A field-validated surrogate crop model for predicting root-zone moisture and salt content in regions with shallow groundwater

Optimum management of irrigated crops in regions with shallow saline groundwater requires a careful balance between application of irrigation water and upward movement of salinity from the groundwater. Few fieldvalidated surrogate models are available to aid in the management of irrigation water under shallow groundwater conditions. The objective of this research is to develop a model that can aid in the management using a minimum of input data that are field validated. In this paper a 2-year field experiment was carried out in the Hetao irrigation district in Inner Mongolia, China, and a physically based integrated surrogate model for arid irrigated areas with shallow groundwater was developed and validated with the collected field data. The integrated model that links crop growth with available water and salinity in the vadose zone is called Evaluation of the Performance of Irrigated Crops and Soils (EPICS). EPICS recognizes that field capacity is reached when the matric potential is equal to the height above the groundwater table and thus not by a limiting hydraulic conductivity. In the field experiment, soil moisture contents and soil salt conductivity at five depths in the top 100 cm, groundwater depth, crop height, and leaf area index were measured in 2017 and 2018. The field results were used for calibration and validation of EPICS. Simulated and observed data fitted generally well during both calibration and validation. The EPICS model that can predict crop growth, soil water, groundwater depth, and soil salinity can aid in optimizing water management in irrigation districts with shallow aquifers.


S1 Potential evaporation and transpiration
As a critical budget term of hydrological cycle, the evapotranspiration has great influence on soil moisture content and crop growth. The reference evapotranspiration (ET 0 ) is calculated by FAO-56 Penman-Monteith method (Allen et al., 1998).
where △ is the slope of vapor pressure curve (kPa℃ -1 ), Rn is the net radiation at the reference grassland (alfalfa) surface (MJ (m 2 ﹒d) -1 ), G is the soil heat flux (MJ (m 2 ﹒d) -1 ), γ is the psychrometric constant (kPa℃ -1 ), T is the mean air temperature (℃), u2 is the wind speed (m s -1 ), e s and e a are the saturation vapor pressure and actual vapor pressure (kPa).The potential evapotranspiration (ET p ) of crop is calculated as: where K c is the crop coefficient but the meaning of this K c is not the same as the K c that described by (Allen et al., 1998). In this study, the calculation of K c is referred to the studies of Sau et al., (2004) and DeJonge et al., (2012).
where LAI is the leaf area index, LAI max is the maximum LAI value, and K cmax is the possible K c with largest leaf area index.
The evapotranspiration includes soil evaporation and crop transpiration. Here, the potential evapotranspiration was partitioned to potential evaporation (E p ) and potential transpiration (T p ) according to the study of (Ritchie et al., 1972). The ratio of E p to T p is according to the crop development stage of the leaf canopy occupied, expressed as τ, where K b is the dimensionless canopy extinction coefficient.

S2 Equations used to calculate phonological parameters in EPICS taken from EPIC
The phonological development of crop in the EPIC model (Williams et al., 1989) is based on daily heat unit accumulation.

Crop growth
The crop height can be calculated with equation: where H t is the crop height (cm) on day t since seeding (cm), H mx is the maximum crop height (cm) and HUF t is the heat factor on day t. HUF t is equal to Where α 1 and α 2 are crop parameters and HUI t is the heat unit index of day t, ranging from 0 at seeding to 1 at physiological maturity.
where PHU is the potential heat units required for crop maturity and HU k is the value of heat unit on day k after seeding that can be expressed as: where T mx,t is maximum temperature (℃) and T mn,t are the minimum temperature (℃) and T b is crop-specific base temperature (℃).

Leaf Area Index (LAI)
The leaf area index (LAI) is the function of heat units, crop stress and crop development stages. The LAI can be calculated from the emergence to the start of leaf area decline: From the start of leaf decline to the end of the growing season, the equation used to estimate LAI can be expressed as where REG is the minimum crop stress factor and LAI mx is the maximum leaf area index, ad is a exponent that governs LAI decline rate for crop, HUI 0 is the HUI value when LAI starts declining and LAI 0 is the actual largest LAI. WS is the water stress factor, T a is the actual transpiration, T p is the potential transpiration. TS is the plant temperature stress factor, T mean is the average daily temperature, T b is the base temperature, T 0 is the crop optimal temperature.

Root Growth
The root length is simulated as the function of heat units and the maximum root depth.
And usually the crop root length will be maximum before the mature stage. The root depth can be calculated by； Where ∆RD t is the variation of root depth at day t (cm), RD mx is the maximum crop root depth (cm).