Groundwater recharge is one of the important factors determining the
groundwater development potential of an area. Even though recharge plays a
key role in controlling groundwater system dynamics, much uncertainty remains
regarding the relationships between groundwater recharge and its governing
factors at a large scale. Therefore, this study aims to identify the most
influential factors of groundwater recharge, and to develop an empirical
model to estimate diffuse rainfall recharge at a global scale. Recharge
estimates reported in the literature from various parts of the world
(715 sites) were compiled and used in model building and testing exercises.
Unlike conventional recharge estimates from water balance, this study used a
multimodel inference approach and information theory to explain the
relationship between groundwater recharge and influential factors, and to predict
groundwater recharge at 0.5∘ resolution. The results show that
meteorological factors (precipitation and potential evapotranspiration) and
vegetation factors (land use and land cover) had the most predictive power
for recharge. According to the model, long-term global average annual
recharge (1981–2014) was 134 mm yr-1 with a prediction error ranging
from -8 to 10 mm yr-1 for 97.2 % of cases. The recharge estimates
presented in this study are unique and more reliable than the existing global
groundwater recharge estimates because of the extensive validation carried
out using both independent local estimates collated from the literature and
national statistics from the Food and Agriculture Organization (FAO). In a water-scarce future driven by increased anthropogenic development, the results from
this study will aid in making informed decisions about groundwater potential
at a large scale.
Introduction
Human intervention has dramatically transformed the planet's surface by
altering land use and land cover and consequently the hydrology associated
with it. In the last 100 years the world population has quadrupled, from
1.7 billion (in 1900) to more than 7.3 billion (in 2014), and is expected to
continue to grow significantly in the future (Gerland et al., 2014). During
the last century, rapid population growth and the associated shift to a
greater proportion of irrigated food production led to an increase in water
extraction by a factor of ∼ 6. This eventually resulted in the
overexploitation of both surface and groundwater resources, including the
depletion of 21 of the world's 37 major aquifers (Richey et al., 2015). This
depletion threatened human lives in many ways, ranging from critical
reductions in water availability to natural disasters such as land
subsidence (Chaussard et al., 2014; Ortiz-Zamora and Ortega-Guerrero,
2010; Phien-Wej et al., 2006; Sreng et al., 2009). Therefore, there is a
need to closely examine approaches for sustainably managing this resource by
controlling withdrawal from the system.
Groundwater recharge is one of the most important limiting factors for
groundwater withdrawal and determines the groundwater development potential
of an area (Döll and Flörke, 2005) Groundwater recharge connects
atmospheric, surface and subsurface components of the water balance and is
sensitive to both climatic and anthropogenic factors (Gurdak, 2008;
Herrera-Pantoja and Hiscock, 2008; Holman et al., 2009; Jyrkama and Sykes,
2007). Various studies have employed different methods to estimate
groundwater recharge including tracer methods, water table fluctuation
methods, lysimeter methods and simple water balance techniques. Some of
these studies input recharge to numerical groundwater models or dynamically
link it to hydrological models to estimate variations under different
climate and land cover conditions (Aguilera and Murillo, 2009; Ali et al.,
2012; Herrera-Pantoja and Hiscock, 2008; Sanford, 2002).
In the last few decades, interest in global-scale recharge analysis has
increased for various scientific and political reasons (Tögl, 2010).
L'vovich (1979) made the first attempt at a global-scale analysis by creating a
global recharge map using baseflow derived from river discharge hydrographs.
The next large-scale groundwater recharge estimate was done by Döll (2002)
who modelled global groundwater recharge at a spatial resolution of
0.50 using the WaterGAP Global Hydrological model (WGHM; Alcamo et
al., 2003; Döll, 2002). In this study, the runoff was divided into fast
surface runoff, slow subsurface runoff and recharge using a heuristic
approach. This approach considered relief, soil texture, hydrogeology and
occurrence of permafrost and glaciers for the runoff partitioning. However,
WGHM failed to reliably estimate recharge in semi-arid regions (Döll,
2002). Importantly, in that study, there was no consideration of the
influence of vegetation which has been reported to be the second most
important determinant of recharge by many researchers (Jackson et al., 2001;
Kim and Jackson, 2012; Scanlon et al., 2005). In subsequent years, several
researchers have attempted to model global groundwater recharge using
different global hydrological models and global-scale land surface models
(Koirala et al., 2012; Scanlon et al., 2006; Wada et al., 2010).
Although a fair amount of research has been carried out to model groundwater
recharge at a global scale, most studies compared results to country-level
groundwater information from the FAO (FAO, 2005). FAO statistics were based
on estimates compiled from national institutions. The data estimation and
reporting capacities of national agencies vary significantly and raise
concerns about the accuracy of the data (Kohli and Frenken, 2015). In
addition, according to FAO AQUASTAT reports, most national institutions in
developing countries prioritise subnational-level statistics over national-level
statistics, and in most cases data are not available for all subnational entities.
This decreases the accuracy of country-wide averages and
raises concerns about the reliability of using them as standard comparison
measures. Only a few studies have validated modelled estimates against small-scale recharge measurements. Döll and Fiedler (2008) used 51 recharge
observations from arid and semi-arid regions to correct model outputs. This
study develops a recharge model and undertakes a more extensive validation
of it using 715 local recharge measurements. Moreover, previous research has
mostly been restricted to studying meteorological influences on recharge,
few studies have systematically explored global-scale factors governing
recharge. Much uncertainty still exists about the relationship between
groundwater recharge and topographical, lithological and vegetation factors.
Without adequate knowledge of these controlling factors, our capacity to
sustainably manage groundwater globally will be seriously compromised.
The major objectives of this study are to identify the most influential
factors of groundwater recharge and to develop an empirical model to
estimate diffuse rainfall recharge. Specifically, to quantify regional
effects of meteorological, topographical, lithological and vegetation
factors on groundwater recharge using data from 715 globally distributed
sites. These relationships are used to build an empirical groundwater
recharge model and then the global groundwater recharge is modelled at a
spatial resolution of 0.5∘× 0.5∘ for the time period 1981–2014.
MethodsDataset
This study is based on a compilation of recharge estimates reported in the
literature from various parts of the world. This dataset is an expansion of
previously collated sets of recharge studies along with the addition of new
recharge estimates (Döll and Flörke, 2005; Edmunds et al., 1991;
Scanlon et al., 2006; Tögl, 2010; Wang et al., 2010). The literature
search was carried out using Google Scholar, Scopus and Web of Science with
related keywords “groundwater recharge”, “deep percolation”, “diffuse
recharge” and “vertical groundwater flux”. Several criteria were considered
in including each study. To ensure that the data reflects all seasons,
recharge estimates for time periods less than 1 year were excluded. The
sites with significant contribution to groundwater from streams or by any
artificial means were also eliminated as the scope of this research was to
model naturally occurring recharge. In order to maximise the realistic
nature of the dataset, all studies using some kind of recharge modelling
were removed from the dataset. After all exclusions, 715 data points spread
across the globe remained (Fig. 1) and were used for further analysis. Of
these studies, 345 were estimated using the tracer method, 123 using the
water balance method and the remaining studies used baseflow method,
lysimeter or water table fluctuation method. This diversity in recharge
estimation has enabled us to evaluate systematic differences in various
measurement techniques. The year of measurement or estimation of recharge
estimates in the final dataset differed (provided as supplementary
material), and ranged from 1981 to 2014 (Fig. 2a). This inconsistency in
the data raised a challenge when choosing the time frame for factors in the
modelling exercise, particularly those showing inter-annual variation.
Moreover, the compiled dataset does not represent all climate zones well
(Fig. 2c), as most of the studies used were done either in arid,
semi-arid or temperate zones. Pasture and cropland were the dominant land
uses in the dataset (Fig. 2b).
Locations of the 715 selected recharge estimation sites and the
corresponding recharge estimation method, used for model building.
Histograms showing frequency of (a) study year, (b) land
use and (c) Köppen–Geiger climate zones for the recharge estimates used.
Description of predictors used for recharge model building.
PredictorsSymbolUnitResolutionTemporalSourceDescriptionReferencespanPrecipitationPmm yr-10.5∘× 0.5∘1981–2014Climatic ResearchMean annualHarris et al. (2014)Unit, Universityprecipitationof East Anglia,United KingdomMeanT∘C0.5∘× 0.5∘1981–2014Climatic ResearchMean annualHarris et al. (2014)temperatureUnit, Universitytemperatureof East Anglia,United KingdomPotentialPETmm yr-10.5∘× 0.5∘1981–2014Climatic ResearchPenman–MonteithHarris et al. (2014)evapotranspirationUnit, Universityreference cropof East Anglia,evapotranspirationUnited KingdomNo. of rainyRd5 arcmin1981–2014AQUAMAPS, FAOAverage number ofNew et al. (2002)dayswet days per yeardefined as having≥ 0.1 mm ofprecipitationSlopeSfraction0.5∘× 0.5∘–Earthdata, NASAMean surface slopeVerdin (2011)Saturatedksatcm day-11∘× 1∘–Earthdata, NASASaturated hydraulicWebb et al. (2000)hydraulicconductivity atconductivity0–150 cm depthSoil waterSWSCmm1∘× 1∘–Earthdata, NASATexture-derived soilWebb et al. (2000)storagewater storage capacitycapacityin soil profile (up to15 m depth)Excess waterEWmm–1981–2014–∑i=112(Pi- PETi)(withoutwhere Pi> PETiirrigation)Aridity indexAI––1981–2014–AI =P/PETClay contentClay%1∘× 1∘–Earthdata, NASA0–150 cm profileDAAC (2016)Bulk densityρbgm cm-31∘× 1∘–Earthdata, NASA0–150 cm profileDAAC (2016)Land useLU–15 arcsec–USGS/LiteratureForest, pasture, cropland,Kim and Jackson (2012),land coverurban/built up, barrenBroxton et al. (2014)
The next step was to identify potential explanatory factors that could
influence recharge (henceforth referred to as predictors). Potential
predictors that were reported in the literature as having some influence on
recharge were identified (Athavale et al., 1980; Bredenkamp, 1988; Edmunds
et al., 1991; Kurylyk et al., 2014; Nulsen and Baxter, 1987; O'Connell et
al., 1995; Pangle et al., 2014). The choice of predictors was made based on
the availability of global gridded datasets and their relative importance in
a physical sense, as informed by the literature. According to the
literature, the water availability on the surface for infiltration and the
potential of the subsurface system to intake water are the two major
controls on recharge. Different variables that can potentially represent
these two factors were chosen as predictors in this study. The water
availability is represented mainly by using meteorological predictors
including precipitation, potential evapotranspiration, aridity index and number
of days with rainfall and vegetation characteristics (land use and land
cover), whereas the intake potential is represented using various quantifiable
characteristics of the vadose zone. We employed 12 predictors comprising
meteorological factors, soil/vadose zone factors, vegetation factors and
topographic factors. However, other factors which could have a sizable
influence on recharge were not included in this study because of
insufficient data. Thus, we did not consider the effects of irrigation
on recharge, limiting the scope of the study to rainfall-induced recharge.
Subsurface lithology which could be another important recharge factor, was
also eliminated from the study, due to a lack of suitable lithological and
geological datasets at a larger scale. Better quality information about
various predictors would have been desirable to enhance the accuracy of
prediction. Details of predictors are given in Table 1.
Data for the chosen predictors corresponding to 715 recharge study sites
were extracted from global datasets. Meteorological datasets (P, T and PET) were
obtained from the Climatic Research Unit, University of East Anglia,
United Kingdom. Even though daily data were available from 1901 to 2014 at a
resolution of 0.5∘× 0.5∘, in this study the mean annual average of
the latest 34 years (1981 to 2014) was used to reduce the inconsistency in
year of recharge measurements in the final dataset. Topographic and soil
data were acquired from the NASA Earth observation dataset. Both datasets
were of 0.5∘× 0.5∘ spatial resolution. A few of the predictors,
including number of rainfall days (Rd) and land use/land cover (LU) data were
obtained from AquaMaps (by FAO) and USGS (United States Geological Survey)
at a spatial resolution of 0.5∘× 0.5∘ and 15 arcmin
respectively. Thus-obtained LU data were compared with land cover reported in
literature and corrected for any discrepancies. The spatial resolution of
the different data used was diverse. This was dealt with by extracting the
values for each recharge site from the original grids using the nearest
neighbour interpolation method. As a result, predictor data extracted for
each recharge site will differ from the actual value due to scaling and
interpolation errors. Out of the 12 predictors LU was not a quantitative
predictor and was transformed into a categorical variable in the modelling exercise.
Recharge model development
With empirical studies, the science world is always sceptical about whether
to use a single best-fit model or to infer results from several better-predicting and plausible models. The former option is feasible only if there
exists a model which clearly surpasses other models, which is rare in the
case of complex systems like groundwater. Usually cross correlation and
multiple controlling influences on the system lead to more than one model
having similarly good fits to the observations. Thus choosing explanatory
variables and model structure is a significant challenge. In the past this
challenge was often addressed using various step-wise model construction
methods, with the final model being selected based on some model fit
criteria that penalise model complexity (Fenicia et al., 2008; Gaganis and
Smith, 2001; Jothityangkoon et al., 2001; Sivapalan et al., 2003). These
approaches were pragmatic responses to the large computational load involved
in trying all possible models. The disadvantage of this method is that the
final model will be dependent on the step-wise selection process used
(Sivapalan et al., 2003). An alternative approach for addressing this high
level of uncertainty in model structure is to adopt a multi-model inference
approach that compares many models (Duan et al., 2007; Poeter and Anderson,
2005). It typically results in multiple final models and an assessment of
the importance of each explanatory variable. Therefore, this approach was
used to develop an understanding of the role of different controlling
factors on recharge in a data-limited condition.
Choosing predictors that are capable of representing the system and
selecting the right models for prediction are the key steps in the
multi-model inference approach. Here, models were chosen by ranking the
fitted models based on performance, and comparing this to the best-performing model in the set (Anderson and Burnham, 2004). This model ranking
also provided a basis for selecting individual predictors. The analysis
progressed through three key stages: exploratory analysis, model building
and model testing.
Multi-model analysis
A multi-model selection process aims to explore a wide range of model
structures and to assess the predictive power of different models in
comparison with others. Essentially, models with all possible combinations
of selected predictors are developed and assessed via traditional model
performance metrics (discussed later). By conducting such an exhaustive
search, multi-model analysis avoids the problems associated with selection
methods in step-wise regression approaches (Burnham and Anderson, 2003).
Importantly, it reduces the chance of missing combinations of predictors
with good predictive performance. However, a disadvantage of this approach
is that the number of predictor combinations grows rapidly with the number
of factors considered. To make the analysis computationally efficient, we
set an upper limit for the number of predictors used. Another problem with
this approach is that it can result in overfitting. To address this issue
we evaluated model performance with metrics that penalise complexity and
tested the model robustness with a cross-validation analysis. The model
development procedure using multi-model analysis is described in detail below.
(a) Exploratory analysis
Firstly, all the chosen predictors were individually regressed against the
compiled recharge dataset. This was carried out with the main objective of
finding the predictors with significant control over recharge and to gain an
initial appreciation of how influential each predictor is compared to the
others. This understanding will aid in eliminating the least influential
predictors from further analysis. Then assumptions involved in regression
analysis, such as linearity, low multicollinearity (important for later
multivariate fitting) and independent identically distributed residuals
were analysed using residual analysis. Following the residual analysis,
various data transformations (square root, logarithmic and reciprocal) were
carried out to reduce heteroscedasticity and improve linearity of the
variables. The square root transformed recharge along with non-transformed
predictors gave the most homoscedastic relationships (results not shown).
Therefore, these transformed values were used in further model-building
exercises. Predictors were selected and eliminated based on statistical
indicators such as adjusted coefficient of determination (Radj2)
value and root mean square error (RMSE).
(b) Model building
Multiple linear regression was employed for building the models as the
transformed dataset did not exhibit any nonlinearity. Furthermore, the
presence of both negative and positive values in the dataset restricted the
applicability of other forms of regression analysis like log-linear and exponential
(Saft et al., 2016). Linear regression is known for its simple and robust
nature in comparison to higher-order analysis. The robustness of linear
regression helped to maintain parsimony together with reasonable prediction
accuracy. A rigorous model-building approach was adopted in order to capture
the interplay between predictors with combined/interactive effects on
groundwater recharge. This is an exhaustive search in which all candidate
models are fitted and inter-compared using performance criteria. In a way,
this modelling exercise used a top-down approach, starting with a simple
model which is expanded as shortcomings were identified (Fenicia et al., 2008).
(c) Model testing
The analysis above provided insight into the relative performance of the
models. However, it is also important to assess the dependence of the
results on the particular sample. Therefore, we conducted a subsample
analysis in which the same method was re-applied to subsamples of the data.
Finally, predictive uncertainty was estimated through leave-one-out cross
validation. In the first case, the whole model development process was
redone multiple times using subsamples of the data. To achieve this, the
entire dataset was randomly divided into 80 and 20 % subsets and
80 % of the data were used for building the model. The predictive
performance of the developed model was tested against the omitted 20 % of
data. This was repeated 200 times in order to eliminate random sampling
error. The leave-one-out cross validation was applied to the best few
individual model structures and provided an estimate of predictive
performance for those particular models. It also gave an indication of data
quality at each point.
In summary the key steps in the multi-model analysis were
selecting predictors;
fitting all possible models consisting different combinations of predictors;
calculating model performance metrics for each model;
calculating the “weight of evidence” for each predictor based on the
performance metric of all models containing that predictor;
testing the predictive performance of the models.
Ranking models and predictors
This part of the analysis has closely followed the approach developed in
Saft et al. (2016). Model performance was evaluated using several
information criteria. These information criteria include a goodness-of-fit
term and an overfitting penalty based on the number of predictors in the
model. In this study we used Radj2, the consistent Akaike
information criterion (AICc) and the complete Akaike information
criterion (CAIC) as the performance evaluation criteria. These criteria differ in
terms of penalising overfitting. Radj2 penalises overfitting the
least, AICc moderately and CAIC heavily. However, when we are unsure of the
true model and whether it overfits or not, there is some advantage in
employing several criteria as it gives insight into how the results depend
on the criteria used. Suitability of the information criteria also varies
with the sample size. CAIC acts as an unbiased estimator for large sample
size with relatively small candidate models, but produces large negative
bias in other cases. Conversely, AICc is well suited for small-sample
applications (Cavanaugh and Shumway, 1997; Hurvich and Tsai, 1989). The
formulas for the above criteria are as follows:
AIC=-2×llf+2×k(Akaike,1974),AICc=AIC+(2×(k-1)×k+2n-k-2)(Hurvichand2Tsai,1989),CAIC=-2×llf+k×(ln(n)+1)(Bozdogan,1987),R2=1-n-1n-k-1×1-R2(Ezekiel,1929;4WangandThompson,2007),
where “llf” is the log-likelihood function, k is the dimension of the model
and n is the number of observations.
When assessing candidate models there are two questions which are of
particular interest. (1) Which models are better? (2) How much evidence
exists for each predictor in predicting recharge? Analysis of the AICc and
CAIC was used to answer both these questions. Models were ranked using
information criteria, with smaller values indicating better performance.
Information criteria are more meaningful when they are used to evaluate the
relative performance of the models (Poeter and Anderson, 2005). Models were
ranked from best to worst by calculating model delta values (Δ) and
model weights (W) as follows:
5Δi=AICi-AICmin,6Wi=exp-0.5×Δi/Σexp-0.5×Δm,
where AICmin is the information criteria value of the best model.
Δi and Wi represent the performance of ith model in comparison
with the best-performing model in the set of M models.
Evidence ratios were then calculated as the ratio of the ith model
weight to the best model weight. They can be used as a measure of the
evidence for the ith model compared to the other models. They also
provide means to estimate the importance of each predictor. This involves
transformation of evidence ratios into a proportion of evidence (PoE) for
each predictor. PoE for a predictor is defined as the sum of weights of all
the models containing that particular predictor. PoE ranges from 0 to 1. The
closer the PoE of a predictor is to 1, the more influential that predictor is.
Summary statistics of potential predictors from the dataset used in this study.
The best model (model 1, Table 3) from the above analysis was used to build a
global recharge map at a spatial resolution of 0.5∘× 0.5∘.
Recharge estimation was done annually for a study period of 34 years
(1981–2014), and the estimated groundwater recharge was then averaged over
the 34-year period to produce a global map. In addition to this, maps
showing percentage of rainfall becoming recharge and the standard deviation of
annual recharge over the 34 years were also generated. As recharge data from
regions with frozen soil were scarce in the model-building dataset, the
model predictions in those regions particularly for regions with
Köppen–Geiger classification Dfc, Dfd, ET and EF were not highly
reliable. EF regions of Greenland and Antarctica were excluded from the
final recharge map due to lack of both recharge and predictor data. However,
the modelled recharge for Dfc, Dfd and ET regions were included because of
the availability of predictor data. In addition, the modelled recharge
values were compared against country-level statistics from FAO (2005) for 153 countries.
Results
The results address three important questions. (1) What are the most
influential predictors of groundwater recharge? (2) What are better
models for predicting recharge? (3) How does groundwater recharge vary over
space and time? The first question was answered by carrying out an
exploratory data analysis and also by estimating the PoE for each predictor,
the second using information criteria and the third by mapping recharge at
0.5∘× 0.5∘ using the best model.
Model fit performance criteria for single predictor regressions.
Exploratory data analysis
Table 2 gives the statistical summary of predictors and groundwater recharge
at 715 data sites. It is apparent from the table that predictors varied
considerably between sites, consistent with inter-site variability in
regional physical characteristics. This variability provided an opportunity
to explore recharge mechanisms in a range of different physical
environments. As we used linear regression to study the one-to-one
relationship of recharge with each of the predictors, RMSE and bias of
fitting were used to identify the predictors with the most explanatory
power. In this case, RMSE values ranged between 23.2 mm yr-1 for P and
30.21 mm yr-1 for S. Predictive potential of meteorological predictors was greater
than for other classes of predictor (Fig. 3). P, AI, EW and ρb
had a negative bias, whereas all other predictors had a positive bias.
Coefficient of predictors used in the top 10 models, ranked based on CAIC.
Proportion of evidence according to AICc and CAIC for
12 predictors (sorted in descending order of PoE).
Multi-model analysisProportion of evidence (PoE) for individual predictors
Figure 4 shows the PoE of the 12 predictors used in this study. According to
this analysis, 3 of the 12 predictors stood out as having the greatest
explanatory power (Fig. 4). Precipitation (P), potential evapotranspiration (PET)
and land use and land cover (LU) had the highest proportions of evidence
(∼ 1). Subsurface percentage of clay (clay) and saturated
hydraulic conductivity (ksat) also had an important influence on
recharge with PoE ∼ 0.4. Aridity index (AI), rainfall days (Rd),
mean temperature (T), bulk density (ρd), slope (S), excess
water (EW) and soil water storage capacity at root zone (SWSC) were in the lower
PoE range (< 0.1 according to both the criteria). There was some
variation in the PoE value of the predictors depending on the performance metric, due to
the diversity in overfitting penalty. However, ranking of the variables was
identical irrespective of the performance metric used. The “best” and
“worst” predictors ranked according to Radj2 were also in
agreement with the PoE analysis (not shown). In addition, results of the
subsample analysis gave similar results (not shown).
Better-performing models
According to information criteria, the performance of models can only be
evaluated relative to the best-performing model in the set. In this study,
as per the model weights, no model exhibited apparent dominance. The
evidence ratio (ratio between the weights of the best model and nth model)
suggested that the best model according to CAIC was only 1.04 times
better than the second best model. However, the evidence ratio increased
exponentially with increase in model rank and there was a clear distinction
between better models and worse models. Similar results were reported by
Saft et al. (2016) in her work for modelling rainfall–runoff relationship
shift. The choice of better models was made by considering the PoE of
individual predictors (refer Sect. 3.2.1) and the number of predictors in
the model (V). Figure 5 shows the performance criteria for the top three
models for different V values. The model performance increased with V up to 6
to 7 depending on the different criteria. After that, AICc, CAIC, RMSE and
Radj2 values remained almost constant, indicating that further
addition of predictors did not improve the model performance. In particular
CAIC shows reaches a minimum at V= 7 and it penalises model complexity more
rigorously. Table 3 illustrates the predictors in the top 10 models selected
based on CAIC. All the top 10 models had V<= 7. P, PET and LU repeatedly
appeared in the predictor list of the top 10 models substantiating their
high predictive capacity, and the top ranked model includes these three
predictors only. In this particular case, top-performing models according to
both information criteria were the same; therefore results from only one
criteria (CAIC) will be discussed.
(a)Radj2, (b) CAIC and (c) RMSE
for the top three models with 1 to 12 predictors and the green
dotted lines representing the number of predictors for the best performance criteria value.
RMSE of sub-sample (a) model fitting and (b) model
prediction of top 10 models according to CAIC.
Model testing
Models ranking from 1 to 10 according to CAIC (Table 3) were tested using
both model testing techniques discussed in Sect. 2.2.1c. Figure 6
depicts model fit and model prediction RMSE values of 200 subsample tests.
It is clear from the box plots that the difference between the RMSE of the
1st and the 10th model during both model fitting and prediction is
less than 1 mm yr-1. In subsample tests, Radj2 of the best model
ranged from 0.42 to 0.56 implying 42 to 56 % of the variance was explained
(please see Sect. 3.2.3 for details on sub-sample testing). The model
errors at each data point ranged from -8 to 28 mm yr-1. However, 97.2 % of
the points had errors between -8 and 10 mm yr-1. Figure 7 shows the
relationship between precipitation and model errors and it is evident from this scatter
plot that model predictions were not greatly influenced by low or high
precipitation. In other words, the model was unbiased by precipitation
trends. Similar checking was done for all other predictors (not shown) which
all showed a similar pattern to precipitation. The dataset was classified
based on recharge estimation techniques and model performance was tested
with results showing no systematic difference (not shown).
(a) Error at each data point along with the corresponding
rainfall obtained using the leave-one-out model testing procedure and (b) Scatter
plot between error at each data point and corresponding precipitation.
Global groundwater recharge
The global long term (1981–2014) mean annual groundwater recharge map at
a spatial resolution of 0.5∘ was made by the model developed in
Sect. 3.2 (Fig. 8). In this study, the best model as defined by CAIC (model 1 in
Table 3) was used to generate the recharge map. However, due to the
similarity in structure of the top 10 models (Table 3), all models were
equally good at predicting groundwater recharge and gave similar results
(not shown). Grid-scale recharge ranged from 0.02 to 996.55 mm yr-1 with
an average of 133.76 mm yr-1. The highest recharge was associated with very
high rainfall (> 4000 mm yr-1). Humid regions such as Indonesia,
Philippines, Malaysia, Papua New Guinea, Amazon, western Africa, Chile,
Japan and Norway had very high recharge (> 450 mm yr-1), whereas
arid regions of Australia, the Middle East and Sahara had very low recharge
(< 0.1 mm yr-1). In humid areas, percentage of rainfall becoming
groundwater recharge (> 40 %) was found to be very high in
comparison to other parts of the world. However, the mean percentage of
rainfall becoming recharge is only 22.06 % across the globe. Among all the
continents, Australia had the lowest annual groundwater recharge rate.
Over the 34 years, global annual mean recharge followed the same pattern as
that of global annual mean precipitation (Fig. 9). Least recharge was
predicted in the year 1987 (groundwater recharge = 95 mm yr-1), where the
annual average rainfall was < 180 mm yr-1. Variation in recharge over
the years was maximal in arid regions of Australia and North Africa
(Fig. 10a). However, the standard deviation of recharge was higher in humid
areas than in arid regions (Fig. 10b). This indicates that standard
deviation did not clearly represent year-to-year variations in recharge.
Potentially, the advantage of using coefficient of variation over standard
deviation is that it can capture variations even when mean values are very
small. In this case precipitation and potential evapotranspiration were the
two major predictors of recharge. Globally, variability in
evapotranspiration is much less than variability in rainfall (Peel et al.,
2001; Trenberth and Guillemot, 1995). Therefore, variability of groundwater
recharge both temporally and spatially is due to variability in
precipitation, which implies that arid regions are more susceptible to
inter-annual variation in groundwater recharge. A comparison of predicted
recharge against country-level recharge estimates from FAO (2005) shows that
the model tends to overpredict recharge, particularly for low recharge
areas. However, due to inaccuracies in the FAO estimates this cannot be
considered as a reliable comparison (Fig. 11a). Recharge estimates from
the best models in the present study were compared to recharge estimates
from the complex hydrological model (WaterGAP; Fig. 11b). Even though
the model in this study overestimates recharge for countries with fewer data
points, the scatter shows a smaller spread compared to the FAO estimates.
Figure 12 shows the country-wide distribution of errors in model prediction
in comparison with FAO statistics. Very high errors were found in countries
with fewer model-building data points. The model considerably overestimated
recharge for Russia, Canada, Brazil, Indonesia, Malaysia and Madagascar.
Long-term (1981–2014) average annual groundwater recharge estimated
using the developed model.
Temporal distribution of total global recharge along with total global
precipitation of corresponding years for a period of 1981 to 2014.
Discussion
The aims of this study were to identify the factors with the most
influence on groundwater recharge, and to develop a global model for
predicting groundwater recharge under limited data conditions, without
extensive water balancing. In this study, an empirical model-building
exercise employing linear regression analysis, multimodel inference
techniques and information criteria was used to identify the most
influential predictors of groundwater recharge and use them to build
predictive models. Finally, a global groundwater recharge map was created
using the developed model. The key findings from this study and their
implications for future research and practice with respect to global
groundwater recharge are discussed below.
One of the findings to emerge is that, out of numerous models developed in
this study there was no single best model for groundwater recharge. Instead,
there were clear sets of better and worse models. However, there were
predictors which stood out as having greater explanatory power. Of the
12 predictors chosen for the analysis, meteorological (P, PET) and vegetation
predictors (LU) had the most explanatory information followed by saturated
hydraulic conductivity and clay content. Thus models using these predictors
ranked higher according to information criteria. It is reasonable that
meteorological factors had the most explanatory information. In most cases,
especially dry regions, groundwater recharge is controlled by the
availability of water at the surface, which is mainly controlled by
precipitation, evapotranspiration and geomorphic features (Scanlon et al.,
2002). Numerous studies agree with this finding. For example, in south-western USA, 80 % of recharge variation is explained by mean annual
precipitation (Keese et al., 2005). However, the influence of meteorological
factors on groundwater recharge is highly site specific (Döll and
Flörke, 2005). The effect of meteorological factors can also depend on
whether the season or year is wet or dry, type of aquifer and irrigation
intensity (Adegoke et al., 2003; Moore and Rojstaczer, 2002; Niu et al., 2007).
Map showing (a) coefficient of variability and (b) standard
deviation of annual groundwater recharge from 1981 to 2014.
Comparison of predicted recharge against country-level estimates from
(a) FAO and (b) WaterGAP model.
Many studies have reported vegetation-related parameters as the second most
influential predictor of groundwater recharge. Vegetation has a high
correlation with other physical variables such as soil moisture, runoff
capacity and porosity, which adds to its recharge explanatory power (Kim and
Jackson, 2012; Scanlon et al., 2005). In this study land use (LU) was used
as a proxy for vegetation. According to the results, LU was found to be one
of the predictors having the highest proportion of evidence (PoE; Fig. 4).
In addition, all the better-performing models included LU as one of the
predictors, which clearly indicates that vegetation is one of the most
influential factors for groundwater recharge. Results indicates that
recharge rates were high where runoff water had greater retention time on the
surface. This was mainly observed in areas with shallow-rooted vegetation like
grasslands. In deep-rooted forest areas recharge was reduced because of
increased evapotranspiration (Kim and Jackson, 2012). However, not all studies
reported are in agreement with vegetation as an important predictor
of recharge. For example, Tögl (2010) failed to find a correlation
between vegetation/land cover and recharge. This may be the result of some
peculiarity in the study dataset. Apart from the predictors discussed above,
depth to groundwater and surface drainage density were also identified as
potential predictors of recharge from literature (Döll and Flörke,
2005; Jankiewicz et al., 2005). Despite this they were excluded from this
study because of the lack of appropriate resolution global datasets.
Global estimates of groundwater recharge.
Model usedSpatialTemporalTotalReferenceresolutionrangeglobalrecharge(km3 yr-1)Empirical model0.5∘1981–201413 600Current studyWaterGAP 20.5∘1961–199014 000Döll (2002)WaterGAP0.5∘1961–199012 666Döll and Flörke (2005)PCR GlobWB0.5∘1958–200115 200Wada et al. (2010)PCR GlobWB0.5∘1960–201017 000Wada et al. (2012)MATSIRO1∘1985–199929 900Koirala et al. (2012)FAO StatisticsCountry1982–201410 613FAO (2016)
Spatial distribution of groundwater recharge residual (FAO estimates less model
estimates) along with recharge sites selected for model building.
The total recharge estimated in this study is strongly consistent with
results from complex global hydrological models. Long-term average annual
recharge was found to be 134 mm yr-1. The total recharge estimated in this
study (13 600 km3 yr-1) was very close to existing estimates of complex
hydrological models except those using MATSIRO, which overestimates recharge
in humid regions (Koirala et al., 2012). The results shown in Table 4
indicate that, compared to existing techniques, the model developed in this
study can make recharge assessments with the same reliability but with fewer
computational requirements. Moreover, the error in recharge prediction in
this study was low, ranging from only -8 to 10 mm yr-1 for 97.2 % of cases.
The global recharge map developed showed a similar pattern to recharge maps
produced using complex global hydrological models. The results of this study
indicate that recharge across the globe varied considerably as a
function of spatial region, and was analogous to global distribution of
climate zones (Scanlon et al., 2002). Humid regions had very high recharge
compared to arid (semi-arid) regions, which is obviously due to the higher
availability of water for recharge. Recharge was also affected by climate
variability and climate extremes at a regional level (Scanlon et al.,
2006; Wada et al., 2012). However, an effect of climate variability on inter-annual recharge at a global scale was not pronounced in our results. The
potential reason for this is that the El Niño Southern Oscillation (ENSO),
the primary factor determining climate variability globally, has
converse effects in different parts of the world. The effects of increased
precipitation in some parts of the world would have been counteracted by
reductions in precipitation in other areas resulting in relatively small
effects on inter-annual variation in global recharge.
Conclusion
This study presents a new method for identifying the major factors
influencing groundwater recharge and using them to model large-scale
groundwater recharge. The model was developed using a dataset compiled from
the literature and containing groundwater recharge data from 715 sites. In
contrast to conventional water balance recharge estimation, a multimodel
analysis technique was used to build the model. The model developed in this
study is purely empirical and has fewer computational requirements than
existing large-scale recharge modelling methods. The 0.5∘ global
recharge estimates presented here are unique and more reliable because of
the extensive validation done at different scales. Moreover, inclusion of a
range of meteorological, topographical, lithological and vegetation factors
adds to the predictive power of the model. The results of this investigation
show that meteorological and vegetation factors had the most predictive
power for recharge. The high dependency of recharge on meteorological
predictors make it more vulnerable to climate change. Although it is a
computationally efficient modelling method, the approach used in this study
has some limitations. Firstly it does not include direct anthropogenic
effects on the groundwater system or recharge by
natural or artificial means, suggesting scope for further future
development. Secondly, the recharge dataset used in this study did not
include data points from frozen regions. Therefore, Greenland and Antarctica
were excluded from the final recharge map. However, the model developed in
this study and the recharge maps produced will aid policy makers in
predicting future scenarios with respect to global groundwater availability.
Data availability
Data used for this study are provided as a Supplement.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-22-2689-2018-supplement.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This project was partially supported by the Australian Research Council
through project FT130100274. The authors would like to acknowledge the
University of Melbourne for providing computational and other technical
facilities for this research, and also the international agencies that
provided the data required for this study.
Edited by: Nandita Basu
Reviewed by: two anonymous referees
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