Estimating water balance components in irrigated agriculture using a combined approach of soil moisture and energy balance monitoring, and numerical modelling

Information on water balance components such as evapotranspiration and groundwater recharge are crucial for water management. Due to differences in physical conditions, but also due to limited budgets, there is not one universal best practice, but a wide range of different methods with specific advantages and disadvantages. In this study, we propose an approach to quantify actual evapotranspiration, groundwater recharge and water inflow, i.e. precipitation and irrigation, that considers the specific conditions of irrigated agriculture in warm, arid environments. This approach does not require direct measurements of precipitation or irrigation quantities and is therefore suitable for sites with an uncertain data basis. For this purpose, we combine soil moisture and energy balance monitoring, remote sensing data analysis and numerical modelling using Hydrus. Energy balance data and routine weather data serve to estimate ET0. Surface reflectance data from satellite images (Sentinel‐2) are used to derive leaf area indices, which help to partition ET0 into energy limited evaporation and transpiration. Subsequently, first approximations of water inflow are derived based on observed soil moisture changes. These inflow estimates are used in a series of forward simulations that produce initial estimates of drainage and ETact, which in turn help improve the estimate of water inflow. Finally, the improved inflow estimates are incorporated into the model and then a parameter optimization is performed using the observed soil moisture as the reference figure. Forward simulations with calibrated soil parameters result in final estimates for ETact and groundwater recharge. The presented method is applied to an agricultural test site with a crop rotation of cotton and wheat in Punjab, Pakistan. The final model results, with an RMSE of 2.2% in volumetric water content, suggest a cumulative ETact and groundwater recharge of 769 and 297 mm over a period of 281 days, respectively. The total estimated water inflow accounts for 946 mm, of which 77% originates from irrigation.


| INTRODUCTION
Information on water balance components is essential in hydrological sciences and related disciplines. It is needed to quantify the replenishment of natural resources and thus forms the basis for sustainable water resources management. For irrigated agricultural systems it helps in irrigation and drainage planning and in distinguishing between blue and green water footprints of crops.
Unfortunately, the possibilities for direct measurements of some balance components such as actual evapotranspiration (Allen et al., 2011;Wang & Dickinson, 2012) and groundwater recharge (Healy, 2010) are quite limited. Therefore, indirect approaches that require less own measurement effort are more frequently applied.
Very common for the approximation of actual evapotranspiration (ET act ) is, for example, the Penman-Monteith equation, which uses routine weather data and information on plant physiology, usually extracted from readily accessible databases (Allen et al., 1998). Indirect methods for estimating groundwater recharge (GWR) include for instance hydrograph analysis, various tracer methods and modelling.
Hydrological models are particularly interesting because they usually provide estimates of all water balance components. However, the reliability of their results depends strongly on the availability and quality of the input data, which therefore constitute the principal source for uncertainties, particularly in data scarce regions.
In addition to ET act and GWR, natural water inflow, that is, precipitation, can also be subject to uncertainties, for instance if there are no precipitation measuring stations in the vicinity or if only spatially integrated data from satellite data (e.g., TRMM, CMORPH) or reanalysis (e.g., ERA5) are available. If imprecise precipitation estimates are then used in models, incorrect parameter estimates and model results may occur (Fraga et al., 2019;Peters-Lidard et al., 2008;Troutman, 1983). For irrigated agricultural systems, irrigation water is also an important but often insufficiently known inflow component (Brocca et al., 2018;Lankford, 2006;Wisser et al., 2008). The degree of uncertainty depends on the type of irrigation. In systems where the water is distributed by a piping system, equipped with flow meters, fairly accurate application rates are available. In many parts of the world, however, there are more rudimentary systems. For example, simple, hand-dug channels for water distribution are very common.
Here, flow rates and transmission losses are often only roughly estimated, based on visual observations, irrigation schedules, and experience (Forkutsa et al., 2009). Irrigation rates become even more uncertain in case of excess irrigation. Here, in addition to inflow rates, drainage rates are required to calculate the net water input into the soil.
Motivated by the problem of inaccurate or unavailable precipitation measurements, Brocca et al. (2013) developed an approach to estimate precipitation amounts by analysing soil moisture changes. To do this, they inverted the soil water balance equation. Water balance components required in addition to soil moisture change were either neglected (evapotranspiration and surface runoff) or estimated using empirical methods (drainage). Soil moisture changes can be derived from in situ observations (Brocca et al., 2015) or from satellite-based radar data (Brocca et al., 2014). Later, this approach was also used to estimate irrigation volumes (Brocca et al., 2018;Dari et al., 2020;Filippucci et al., 2020).
The aim of the present study is to present a method that allows a reliable estimation of the water balance components ET act , GWR, and water inflow (precipitation and irrigation) with moderate measurement efforts. This approach is particular suitable for irrigated areas, where irrigation water inflows are insufficiently known and difficult to measure. For this purpose, we apply a combined approach of soil moisture and radiation balance monitoring, remote sensing data analysis, and numerical modelling. Unknown irrigation amounts are estimated based on soil moisture data and an inversion of the soil water balance equation. This is accompanied by an iterative process in which other required water balance components are estimated stepwise by numerical modelling using Hydrus (Šimů nek et al., 2008).

| STUDY SITE
We apply this approach to an agricultural test field of the University of Agriculture Faisalabad in Punjab, Pakistan, which is part of the Lower Chenab Canal (LCC) system ( Figure 1; Becker et al., 2019). The test field has a dimension of 110 m × 30 m and the crop cycle during our investigation period from July 2018 to June 2019 is cotton (Kharif season, monsoon) and wheat (Rabi season, inter-monsoon). The water allocation is realized with the Warabandi system (Narain, 2008) and applied to the plants by flood irrigation. While for the total LCC system and its larger irrigation subdivisions fairly precise canal supplies are known, on the field-scale only sparse data are available on irrigation operations and irrigation volumes (Ahmad et al., 2009). The longterm (1981-2019) average annual air temperature, precipitation and potential evaporation of the study site are 24.6 C, 540 mm and 2540 mm, respectively (Muñoz Sabater, 2019). The soil type is classified as sandy loam (locally termed Farida), which is the most abundant soil type in the LCC system (Awan & Ismaeel, 2014).
According to Köppen-Geiger, the climate in the Punjab region is generally classified as hot arid (Kottek et al., 2006), and only irrigation water allows intensive agriculture. Overall, this makes the Punjab region with the Indus Basin Irrigation System one of the largest closed irrigation areas with the world's second largest blue water footprint of 50 Gm 3 a −1 after Utter Pradesh (Ganges) and before California (Mekonnen & Hoekstra, 2011). The main irrigation water source for the Punjab is surface water from the Indus and its tributaries. However, measures against waterlogging (Bhutta & Smedema, 2007), steadily rising irrigation water demand, substantial transmission losses in the canal distribution system (Chaudhry, 2015), not demandoriented water allocation (Basharat & Tariq, 2013), and large differences between up and downstream water availability (Kazmi et al., 2012) lead to an increasing exploitation of local groundwater resources (Habib, 2004). In addition to falling groundwater levels, the Punjab is strongly affected by increasing soil and groundwater salinization (Bhutta & Smedema, 2007), which is a quite typical phenomenon of irrigated agriculture in arid regions (Foster et al., 2018). In order to counteract these trends and make agriculture in this region more sustainable, management adjustments are necessary, which require a quantification of the water balance components.

| Monitoring and soil sampling
A monitoring station was installed in July 2018 on a test field of the University of Agriculture Faisalabad (UAF) in Pakistan ( Figure 1). The station is located at 73 04 0 17.7 00 N, 31 26 00 21.3 00 E and is equipped with the following devices: 1. one net radiometer (NR-Lite2, Kipp & Zonen), mounted at a height of 2.5 m to a vertical pipe; 2. one self-calibrating soil heat flux plate (HFP01SC, Hukseflux), installed in a depth of 8 cm below ground level (b.g.l.); 3. four soil moisture and temperature sensors (CS650, Campbell Scientific), installed in a depth of 10, 20, 40 and 80 cm b.g.l., respectively; 4. one data logger (CR800, Campbell Scientific), mounted to the vertical pipe of the net radiometer and set to a 1-min recording interval; 5. one 12 V battery with a capacity of 4.2 Ah.
This station was in operation from 3 July 2018 to 1 June 2019. Due to empty batteries or full memory storage the records show some gaps. The cumulative gap length is 51 days, and the number of full days with records is 281. This database is available via https://doi. pangaea.de/10.1594/PANGAEA.921389 (Schulz, 2020).
Additionally, routine weather data such as air temperature (minimum, maximum and mean), relative humidity, precipitation, class A pan evaporation, sun shine duration, and wind speed are available from a nearby (<100 m) weather station.
During the installation of the monitoring station, we took three undisturbed soil samples using 250 mL soil sample rings in depths of 10, 40 and 80 cm b.g.l., respectively. The samples were oven-dried at 105 C for 24 h and weighted to derive the bulk density. Subsequently, the three sub-samples per layer were combined and wet sieved with various mesh sizes to quantify the mass fractions for particle diameters larger than 63 μm. For particle diameters smaller than 63 μm, we carried out a sedimentation analysis. Results are given in the Table S1.

| Overview of data processing methodology
To estimate the water balance components ET act , GWR, and water inflow we apply an approach, which comprises a series of data processing steps ( Figure 2). First, we estimate reference crop evapotranspiration (ET 0 ) using energy balance data from our monitoring station and routine weather data. Subsequently, surface reflectance data from satellite images (Sentinel-2) are used to derive time-variable plant-specific information such as leaf area index (LAI), which then serves to partition ET 0 into energy limited evaporation (E max ) and transpiration (T max ). The next step is a first approximation of the inflow Afterwards, we perform a first series of forward simulations of the water flow in the unsaturated zone and the root water uptake using Hydrus. The upper boundary conditions for this model are first approximations of the water inflow, E max , and T max . To further account for soil parameter uncertainties, we run simulations with a quite wide range of a priori estimates of van Genuchten parameters, derived from a soil texture analysis. This first modelling step yields a range of estimates for ET act and drainage (flux at 1 m b.g.l.), which are then used to better estimate the inflow from the inverted soil water balance equation. The final step is to incorporate these improved inflow estimates into the model and calibrate the soil parameters by inverse modelling. Here, the observed soil moisture data form the reference figure for calibration.
Forward simulations with calibrated soil parameters and improved inflow estimates result in final estimates for ET act and GWR. A detailed description of all processing steps is given in the following sections.

| Radiation balance
The amount of energy, which is available for the latent heat (LE) and the sensible heat (H), is defined by the one-dimensional surface energy balance (Equation 1, Hartmann, 2016).
While the net radiation (Rn) is directly measured by the net radiometer, the estimation of the ground heat flux (G) requires some computation. The heat flux, which we measure with our monitoring station, is the flux in a depth of 8 cm (G 8cm ). To derive the ground heat flux, we need to account for a storage term (S heat ), which describes the change of heat stored in the layer above the heat flux plate (Equation 2).
The storage term depends on the volumetric heat capacity of the moist soil (C s ) and is defined in Equation (3) (Hartmann, 2016).
Estimates for the soil temperature change (dT s ) over the time period (dt) as well as the volume fraction of water (f s ) of the upper soil layer with a thickness (dz) of 8 cm base on records from the uppermost (10 cm b.g.l.) soil moisture and temperature sensor. The product of the soil density (ρ s ) and the volume fraction of soil (f s ) is the previously determined bulk density. The specific heat capacity of most dry mineral soils (c s ) and of water (c w ) are 837 and 4190 J kg −1 K −1 , respectively, and the density of water (ρ w ) is assumed to be 1.00 g cm −3 (Hanks, 1992).
Overview of data processing methodology

| Leaf area index and rooting depth
Leaf area index (LAI) and rooting depth are plant characteristics, which are required to quantify transpiration, that is, LAI serves for partitioning of evapotranspiration (Allen et al., 1998) and rooting depth defines the soil depth from which plants can take up water (Feddes et al., 1976).
Leaf area indices (LAI) for our test site are estimated using red and near-infrared reflectance data. This approach was introduced by Clevers (1989) and bases on an empirically derived linear relationship (Equation 4) between LAI [m 2 m −2 ] and the weighted difference vegetation index (WDVI).
Furthermore, Clevers (1989) suggests to calculate the WDVI using red (R 670 ) and near-infrared (R 870 ) reflectance data of the plant canopy and the soil (R 670,soil and R 870,soil ), respectively (Equation 5).
Given the availability of high-resolution satellite data, Clevers et al. (2017) revisited this approach and proofed its usability with space-borne multispectral reflectance data from the Sentinel-2 satellite mission. An advantage of this approach, especially for small-scale applications such as in the presented case, is the relatively high spatial resolution of 10 m of the required spectral information, that is, band 4 (665 nm) and band 8 (842 nm).
For this study, 65 sets of satellite images are analysed, covering our monitoring period from 10 July 2018 to 1 June 2019. To allow for the further use of these scenes, the data are converted from top-of-atmosphere into top-of-canopy reflectance using the atmospheric correction procedure sen2cor (Louis et al., 2016). Afterwards, images with haze or clouds covering our test field are excluded. For the remaining images, reflectance values of band 4 and 8 are extracted from the pixel at the location of our monitoring station. To calculate the slope of the soil line (C in Equation 5) we use averages of the band values at the same location of images at times between cropping periods, that is, with bare soil.
Rooting depth (r d ) is assumed to be proportional to the soil cover fraction (SCF; Equation 6; Wongkaew et al., 2018).
Plant-specific canopy extinction coefficients (K b ) are also available from Allen et al. (1998). The extinction coefficients for cotton and wheat are 0.65 and 0.55, and the maximum rooting depths are 1.35 m and 1.65 m, respectively.

| Energy-limited evapotranspiration
Estimates of energy-limited (soil) evaporation and energy-limited transpiration, that is, not limited by the availability of water, are derived from methods suggested in the FAO Irrigation and Drainage Paper No. 56 (Allen et al., 1998). Parts of these methods are slightly adapted to better meet the requirements of the numerical simulation tool Hydrus. First, reference crop evapotranspiration (ET 0 ) is calculated based on the FAO Penman-Monteith method, thoroughly described by Allen et al. (1998), using data from our monitoring station (Rn and G) and routine weather data from the nearby weather station. In order to separate ET 0 into a plant-specific and energy-limited transpiration and evaporation component, we applied the dual crop coefficient approach. Here, transpiration is calculated without considering limitations in soil water availability and thus, constitutes maximum possible transpiration (T max ), Equation (8).
The basal crop coefficient (K cb ) characterizes the growth stage of the plant and can be derived from the time-variable LAI (Equation 9).
K c min is the minimum crop coefficient for bare soil (K c = 0.15) and K cb full is the plant-specific K cb during the mid-season at peak plant height. K cb full for cotton and wheat are 1.15 and 1.1, respectively (Allen et al., 1998).
Evaporation from the soil (E) depends strongly on the growth stage of the plant, that is, the more of the soil surface is covered by plants, the lower the evaporation. In contrast to the previous calculation of transpiration, evaporation additionally bases on the availability of soil water for evaporation, described by the evaporation reduction Equation 10). However, for further use in Hydrus we are only interested in the energy-limited (maximum possible) evaporation (E max ). Therefore, we set K r to its maximum value of 1, which results in Equation (11).
The maximum crop coefficient (K c max ) represents the upper limit for the actual evapotranspiration, considering the constraints of the available energy (Equation 12).
Wind speed at 2 m height (u 2 ) and daily minimum relative humidity (RH min ) are obtained from the nearby weather station. The mean plant heights during mid or late season stages (h) for cotton and wheat are 1.2 m and 1.0 m, respectively (Allen et al., 1998 . . .
To allow a comparative analysis to the estimation of energy-limited evaporation and transpiration described above, which bases on energy balance data from our monitoring station and routine weather data from the nearby weather station, we apply two alternative methods.
First, we followed the same procedure as described above, but for the estimation of ET 0 we use only data from the nearby weather station, that is, air temperature, relative humidity, wind speed and sunshine hours (Allen et al., 1998). Second, we calculate the theoretical maximum available energy for evapotranspiration (LE + H), using only data from our monitoring station, that is, Rn and G. Here, the temperaturedependent latent heat of vaporization was calculated using the temperature recordings of the upper CS650 sensor and an approach proposed by Henderson-Sellers (1984). These two alternative methods are evaluated by comparing them to the previously presented approach and may serve as an alternative when not all required data are available.

| First approximation of inflow
For days with observed positive changes in soil water storage, we assume that either precipitation or irrigation must have taken place.
For these days we calculate the amount of water inflow (sum of irrigation and precipitation) using the water balance of the first meter of the unsaturated zone (Equation 14).
Daily changes of soil moisture storage in the upper 1 m (dS 1m ) result from the water volume stored at the end of the day (t) minus the water volume stored at the end of the previous day (t-1). To estimate these water volumes, first, temperature corrected (Campbell Scientific, 2018)  Since we do not know too much about the variables flux 1m (flux at 1 m depth, previously referred to as drainage) and ET act , for now, we apply the initial assumption flux 1m = 0 and ET act = E max + T max .
This step serves only for a first estimation of the inflow and in second step better estimates of flux 1m and ET act will be available. Nevertheless, we expect that this assumption is not too far from reality. On a daily basis, the expected flux 1m is quite low compared to the relatively large, periodically applied inflow quantities that are common in flood irrigation. Moreover, irrigation contributes to a constant water supply for evaporation, which allows the assumption that evapotranspiration is mostly energy-limited. respectively. Parallel to the flow modelling, root water uptake is simulated using the Feddes model (Feddes et al., 1976). Parameter of the Feddes model for cotton and wheat base on values provided by Taylor and Ashcroft (1972), cited in Forkutsa et al. (2009)

| Final estimation of inflow
Final estimates of inflow are derived from a first model application.
The van Genuchten parameters (VGP) and the saturated hydraulic conductivity (Ks) of the model are not yet calibrated and only a priori estimates based on the particle size distribution and the bulk density are available. These estimations are predicted by pedotransfer functions implemented in the Rosetta model (Schaap et al., 2001;Zhang & Schaap, 2017). This is an elegant and frequently used approach. However, due to its empirical nature (pedotransfer functions are derived from a neural network analysis of a soil database), it is associated with uncertainties that are quantified with the standard deviations (σ) resulting from a bootstrap-resampling method (Zhang & Schaap, 2017). In this study, except for the saturated water content (θ s ), the range of the a priori estimation of the hydraulic parameters is defined as their mean predicted value ±2Á Á Áσ. Due to intense irrigation, that is, high availability of water, we assume that the highest observed volumetric water content is a good estimate for θ s .

| Parameter optimization
With an estimation of the inflow boundary condition and a quantification of its uncertainty, we can carry out an optimization of the hydraulic parameters. For this purpose, we apply an inverse modelling approach using the PEST (Model-Independent Parameter Estimation and Uncertainty Analysis) tool (Doherty, 2015). Here we employ the global optimization tool CMA-ES (Covariance Matrix Adaptation Evolution Strategy) to minimize the objective function, that is, the sum of squared residuals of simulated and observed volumetric soil moisture (Hansen, 2006). In analogy to the estimation of the inflow uncertainty, we use the mean predicted value ±2Á Á Áσ from the Rosetta model as the parameter range for the VGPs and K s during optimization. θ s is an exception here as well. This parameter is kept constant on its a priori estimated value, that is, the highest observed volumetric water content. The optimization procedure is applied for the minimum, mean fraction is 16%. Typically, it is assumed that the magnitude of the ground heat flux in day periods is very small and may therefore be neglected (Allen et al., 1998). However, this seems to be too much of a simplification for our system. A possible explanation can be found in the specific conditions for our test site. Due to the intensive irrigation, our soil is almost always moist, which results in a rather high heat capacity of our soil, since the specific heat capacity of water is more than four times higher than that of mineral soil (Hanks, 1992). Combined with a high but variable energy input due to climatic conditions, this can result in a high energy storage in the soil, which does not allow for quick heat equalization.

| Leaf area index and rooting depth
The basis for estimating LAI and rooting depth is the canopy or soil reflection data from the Sentinel 2 satellite mission. After sorting out the images with haze or cloud cover over our test field, 11 images for cotton, 9 images for wheat and 7 images for bare soil remained for

| Energy-limited evapotranspiration
Energy-limited evapotranspiration (E max + T max ) show pronounced inter-annual variabilities with higher rates during the hot summer months (up to almost 10 mm day −1 ) and significantly lower rates during the temperate winter months (Figure 4b). The partitioning of evapotranspiration is based on the dual crop coefficient concept. Like the rooting depth, crop coefficients highly depend on the LAI. The more photosynthetically active leaves the plant has, the larger the basal crop coefficient (K cb ) and thus the higher the share of transpiration. In case of bare soil, K cb is zero and only evaporation takes place.
On average, the sum of K cb and the share for E max (K c max − K cb ) is 1.11 (Figure 4a). This means that the energy-limited evapotranspiration of our test site is 11% higher than the reference crop evapotranspiration (ET 0 ), that is, ET act of short, green and well-watered grass.
This is quite an important observation, as it is not uncommon to use ET 0 as so called potential evapotranspiration, which then defines the upper limit for actual evapotranspiration in Hydrus (Šimů nek et al., 2013). In most cases this is a well working assumption.
However, in cases with a high energy input, tall crops and almost permanent excess of water, for example, through irrigation, actual evapotranspiration may easily exceed ET 0 (Kirkham, 2014;Rosenberg, 1974).
Noteworthy findings also result from the comparison of the different possibilities to estimate evapotranspiration. For our study, we used energy-limited evaporation (E max ) and transpiration (T max ) estimates derived from methods proposed in the FAO Irrigation and Drainage Paper No. 56 (Allen et al., 1998) using energy balance data, that is, Rn and G, from our monitoring station as well as routine weather data from the nearby weather station. Additionally, we estimated the energy-limited evapotranspiration with two alternative methods. One of them uses only energy balance data from our F I G U R E 4 (a) Temporal evolution of LAI, rooting depth and crop coefficient components. (b) Daily sums of energy-limited evaporation (E max ) and transpiration (T max ), and alternative estimates for energy limited evapotranspiration estimates monitoring station and the other one uses only routine weather data.
Results from the two alternative methods show a similar pattern as our approach (Figure 4b). The root mean square error (RMSE) of the FAO approach using only routine weather data and the approach using only energy balance data compared to the FAO approach based on both data sets are 0.73 mm and 0.69 mm, respectively. While the first mentioned alternative seems to slightly overestimate the energylimited ET (mean error of +0.23 mm), the energy balance approach shows on average almost no difference (−0.04 mm). At first, the even better performance of the energy balance approach is somewhat surprising, as it neglects any energy loss or input through sensible heat flux (H). However, the special conditions of our study area, that is, almost constantly well-irrigated soil and relatively high temperatures, associated with low advection and low Bowen ratios, may explain this finding (McMahon et al., 2013;Priestley & Taylor, 1972).  Table S1 and S3, respectively.
Not surprisingly, the derived initial set of ET act and flux 1m estimates show a rather wide range (Figure 5a). During the modelling period from16 August 2018 to 4 May 2019, the mean initial ET act and the mean initial flux 1m are 3.5 and 0.8 mm day −1 with a relative uncertainty range of 64% and 246%, respectively. At first glance, these uncertainties seem to be quite large. However, these values are only used for inflow estimation, and compared to the relatively large soil moisture changes of up to almost 150 mm day −1 this first impression is somewhat relativized. Finally, Equation (14) is applied to calculate three inflow time series using the mean, minimum and maximum values of dS, initial ET act , and initial flux 1m , respectively. The final inflow estimates range from small events of only a few millimetres up to events of more than 150 mm (Table S5, Figure 6).
Comparing the uncertainty range of the first approximation of inflow (introduced by the application of different interpolation schemes) and the final inflow estimates (based on both, interpolation and a priori soil parameter uncertainty) provides information about the sensitivity of the different interpolation methods and soil parameters. While the first approximation of the inflow shows a mean relative uncertainty of 9.5%, it increases to 23.8% for the final estimates (compare Table S2 and S5). This suggests that both sources of uncertainty are quite similarly sensitive.

| Parameter optimization
The second stage is the VGP optimization. With the exception of the saturated water content (θ s ), the upper and lower parameter limits

| Comparison of results with observed data
From the nearby weather station, daily precipitation amounts are available for our modelling period. These data are used to identify precipitation events in the simulated inflow time series, that is, inflow events that occur during a day or the following day when precipitation is recorded are attributed to precipitation. Thus, a comparison between measured and simulated precipitation is enabled. Generally, the measured precipitation pattern matches well with the one we estimated from the water balance. Except for a few small precipitation events (<5 mm) all precipitation events could be captured ( Figure 6).
The reason for not detecting these small events is that low precipitation can be balanced out by evaporation during the day, that is, no positive change in daily soil moisture storage is observed. Nevertheless, the sums of the measured precipitation are within the error range of those simulated during cotton and wheat cultivation (

| CONCLUSION
This study presents a method for estimating water balance components with moderate measurement efforts. We focus on the specific requirements of irrigated agriculture in semi-arid and arid environments. A particular aspect is that we do not need measurements of irrigation nor precipitation quantities to establish the water balance. This is quite useful as many irrigated areas lack the basic knowledge of these inflows.
The final estimations of the actual evapotranspiration and groundwater recharge base on simulations with the numerical model Hydrus. This is also beneficial since models have predictive power and simulations could be performed to test different management scenarios, for example, different irrigation practices or crop cycles. Although the presented method of the inflow estimation could also be applied to solely rainfed systems, it can be reasonably assumed that precipitation can be measured more simply and with much lower uncertainties, for example, with a rain gauge. However, it is different for irrigation. Theoretically, measurements are not complicated here either (simple flow meters would often be sufficient), but they would be needed for each field separately and farmers would have to keep accurate records. Moreover, irrigation water distribution over the field can vary considerably. This can lead to uncertainties if only one specific point is to be examined, as it is common, for example, in one-dimensional process analysis. Finally, the decision whether the presented approach is suitable depends on the research question and the available data. In this context, the two alternative methods for estimating energy limited evapotranspiration are also worth mentioning. If an accurate determination of evapotranspiration is not the primary goal, but only an estimation of irrigation or groundwater recharge, one of the presented alternatives can also be applied. They require less data and the differences between the methods are quite small compared to irrigation amounts.
Moreover, this study could show some shortcomings in frequently applied assumptions such as using ET 0 as the upper limit for actual evapotranspiration or neglecting the ground heat flux in the energy balance. For most cases these assumptions might work and constitute valid simplifications. However, for irrigated agricultural systems with a high but variable energy input, as common in arid regions, they seem to be too much of a simplification and should be avoided.
For our study area, but also for other irrigation systems in arid environments, the complex interplay of different aspects such as waterlogging and salinity control, preservation of drinking water resources and reduction of the blue water footprint while ensuring agricultural productivity requires finely tuned management. A profound knowledge of the hydrological processes and a reliable quantification of the water balance components are essential for this.