reaches of Heihe River Basin

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Article Modeling Regional Soil Water Balance in Farmland of the Middle Reaches of Heihe River Basin

Jiang Li 1,2, Xiaomin Mao 1,*, Songhao Shang 2 ID and Tammo S. Steenhuis 3 ID

1 Centre for Agricultural Water Research in China, College of Water Resources and Civil Engineering, China Agricultural University, Beijing 100083, China; [email protected] 2 State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China; [email protected] 3 Department of Biological and Environmental Engineering, Riley-Robb Hall, Cornell University, Ithaca, NY 14853, USA; [email protected] * Correspondence: [email protected]; Tel.: +86-10-6273-8498

Received: 12 September 2017; Accepted: 31 October 2017; Published: 3 November 2017

Abstract: Quantifying components of soil water balance in farmland of the middle reaches of Heihe River Basin is essential for efﬁciently scheduling and allocating limited water resources for irrigation in this arid region. A soil water balance model based on empirical assumptions in the vadose zone of farmland was developed and simulation results were compared/validated with results by the numerical model HYDRUS-1D. Results showed a good coherence between the simulated results of the water balance models and the HYDRUS-1D model in soil water storage, evapotranspiration, deep percolation and groundwater recharge, which indicated that the water balance model was suitable for simulating soil water movement in the study area. Considering the spatial distribution of cropping patterns, groundwater depth and agricultural management, ArcGIS was applied for the pre-/post-processing of the water balance model to quantify the spatial distribution of components of soil water balance in the major cropland in middle reaches of Heihe River Basin. Then, distributions of components of soil water balance in the major cropland under different water-saving irrigation practices during the growing season were predicted and discussed. Simulation results demonstrated that evapotranspiration of the main crops would be more prominently inﬂuenced by irrigation quota under deep groundwater depth than that under shallow groundwater depth. Groundwater recharge would increase with the increase of irrigation quota and decrease with the increase of groundwater depth. In general, when groundwater depth reached 3 m, groundwater recharge from root zone was negligible for spring wheat. While when it reached 6 m, groundwater recharge was negligible for maize. Water-saving irrigation practices would help to reduce groundwater recharge with a slight decrease of crop water consumption.

Keywords: water balance model; HYDRUS-1D; soil water balance; ArcGIS; Heihe River Basin

1. Introduction Quantifying the components of soil water balance in farmland is essential in arid regions with limited water resources. It can provide a basis for efﬁcient irrigation scheduling and optimum water resource allocation [1–5]. Soil water balance in the vadose zone of farmland would be inﬂuenced by water-saving irrigation practices. The main components of soil water balance in farmland mainly include irrigation/precipitation, surface runoff, evaporation, transpiration, water exchange between root zone and the lower zone, variation of soil water storage, and lateral seepage to adjacent land [6,7]. Field experiments have been widely conducted to quantify soil water balance in farmland [8–13]. Weighing lysimeters, eddy covariance and Bowen ratio systems are frequently used to estimate

Water 2017, 9, 847; doi:10.3390/w9110847 www.mdpi.com/journal/water Water 2017, 9, 847 2 of 21 evapotranspiration [14–16]. The variation of the water table is monitored to calculate groundwater recharge [17]. Soil water content measured by neutron probe, time-domain reflectometer, or oven drying is usually used to obtain soil water storage [18]. However, experiments are expensive, time-consuming and site specific. Thus, simulation models were established to predict soil water content and calculate the transformation of water input in a farmland vadose zone [19–24]. Hydrodynamic models and water balance models are two main types of models for simulating soil water movement [25,26]. Hydrodynamic models for vadose zones are based on the Richards equations combining mass conservation and Darcy’s law [27,28]. These models have sound physical bases and can describe detailed soil water movement. One of popular hydrodynamic models is HYDRUS-1D [29,30]. Soil water balance models are based on the concept of mass balance, which consider the total soil water quantity into and out of the target zone [31,32]. These models are widely used in agricultural water management because they perform as well as hydrodynamic models and require less input parameters and can be easily used at field scale [33–35]. For irrigated farmland on regional scales, especially for the arid zone, large spatial variation of soil texture, irrigation and groundwater exists, which leads to differences in the soil water balance of the root zone [36,37]. Because of scale-matching problems, hydrological models were usually achieved by using a regional groundwater flow model with the rough estimation of evapotranspiration on land surface [38], or by the coupling of several models, e.g., Modflow and SWAP [39], Modflow and HYDRUS [40]. Most of the hydrodynamic models for a vadose zone are applied at point or field scale. Because of excess the computer time and detailed subsoil characteristics required, those models cannot be applied at regional scale where spatial variability in crop, soil and irrigation practices should be included [41,42]. Only when vadose water balance models can be up-scaled to a regional scale can the full impacts/benefits of this kind model be realized in irrigated farmland [43,44]. Geographic Information Systems (GIS) can be used to extend vadose applications to the regional scale through loose, close or embedded coupling. Previous studies on GIS-coupled models usually focused on certain areas and the purpose of them was always to simulate the runoff or groundwater balance. For example, Wang et al. [45] used GIS with T-M water balance model to calculate the water balance and obtained the runoff in the Jinyangchuan watershed. Portoghese et al. [46] and Tilahun and Merkel [47] coupled GIS with water balance models and calculated groundwater balance. In arid zones, there are no quantities of surface runoff produced by rainfall like there are in humid areas. In these regions, most of the water recourses are used for agriculture and water is usually diverted from canals/rivers to farmland, and consumed largely by evaporation/transpiration. Under these conditions, the most popular hydrological models, which are good at simulating surface runoff processes, such as SWAT, SHE, VIC model, etc., should be improved or modified when used in such regions [48]. Especially when water-saving practices are taken in this region, the hydrological processes would be influenced by human control. Therefore, it is necessary to develop some models that are specifically suitable for these regions. For this purpose, in this study we proposed a field scale soil water balance model which requires fewer parameters and less computer time/memory than the commonly used soil water dynamic models, e.g., HYDRUS-1D. It can be easily integrated into GIS for regional scale quantifications. Then this method was applied in the middle reaches of Heihe River Basin, to investigate the impacts of water-saving irrigation practices on the soil water balance of farmland. First, the soil water balance model was evaluated by comparing with those simulated by HYDRUS-1D. Then, the model was loosely coupled with ArcGIS for the pre-/post-processing for regional-scale calculations. Finally, the soil water balance in the vadose zone is discussed under different groundwater depths with various water-saving irrigation practice applications. Water 2017, 9, 847 3 of 21 Water 2017, 9, 847 3 of 21 2. Materials and Methods 2. Materials and Methods 2.1. Study Area and Data Collection 2.1. Study Area and Data Collection The study area is the middle reaches of Heihe River Basin, which is located in the arid region of northwestThe study China area and is covers the middle 17 irriga reachestion districts. of Heihe Figure River 1 Basin,showswhich the distribution is located of in landscape the arid region units inof northwestthis area, including China and the covers main 17 crops, irrigation forest, districts. grassland, Figure bare1 showssoil and the surface distribution water, of which landscape were obtainedunits in this from area, land including use map the and main cropping crops, patterns forest, grassland, based on bareremote soil sensing and surface data water,from the which Western were Databaseobtained from(http://www.heihedata.or land use map and croppingg/). The patternsstudy area based is 6736 on remotekm2 consisting sensing dataof 38% from farmland, the Western 14% forest/grassDatabase (http://www.heihedata.org/ land, 4% river and flood plain,). The and study 41% area bare is soil. 6736 Most km2 ofconsisting the cultivated of 38% lands farmland, were 14%planted forest/grass with maize land, and 4% spring river wheat, and flood which plain, accounted and 41% for bare over soil. 50% Most of the of farmland. the cultivated The other lands crops were includeplanted barley, with maize interplant and spring of spring wheat, wheat which and accounted maize (relay for overstrip 50%interplant of the in farmland. this region The for other the purposecrops include of improving barley, interplant crop economic of spring production wheat and in maizethis region), (relay and strip others interplant (mainly in this various region kinds for the of vegetables).purpose of improving The intensive crop planting economic area production is distributed in this in region),the southern and othersand middle (mainly irrigation various districts. kinds of Tablevegetables). 1 shows The the intensive classification planting of soil area texture is distributed based on in our the survey southern in 2014, and middlewhich demonstrated irrigation districts. that inTable most1 shows areas the it classificationis loam at 0–100 of soil cm texture soil layer, based onand our loam, survey sand in 2014,or cobble which stone demonstrated in deep thatlayers. in Therefore,most areas the it is soil loam types at 0–100 are grouped cm soil layer, into andthree loam, types sand (T1, orT2 cobble and T3) stone and in locations deep layers. are Therefore,shown in Figurethe soil 1. types are grouped into three types (T1, T2 and T3) and locations are shown in Figure1.

Figure 1. Geographic locations, land use andand crop patterns in the studystudy area.area.

Crop growth in theTable study 1. areaResults mainly of soil relies survey on on irrigation, the layered and soil agriculturalsamples. irrigation generally takes over 90% of the total water resources, with over 85% of the irrigation water coming from the 0–100 cm 100–140 cm Heihe River [49Soil]. With Type the implementation of the Water DiversionNumber of Plan Sample [50], Sites the amount of water diverted from the Heihe River to theSoil middle Texture reaches of the basin has reduced by one-third since the year 2001. Table2 showsT1 the statisticsLoam of irrigationLoam depths for the main crops 11 in each irrigation districts during the year 2000T1 to 2010. It canLoam be seen thatSandy irrigation loam depth for maize 4 is normally higher than that for spring wheat. ThereT1 are bigLoam differences betweenSilt loam irrigation depths 12 for the same crop in different irrigation districts. InT1 the sameLoamy irrigation sand district, Silt the loam main crop usually has 1 a big variation of irrigation amounts because ofT1 climate or Loamy human sand factors. Sandy loam 1 T1 Sandy loam Loam 6 T1 Sandy loam Sandy loam 12 T1 Sandy loam Silt loam 6 T1 Silt loam Loam 7 T1 Silt loam Sandy loam 2 T1 Silt loam Silt loam 57

Water 2017, 9, 847 4 of 21

Table 1. Results of soil survey on the layered soil samples.

0–100 cm 100–140 cm Soil Type Number of Sample Sites Soil Texture T1 Loam Loam 11 T1 Loam Sandy loam 4 T1 Loam Silt loam 12 T1 Loamy sand Silt loam 1 T1 Loamy sand Sandy loam 1 T1 Sandy loam Loam 6 T1 Sandy loam Sandy loam 12 T1 Sandy loam Silt loam 6 T1 Silt loam Loam 7 T1 Silt loam Sandy loam 2 T1 Silt loam Silt loam 57 T2 Loamy sand Sand 4 T2 Sandy loam Loamy sand 4 T2 Sandy loam Sand 3 T2 Silt loam Loamy sand 1 T3 Loam Cobble stone 2 T3 Sandy loam Cobble stone 12 T3 Silt loam Cobble stone 14

Table 2. Basic statistics of irrigation depths for the main crops in different irrigation districts (unit: mm).

Irrigation Depths for Spring Wheat Irrigation Depths for Maize Irrigation District Minimum Maximum Average Minimum Maximum Average Daman 369 545 443 495 698 612 Yingke 417 519 465 603 738 686 Xijun 449 551 509 561 729 629 Shangsan 462 560 514 557 810 669 Anyang 480 561 513 228 600 484 Huazhai 222 405 342 375 608 479 Pingchuan 540 675 620 623 1155 776 Banqiao 480 750 671 623 1080 875 Yanuan 540 780 698 623 975 897 Liaoquan 533 705 670 810 1184 928 Shahe 432 600 530 629 900 785 Liyuanhe 432 660 496 629 842 697 Youlian 543 615 586 819 975 919 Liuba 510 615 578 788 1028 935 Luocheng 495 630 582 840 990 905 Xinba 525 675 587 675 975 797 Hongyazi 488 684 587

The middle reaches of the Heihe River basin have temperate arid climate with the mean annual temperature varying from 0 ◦C to 5 ◦C. Meteorological data, i.e., precipitation, relative humidity, sunshine hours, average temperature, minimum air temperature, maximum air temperature and wind speed at Zhangye weather station (38◦560 E, 100◦260 N, 1482.7 m) were obtained from China Meteorological Data Sharing Service System (http://cdc.nmic.cn/home.do). Figure2 shows the annual precipitation and reference evapotranspiration from the year 2000 to 2014 at Zhangye weather station. Obviously the annual precipitation is below 250 mm and the annual reference evapotranspiration is above 1000 mm. The average groundwater level is in the range of 1300 m to 1690 m above mean sea level. WaterWater 20172017,, 99,, 847 847 55 of of 21 21 Water 2017, 9, 847 5 of 21

Figure 2. Annual reference evapotranspiration and precipitation in the study area during the year Figure 2. Annual reference evapotranspiration and precipitation in the study area during the year Figure2000 2. Annualto 2014. reference evapotranspiration and precipitation in the study area during the year 20002000 to to 2014. 2014. 2.2. Model Description and Related Parameters 2.2. Model Description and Related Parameters 2.2. Model Description and Related Parameters 2.2.1. Water Balance Models in Vadose Zone 2.2.1. Water Balance Models in Vadose Zone 2.2.1. WaterTo Balancequantify Models crop water in Vadose consumption, Zone deep percolation from root zone and groundwater Torecharge quantify in farmland, crop water we consumption,developed a corresponding deep percolation soil water from balance root zone model and [51], groundwater which is similar recharge To quantify crop water consumption, deep percolation from root zone and groundwater in farmland,to the previous we developed study [52]. a The corresponding model was briefly soil water illustrated balance here. model The vadose [51], zone which is divided is similar into to the rechargeprevioustwo inparts study farmland, in [ 52vertical]. The we direction, modeldeveloped was i.e., brieﬂyroota corresponding zone illustrated (from 0 m soil here. to 1 water m The below vadosebalance ground zone model surface) is divided[51], and which buffer into is twozone similar parts toin the vertical(from previous direction,1 m belowstudy i.e., soil[52]. rootsurface The zone model to (fromgroundwater was 0 m briefly to 1level, m illustrated below because ground groundwaterhere. surface) The vadose table and depth bufferzone isis zone generallydivided (from into 1 m twobelow partsgreater soil in surface thanvertical 1 tom direction, groundwaterin the farmland i.e., level,root of the zone because study (from area groundwater 0). mFigure to 1 m3 shows below table depththe ground water is generally surface)balance in and greater the buffervadose than zone 1 m (fromin thezone 1 farmland m of below farmland. of soil the surface study area). to groundwater Figure3 shows level, the because water balance groundwater in the vadose table depth zone ofis farmland.generally greater than 1 m in the farmland of the study area). Figure 3 shows the water balance in the vadose zone of farmland. ET

P EIT Ground surface

Root zoneP I Qs Ground surface WR

Root zone Buffer zone Q WB Qs WR Groundwater level

Buffer zone Q FigureFigure 3. 3.Water WWaterB balance balance inin vadosevadose zone zone of of farmland. farmland. Groundwater level In rootIn root zone, zone, water water balance balanc cane can be be described described byby [53] [53] WPIETQt (1) Figure 3. Water∆WR =balanceRs(P+ inI − vadoseET − zoneQs) ·of∆ farmland.t (1)

where ΔWR is the changes of water storage in root zone (mm) (positive means increase), Δt is time whereInstep ∆rootW (day),R zone,is theP wateris changes precipitation balanc of watere can(mm/day), be storage described I is in irrigation root by zone[53] depth (mm) (mm/day), (positive ET means is evapotranspiration increase), ∆t is time step (day),(m/day),P andis precipitation Qs is flux (called (mm/day), percolationI here)is irrigation between root depth zone (mm/day), and buffer zoneET is (mm/day). evapotranspiration Qs can WPIETQt (1) (m/day),be calculated and Qs isby ﬂux Equation (called (2) percolation [54]. Rs here) between root zone and buffer zone (mm/day). Qs can be calculated by Equation (2) [54]. where ΔWR is the changes of water storage in root zone (mm) (positive means increase), Δt is time step (day), P is precipitation (mm/day), I is irrigation!b depth (mm/day), ET is evapotranspiration WR (m/day), and Qs is flux (called percolationQ = a here)· betwee· (nW root− zoneW ) and buffer zone (mm/day). Qs can(2) s W R Rc be calculated by Equation (2) [54]. R f

Water 2017, 9, 847 6 of 21

where WR is the actual water storage in root zone (mm), WRf = θf·LR is the field water capacity of root 3 3 zone, θf is soil water content at field capacity (mm /mm ) and is set as 0.25 for loam [55], LR is the depth of root zone (mm), WRc is the critical value of water storage for water exchange with buffer zone, which is related with field water capacity and groundwater table depth, and usually considered to be constant when groundwater table depth is great. a and b are empirical coefficients (dimensionless), which are related with soil texture and set as 0.11 and 2.5, respectively [56]. Note that Qs > 0 indicates deep percolation, while Qs < 0 means upward recharge from buffer zone to root zone. ET is determined by crop types, growing seasons, atmosphere condition and soil moisture status [57], which is ET = Ks·Kc·ET0 (3) where ET0 is reference evapotranspiration (mm/day) and can be calculated by the Penman-Monteith equation recommended in Allen et al. [57]. Kc is crop coefficient (dimensionless), which varies with specific crop characteristics and growing stage, and is normally obtained through field experiments. The values of Kc for typical crops are obtained according to previous research in the study area [58]. Ks is soil water stress coefficient (dimensionless) and can be described by Equation (4) [59]:

ln(A + 1) K = w (4) s ln 101

θ − θw Aw = × 100 (5) θ f − θw

3 3 where θ = WR/LR is the average soil water content in root zone (mm /mm ), and θw is wilting soil water content (mm3/mm3), which was set as 0.09 for loam [60] in this study. The buffer zone or the area between root zone and groundwater, we assume that it had water connection with root zone through Qs and the surplus water in this zone would recharge to groundwater. Groundwater table depth in most area of the study region is over 3 m. Hence, the phreatic evaporation, i.e., the upward ﬂux from groundwater to root zone, is negligible [61,62]. The water balance and related terms can be calculated from.

∆WB = (−Q + Qs) · ∆t (6)

If WB + QS > WBf, Q = WB + QS − WBf (7)

If WB + QS < WBf, Q = 0 (8) where ∆WB is the changes of water storage in buffer zone (mm) (positive means increase), WB and WBf are actual water storage and ﬁeld water capacity of buffer zone (mm), Q is groundwater recharge per day (mm).

2.2.2. HYDRUS-1D Model HYDRUS-1D is one of hydrodynamics models, which can simulate one-dimensional water transport in variable saturated porous media. This model has been successfully used to simulate water ﬂow in the middle reaches of Heihe River Basin [63–66]. Therefore, in this study, results simulated by HYDRUS-1D were used to validate the calculations of water balance models. The soil water equation in HYDRUS-1D model is the Richards equation

∂θ ∂ ∂h = K(h) + 1 − S(h) (9) ∂t ∂z ∂t where t is time (day), θ is volumetric water content (mm3/mm3), h is water pressure head (mm), z is vertical coordinate axis (mm), K(h) is hydraulic conductivity (mm/day), and S(h) is water sink term Water 2017, 9, 847 7 of 21

(mm/day). The van Genuchten-Mualem (VG-M) equation [67,68] models the variation of K(h) with soil water content where ( θs−θr θr + n m h < 0 θ(h) = [1+|αh| ] (10) θs h ≥ 0

 h mi2  K S l 1 − 1 − S 1/m h < 0 K(h) = s e e (11)  Ks h ≥ 0

θ − θr Se = (12) θs − θr

m = 1 − 1/n , n > 1 (13) where θr and θs are residual and saturated water content, respectively, Ks is saturated hydraulic conductivity, Se is effective saturation and α, n and l are empirical coefﬁcients (the inverse of the air-entry value, a pore-size distribution index and a pore-connectivity parameter, respectively). The sink term S(h) in Equation (9) is actual root-water uptake (equal to actual transpiration), obtained from the Feddes equation [69]

S(h) = α(h) · b(z) · Tp (14) where root-water uptake stress response function α(h) is a prescribed dimensionless function of the soil water pressure head h (0 ≤ α(h) ≤ 1), b(z) is normalized root-water uptake distribution, and Tp is potential transpiration rate. The potential crop evapotranspiration (ETp) was obtained from Equation (15) [57]

ETp = ET0 · Kc (15) where ET0 is reference evapotranspiration (mm/day), Kc is crop coefﬁcient, which can be obtained from previous study [70]. ETp was then divided into potential evaporation (Tp) and potential transpiration (Ep). This partitioning was achieved using crop leaf area index (LAI) based on Beer Equation [71], where c is empirical parameter. −cLAI Ep = ETp × e (16)

−cLAI Tp = ETp × 1 − e (17)

2.2.3. Model Setup and Input Parameters The vadose zone of farmland from ground surface to groundwater level with either maize or spring wheat crop was selected as the simulation domain. Based on observed groundwater depths under farmland, depths to groundwater of 2 m, 3 m, 4 m, 5 m and 6 m were used. As seen in Table1 and Figure1, most of the soil texture in the study area is T1. Therefore, the common soil type loam was used in HYDRUS-1D for model validation. The initial condition for HYDRUS-1D model was assumed to be in hydrostatic condition, therefore the soil matric potential decreased with the increase of elevation. Soil water storage of root zone and buffer zone under the initial condition in HYDRUS-1D model was taken as the input to the water balance model for initial conditions. The upper boundary condition for HYDRUS-1D was the atmospheric boundary condition, including precipitation, evaporation and irrigation (with transpiration as the sink term). The lower boundary was at the free surface of groundwater. We assumed that the groundwater level did not ﬂuctuate during the simulation period. So the lower boundary for HYDRUS-1D was set as stable pressure head boundary (pressure head was 0 m). The distribution of potential root-water uptake over root zone was derived from potential transpiration, Water 2017, 9, 847 8 of 21 where the actual uptake and transpiration would be simulated considering root distribution and soil water condition in root zone. We assumed that the root was uniformly distributed within the underground 1 m depth (i.e., root zone). The simulation period was 152 days and 123 days for maize and spring wheat, respectively, according to the investigation of local planting custom. Irrigation schedules commonly used by farmers for maize and spring wheat were obtained from previous study [72] and shown in Table3. Soil hydraulic parameters for VG-M model and parameters of water stress response function in Feddes model were set as the default values for loam in HYDRUS [29,73]. Values of crop coefﬁcients are from previous research in the same study area and shown in Table4[74].

Table 3. Irrigation schedules for maize and spring wheat (DAS means days after sowing).

First Second Third Fourth Crops Irrigation Irrigation Irrigation Irrigation DAS DAS DAS DAS Depth (mm) Depth (mm) Depth (mm) Depth (mm) Maize 34 160 61 230 90 230 113 230 Spring wheat 33 165 61 150 89 150

Table 4. Parameters for models.

Parameters Maize Spring Wheat 3 3 θr (cm /cm ) 0.005 0.005 3 3 θs (cm /cm ) 0.4 0.4 a 0.036 0.036 VG-M model n 1.56 1.56 Ks (cm/day) 24.96 24.96 l 0.5 0.5

h1 (cm) −15 0 h2 (cm) −30 −1 Feddes model h3(high) (cm) −325 −500 h3(low) (cm) −600 −900 h4 (cm) −8000 −16,000 Seeding to Trefoil 0.43 0.48 Trefoil to Jointing 1.32 0.76 Crop coefﬁcients (K ) C Jointing to Heading 1.47 1.05 Heading to Mature 0.9 0.84

2.3. Methodology of Extending the Local Water Balance Model Simulation Results to Regional Scale The soil water balance at the regional scale was obtained by loose coupling between water balance models for each unit and ArcGIS. ArcGIS software was used as a pre-/post-processor to generate and organize the input data as well as display the output data. For details, the spatial distribution of cropping patterns, groundwater depths and agricultural management in the study area were grouped into small units under the ArcGIS by its function of UNION, i.e., for each unit it had the same crop type, groundwater depth range and irrigation schedule. Then, the data files in ArcGIS were transferred into Microsoft Excel. The Excel file was used as the reference to generate the water balance models’ input project files. Further, water balance models were run to calculate components of soil water balance for each unit, and the outputs of models were transferred back to the Excel file and then into ArcGIS by the function of JOIN. Lastly, ArcGIS was used to present the spatially distributed simulation results.

2.4. Scenario Design The water balance model was used to simulate farmland soil water movement under different groundwater depths (from 2 m to 6 m) or various irrigation quotas. Irrigation depths ranged from Water 2017, 9, 847 9 of 21 450 mm to 1300 mm for maize and 280 mm to 750 mm for spring wheat, respectively. Then, regional farmland soil water balance in the major cropland under water-saving irrigation practices in the studyregional area farmland was predicted soil water as deficit balance irrigation in the major is one cropland of the useful under water water-saving saving irrigation irrigation practices practices in in aridthe studyregions. area was predicted as deficit irrigation is one of the useful water saving irrigation practices in aridFor regions.regional scales, average irrigation amounts of maize or spring wheat during the years 2000 to 2010For for regional each irrigation scales, averagedistrict (shown irrigation in amountsTable 2) were of maize selected or spring as the wheatirrigation during quotas the under years 2000the statusto 2010 quo for scenario. each irrigation The irrigation district schedule (shown (i.e., in Table times2) of were irrigation, selected the as irrigation the irrigation days quotasafter seeding under andthe the status proportion quo scenario. of irrigation The irrigation amount schedulein each irrigation (i.e., times event) of irrigation, was the same the irrigation with the irrigation days after scheduleseeding in and Section the proportion 2.2.3. The irrigation of irrigation water amount application in each were irrigation decreased event) to 80% was and the 60% same under with the the conditionsirrigation scheduleof scenario in SectionA and scenario2.2.3. The B, irrigation respectively. water The application mean of weremetrological decreased data to 80%at Zhangye and 60% weatherunder the station conditions during of the scenario period A from and scenario2000 to 201 B, respectively.0 were used Thein all mean scenarios of metrological (i.e., status data quo, at scenarioZhangye A weather and scenario station B). during the period from 2000 to 2010 were used in all scenarios (i.e., status quo, scenario A and scenario B). 3. Results and Discussion 3. Results and Discussion 3.1. Model Validation 3.1. Model Validation In this section, HYDRUS-1D model was used to validate water balance models. The results of componentsIn this section,of water HYDRUS-1D balance, such modelas soil waswater used storage, to validate evapotranspiration water balance, deep models. percolation The results from of rootcomponents zone to buffer of water zone balance, and groundwater such as soil rech waterarge storage, were compared evapotranspiration, between these deep two percolation models. from root zone to buffer zone and groundwater recharge were compared between these two models. 3.1.1. Soil Water Storage 3.1.1. Soil Water Storage Results of soil moisture in root zone simulated by HYDRUS-1D and water balance model have good Resultsagreements of soil (Figure moisture 4). inFluctuations root zone simulatedof soil moisture by HYDRUS-1D in root zone and consistently water balance reflected model havethe irrigationgood agreements events. Soil (Figure moisture4). Fluctuations increased rapidly of soil after moisture irrigation in rootor precipitation, zone consistently and then reflected fell down the becauseirrigation of events. deep Soilpercolation moisture or increased evapotranspira rapidly aftertion. irrigationIn the earlier or precipitation, stage of andgrowing then fellperiod, down transpirationbecause of deep rate percolation was relatively or evapotranspiration. small with non-flourished In the earlier leaves, stage which of growing led to slowly period, declined transpiration soil moisture.rate was With relatively the growing small with of crops, non-flourished the transpirat leaves,ion rate which and led root-water to slowly uptake declined increased, soil moisture. which leadWith to the a sharper growing drop of crops,of soil themoisture transpiration in root zone rate. and At the root-water end of crop uptake growing increased, period, which soil moisture lead to a insharper the root drop zone of declined soil moisture slowly in because root zone. of the At thesmall end transpiration of crop growing by withered period, soilleaves moisture when crops in the beganroot zone to mature. declined slowly because of the small transpiration by withered leaves when crops began to mature.

(a) 50 50 40 40 25 25 ) 30 30 Soil (%) mm ( (%)

moisture 20 20

0 0 Water (mm) storagein -25 -25 buffer zone 10 10 Soilmoisture in buffer in zone -50 -50 0 0 Waterstorage -75 -75 -10 -10 -100 -100 -20 -20 recharge (mm/day) Deep

(mm/day) Spring wheat -125 Maize -125 -30 -30 Groundwater recharge (mm/day)

GW: 2 m (mm/day)

GW: 2 m percolation Deep percolation -40 -40 -150 -150 Groundwater 0 30 60 90 120 150 0 306090120 Days after sowing Days after sowing HM_Soil moisture in root zone HM_Water recharge from root zone WM_Soil moisture in root zone WM_Water recharge from root zone HM_Water storage in buffer zone HM_Deep percolation WM_Water storage in buffer zone WH_Deep percolation

Figure 4. Cont.

Water 2017, 9, 847 10 of 21 Water 2017, 9, 847 10 of 21

(b) 75 75 55 55 50 50 ) 45 45 Soil mm (%) 35 35 25 25 ( Water Water moisture storage in in storage (%) (mm)

0 0 buffer zone 25 25 15 15 in buffer in zone

-25 -25 storage Water Soil moisture Soil -50 -50 5 5 -75 -75 -5 -5 -100 -100 -15 -15 recharge (mm/day) Spring wheat

Maize Deep

(mm/day) -25 -25 -125 -125 Groundwater (mm/day) GW: 3 m GW: 3 m recharge (mm/day) percolation -35 -35 Deep percolation -150 -150 Groundwater 0 306090120150 0 306090120 Days after sowing Days after sowing HM_Soil moisture in root zone HM_Water recharge from root zone WM_Soil moisture in root zone WM_Water recharge from root zone HM_Water storage in buffer zone HM_Deep percolation WM_Water storage in buffer zone WH_Deep percolation

(%) 40 40 0 0 30 30 (mm) buffer zone in bufferin zone Waterstorage -25 Soil moisture 20 20 -50 -50 10 10 Waterstoragein -75 0 0

Deep -100 Maize -100 -10 -10

(mm/day) Spring wheat Deep recharge percolation -125 GW: 4 m (mm/day) -20 -20

(mm/day) GW: 4 m Groundwater percolation -150 -150 recharge -30 -30 (mm/day)

0 306090120150 0 306090120Groundwater Days after sowing Days after sowing HM_Water recharge from root zone HM_Soil moisture in root zone WM_Soil moisture in root zone WM_Water recharge from root zone HM_Water storage in buffer zone HM_Deep percolation WM_Water storage in buffer zone WH_Deep percolation

(d) 125 125 80 80 70 70 60 60 75 75

(%) 50 50 (mm) (%)

40 40 (mm) Soil moisture Soil

in bufferin zone 30 30 Water storage storage Water buffer zone

25 25 moistureSoil 20 20 10 10 in storage Water -25 -25 0 0 Maize -10 Spring wheat -10 Deep GW: 5 m -20 -20 (mm/day)

recharge GW: 5 m Deep (mm/day) percolation -75 -75 -30 -30 recharge Groundwater (mm/day) (mm/day) 0 306090120150 percolation 0 306090120 Groundwater Days after sowing Days after sowing HM_Soil moisture in root zone HM_Water recharge from root zone WM_Soil moisture in root zone WM_Water recharge from root zone HM_Water storage in buffer zone HM_Deep percolation WM_Water storage in buffer zone WH_Deep percolation

(e) 125 125 90 90 80 80 70 70 75 75 60 60 (%) (%) (mm) 50 50 40 40 (mm) Soil moisture Soil in bufferin zone Soil moisture Soil 25 25 storage Water 30 30 in buffer in zone 20 20 storageWater 10 10 -25 -25 0 0 Maize -10 Spring wheat -10 Deep Deep GW: 6 m -20 -20 Deep GW: 6 m recharge (mm/day) (mm/day) percolation

-75 -75 -30 -30 recharge (mm/day) (mm/day) percolation Groundwater

0 306090120150 0 30 60 90 120 Groundwater Days after sowing Days after sowing HM_Soil moisture in root zone HM_Deep percolation WM_Soil moisture in root zone WM_Deep percolation HM_Water storage in buffer zone HM_Recharge to groundwater WM_Water storage in buffer zone WH_Recharge to groundwater

FigureFigure 4. Simulation4. Simulation results resultsof of soilsoil moisture,moisture, water water storage storage in inbuffer buffer zone, zone, deep deep percolation percolation and and groundwatergroundwater recharge recharge for for summer summer maizemaize and spring spring wheat wheat under under thethe conditions conditions of groundwater of groundwater depthsdepths at 2 at m 2 (ma), (a 3), m 3 m (b (),b), 4 4 m m ( c(c),), 55 mm ( (d)) and and 6 6m m (e ()e (For) (For deep deep percolation percolation and groundwater and groundwater recharge, recharge, negativenegative values values mean mean downward. downward. HMHM meansmeans the the results results simulated simulated by byHYDRUS-1D, HYDRUS-1D, WM WMmeans means the the results calculated by water balance model, and GW means groundwater depth). results calculated by water balance model, and GW means groundwater depth). Soil moisture in the root zone was relatively low because of less precipitation at the beginning Soil moisture in the root zone was relatively low because of less precipitation at the beginning of the crop-growing period, before irrigation. During this period, soil moisture calculated by water of the crop-growing period, before irrigation. During this period, soil moisture calculated by water balance model was larger than that simulated by HYDRUS-1D. It is possibly because the empirical balance model was larger than that simulated by HYDRUS-1D. It is possibly because the empirical equation used in the water balance model is not powerful and accurate enough to reflect water stress on root uptake. The discrepancy of results between these two models becomes larger when groundwater becomes deeper. The largest error in moisture content between these two models were 2% and 3% for Water 2017, 9, 847 11 of 21 equation used in the water balance model is not powerful and accurate enough to reflect water stress on root uptake. The discrepancy of results between these two models becomes larger when groundwater becomes deeper. The largest error in moisture content between these two models were Water2% and2017 ,3%9, 847 for maize and spring wheat, respectively. After irrigation, soil moisture in the root11 zone of 21 increased rapidly. The peak values simulated by the water balance model were larger than those by HYDRUS-1D. Results calculated by water balance model were lower than results by HYDRUS-1D maize and spring wheat, respectively. After irrigation, soil moisture in the root zone increased rapidly. during these periods, because the water balance model was more sensitive to groundwater recharge The peak values simulated by the water balance model were larger than those by HYDRUS-1D. Results than HYDRUS-1D. At the end of the crop-growing period, soil moisture calculated by these two calculated by water balance model were lower than results by HYDRUS-1D during these periods, models was similar. because the water balance model was more sensitive to groundwater recharge than HYDRUS-1D. Soil water storage in the buffer zone calculated by these two models (see Figure 4) after sowing At the end of the crop-growing period, soil moisture calculated by these two models was similar. and before harvest was close. Each time, before irrigation, soil in the root zone was dry with relatively Soil water storage in the buffer zone calculated by these two models (see Figure4) after sowing low negative soil potential that tended to suck water from the buffer zone. Therefore, soil water and before harvest was close. Each time, before irrigation, soil in the root zone was dry with relatively storage in the buffer zone declined slowly. After irrigation, soil water in the root zone would increase low negative soil potential that tended to suck water from the buffer zone. Therefore, soil water storage sharply with water input, and decrease greatly in the first few days by deep percolation. In the water in the buffer zone declined slowly. After irrigation, soil water in the root zone would increase sharply balance model, deep percolation was calculated based on the empirical equation (Equation (2)), with water input, and decrease greatly in the first few days by deep percolation. In the water balance where deep percolation would occur when the soil water storage became larger than the critical value model, deep percolation was calculated based on the empirical equation (Equation (2)), where deep of water storage WRc. This empirical equation did not consider the feedback of soil water in the buffer percolation would occur when the soil water storage became larger than the critical value of water zone on deep percolation, while the Richards equation-based models such as HYDRUS-1D would storage W . This empirical equation did not consider the feedback of soil water in the buffer zone capture thisRc phenomenon, i.e., deep percolation would be hindered with the increase of soil water in on deep percolation, while the Richards equation-based models such as HYDRUS-1D would capture the lower soil zone (buffer zone). As a result, the fluctuation of water storage calculated by the water this phenomenon, i.e., deep percolation would be hindered with the increase of soil water in the balance model was greater than that by HYDRUS-1D. Despite the differences, the trend of simulation lower soil zone (buffer zone). As a result, the fluctuation of water storage calculated by the water results by the water balance model was similar to those by HYDRUS-1D and the results were in balance model was greater than that by HYDRUS-1D. Despite the differences, the trend of simulation reasonable agreement. results by the water balance model was similar to those by HYDRUS-1D and the results were in reasonable3.1.2. Evapotranspiration agreement. (ET) 3.1.2.Figure Evapotranspiration 5 shows the (ET)results of evapotranspiration (ET) calculated by these two models under different groundwater depths. ET calculated by these two models had the same trends, which Figure5 shows the results of evapotranspiration (ET) calculated by these two models under presented as pulsed fluctuations with irregular peak values. The fluctuation of ET was related to the different groundwater depths. ET calculated by these two models had the same trends, which presented climate and irrigation [75]. ET of both maize and spring wheat decreased with increasing as pulsed fluctuations with irregular peak values. The fluctuation of ET was related to the climate groundwater depth under the same climate and irrigation. The total ET for maize was in the range of and irrigation [75]. ET of both maize and spring wheat decreased with increasing groundwater depth 569 mm to 591 mm calculated by water balance model and 570 mm to 578 mm by HYDRUS-1D (Table under the same climate and irrigation. The total ET for maize was in the range of 569 mm to 591 mm 5). As to spring wheat, the total ET was in the range of 401 mm to 422 mm calculated by water balance calculated by water balance model and 570 mm to 578 mm by HYDRUS-1D (Table5). As to spring model and 431 mm to 438 mm by HYDRUS-1D. The results are consistent with results simulated by wheat, the total ET was in the range of 401 mm to 422 mm calculated by water balance model and the other study in the same region. For example, Zhu [76] obtained that ET for maize was in the range 431 mm to 438 mm by HYDRUS-1D. The results are consistent with results simulated by the other of 496 mm to 580 mm, whereas for spring wheat it was from 484 mm to 524 mm in the Yingke study in the same region. For example, Zhu [76] obtained that ET for maize was in the range of 496 mm irrigation district. It indicated that water balance models were able to simulate ET for the main crops to 580 mm, whereas for spring wheat it was from 484 mm to 524 mm in the Yingke irrigation district. in the study area. It indicated that water balance models were able to simulate ET for the main crops in the study area.

(a) 12 (f) 12 HYDRUS WBM Maize HYDRUS WBM Spring wheat 10 GW: 2 m 10 GW: 2 m 8 8

6 6 (mm/day)

ET 4 4 ET (mm/day) 2 2

0 0 0 15 30 45 60 75 90 105 120 135 150 0 153045607590105120 Days after sowing Days after sowing

Figure 5. Cont.

WaterWater2017 2017,,9 9,, 847847 1212 ofof 2121

(b) 12 (g) 12 HYDRUS WBM Maize HYDRUS WBM Spring wheat 10 GW: 3 m 10 GW: 3 m 8 8

6 6

4 4 ET (mm/day) ET (mm/day) 2 2

0 0 0 15 30 45 60 75 90 105 120 135 150 0 153045607590105120 Days after sowing Days after sowing

6 6

ET (mm/day) 4 4 ET (mm/day) 2 2

0 0 0 15 30 45 60 75 90 105 120 135 150 0 153045607590105120 Days after sowing Days after sowing

(d) 12 (i) 12 HYDRUS WBM Maize HYDRUS WBM Spring wheat 10 GW: 5 m 10 GW: 5 m 8 8

6 6

4 4 ET (mm/day) ET (mm/day) 2 2

0 0 0 153045607590105120135150 0 15 30 45 60 75 90 105 120 Days after sowing Days after sowing

(e) 12 (j) 12 HYDRUS WBM Maize HYDRUS WBM Spring wheat 10 GW: 6 m 10 GW: 6 m 8 8

6 6

4 4 ET (mm/day) ET (mm/day) 2 2

0 0 0 153045607590105120135150 0 153045607590105120 Days after sowing Days after sowing

FigureFigure 5.5. ResultsResults ofof evapotranspirationevapotranspiration (ET)(ET) forfor summersummer maizemaize underunder thethe conditionsconditions ofof groundwatergroundwater depthsdepths atat 22 mm ((aa),), 33 mm ((bb),), 44 mm ((cc),), 55 mm ((dd)) andand 66 mm ((ee),), andand forfor springspring wheatwheat underunder thethe conditionsconditions ofof groundwatergroundwater depthsdepths at at 2 2 m m (f (),f), 3 m3 m (g (),g 4), m4 m (h ),(h 5), m 5 (mi) and(i) and 6 m 6 (jm) (GW(j) (GW means means groundwater groundwater depth depth and WBMand WBM means means water water balance balance model). model).

TableTable 5.5.Results Results ofof evapotranspiration,evapotranspiration, deepdeep percolationpercolation andand groundwatergroundwater rechargerecharge underunder differentdifferent groundwatergroundwater depthsdepths calculated calculated by waterby water balance balance model model and HYDRUS-1D and HYDRUS-1D (unit: mm/growing (unit: mm/growing season). season). Groundwater Depth Component Crops Model Groundwater Depth Component Crops Model 2 m 3 m 4 m 5 m 6 m 2 m 3 m 4 m 5 m 6 m Water balance model 591 586 581 574 569 Maize Water balance model 591 586 581 574 569 Maize HYDRUS-1D 578 574 572 571 570 Evapotranspiration HYDRUS-1D 578 574 572 571 570 Evapotranspiration Water balance model 422 424 417 409 401 Spring wheat Water balance model 422 424 417 409 401 Spring wheat HYDRUS-1D 439 435 433 432 431 HYDRUS-1D 439 435 433 432 431 Water balance model 406 374 360 354 350 Maize HYDRUS-1D 417 385 366 357 349 Deep percolation Water balance model 155 119 107 103 102 Spring wheat HYDRUS-1D 138 105 89 78 70

Water 2017, 9, 847 13 of 21

Table 5. Cont.

Groundwater Depth Component Crops Model 2 m 3 m 4 m 5 m 6 m Water balance model 406 374 360 354 350 Maize HYDRUS-1D 417 385 366 357 349 Deep percolation Water balance model 155 119 107 103 102 Spring wheat HYDRUS-1D 138 105 89 78 70 Water balance model 428 326 182 27 0 Maize HYDRUS-1D 417 312 158 4 0 Groundwater recharge Water balance model 164 63 0 0 0 Spring wheat HYDRUS-1D 133 28 0 0 0

3.1.3. Deep Percolation The ﬂuctuation trends of deep percolation from root zone to buffer zone calculated by these two models are similar (see Figure4). Before irrigation, soil water in the root zone was small and water in the buffer zone would ﬂow upwards to the root zone. After irrigation, water in the root zone would seep to the buffer zone immediately. The total volume of deep percolation during the crop-growing period declined with the increase of groundwater depths (Table5). It was within the range of 349 mm to 417 mm calculated by HYDRUS-1D and from 350 mm to 406 mm simulated by water balance model for maize. In the zone with shallow groundwater depth, results for maize simulated by HYDRUS-1D were larger than those calculated by water balance model. With the increase of groundwater depth, deep percolation calculated by these two models becomes closer. As for spring wheat, each peak value after irrigation simulated by HYDRUS-1D was smaller than that by the water balance model, which resulted in larger total deep percolation by water balance model than that by HYDRUS-1D model. It was in the range of 70 mm to 138 mm calculated by HYDRUS-1D and 102 mm to 155 mm simulated by water balance model for spring wheat.

3.1.4. Groundwater Recharge Results of groundwater recharge calculated by the water balance model were larger than those simulated by HYDRUS-1D (shown in Figure4 and Table5). The reason was that the upward water flow from groundwater to the vadose zone (i.e., phreatic evaporation) was ignored in the water balance model. In HYDRUS-1D, the lower boundary was set as constant pressure head of 0 m. Under this condition, there would be phreatic evaporation from groundwater to root zone especially before irrigation when the water storage in the vadose zone was low. For this reason, the cumulated groundwater recharge by HYDRUS-1D was less than that by the water balance model. However the difference of recharge results between these two models were in the range of 12 mm to 35 mm, which is less than 7% of the total water input in farmland. It confirmed the previous study by Gao et al. [77,78] that during the growing season, upward flux was only a small percentage of overall flux. It indicated that water balance model was capable of simulating groundwater recharge of the main crops in the study area. Groundwater recharge of the main crops declined with the increase of groundwater depth. The results calculated by the water balance model shows that there would be water recharge to the groundwater after irrigation, which was consistent with previous studies that excess precipitation and irrigation would recharge to aquifers [62]. The peak values of groundwater recharge simulated by HYDRUS-1D were smaller than those calculated by water balance model and the fluctuations were milder. For maize, the groundwater recharge was in the range of 4 mm to 417 mm simulated by HYDRUS-1D, and 27 mm to 428 mm calculated by the water balance model. Under the condition of 6 m groundwater depth, groundwater recharge was zero for maize. As for spring wheat, groundwater recharge over the growing season was 133 mm simulated by HYDRUS-1D and 164 mm calculated Water 2017, 9, 847 14 of 21 by the water balance model under the condition of 2 m groundwater depth. It reduced to 27 mm (by HYDRUS-1D) and 63 mm (by water balance model) when the groundwater depth increased to 3 m. Groundwater recharge in the spring wheat was zero when groundwater depth was over 4 m. Results in this section showed that calculations of soil water storage, evapotranspiration, deep percolation and water recharge from root zone to buffer zone by the water balance model were in reasonable agreement with the results simulated by HYDRUS-1D, which indicated that water balance models were capable of being used to predict soil water balance under various conditions.

3.2. SoilWater Water 2017, 9, Balance847 under Different Groundwater Depths 14 of 21 3.2.Results Soil Water of soil Balance water under balance Different in the Groundwater root zone underDepths loam texture for each cropland unit calculated by waterResults balance of modelssoil water are balance shown in Figurethe root6. zone Evapotranspiration under loam texture for maizefor each was cropland not sensitive unit to the variationcalculated ofby groundwaterwater balance depths.models are The shown water in inputFigure (irrigation6. Evapotranspiration plus precipitation) for maize was in the not maize fieldsensitive was 965 to mm theand variation around of groundwater 60% of it was depths. consumed The water by evapotranspiration. input (irrigation plus Meanwhile, precipitation) for in spring wheat,the evapotranspirationmaize field was 965 mm decreased and around with 60% the of increaseit was consumed of groundwater by evapotranspiration. depth. Under Meanwhile, the condition of 2 mforgroundwater spring wheat, evapotranspiration depth, evapotranspiration decreased accountedwith the increase for 75% of groundwater of the total water depth. input Under (564 the mm). condition of 2 m groundwater depth, evapotranspiration accounted for 75% of the total water input When groundwater depth was 6 m, the ratio declined to 71%. The volume of water transfer from (564 mm). When groundwater depth was 6 m, the ratio declined to 71%. The volume of water transfer root zone to buffer zone decreased with the increase of groundwater depth for both maize and spring from root zone to buffer zone decreased with the increase of groundwater depth for both maize and wheat.spring The wheat. proportion The proportion of water of recharge water recharge from root from zone root to zone buffer to buffer zone zone on the on totalthe total water water input input ranged fromranged 36 to 42%from for36% maize. to 42% In for the maize. spring In the wheat spring field, wheat the field, proportion the proportion of water of water recharge recharge from from root zone to bufferroot zone zone to would buffer decreasezone would from decrease 27 to from 18% 27% with to the 18% groundwater with the groundwater depth increased depth increased from 2 m to 6 m.from Under 2 m the to current6 m. Under irrigation the current schedules, irrigation water schedules, use efficiency water use of efficiency spring wheat of spring was wheat more was effective thanmore maize. effective than maize.

125 75 Irrigation plus precipitation 25 Evapotranspiration

(cm) -25 Water storage -75 Deep percolation -125

Water consumption/supply MS MS MS MS MS 2m 3m 4m 5m 6m Groundwater depth

FigureFigure 6. Soil 6. Soil water water consumption consumptionand and supplysupply in in root root zone zone (positive (positive means means supply, supply, negative negative means means consumption,consumption, M meansM means maize maize and and S S means means spring wheat). wheat).

FigureFigure7a shows 7a shows results results of of the the water water budgetbudget in th thee buffer buffer zone zone for for main main crops crops in the in study the study area. area. TermsTerms of the of the water water budget budget in in the the buffer buffer zonezone illustratedillustrated large large differences differences when when groundwater groundwater depth depth changed.changed. When When groundwater groundwater depthdepth was less less than than 3 3m, m, water water storage storage in the in thebuffer buffer zone zonewould would decreasedecrease and waterand water from from the root the zoneroot wouldzone would continue continue seeping seeping to groundwater to groundwater (i.e., deep (i.e., percolation). deep percolation). When groundwater depth becomes deeper, water discharged from the root zone would When groundwater depth becomes deeper, water discharged from the root zone would stay in the stay in the buffer zone and lead to less deep percolation. In the maize field, over 80% of the water buffer zone and lead to less deep percolation. In the maize field, over 80% of the water discharged discharged from the root zone would seep into groundwater directly when groundwater depth was from3 them. When root groundwater zone would depth seep was into 4 m groundwater or 5 m, there would directly be when50% or groundwater7% of the water depth discharged was 3 m. Whenfrom groundwater the root zone depth seeping was into 4groundwater. m or 5 m, thereWhen wouldgroundwater be 50% increased or 7% to of 6 m, the all water of the dischargedwater fromdischarged the root zone from seepingthe root zone into would groundwater. stay in the When buffer groundwater zone. In the spring increased wheat tofield, 6 m, all all the of water thewater dischargeddischarged from from the the root root zone zone would would stay in in the the buffer buffer zone zone. when In groundwater the spring wheat depth field,was over all the3 m. water dischargedNote that from in this the study root zone(as shown would in Figure stay in 7a) the we buffer assumed zone the when initial groundwater soil water of farmland depth was was over at 3 m. Notethe that hydrostatic in this study condition (as shown after a inlong Figure period7a) of we laying assumed fallow the through initial the soil winter. water For of farmlandsome places was at the hydrostaticthere might be condition flood irrigation after a(e.g., long fall period irrigation of layingand winter fallow irrigation through in the the late winter. autumn For period) some to places leach salts and to restore water for springtime. Under those conditions, the initial soil water content there might be flood irrigation (e.g., fall irrigation and winter irrigation in the late autumn period) to might be much larger than the assumption in Figure 7a. We assumed under this condition that soil leachwater salts in and the tobuffer restore zone water was at for field springtime. capacity when Under crop thosewas planted. conditions, Thus, theresults initial showed soil that water deep content percolation from root zone to buffer zone was nearly equal for various groundwater depths (Figure 7b). Almost all the deep percolation would enter groundwater, which was different from results under hydrostatic condition.

Water 2017, 9, 847 15 of 21 might be much larger than the assumption in Figure7a. We assumed under this condition that soil waterWater 2017 in the, 9, 847 buffer zone was at ﬁeld capacity when crop was planted. Thus, results showed that15 deep of 21 percolation from root zone to buffer zone was nearly equal for various groundwater depths (Figure7b). Almost all the deep percolation50 would enter groundwater, which was different(a) from results under hydrostaticWater 2017 condition., 9, 847 30 15 of 21 Deep percolation 10 50 (a) -10 Groundwater recharge

(cm) 30 -30 Deep percolation 10 Water storage -50-10 Groundwater recharge

(cm) MS MS MS MS MS Water consumption/supply -30 2m 3m 4m 5m 6m Water storage -50 Groundwater depth MS MS MS MS MS Water consumption/supply 50 2m 3m 4m 5m 6m (b) Groundwater depth 30 50 Deep percolation(b) 10 30 -10 DeepGroundwater percolation recharge

(cm) 10 -30 -10 GroundwaterWater storage recharge (cm) -50-30 MS MS MS MS MS Water storage Water consumption/supply -50 2m 3m 4m 5m 6m MSGroundwater MS MS depth MS MS Water consumption/supply 2m 3m 4m 5m 6m Groundwater depth Figure 7. Soil water consumption and supply in buffer zone with the initial condition of (a) Figure 7. Soil water consumption and supply in buffer zone with the initial condition of (a) hydrostatic hydrostaticFigure 7.condition Soil water andconsumption (b) harvest and supplycondition in buffer (positive zone withmeans the initialsupply, condition negative of (ameans) condition and (b) harvest condition (positive means supply, negative means consumption, M means consumption,hydrostatic M conditionmeans maize and and(b) Sharvest means springcondition wheat). (positive means supply, negative means maizeconsumption, and S means M spring means wheat).maize and S means spring wheat). 3.3. Soil Water Balance under Various Irrigation Depths 3.3. Soil3.3. WaterSoil Water Balance Balance under under Various Various Irrigation Irrigation Depths Depths InIn thetheIn arid aridthe arid area,area, area, cropcrop crop productivityproductivity productivity wouldwould would bebe inﬂuencedinflinfluenceduenced greatly greatlygreatly by byby soil soilsoil water waterwater stress stressstress in the inin root thethe rootroot zonezonezone becausebecause because ofof lessless of less irrigationirrigation irrigation andand and high high evapotranspiration.evapotrans evapotranspiration.piration. While While there there was was inappropriate inappropriate irrigation, irrigation, suchsuch suchasas excessiveexcessive as excessive irrigation,irrigation, irrigation, inin in somesome some places,places, places, some somesome ofof thethe irrigated irrigatedirrigated water waterwater would wouldwould be consumedbebe consumedconsumed by soil byby soilsoil evaporation,evaporation,evaporation, oror percolatepercolateor percolate toto to groundwatergroundwater groundwater andandand resultresult in inin the thethe waste wastewaste of of ofvaluable valuablevaluable water waterwater resources resourcesresources and andand possiblypossiblypossibly fertilizerfertilizer fertilizer andand and pesticides.pesticides. pesticides. ThereforeTh Thereforeerefore ititit isis necessarynecessary to toto study studystudy soil soilsoil water waterwater movement movementmovement and andwaterand waterwater balancebalancebalance inin thethe in vadosevadosethe vadose zonezone zone underunder under differentdifferent different irrigation irrigationirrigation schedulesschedules withwith with variousvarious various irrigationirrigation irrigation depths. depths.depths. In this InIn thisthis section, components of the soil water balance in loam under different conditions were simulated section,section, componentscomponents of of the the soil soil water water balance balance in loamin loam under under different different conditions conditions were simulatedwere simulated using using water balance models. Results of evapotranspiration, variation of soil water storage in the waterusing balancewater balance models. models. Results ofResults evapotranspiration, of evapotranspiration, variation ofvariation soil water of storagesoil water in the storage vadose in zone the vadose zone and groundwater recharge for maize and spring wheat are shown in Figure 8. andvadose groundwater zone and groundwater recharge for maize recharge and for spring maize wheat and arespring shown wheat in Figureare shown8. in Figure 8.

Figure 8. Cont.

Water 2017, 9, 847 16 of 21 Water 2017, 9, 847 16 of 21

FigureFigure 8.8. Results of evapotranspiration for maize (a) andand springspring wheatwheat ((b),), variationvariation ofof soilsoil waterwater storagestorage inin vadosevadose zone zone for for maize maize (c )(c and) and spring spring wheat wheat (d ),(d and), and groundwater groundwater recharge recharge for maizefor maize (e) and (e) springand spring wheat wheat (f) in ( differentf) in different irrigation irrigation quota quota under under various various groundwater groundwater depths. depths.

EvapotranspirationEvapotranspiration of maize waswas largerlarger thanthan thatthat ofof springspring wheat,wheat, andand evapotranspirationevapotranspiration increasedincreased withwith thethe increaseincrease ofof irrigationirrigation amountamount for the samesame groundwatergroundwater depth (Figure 88a,b).a,b). EvapotranspirationEvapotranspiration hadhad a a greater greater dependence dependence on on the the amount amount of waterof water applied applied when when groundwater groundwater was nearwas near 6 m depth6 m depth than than when when groundwater groundwater was was shallow. shallow. For For example, example, reducing reducing the the irrigation irrigation depth depth by 60%,by 60%, evapotranspiration evapotranspiration for for maize maize decreased decreased by 8%by 8% when when groundwater groundwater depth depth was was 2–3 2–3 m, m, 9% 9% at 4at m 4 groundwaterm groundwater depth depth and and 10% 10% at 5–6 at m.5–6 When m. When irrigation irrigation application application was reducedwas reduced to 80% to in 80% the maizein the ﬁeld,maize evapotranspiration field, evapotranspi wouldration decreasewould decrease by 2% under by 2% all unde the groundwaterr all the groundwater depths. When depths. irrigation When increasedirrigation byincreased 20% or 40%,by 20% evapotranspiration or 40%, evapotranspiration of maize would of maize increase would by 0.5% increase to 0.6% by for0.5% groundwater to 0.6% for depthsgroundwater of 2 m depths and 0.7% of 2 m to and 0.9% 0.7% for ato groundwater0.9% for a groundwater table between table 5 between and 6 m. 5 and For 6 springm. For wheat,spring evapotranspirationwheat, evapotranspiration would decrease would bydecrease 4% to 6%by when4% to irrigation 6% when water irrigation application water was application decreased was by 20%decreased to 40% by and 20% it wouldto 40% increaseand it would by 1% increase to 2% whenby 1% irrigation to 2% when water irrigation application water was application increased was to 120%increased to 140%. to 120% to 140%. SoilSoil waterwater storagestorage wouldwould decreasedecrease (negative(negative values)values) whenwhen groundwatergroundwater waswas deepdeep withwith deﬁcitdeficit irrigationirrigation (Figure(Figure8 8c,d).c,d). InIngeneral, general,soil soilwater waterstorage storage tendedtended toto increaseincrease during during the the growing growing season season whenwhen irrigationirrigation amountsamounts werewere highhigh andand groundwatergroundwater waswas deepdeep withwith thickthick bufferbuffer zone.zone. GroundwaterGroundwater rechargerecharge wouldwould increaseincrease withwith thethe decreasedecrease ofof groundwatergroundwater depthdepth andand thethe increase ofof thethe irrigationirrigation waterwater applicationsapplications (Figure(Figure8 8e,fe,f).).Under Underthe thesame samegroundwater groundwater depths, depths, groundwatergroundwater rechargerecharge ofof maizemaize waswas largerlarger thanthan thatthat ofof springspring wheat.wheat.

3.4.3.4. Soil Water BalanceBalance inin thethe MajorMajor CroplandCropland underunder WaterWater SavingSaving IrrigationIrrigation PracticesPractices inin thethe MiddleMiddle Reaches ofReaches Heihe Riverof Heihe Basin River Basin ResultsResults ofof evapotranspiration, evapotranspiration, variation variation of soil of watersoil storagewater storage and groundwater and groundwater recharge simulatedrecharge 2 bysimulated the water by balance the water model balance in the model major croplandin the major (covering cropland 1275 km(covering) in the 1275 middle km reaches2) in the of middle Heihe Riverreaches Basin of Heihe are shown River inBasin are shown in Figure 9. FigureFigure9 9shows shows that that evapotranspiration evapotranspiration in the in north the (e.g.,north Anyang (e.g., Anyang Irrigation Irrigation District andDistrict Huazhai and IrrigationHuazhai Irrigation District) wasDistrict) less thanwas thatless than in other that irrigation in other irrigation districts under districts the under same scenario.the same Withscenario. the implementationWith the implementation of water-saving of water-saving irrigation irrigation practices, evapotranspirationpractices, evapotranspiration decreased decreased with the reduction with the reduction of irrigation water application, especially in the middle of the study area, such as in the Liyuanhe Irrigation District. Under the status quo, the total evapotranspiration of farmland

Water 2017, 9, 847 17 of 21

of irrigationWater 2017 water, 9, 847 application, especially in the middle of the study area, such as in the17 Liyuanhe of 21 Irrigation District. Under the status quo, the total evapotranspiration of farmland cultivated with maizecultivated and spring with wheat maize inand the spring study wh areaeat in was the study 7.06 × area10 was8 m 37.06; it would× 108 m3; slightly it would decrease slightly decrease by 2% and 5% whenby 2% the and irrigation 5% when quota the irrigation cut down quota to 80% cut and down 60%, to respectively.80% and 60%, Groundwater respectively. Groundwater recharge in most croppedrecharge ﬁelds in was most less cropped than 30fields mm. was Under less than the status30 mm. quo, Under the the recharge status quo, in some the recharge places inin thesome north and middleplaces in of the the north study and area middle (e.g., of the the Shahestudy area Irrigation (e.g., the district Shahe andIrrigation the Liyuanhe district and Irrigation the Liyuanhe District) Irrigation District) was greater than 450 mm. The total amount of groundwater recharge of the main was greater than 450 mm. The total amount of groundwater recharge of the main crops reduced with crops reduced with the decrease of irrigation quotas. It would decrease from 1.68 × 108 m3 in status × 8 3 3 × 8 3 the decreasequo, to 1.0 of3 irrigation× 108 m3 and quotas. 4.75 × 10 It8 wouldm3 under decrease Scenario from A and 1.68 Scenario10 B.m Underin status the status quo, quo, to 1.0 excessive10 m 8 3 and 4.75irrigation× 10 wouldm under lead Scenarioto the increase A and of Scenario soil water B. storage Under in the the status vadose quo, zone excessive (2.89 × 10 irrigation8 m3), when would 8 3 lead toirrigation the increase amount of soilreduced water to storage 80% or in60%, the vadosethe volumes zone would (2.89 × be10 decreasedm ), when by 43% irrigation and 86%, amount reducedrespectively. to 80% or 60%, the volumes would be decreased by 43% and 86%, respectively. Figure9.

FigureFigure 9. Results 9. Results of evapotranspirationof evapotranspiration ( a(a),), groundwatergroundwater recharge recharge (b ()b and) and variation variation of soil of soilwater water storagestorage in vadose in vadose zone zone (c) in(c) thein the farmland farmland cultivated cultivated withwith maize maize and and spring spring wheat wheat of study of study area area under under differentdifferent water water saving saving irrigation irrigation practice practice scenarios. scenarios.

4. Conclusions4. Conclusions To studyTo study the the soil soil water water balance balance inin farmland of of the the middle middle reaches reaches of the of Heihe the HeiheRiver Basin, River we Basin, proposed a corresponding soil water balance model and the simulation results were compared with we proposed a corresponding soil water balance model and the simulation results were compared the results calculated by the hydrodynamic model HYDRUS-1D. Then, components of soil water with the results calculated by the hydrodynamic model HYDRUS-1D. Then, components of soil balance under different conditions of groundwater depths and irrigation quotas during the growing waterseason balance of undermain crops different were conditionsanalyzed using of groundwatercorresponding depthswater balance and irrigation models. With quotas pre-/post- during the growingprocessing season by of mainArcGIS, crops the werewater analyzedbalance models using were corresponding further applied water for balance predicting models. the spatial With pre- /post-processingdistribution of by evapotranspirati ArcGIS, the wateron, groundwater balance models recharge were furtherand variation applied of forsoil predicting water storage the spatialin distribution of evapotranspiration, groundwater recharge and variation of soil water storage in Water 2017, 9, 847 18 of 21 farmland of the whole middle reaches under different water-saving irrigation practice scenarios. Conclusions are drawn as follows:

(1) A good coherence was shown between the simulated results of the water balance models and HYDRUS-1D model in soil water storage, evapotranspiration, deep percolation from the root zone and groundwater recharge, indicating that the water balance models were suitable to simulate soil water movement in the vadose zone cultivated with maize or spring wheat in the study area. (2) Results of simulations under different groundwater depths showed that components of soil water balance in the root zone for maize was not sensitive to the variation of groundwater depths. Meanwhile, for spring wheat, the volume of evapotranspiration was decreased with the increase of groundwater depth. More water deep percolation from the root zone would stay in the buffer zone and led to less groundwater recharge when groundwater depth was larger. When groundwater depth reached 3 m for spring wheat and 6 m for maize, groundwater recharge from farmland to aquifer was negligible. (3) Results of simulations under different irrigation quotas with various groundwater depths showed that evapotranspiration of the main crops in the study area would be more prominently influenced by irrigation quota under deep groundwater depth than that under shallow groundwater depth. Groundwater recharge of farmland would increase with the increase of the irrigation quota. (4) Results of scenario simulations under different water-saving irrigation practices showed that groundwater recharge in farmland cultivated with maize and spring wheat would sharply decrease with the implementation of deficit irrigation. Evapotranspiration of the main crops in the study area would be slightly reduced under deficit irrigation.

Note that the proposed soil water balance model is validated by HYDRUS-1D. Generally speaking it is insufﬁcient to validate one proposed model by the other model without calibrations. Despite the fact that HYDRUS-1D is a popular model and has been successfully used in previous research in this region, to ensure our study results more sound and reliable, data regarding regional soil water balance need to be collected or monitored to further validate the models.

Acknowledgments: This work was supported by Projects of National Natural Science Foundation of China (Grant No. 91425302, 51379207) and the Program of Introducing Talents of Discipline to Universities (B14002). Author Contributions: J.L. and X.M. designed the study; J.L. did the simulations and analyzed the data; J.L. and X.M. wrote the paper; S.S. and T.S.S. contributed to the model design and discussed the results. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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