Journal of Hydrology 641 (2024) 131771

Contents lists available at ScienceDirect

Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol

An integrated approach to obtain high-precision regional root water
uptake maps
Yuqi Liu a , Jirka Šimůnek b , Renkuan Liao a, *abCollege of Land Science and Technology, China Agricultural University, Beijing 100193, PR China
Department of Environmental Sciences, University of California Riverside, CA 92521, USA

A R T I C L E I N F O

A B S T R A C T

This manuscript was handled by Corrado Corradini, Editor-in-Chief, with the assistance ofSaket Pande, Associate Editor

Root water uptake (RWU) is exceptionally difficult to determine in situ due to its unique nature of occurring
underground. Accurately characterizing the spatial–temporal characteristics of RWU at a regional scale remains asignificant challenge, and high-precision regional-scale RWU maps have not yet been reported. In this study, wedevelop a novel approach that integrates the Google Earth Engine (GEE) platform, mathematical models, andmachine learning algorithms to generate high-precision regional maps of maize RWU in China’s primary maize
production area. The GEE platform was used to extract essential parameters such as soil properties, leaf areaindex, and growth period. These variables, along with meteorological data from 122 agricultural meteorologicalstations, were used to calculate RWU at a point scale using the Hydrus-1D and AquaCrop models. Finally, we
utilized Hydrus-calculated point-scale RWU fluxes, along with 31 covariates extracted from the GEE platform, in
conjunction with the CatBoost algorithm to develop a machine-learning model for estimating regional-scale
RWU. The accuracy of the developed machine-learning model was validated using statistical measures, suchas a mean absolute error (0.0299 cm d− 1), a root mean squared error (0.0398 cm d− 1), and the correlation
coefficient (0.9178). The model was then applied to generate high-precision (500 m × 500 m) regional-scale
RWU maps from 2015 to 2019. Additionally, our analysis identified several parameters, including TempDew(i.e., 2-m dewpoint temperature), SurfaceSM (i.e., top layer soil moisture), TempMax (i.e., max 2-m air temperature), and Latitude, as key factors influencing regional-scale RWU. This approach provides a robust strategy
for accurately generating regional-scale RWU maps, even with limited data. Furthermore, it can be extended toobtain other regional indices, offering valuable insights for various real-world applications.

Keywords:
Google earth engine
Hydrus-1D
AquaCrop
Machine learning
Soil water management

1. Introduction
Approximately 70 % of freshwater resources are consumed by agriculture (Steduto et al., 2012). The rate of water uptake by crop roots
plays a pivotal role in determining water availability in the root zone
and influences the water balance within agricultural ecosystems. Gaining a deeper understanding of the root water uptake (RWU) rate is
crucial for comprehending the functionality of root systems, the dynamics of nutrient uptake, and the overall health and resilience of cropcommunities (Wang and Smith, 2004). Accurately quantifying andmapping the spatio-temporal characteristics of RWU at a regional scale
can offer valuable insights into the water requirements of various crops(Faria et al., 2010). This information can enable the optimization ofirrigation strategies and facilitate the assessment of the impact of water
stress on crop productivity (Green et al., 2006). Furthermore, thisknowledge can assist in identifying areas with high water demand,prioritizing water allocation, and ensuring the optimal use of limited
water resources, especially in regions prone to drought or where water isscarce (Fernández García et al., 2020).
However, obtaining regional-scale RWU still presents several significant challenges. Current RWU measurement techniques, including
lysimeters, stable isotope tracing, and sap flow sensors, often involve
invasive and localized procedures. Conducting large-scale RWU measurements to capture RWU spatial and temporal variability can be timeconsuming and labor-intensive, demanding extensive fieldwork, datacollection, and analysis (Oerter and Bowen, 2017). These methods alsofind it challenging to fully capture the intricacy of root-soil interactions
and the impact of environmental conditions on RWU. Moreover,developing models and methodologies that can scale up and generalize
RWU from localized measurements to a regional scale is a complex task

* Corresponding author.
E-mail address: renkuanliao@163.com (R. Liao).
https://doi.org/10.1016/j.jhydrol.2024.131771
Received 23 December 2023; Received in revised form 8 May 2024; Accepted 21 July 2024
Available online 14 August 20240022-1694/© 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Y. Liu et al.

Journal of Hydrology 641 (2024) 131771(Kumar et al., 2015). It requires a comprehensive understanding of theunderlying processes and interactions. The scaling-up process necessitates the integration of relevant data affecting RWU from various sources, such as soil properties, water contents, root distributions anddensities, and climatic conditions (Molz and Remson, 1971; Luo et al.,2003). However, this can be difficult due to issues related to data
availability, resolution, quality, and compatibility.
Therefore, developing non-invasive and high-resolution techniques
and reasonable scaling-up methods is crucial for accurately obtaining
regional-scale RWU. Soil water flow models embedded with RWU
functions, such as Hydrus and SWAP, are the most commonly used tools
for the non-invasive evaluation of RWU (de Willigen et al., 2012;
Camargo and Kemanian, 2016; Sharmiladevi and Ravikumar, 2021;
Dong et al., 2023). These well-developed models, combined with fieldmeasured data, including leaf area indices, root depths, and growing
periods, have been effectively applied to calculate the point-scale RWU
of maize, rice, and wheat (Hou et al., 2017; Jha et al., 2017; Hatiye et al.,2018), among other crops.
However, obtaining measured crop growth data is also quite difficultand labor-intensive. Therefore, when only limited measured crop
growth data are available, crop growth models, such as APSIM, DSSAT,
and AquaCrop, are utilized to provide necessary crop growth data (Joneset al., 2003; Keating et al., 2003; Steduto et al., 2009). For example,
Kanda et al. (2021) obtained cowpea growth parameters using the
AquaCrop model, which were then used in the Hydrus-2D model tosimulate RWU under different irrigation management. Similarly, Shelia
et al. (2018) coupled the DSSAT and Hydrus-1D models to obtain soybean and peanut growth parameters to calculate RWU. Wang et al.
(2021) applied the APSIM model to get maize growth parameters for theHydrus-1D model to estimate RWU. These multiple applications indicatethat a non-destructive and labor-saving acquisition of point-scale RWU
can be achieved.
IDW (inverse distance weighted) and kriging interpolations are themost popular methods to aggregate point-scale data to a regional scale(Belkhiri et al., 2020; Yanto et al., 2022; Bel-Lahbib et al., 2023). Thesemethods rely on the principle of similarity, using a semivariance function (semivariograms) and known point data to interpolate unknown
point data in space (Li and Heap, 2011). However, these methods
require a sufficient number of known data points to ensure the accuracyof interpolation results (Zhu et al., 2018). Moreover, the spatial differences in soil and climate characteristics at the regional scale could resultin significant interpolation errors in methods that rely solely on theprinciple of similarity. Fortunately, the Google Earth Engine (GEE)
platform provides an online platform for manipulating a large amount of
global-scale geospatial data (Gorelick et al., 2017). This platform canconveniently store petabytes of data, including climate data and soil
properties at regional and global scales (Amani et al., 2020). With the
GEE platform’s powerful geographic and meteorological informationacquisition capabilities, accurate regional-scale maps, such as thenational-scale cropland map, the high-resolution soil attributes map,and the regional soil water content map, can be obtained (Htitiou et al.,2021; Poppiel et al., 2021; Yu et al., 2022). However, no quantitative
study has used the GEE platform to get regional-scale RWU maps.
The objective of this study is to develop a robust approach that integrates the GEE platform, mathematical models, and machine learningalgorithms to generate high-precision regional-scale RWU maps. Twomathematical models, Hydrus-1D and AquaCrop, are first utilized to
calculate RWU for each point. Soil characteristics and geographical andmeteorological covariates extracted from the GEE platform corresponding to these points are then used to train a machine-learning modelusing the CatBoost algorithm to estimate regional-scale maize RWU.

2. Materials and methods
2.1. Study area
The primary rain-fed maize-producing area in Northeast China(31◦ 23′04″–53◦ 33′39″ N, 97◦ 10′18″–134◦ 46′32″ E) is considered to validate the effectiveness of our developed approach (Fig. 1). This region
encompasses Heilongjiang, Jilin, Liaoning, Inner Mongolia Autonomous
Region, Hebei, Henan, Shandong, Shanxi, Beijing, Tianjin, and Shaanxi
provinces, as derived from China maize phenological dataset from 2000
to 2019 (Luo et al., 2020). According to the National Bureau of Statisticsof China, the 2022 maize production in this area exceeded 2.2 billion
tons, accounting for over 80 % of the country’s total maize production.
We selected 122 meteorological stations to collect measured meteorological data across the study area. These stations were evenly distributedin the study area to ensure their representativeness (Fig. 1).
2.2. The integrated approach
We developed a novel integrated approach that combines the GEE
platform, mathematical models, and machine learning algorithms toestimate regional-scale actual RWU. The flowchart illustrating thisapproach is presented in Fig. 2. Initially, we selected 122 representative
meteorological stations, and their corresponding longitude and latitude
coordinates were uploaded to the GEE platform to extract essential parameters, including soil properties, leaf area index, and growth period.
These parameters, along with meteorological data from 122 agriculturalmeteorological stations, were applied to calculate point-scale RWU
using the Hydrus-1D and AquaCrop models. Since Hydrus-1D canaccurately simulate soil moisture movement based on detailed hydraulicparameter information in each layer of soil, and the AquaCrop model
can accurately simulate the crop growth process with fewer parameters,
the coupled model uses Hydrus-1D Provide detailed multi-layer soil
hydraulic parameters for AquaCrop, and use the crop parameters provided by AquaCrop to import into Hydrus-1D to calculate point-scale
RWU, along with 31 covariates extracted from the GEE platform, were
employed in conjunction with the CatBoost algorithm to develop amachine-learning model for estimating regional-scale RWU.
2.3. Calculation of point-scale RWU
Several variables and parameters, such as precipitation (Prec),reference evapotranspiration (ET0), LAI, and rooting depth, need to be
input as time-variable boundary conditions into Hydrus-1D to calculate
daily point-scale RWU (for years 2015–2019) for the 122 agriculturalmeteorological stations (Simunek et al., 2005; Šimůnek et al., 2016). The
root growth of maize is characterized in Hydrus-1D using a root distribution function (Hoffman and Van Genuchten, 1983). Daily precipitation data can be obtained from the agricultural meteorological stations,while daily ET0 can be estimated using the Penman-Monteith equation(Allen et al., 1998). The LAI values and root depths used as input in
Hydrus-1D were obtained from the AquaCrop-OSpy model (Kanda et al.,2018). The depth of each soil profile was set to 250 cm, and theboundary conditions (BC) were assigned to an atmospheric BC at the soil
surface and a free drainage BC at the lower boundary. In addition, themaize in the study area was assumed to be rain-fed, and no artificial
irrigation was carried out.
The sand content, clay content, soil bulk density, and field capacity
were extracted from the GEE platform to estimate soil hydraulic parameters using the Rosetta module (Schaap et al., 2001) of Hydrus-1D.
These parameters are then used in the van Genuchten-Mualem (1980)
equations to describe water retention and soil hydraulic conductivity
functions. The van Genuchten-Mualem equations are described asfollows:2

Y. Liu et al.

Journal of Hydrology 641 (2024) 131771

Fig. 1. Overview of the study area. (a) The location and layout of the study area; (b) The distribution of maize production areas and meteorological stations.

θ(h) =⎧⎪⎨ θr +⎪⎩(θs − θr )m,
(1 + |αh|n )K(h) = Ks Sle 1 −
Se =

h⩾0

θs ,
[

(

h<0

) ]2
1/m m

1 − Se(θs − θr )(θ − θr )⎧1.66667⎪⎪⎪,z > L − 0.2LR
⎪
⎪
⎪
⎨ LR
B(z) = 2.08333⎪, L − LR > z > L − 0.2LR
⎪
⎪
LR
⎪
⎪
⎪
⎩
0,
z⩽L − LR(1)(2)

where A(h) and B(z) are the water stress response function (Feddes,
1980) and root growth function (Hoffman and Van Genuchten, 1983),
respectively, and Tp is the potential transpiration rate (cm day− 1), which
can be calculated using reference evapotranspiration (ET0), the extinction coefficient k (usually considered with a value of 0.4 for maize), and
LAI obtained using the Aquacrop crop growth module (Belmans et al.,
1983; Liu and Xie, 1998). In the stress response function A(h), h1 and h4
are anaerobiosis and wilting point pressure heads, respectively, and h2
and h3 are the pressure heads defining the optimal moisture range for
RWU. In this study, these parameters are extracted from the Hydrus-1D
database (Wesseling et al., 1991). Finally, in the root growth function B(z), L is the vertical coordinate of the soil surface (cm), and LR is the root
depth (cm). Note that the actual transpiration rate is obtained by integrating the actual root water uptake rate S across the root zone. This
study uses the term point-scale RWU to represent the actual transpiration rate (de Melo and de Jong van Lier, 2021).
The root depth and LAI are estimated using the AquaCrop crop
growth module (Kelly and Foster, 2021). Aquacrop uses the canopy
cover (CC) to describe the leaf development process instead of LAI. The
LAI values are thus obtained in the subsequent step using the adjusted
empirical relationship for maize (Hsiao et al., 2009).

(3)

where θs and θr are the saturated water content (cm3 cm− 3) and theresidual water content (cm3 cm− 3), respectively, Ks is the saturated
hydraulic conductivity (cm day− 1), Se is the effective saturation watercontent. α, m, and n are empirical parameters, which can be obtained
through the Rosetta module, and l is a tortuosity parameter in the conductivity function, usually assumed to be equal to 0.5.
RWU is accounted for in the Richards equation (1931) by the sinkterm S(z,t), which represents the amount of water removed from a unitof soil volume per unit of time due to RWU. The Richards equation andrequired initial conditions can be described as follows:⎧⎪⎨ ∂θ = ∂ [K(h)(∂h − 1)] − S
∂t ∂z
∂z
(4)
⎪
⎩
h(z, 0) = h0 (z)where θ is the volumetric water content (cm3 cm− 3), z is the verticalspace coordinate (cm), K(h) is unsaturated hydraulic conductivity
function (cm day− 1), h is the soil water pressure head (cm), h0(z) is theinitial soil water pressure head (cm), t is time (day), and S is a generalsink-source term accounting for RWU (cm3 day− 1) described as follows:
S = A(h)B(z)Tp(5)

Tp = ETo (1 − exp(− kLAI))(6)⎧h − h1⎪⎪⎪,h1 > h > h2⎪⎪h⎪
2 − h3⎪⎪⎪⎨1h3 > h > h2
A(h) =
⎪
h
−
h
⎪
4
⎪
,
h3 > h > h4⎪⎪⎪
h3 − h4⎪⎪⎪⎩ 0,
h > h1 or h < h4

(7)

(8)

CC = 1.005 × [1 − exp(− 0.6LAI)]1.2(9)The procedure for obtaining LAI and root depth values is described asfollows:
1) Set the meteorological parameters, including daily minimum temperature, maximum temperature, precipitation, and reference
evapotranspiration.
2) Set soil parameters, including sand, silt, and clay content required todetermine soil texture type, and field capacity (obtained from the
GEE platform), and soil hydraulic conductivity (obtained from the
Rosetta module of Hydrus-1D).
3) Obtain phenology information on maize from the GEE platform foreach point.
4) Define the initial soil water conditions equal to field capacity.

3

Y. Liu et al.

Journal of Hydrology 641 (2024) 131771

Fig. 2. The flowchart of the developed approach for generating regional-scale RWU maps.

5) Perform simulations from 2015 to 2019, saving crop growth files
locally to extract daily values of LAI and root depth data.

decision trees approach, supports both numerical and categorical features (Prokhorenkova et al., 2018). More specifically, most algorithms
based on the gradient-boosting decision tree (GBDT) method generate abase learner in each iteration, and as the number of iterations increases,
the next base learner is trained on the gradient of the previous learner,
but at each iteration the data points and target values used in this iteration are the same as those used in building the model, which will undoubtedly lead to a deviation between the estimated gradient and thetrue gradient. CatBoost advances the ordered-boosting method toseparately sample each step in the boosting process, thereby avoiding
gradient offsets in the estimation process, therefore, CatBoost has superior quality compared to other GBDT algorithm (Dorogush et al.,2018; Prokhorenkova et al., 2018). In this study, we utilized thisAfter using Hydrus-1D and Aquacrop to carry out RWU simulations
for the selected 122 stations, the RWU values, longitude, and latitude ofeach point from 2015 to 2019 were included in the shp files and imported into ArcMap (v. 10.8). Then, the hot and cold spot analysis was
performed to determine the spatial distribution characteristics of highand low RWU values (Songchitruksa and Zeng, 2010).
2.4. Scaling up point-scale RWU to regional RWU
The CatBoost algorithm, based on the gradient boosting over4

Y. Liu et al.

Journal of Hydrology 641 (2024) 131771

algorithm to construct a machine-learning model using information
about simulated RWU and 31 local covariates at 122 locations over five
years (2015 to 2019). The 31 covariates were extracted from the GEE
platform to train and test the CatBoost algorithm, thereby developing
machine learning models for upscaling RWU. The procedure for
upscaling is as follows (Gavrilidis et al., 2022):

2) The latitude and longitude of points are uploaded to the GEE platform, and the covariate parameters required for modeling are
extracted.
3) The extracted covariate parameters are aggregated, and the regional
RWU estimation model is run to obtain RWU at each point for years
from 2015 to 2019.
4) The points containing RWU estimates are imported into ArcGIS forpoint-to-raster mapping.

1) The 31 covariate parameters for each simulation point are cyclicallyextracted using the GEE platform and saved locally using Google
Drive.
2) The calculated point-scale RWU values and the covariates extracted
by the GEE platform are combined for data aggregation.
3) The point-scale RWU values are used as the label for the CatBoost
model. The 31 covariates extracted from GEE are utilized as features
to construct the CatBoost model. The TPE (Tree-Structured Parzen
Estimator) optimization is employed to select hyperparameters,
optimizing the number of iterations, tree depth, and learning rate
(Bentéjac et al., 2021).
4) A sliding time window is used to divide the aggregated data intotraining and test sets. This ensures that each year’s data can be utilized as training samples, allowing for a comprehensive explorationof the correlation between the data.
5) The TPE-optimized hyperparameters are passed into the CatBoost
model to construct the regional RWU estimation model. This model
serves as the basis for subsequent spatial mapping.

2.6. Data acquisition
The covariate parameters used in the modeling are extracted fromthe GEE platform, including soil parameters, meteorological data,
elevation data, and soil moisture data. After uploading the locations of
122 meteorological stations in the shape file format to the GEE platform,
values of the dataset from 2015 to 2019 are extracted in a loop andexported to the local drive via Google Drive for machine-learningmodeling purposes (Tamiminia et al., 2020). The covariate data obtained in this study are described as follows:
1) Soil parameters dataset: The data is obtained from the OpenLandMap
dataset, including the surface soil’s and root zone’s clay content(denoted as SurfaceClay and RootzoneClay, respectively), sandcontent (SurfaceSand and RootzoneSand), field capacity (SurfaceFCand RootzoneFC), and soil bulk density (SurfaceBD and RootzoneBD)(Hengl, 2018a–c; Hengl and Gupta, 2019). Each parameter is obtained for 6 standard depths (0, 10, 30, 60, 100, and 200 cm) at aresolution of 250 m. The variables differ only in terms of depth. To
prevent mutual interference between variables, the soil parameters
for the 0 cm depth represent surface parameters. The remaining
depths are averaged and used as rootzone parameters, serving as
covariates for modeling.
2) Altitude dataset: The data is obtained from the SRTM Digital
Elevation Data, Version 4, providing elevation at a resolution of 90 m
(Jarvis et al., 2008). When extracting altitude data for each point, thelatitude and longitude information of the point is also extracted tosupplement the geographic location factor in the covariate.
3) Daily climate dataset: The data is obtained from ERA5 Daily
Aggregates-Latest Climate Reanalysis produced by the ECMWF/
Copernicus Climate Change Service dataset (Service (C3S), 2017). It
includes various variables such as mean 2-m air temperature(TempMean), max 2-m air temperature (TempMax), min 2-m airtemperature (TempMin), 2-m dewpoint temperature (TempDew),
total precipitation (TotalPrec), mean sea level pressure (Prs), surfacepressure (SurPrs), 10 m u-component of wind (Wind10U), and 10 m
v-component of wind (Wind10V).
4) Soil moisture dataset: The data is obtained from the SPL4SMGP.007
SMAP L4 Global 3-hourly 9-km Surface and Root Zone Soil Moisturedataset (Model, n.d.). It includes various variables such as top layer
soil moisture (SurfaceSM), mean land surface temperature (SurfaceTemp), root zone soil moisture (RootzoneSM), evapotranspiration(ET), overland runoff (Runoff), baseflow, soil water infiltration rate
(Infiltration), net downward shortwave flux over land (Shortwave),
net downward longwave flux over land (Longwave), vegetation
greenness fraction (Greenness), and vegetation leaf area index (LAI).
Since the time resolution of this data set is 3 h, the data is aggregatedby summing and averaging over a day to match the daily scale data
used for modeling.

The CatBoost machine learning model was developed in a training
environment consisting of a graphics workstation with the following
specifications: CPU: Intel(R) Core(TM) i9-12900H CPU @ 3.00 GHz,
GPU: NVIDIA GeForce RTX A2000, and RAM: 64 GB. The model training
was performed using the Anaconda platform as the base platform,
JupyterLab as the code integration development tool, and the underlying Python version is 3.8.
After establishing the model, the feature importance analysis and theSHapley Additive exPlanations (SHAP) analysis were used to elucidate
the contribution rate of 31 covariates involved in the modeling to themodel output. In the CatBoost algorithm, three methods for calculating
feature importance scores are provided: Prediction Values Change, Loss
Function Change, and Internal Feature Importances. For this study, thePrediction Values Change method is employed to calculate featureimportance scores. This approach assesses the impact of alterations in
the values of each feature involved in the modeling on the model prediction results, thereby providing a ranking of feature importancescores. Although not as precise as the other two methods, it significantly
reduces computation time and yields faster score rankings. Conversely,
the SHAP method not only provides feature importance rankings but
also elucidates the impact（whether positive or negative）of eachfeature value change on the model prediction results. While SHAP
method offering more accurate results, this method requires more timeintensive calculations. Therefore, to swiftly obtain feature importanceranking and interpretable results regarding feature ranking, the aforementioned methods have been chosen for this study. The principles andprocedures of these two analysis methods have been described in thepreviously published studies (Slack et al., 2020; Zien et al., 2009).
2.5. Generation of regional RWU maps
ArcGIS (10.8) was used in this study to generate regional RWU maps.
Since the developed RWU estimation model only requires the extractionof covariates from corresponding points to complete the estimation
process, the methods can be described as follows:

Covariates are extracted from the above-discussed datasets to provide data support for machine learning models. The statistics of pointscale RWU values and covariates are presented in Table 1.

1) The cultivated land within the study area is rasterized with a resolution of 500 m, and the central point of each raster cell is extracted
as the covariate extraction point.

2.7. Error analysis
The mean absolute error (MAE) and the root mean squared error
5

Y. Liu et al.

Journal of Hydrology 641 (2024) 131771

Table 1The statistics of 31 covariates and point-scale RWU values.
Indicator
SurfaceBD
RootzoneBD
SurfaceClay
RootzoneClay
Elevation
SurfaceFC
RootzoneFC
LatitudeLongitude
SurfaceSand
RootzoneSand
Prs
SurfacePrs
TempDew
TempMax
TempMean
TempMin
TotalPrec
Wind10U
Wind10V
BaseflowET
Greenness
Infiltration
LAI
Longwave
Runoff
SurfaceTemp
Shortwave
RootzoneSM
SurfaceSM
RWU

Unit
3

g/cm
g/cm3
%
%
m
%
%
decimaldecimal
%
%
kPa
kPa
◦
C
◦
C
◦
C
◦
C
mm/d
m/s
m/s
mm/d
mm/d
%
mm/d
–
W/m^2
mm/d
◦
C
W/m^2
%
%
cm/d

Mean

SD

Min

Median

Max

1.28
1.40
20.81
22.10
313.76
29.84
28.01
41.12
120.31
39.57
39.49
101.58
96.95
0.99
14.86
9.60
4.65
0.18
0.71
0.08
0.00
1.64
0.83
1.47
0.63
− 68.660.28
9.18
150.97
0.50
0.41
0.05

0.11
0.06
4.53
4.64
344.87
4.01
3.06
4.32
6.10
8.17
8.21
1.02
4.73
14.28
13.44
13.40
13.65
0.56
1.77
2.12
0.04
1.45
0.10
4.60
0.65
24.29
1.52
13.96
74.14
0.12
0.15
0.11

0.99
1.21
11.00
12.60
7.04
22.00
21.00
32.80
108.24
25.00
24.40
98.21
82.91
− 39.40− 28.38− 34.18− 40.33
0.00− 7.38− 13.160.00− 0.87
0.39
0.00
0.00
− 149.87
0.00− 38.10
1.99
0.15
0.05
0.00

1.31
1.42
21.00
22.00
173.75
30.00
28.20
41.55
119.91
38.00
38.20
101.51
98.57
2.03
17.56
12.00
6.66
0.00
0.62
0.03
0.00
1.20
0.84
0.02
0.35
− 69.88
0.01
11.61
148.37
0.50
0.40
0.00

1.45
1.55
32.00
33.00
1454.54
40.00
37.00
49.46
132.91
62.00
63.20
105.77104.29
27.80
41.97
35.84
30.93
18.65
9.32
9.63
1.75
9.34
0.99
141.374.41
10.01
104.0437.52
318.76
0.96
0.94
0.67

(RMSE) are used for error analysis. Their calculation formulas aredescribed as follows:
MAE =

m
1 ∑
|(yi − zi )|m i=1

RMSE =√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
m1 ∑(yi − zi )2
m i=1

(10)

(11)

where m is the number of data points, and yi and zi refer to the i-th
calculated and predicted values, respectively.
3. Results
3.1. Point-scale RWU
Point-scale maize RWU at 122 meteorological stations from 2015 to2019 were calculated using the Hydrus-1D and AquaCrop models. The
spatial clustering patterns of point-scale RWU with high or low values
were investigated using a hot and cold spot analysis. The hot and cold
spot analysis results reflect the strength and distribution characteristicsof the RWU capacity. The results revealed an apparent clustering patternof point-scale RWU values. Hot spot clusters, indicating higher RWU
values, were found in mid to high-latitude areas such as Heilongjiang,
Jilin, Inner Mongolia, Shanxi, and Hebei provinces. On the other hand,
cold spot clusters, representing lower RWU values, were observed in
low-latitude areas, including Hebei, Shandong, and Henan provinces(Fig. 3). We determined that these differences in RWU values in the hot
and cold spot locations were influenced by latitude. Furthermore, thewater uptake capability of maize in higher latitude locations wasstronger.
Fig. 4 shows the cumulative annual RWU during 2015–2019 averaged for all hot-spot and cold-spot locations, further highlighting theirdifferences. Specifically, the initial time for RWU in the high-latitudeFig. 3. Hot and cold spot analysis of point-scale RWU values (Ci: confidence interval).

locations (hot spots) was earlier than in the low-latitude locations(cold spots), with an average of 26 days earlier. The time series of thesimulated daily RWU values during 2015–2019 for all hot-spot and coldspot locations also aligns with this trend (Fig. S1). Additionally, from2015 to 2019, the average annual cumulative RWU values in hot-spot
and cold-spot locations showed an increasing gap. The gap for the
average annual cumulative RWU values from 2015 to 2016 is 0.08–0.26
cm/year, while from 2017 to 2019, it is 2.42–5.22 cm/year. Considering
the current global warming scenario, this may be related to the variations in maize potential RWU response to a temperature increase across6

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Journal of Hydrology 641 (2024) 131771

different latitudes. The potential mechanism is examined in detail in thediscussion section.
3.2. Regional-scale RWU
The CatBoost machine learning algorithms were used to successfully
develop a regional estimation model for maize RWU using RWU values
calculated at 122 locations and 31 spatial covariates obtained from GEE.
A hyperparameters optimization procedure was performed to ensure theaccuracy of the developed model. The results demonstrated that the
optimal hyperparameters, compared to the default hyperparameters,
significantly enhanced the estimation accuracy of RWU values(Table S1). Furthermore, the optimized hyperparameters determinedthe developed model’s most suitable number of iterations (243), tree
depth (9), and learning rate (0.6874), which are all the CatBoost machine learning algorithm parameters.
Moreover, we assessed the significance of various covariates formodel accuracy. Feature importance scores of 31 covariates wereanalyzed to determine the variables (with higher scores) with a higher
impact on changes in the output value of the model. Meteorological data
(specifically TempDew and TempMax), spatial location information (i.
e., Latitude), and surface soil moisture (i.e., SurfaceSM) were determined to be the primary covariate factors influencing regional RWU
estimation (Fig. 5).
To further elucidate the contribution rate of each covariate factor tothe model output, we conducted the SHapley Additive exPlanations(SHAP) analysis, which evaluates the impact of covariates in eachsample by calculating the marginal contribution to the model output.
The SHAP results are generally consistent with the covariates importance analysis results, highlighting that TempDew, TempMax, andLatitude significantly impact the RWU predictions (Fig. 6). Furthermore,their contributions to estimating regional RWU values are similar,
meaning that higher values of these covariate factors result in larger
RWU values.
By utilizing the developed regional estimation model, we could
compute the regional RWU, with their average values depicted in Fig. 7.
The annual variation patterns of RWU align with the growth pattern ofmaize. The predicted values (calculated by the developed machinelearning model) and measured values (calculated by Hydrus-1D and
AquaCrop) exhibit a significant positive correlation at a 99 % confidence
level (p < 0.01), indicating excellent accuracy of the model in estimating
RWU values (Fig. 7). The average mean absolute error (MAE) and root
mean squared error (RMSE) for RWU are 0.0299 and 0.0398 cm d− 1,
respectively. The interannual average MAE and RMSE values varied
from 0.0262 to 0.0334 and 0.0346–0.0456 cm d− 1, respectively, which
exhibited a consistent amplitude without significant fluctuations(Fig. S2). This suggests that estimated RWU values remain relatively
stable over time. Regarding the spatial error, the range of MAE and
RMSE values for RWU varied from 0.0286 to 0.0533 and 0.0558–0.0781
cm d− 1, respectively (Fig. S3). The developed model demonstrates good
performance in terms of spatial estimations, with minimal differences in
MAEs between different provinces.
3.3. Regional RWU maps
Using the developed regional RWU estimation model, we generated
high-precision (500 m × 500 m) regional RWU maps from 2015 to 2019
(Fig. 8). Specifically, we focused on displaying the RWU values from
May to September of each year (i.e., the main growth period for maizeduring each year), providing a detailed depiction of the monthly variation pattern of RWU. Overall, RWU shows similar trends during
different months of different years between 2015 and 2019. These maps
exhibit an increasing trend in RWU in early summer, reaching its peak in
July, followed by a decrease over time.
Although the overall trend of RWU in different years is similar, there
are still differences in their spatial distribution characteristics. Due toFig. 4. Cumulative annual RWU averaged over hot and cold spots during 20152019 (top to bottom).

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Journal of Hydrology 641 (2024) 131771

Fig. 5. Feature importance scores for variables considered in the CatBoost machine learning algorithm in the RWU regression model.

extreme climate phenomena occurring in certain locations in specificyears, the RWU values in these locations have shown significant differences compared to other locations. Except for climate conditions,these differences in RWU also signify the influence of diverse soil andmanagement conditions on maize water uptake. The generated regional
RWU maps provide comprehensive insights into root water uptake at theregional scale, offering valuable information for understanding the dynamics of crop water uptake and soil water scarcity. Some specificapplication cases of these maps were analyzed in the discussion section.

put forward to discern the critical factors impacting regional-scale RWU.
The top four covariates identified in this study in both analyses, i.e.,
TempDew, SurfaceSM, TempMax, and Latitude, are considered the key
influencers.
These findings partially challenge the previous understanding ofvarious factors influencing point-scale RWU in field or pot experiments.
Previously, numerous reports on point-scale RWU suggested that soil
hydraulic characteristics and soil moisture were the primary factors
affecting RWU (Puig-Sirera et al., 2023; Yang et al., 2022). While wetend to agree with this view concerning point-scale RWU, we believethat comprehending RWU at different scales (point-scale and regionalscale) may yield different conclusions.
We cannot find similar comparative studies since this is the firststudy estimating daily RWU at a regional scale. Crop transpiration, a
result of RWU, is indicative of the RWU pattern, and most models
dealing with RWU and transpiration consider the two to be numericallyequivalent (de Melo and de Jong van Lier, 2021; Aston and Lawlor,
1979). Herein, to make a comparison, we have examined many quantitative studies on crop transpiration at a regional scale, which indicatethat atmospheric moisture, pressure, temperature, and precipitation are
key factors affecting crop transpiration at a regional scale (Christensen

4. Discussion
4.1. Key covariates affecting regional RWU estimation
We collected a large amount of data to perform an importanceranking analysis (Fig. 5) and the SHAP analysis (Fig. 6) for assessing theimpacts of 31 covariate factors on the accuracy of estimating regional
RWU (Lipovetsky and Conklin, 2001; Slack et al., 2020). Thesenumerous data are repeatedly used to train the CatBoost machinelearning algorithms to achieve optimal accuracy, thereby identifying
key influencing factors for regional-scale RWU. This is the first evidence
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Journal of Hydrology 641 (2024) 131771

Fig. 6. The SHAP analysis for RWU.

Fig. 7. Calculated (by HYDRUS) and predicted (using the machine-learning algorithm) RWU as well as the error analysis during 2015-2019 (left to right). The top
figures display average RWU values for all 122 stations.

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Journal of Hydrology 641 (2024) 131771

Fig. 8. High-resolution spatiotemporal maps of RWU from May to September (left to right) during 2015-2019 (top to bottom)

et al., 2008; Kropp et al., 2017; Kukal and Irmak, 2023; Peng et al.,2011). These factors that affect regional-scale transpiration haveimportant reference significance for our understanding of regional-scale
RWU.
This study identifies TempDew as the most influential covariate
factor for estimating regional-scale RWU. TempDew, denoting dew
point temperature, represents the temperature to which the air must becooled (at constant pressure) to reach a relative humidity (RH) of 100 %(Wood, 1970). At this point, the air can no longer hold water in its gas
form, leading to the condensation of water vapor into liquid form, suchas fog or precipitation. A higher dew point indicates more moisture in
the air, resulting in a more humid environment (Zounemat-Kermani,2012). Therefore, TempDew strongly correlates with atmospheric humidity, pressure, and precipitation events, enabling tracking changes in
the atmospheric moisture holding capacity (Wasko et al., 2018; Pumo
and Noto, 2021). This is consistent with the aforementioned factors
affecting regional-scale transpiration.
On the other hand, latitude is a key covariate factor for estimating
regional-scale RWU. The hot and cold spot analysis results discussed
above support the significance of latitude for regional-scale RWU. RWU
exhibits distinct latitude-dependent patterns, with higher RWU clusters

predominantly located in mid and high-latitude areas, while lower RWU
clusters are observed in low-latitude areas. In this study, the significant
difference in latitude, approximately 22◦ between the northern andsouthern ends of the study area, results in an uneven distribution ofwater and heat resources, affecting the phenology and RWU of maize(Muchow, 1989a, 1989b). Similar studies have also demonstrated that
latitude plays a significant role in the developmental stages of maize,
consequently impacting its RWU (Liu et al., 2013).
This conclusion also differs from previous studies, which generally
suggested that crop growth (the capability of RWU) in high-latitude andlow-latitude areas is lower compared to middle-latitude areas (Afuakwa
et al., 1984; Baloch et al., 2021). Higher RWU observed in high-latitude
areas may be attributed to the current global warming. Global warming
has intensified the already hot conditions in low-latitude areas, making
them even hotter and drier (Peltonen-Sainio et al., 2016). Excessive heatcan reduce crop yields by lowering RWU due to unfavorable climaticconditions (Meng et al., 2014; Williams et al., 2012). Conversely, highlatitude areas have experienced warming, and a warmer climate canenhance crop yields by promoting RWU. The report released by theWorld Meteorological Organization (WMO) has shown that the period
from 2015 to 2019 was the hottest five-year period, and greenhouse gas
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Journal of Hydrology 641 (2024) 131771

concentrations in the atmosphere also rose to record levels (Siegmund
et al., 2020). This high-intensity warming may reverse the original trendof higher RWU at low latitudes and lower RWU at high latitudes,
increasing RWU at high-latitude locations (i.e., at hot spots).

scale, which intuitively reflects whether crops are in a state of water
scarcity on a spatial scale. We found that most of the key factors
affecting regional-scale RWU are meteorological factors. Therefore, toverify the accuracy of the generated RWU maps, we chose the precipitation and evapotranspiration-driven indicator, the so-called standardized precipitation evapotranspiration index (SPEI), for comparison. The
SPEI index has a wide range of applications to reflect regional drought
conditions (Beguería et al., 2014; Stagge et al., 2015). We selected thegenerated RWU maps for July 2015, 2017, and 2019 for comparison,
showing a relatively consistent spatial distribution pattern for bothvariables, with lower values in the north and higher values in the south(Fig. 9). However, the SPEI index has a spatial resolution of 55660 m anda monthly cadence, while our product has the advantage of having aspatial resolution of 500 m and can be obtained at a daily scale. Our
product can achieve a more accurate and real-time reflection of regional

4.2. High-precision regional RWU maps and their application
The approach proposed in this manuscript enables the generation ofdaily spatial distribution maps of maize RWU at a resolution of 500 m or
higher. However, our investigation revealed that published articles only
report calculated point-scale RWU (Kanda et al., 2021; Shelia et al.,2018; Sulis et al., 2019; Wang et al., 2021), and no similar studies orcommercial products are available. Consequently, high-precision
regional RWU maps have not yet been reported.
The developed approach can directly produce RWU at a regional

Fig. 9. Comparison of RWU maps generated by the proposed model and the SPEI index produced by SPEIbase. (a, c, e) The RWU maps produced by the proposedmodel for July 2015, 2017, and 2019, respectively. (b, d, f) The SPEI maps produced by SPEIbase for July 2015, 2017, and 2019, respectively.
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Journal of Hydrology 641 (2024) 131771

drought conditions.
The generated RWU maps can be used to recognize and validate
extreme meteorological events. For example, the published reportdemonstrated that the precipitation in the Liaoning province decreased
by 78.7 % in July 2015, which caused a significant reduction in soil
moisture (Liao et al., 2016). This event can be reflected in lower RWU
values in July 2015 in our generated regional-scale RWU map (Fig. 8).
Similarly, another previous report showed that precipitation in western
northeast China and western Inner Mongolia decreased by 30–80 %from April to late July 2017, and the temperature increased by 1–2 ◦ C(Feng et al., 2018). This decreased RWU is also reflected in the generated
regional-scale RWU map (Fig. 8). Furthermore, we have recognized an
extreme meteorological event (e.g., lower RWU values) in the westernpart of the Shandong province in July 2019 (Fig. 8). Our investigation
revealed that this can be attributed to an intense heatwave that lasted fora month, which was the most severe event in this area since 1961 (Zenget al., 2020). According to the covariate importance ranking discussed
above, TempDew is the most important indicator for estimating regionalroot water uptake and is closely correlated with atmospheric temperature and precipitation events (Bui et al., 2019). SurfaceSM and TempMax emerge as the second and third most significant factors in regionalscale RWU calculations, following TempDew. The validation of these
real-world cases demonstrated that the main identified factors (e.g.,
TempDew, SurfaceSM, and TempMax) greatly impact estimatedregional-scale RWU.
Our newly developed approach, combined with future climatechange scenarios, can also predict future regional-scale RWU anddrought degrees. This is of great significance for guiding the optimization of regional agricultural water resource management.

Data availability
All data needed to evaluate the conclusions in the paper are present
in the paper and/or the Supplementary Materials. The data and code forthis study can be connected through the email address to obtain(renkuanliao@163.com or renkuanliao@cau.edu.cn).
Acknowledgements
Funding: This work was supported by the Chinese Universities Scientific Fund (15053343).
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.jhydrol.2024.131771.
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5. Conclusion
We propose a novel approach integrating the GEE platform, mathematical models, and machine learning algorithms to calculate regional
RWU. Mathematical models, which consider the complexity of root-soilclimate interactions, are utilized to accurately calculate RWU at the
point scale, offering a non-invasive, time-efficient, and labor-saving
method. By harnessing the capabilities of the GEE platform forextracting and fusing multi-source data and incorporating machinelearning algorithms to use the amassed data for training, we achieve areasonable upscaling of RWU from the point scale to the regional scale.
TempDew, SurfaceSM, TempMax, and Latitude were identified as critical factors influencing regional RWU. The developed model for estimating regional RWU has been validated to have high accuracy,
enabling the generation of high-precision (500 m × 500 m) regional
RWU maps for 2015 to 2019. These findings will facilitate a morecomprehensive understanding of root water uptake patterns and theirvariability across different spatial and temporal scales, significantly
contributing to optimizing water resource management strategies.
CRediT authorship contribution statement
Yuqi Liu: Writing – review & editing, Writing – original draft,
Visualization, Software, Investigation, Data curation. Jirka Šimůnek:Writing – review & editing, Writing – original draft, Investigation.
Renkuan Liao: Writing – review & editing, Writing – original draft,
Supervision, Resources, Project administration, Methodology, Funding
acquisition, Formal analysis, Conceptualization.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

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