Abstract
Parameterisation of unsaturated flow models for estimating spatial-scale groundwater recharge is usually reliant on expert knowledge or best-estimated parameters rather than robust uncertainty analysis. This study chose the Campaspe catchment in southeastern Australia as a field example and examined the uncertainty of spatial groundwater recharge by performing uncertainty analysis. The study area was first divided into 13 zones according to different vegetation types, soil groups and precipitation. Individual models were then established for these zones using the biophysically based modelling code WAVES (Water Atmosphere Vegetation Energy and Solutes), which is capable of simulating unsaturated flow. The Monte Carlo method, together with the Latin-Hypercube sampling technique, was employed to perform uncertainty analysis by comparing modelled monthly evapotranspiration (ET) to MODIS ET. The results show that the common one-estimate-per-site approach can still identify the spatial pattern of groundwater recharge in the study area due to the presence of a precipitation pattern. In comparison, the uncertainty analysis not only identifies the spatial pattern, but also provides confidence levels in groundwater recharge that are critical for water resources management. The results also show that recharge absolute uncertainty is directly proportional to the amount of water input, but relative uncertainty in recharge is not. This study indicates that spatial recharge estimation without model calibration or knowledge of model uncertainty could be highly uncertain. MODIS ET can be used to reduce recharge uncertainty, but it is unlikely to lower the recharge uncertainty by a large extent because of the MODIS ET estimation error.
Résumé
Le paramétrage des modèles d’écoulements non saturés pour estimer la recharge des eaux souterraines à l’échelle spatiale dépend habituellement de connaissances d’experts ou de paramètres les mieux estimés plutôt que d’une analyse d’incertitude robuste. Cette étude a choisi le bassin versant de Campaspe dans le sud-est de l’Australie comme un exemple de terrain et a examiné l’incertitude de la recharge spatialisée des eaux souterraines en réalisant une analyse d’incertitude. La zone d’étude a été tout d’abord divisée en 13 zones en considérant les différents types de végétation, de groupes de sol et des précipitations. Des modèles individuels ont été ensuite établis pour ces zones en utilisant le code de modélisation WAVES (Water Athmosphere Vegetation Energy and Solutes) basé sur la biophysique, qui est. capable de simuler les écoulements non saturés. La méthode Monte Carlo, associé à la technique d’échantillonnage Latin-Hypercube, a été employée pour réaliser l’analyse d’incertitude en comparant l’évapotranspiration (ET) modélisée au pas de temps mensuel à l’ET MODIS. Les résultats montrent que l’approche commune à une estimation par site peut encore identifier la configuration spatiale de la recharge des eaux souterraines dans la zone d’étude en raison de la présence d’un modèle de précipitation. En comparaison, l’analyse d’incertitude n’identifie pas seulement une configuration spatiale, mais fournit des niveaux de confidence dans la recharge des eaux souterraines qui sont importantes pour la gestion des ressources en eau. Les résultats indiquent également que l’incertitude absolue concernant la recharge est. directement proportionnelle à la quantité d’eau qui s’infiltre, mais l’incertitude relative dans la recharge ne l’est. pas. Cette étude indique que l’estimation de la recharge à l’échelle spatiale sans calibration du modèle ou sans connaissance de l’incertitude du modèle pourrait être fortement incertaine. MODIS ET peut être utilisé pour réduire l’incertitude sur la recharge, mais il est. peu probable qu’il puisse abaisser l’incertitude sur la recharge en grande partie en raison de l’erreur d’estimation de MODIS ET.
Resumen
La parametrización de los modelos de flujo no saturado para estimar la recarga del agua subterránea a escala espacial generalmente depende del conocimiento experto o de los parámetros mejor estimados en lugar de un sólido análisis de incertidumbre. Este estudio eligió la cuenca de drenaje de Campaspe en el sureste de Australia como un ejemplo de campo y examinó la incertidumbre de la recarga espacial del agua subterránea mediante la realización de un análisis de incertidumbre. El área de estudio se dividió en principio en 13 zonas según los diferentes tipos de vegetación, los grupos de suelos y la precipitación. Luego se establecieron modelos individuales para estas zonas utilizando el código de modelado WAVES (Water Atmosphere Vegetation Energy and Solutes), basado en la biofísica, que es capaz de simular el flujo no saturado. El método de Monte Carlo, junto con la técnica de muestreo Latin-Hypercube, se empleó para realizar el análisis de incertidumbre mediante la comparación de la evapotranspiración (ET) mensual modelada con MODIS ET. Los resultados muestran que el enfoque común de una estimación por sitio puede identificar el patrón espacial de recarga del agua subterránea en el área de estudio debido a la presencia de un patrón de precipitación. En comparación, el análisis de incertidumbre no solo identifica el patrón espacial, sino que proporciona niveles de confianza para la recarga del agua subterránea que son críticos para la gestión de los recursos hídricos. Los resultados también muestran que la incertidumbre absoluta de la recarga es directamente proporcional a la cantidad de ingreso de agua, pero no la incertidumbre relativa en la recarga. Este estudio indica que la estimación de la recarga espacial sin calibración del modelo o el conocimiento de la incertidumbre del modelo podría ser altamente incierto. MODIS ET se puede usar para reducir la incertidumbre de la recarga, pero es poco probable que reduzca la incertidumbre de la recarga en gran medida debido al error de estimación MODIS ET.
摘要
估算空间尺度地下水补给的非饱和水流模型的参数化通常依赖于专门知识或者最好的估算参数,而不是依赖于强大的不确定性分析。本研究选择澳大利亚东南部Campaspe流域作为一个野外实例,通过进行不确定性分析检查了空间地下水补给的不确定性。根据不同的植被类型、土壤组和降水情况,首先把研究区分为13个区。然后采用基于生物物理学上的模拟编码WAVES(水大气植被能量和溶质)为这些区建立了各自的模型,该模型能够模拟非饱和水流。通过比较模拟的每月蒸发蒸腾和MODIS ET,采用蒙特卡洛法以及拉丁超立方抽样技术进行不确定性分析。结果显示,由于存在着降水模式,普通的一地一估算方法仍然能确定研究区地下水补给的空间模式。相比之下,不确定性分析不仅能够确定空间模式,而且还能提供地下水补给中的置信级别,这对于水资源管理至关重要。结果还显示,补给绝对不确定性与水输入量成正比,但是补给的相对不确定性并不是如此。本研究表明,没有模型校正或模型不确定性知识的空间补给估算可能高度不确定。MODIS ET可用于减少补给不确定性,但是由于MODIS ET估算误差,很可能在很大程度上降低补给不确定性。
Resumo
Parametrização de modelos de fluxo de zona não saturada para estimativa da recarga de águas subterrâneas em escala espacial é normalmente dependente em conhecimento especializado ou parâmetros otimamente estimados ao invés de análise de incerteza. Esse estudo escolheu a bacia Campaspe na porção sudoeste da Austrália como exemplo de campo e examinou a incerteza da recarga de águas subterrâneas espacial através da análise de incerteza. A área de estudo foi primeiro dividida em 13 zonas de acordo com os tipos diferentes de vegetação, grupos de solos e precipitação. Modelos individuais foram então estabelecidos para essas zonas utilizando o código de modelagem baseado em biofísica WAVES (Águas Atmosfera Vegetação Energia e Solutos), queé capaz de simular o fluxo em zona não saturada. O método de Monte Carlo, em conjunto com a técnica de amostragem Latin-Hypercube foram empregados para fazer a análise de incerteza, comparando evapotranspiração (ET) mensalmente modelada e ET do MODIS. Os resultados demonstram que a abordagem comum de uma estimativa por local ainda pode identificar que o padrão espacial da recarga de águas subterrâneas na área estudada pela presença de um padrão de precipitação. Em comparação, a análise de incerteza não apenas identifica o padrão espacial, mas provém níveis de confiança na recarga de águas subterrâneas que são criticos para o gerenciamento dos recursos hídricos. Os resultados também demonstram que a incerteza absoluta da recarga está diretamente proporcional à quantidade de entrada de água, mas a incerteza relativa não o é. Esse estudo indica que estimar recarga espacial sem a calibragem do modelo ou conhecimento da incerteza do modelo poderia ser altamente incerto. ET do MODIS pode ser utilizada para reduzir a incerteza da recarga, mas é improvável que reduza a incerteza da recarga por uma grande extensão por causa do erro de estimativa da ET do MODIS.
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Introduction
Diffuse groundwater recharge occurs below the root zone and over large areas when water input (precipitation and irrigation) is greater than demands for evapotranspiration. Although it is usually a small fraction of water input (particularly in arid and semiarid regions), it plays a significant role in replenishing aquifers. Recharge is known to vary spatially (and temporally) because of spatial distributions of controlling factors including climate, soil and vegetation (Keese et al. 2005; Kim and Jackson 2012; Scanlon et al. 2006). Hence, mapping and understanding spatial distributions of groundwater recharge is a key step for many types of hydrologic assessments including aquifer replenishment rates, groundwater flow modelling, conjunctive surface-water/groundwater management, climate change impacts, and agricultural pollutant control. Many recharge maps at varying scales have been produced over the past decades, e.g., Spain (Alcalá and Custodio 2014), Australia (Crosbie et al. 2013), Bangladesh (Shamsudduha et al. 2011), Ireland (Williams et al. 2011) and globally (Döll and Fiedler 2008).
Mapping spatial recharge could be conducted with two approaches. The first approach requires the preparation of gridded maps of input variables. Spatial recharge is then calculated for all grid cells or areas with the same land features using a recharge estimation method such as water balance modelling (Anuraga et al. 2006; Batelaan and De Smedt 2001; Dripps and Bradbury 2010; Hartmann et al. 2015; Westenbroek et al. 2010) or chloride mass balance (Alcalá and Custodio 2014, 2015)—for example, Alcalá and Custodio (2014) produced raster maps for chloride deposition rate, and chloride mass fluxes for runoff and groundwater. They then compute groundwater recharge for all grid cells using the chloride mass balance method. The second approach requires the derivation of groundwater recharge at individual locations using various methods including water balance modelling (Crosbie et al. 2010a; Keese et al. 2005), chloride mass balance (Crosbie et al. 2017), Darcy method (Nolan et al. 2003) or unsaturated zone tracer tests (Chand et al. 2004). Recharge rates estimated from these local-scale methods are then upscaled to entire study areas using upscaling techniques—for example, Keese et al. (2005) estimated recharge for dozens of sites using an unsaturated flow model (UNSAT-H) and recharge estimates were then upscaled to the entire Texas region (USA) by building a power-law correlation between recharge and precipitation. Among these recharge studies, water balance modelling is the most widely used method.
Although recharge mapping has been widely performed across the world, only a limited number of studies have performed a formal assessment of the uncertainty of recharge maps (Alcalá and Custodio 2014, 2015; Crosbie et al. 2017; Hartmann et al. 2015; Westerhoff et al. 2018). Crosbie et al. (2017) examined the spatial uncertainty of recharge estimated from the chloride mass balance (CMB) method. The uncertainty of recharge in the CMB method results from the uncertainties of rainfall chloride deposition rate, chloride concentration in surface runoff, and chloride concentration in groundwater. The spatial recharge uncertainty was calculated from 1,000 recharge raster maps, each using regression kriging with thousands of point estimates of recharge upscaled using rainfall and geology as covariates. Alcalá and Custodio (2014, 2015) also examined spatial recharge uncertainty across the Spanish continent for the CMB method. Unlike Crosbie et al. (2017), they first interpolated the uncertainty of the input variables to grid cells using ordinary kriging and then computed the spatial uncertainty of recharge for each grid cell using a linear error propagation method. Hartmann et al. (2015) computed recharge and the relevant uncertainty for karstic regions across Europe and the Mediterranean using a simple tipping bucket model together with a Monte Carlo approach. Westerhoff et al. (2018) estimated national groundwater recharge across New Zealand where recharge uncertainty was computed using the same linear error propagation method as that in Alcalá and Custodio (2014, 2015). The common feature of these studies is that they used very simple methods requiring a limited number of parameters and short runtime to complete one forward run. Computational burden and modelling complexity increase dramatically for many water-balance-modelling analyses and approaches. This is particularly true for unsaturated flow modelling which may need dozens of parameters and also have to solve the Richards equation (Keese et al. 2005; Crosbie et al. 2010).
Apart from computational constraints, the primary reason for not including formal uncertainty assessments is that recharge maps are usually used in a relative rather than absolute sense, i.e. to identify high, medium and low recharge areas instead of finding precise recharge rates in a particular location or region. Most prior studies attempted to identify spatial recharge patterns by discretising an area into regular grid cells and computing one recharge estimate per grid cell (Anuraga et al. 2006; Westenbroek et al. 2010; Batelaan and De Smedt 2001). Xie et al. (2018) performed theoretical analysis of potential recharge uncertainty at a semi-arid location where soil type is clay loam and land cover is largely annual pasture. They reported that the point-scale recharge estimated from water-balance modelling could be very uncertain due to uncertainties of input variables and also uncertainties of observation time series used for model calibration. Without an uncertainty assessment, expert knowledge will guide the selection of different parameters and determine the reasonableness of the resulting groundwater recharge. As the expert knowledge is highly dependent upon prior experience and personal understanding, different assessors may produce varying recharge estimates between the upper and lower bounds of a potential uncertainty range; hence, it is important to examine spatial recharge uncertainty (e.g., Crosbie et al. 2017). Uncertainty results (mean, standard deviation and various percentiles) allow for a more consistent assessment of spatial recharge and its uncertainty.
This study attempted to quantify spatial recharge uncertainty estimated from unsaturated flow modelling. Uncertainty analysis in recharge assessment has rarely been performed for unsaturated flow modelling. As a first systematic and quantitative study on regional-scale recharge uncertainty assessment, the main objective was to assess the importance of uncertainty analysis for recharge mapping. A commonly used numerical tool—Water Atmosphere Vegetation Energy and Solutes (WAVES) code—was employed to perform recharge modelling. WAVES is capable of simulating unsaturated flow and has been widely used to assess the response of groundwater recharge to land use changes (Zhang et al. 1999) and climate change (Crosbie et al. 2010a). In this study, the study region was divided into a number of recharge zones with the same land and atmospheric features as performed by Anuraga et al. (2006). One numerical model was established for each recharge zone. Recharge uncertainty analysis was then performed for each recharge zone using the Monte Carlo approach. Spatial recharge and its uncertainty were assessed by examining recharge statistics of all the recharge zones.
Field site description
This study focussed on the Campaspe catchment in southeast Australia. The catchment covers 7,949 km2 and forms the southern edge of the Murray-Darling Basin (Fig. 1). It extends from the Great Dividing Range in the south to the floodplains of the Campaspe and Murray rivers in the north. Soils are mostly Sodosols and Vodosols with varying thicknesses according to the Australian Soil Classification system (Isbell 1996).
In the southern upland area, aquifers are usually unconfined and fractured. Water-table depth ranges from 10 to 40 m. In the riverine plains, two main aquifers occur: a shallow unconfined aquifer with interbedded sand and clay (Shepparton Formation), and a deep semi-confined aquifer consisting of coarse sand (Calivil Formation). The water table in the shallow aquifer is usually 10–15 m below the land surface, whilst the piezometric surface of the deep aquifer is often lower than the water table. The difference in the hydraulic heads between the two aquifers leads to a general trend of downward flow (CSIRO 2008).
Overall, there is a decreasing trend from south to north in average precipitation (from 1,075 to 389 mm/y) and an increasing trend in average potential evapotranspiration (from 1,181 to 1,757 mm/y) based on a standard 30-year (1961–1990) climatology (Australian Government 2010). Precipitation occurs episodically throughout the year, with mean monthly precipitation about 30% higher in the months from May to October than in the other months; however, extreme precipitation events can occur at any time. In comparison, potential evapotranspiration (PET) has a clear seasonal trend. PET reaches peak at around 12 mm/day in the summer months (December to February) and is only about 1 mm/day in the winter months (June to August). Most parts of the catchment have been developed for farming, including dryland crops, dryland pasture and irrigated crops.
Methods
Numerical modelling
The Water Atmosphere Vegetation Energy and Solutes (WAVES) code (Zhang and Dawes 1998) was chosen to examine potential groundwater recharge. WAVES is a biophysically based model, designed to simulate several balances (energy, water, carbon and solute balances) of a one-dimensional (1D) soil-vegetation-atmosphere system simultaneously. It can predict the dynamic interactions and feedbacks between different processes. Hence, it is well suited to investigations of hydrological and ecological responses to changes in land management and climatic variation. In WAVES, groundwater recharge is computed in the form of deep drainage (the residual of a soil water balance), where actual evapotranspiration is further constrained by solving a simultaneous energy balance. It is believed that the simulation of multiple processes can improve the accuracy of groundwater recharge. The reader is referred to the WAVES manual for the details of the methodology employed and its numerical implementation (Zhang and Dawes 1998).
Data collection
The WAVES model requires three types of input data for model simulations as well as field observations for model calibration. The input data include climatic variables on a daily time step, soil hydraulic parameters and vegetation parameters.
Climate
Historical daily meteorological data were obtained from the gridded climate surfaces spatially interpolated from ground-based observational data and managed by the Queensland Department of Natural Resources and Water (Jeffrey et al. 2001). Each dataset contains all variables commonly recorded at a weather station, including precipitation, air temperature, solar radiation, pan evaporation, vapour pressure and humidity. The variable vapour pressure deficit needed by WAVES was calculated from the measured temperature and vapour pressure according to Grayson et al. (1998). The gridded climate data have a resolution of 0.05° (approximately 5 km). Ideally, recharge should be estimated for each grid cell, but because of the computational burden caused by Monte Carlo simulations, it was decided to use three sites of weather data (Fig. 2a). The original long-term average precipitation map shown in Fig. 2a was used to scale estimated recharge to the whole catchment.
Vegetation
Vegetation parameters are an important requirement of WAVES modelling. Dawes and Zhang (1998) performed a thorough literature review of all vegetation parameters for all the vegetation types including C3 annual pasture, C3 perennial pasture, trees etc. They compiled a table of all the relevant parameters with upper and lower limits for each vegetation type. These uncertainties reflect the likely ranges of parameters based on published studies. In this study, three representative vegetation types (annual pasture, perennial pasture and trees) were chosen which is in keeping with previous studies (Crosbie et al. 2010a; McCallum et al. 2010). These three vegetation types form four land use types including annual pasture (non-irrigated), perennial pasture, trees (sometimes with perennial pasture as understorey) and irrigated annual pasture. The irrigation amount was simulated by specifying the depth of water at the land surface (approximately 20 mm, based on interviews with local farmers) once every fortnight between October and March. The total amount of irrigation was 240 mm. The uncertainty ranges of most vegetation parameters were taken from the table in Dawes and Zhang (1998) with only a few parameter ranges modified after additional literature review. The modification of these parameters was to better reflect these vegetation types in a semi-arid environment in southeast Australia and modified parameters are indicated in Table 1.
Spatial recharge estimation requires the spatial distributions of all the vegetation types. This information was derived from a raster map of ‘Catchment Scale Land Use of Australia’ (50-m resolution) published by the Department of Agriculture and Water Resources of the Australian Government (2016). This catchment-scale land-use map has detailed 18 land use types. It was not possible to take into account all the land use types in the WAVES model because vegetation parameters for many land use types are not available. Hence, the raster map was classified by reducing the land use types to the four types already discussed based on the nature of their water use (Fig. 2b)—for example, grazing modified pasture, grazing native vegetation, protected areas and land in transition are treated as annual pasture, whereas nature conservation, production forestry, plantation forestry and horticulture are grouped together as trees. Note that this classification and grouping requires an understanding of the water use of different land use types.
Soil
Soil parameters are also important for WAVES because they are required to solve the Richards equation. The Terrestrial Ecosystem Research Network (2018) provides several Australia-wide soil attributes (including clay content, silt content, sand content used in this study) at 6 depth intervals (0–0.05, 0.05–0.15, 0.15–0.3, 0.3–0.6, 0.6–1.0 and 1.0–2.0 m). Consistent with prior studies (e.g. Crosbie et al. 2010a), soil profiles were simplified to topsoil (top 0.3 m) and subsoil (depth range of 0.3–2.0 m). After the simplification of soil layers, the clay content of both the topsoil and subsoil was averaged to create a single clay content map. All the grid cells with clay content smaller than the median clay content are classified as soil group 1 (loam), whereas all the grid cells with clay content larger than the median are soil group 2 (clay loam, Fig. 2c). This operation led to averaged percent clay, silt and sand as shown in Table 2. It should be noted that clay content was used to determine soil groups, as it plays an important role in affecting deep drainage (Kennett-Smith et al. 1994; Wohling et al. 2012). That is, increases in clay content lead to decreases in permeability and increases in water holding capacity, and hence reduction in deep drainage.
The soil retention model developed by Broadbridge and White (1998) was used by WAVES. In this study, soil hydraulic parameters were derived for both topsoil and subsoil using the method documented by Carsel and Parrish (1988). The method estimates both soil retention curve parameters and saturated conductivity simultaneously through a joint probability distribution method for different soil textural classes, because evidence has shown that these parameters are correlated. This method facilitates the uncertainty analysis in this study, as it is capable of producing numerous combinations of different soil hydraulic parameters. The classifications above resulted in 13 recharge zones (Table 3). The three digits in each zone code represent climate, vegetation and soil respectively. In the vegetation column, perennial pasture acts as the understorey of trees if it is listed together with trees. The soil column lists both topsoil and subsoil textures.
MODIS ET
In this study, MODIS monthly ET (actual ET) was used for model calibration. For regional-scale recharge estimation, MODIS ET data are available at an appropriate scale (1 km2). Monthly MODIS ET datasets for a period between 2003 and 2013 (inclusive) were downloaded from the website of MODIS Global Evapotranspiration Project (2018). The ET time series for different recharge zones were derived from the raw MODIS ET data sets using the recharge zone map created in the preceding text. Figure 3 presents monthly ET time series for four major recharge zones. (The recharge zones are explained in the following section.) As can be seen, larger precipitation results in larger ET (compare ET in Zone HAL to smaller ET in other zones). It is acknowledged that different MODIS ET products are available using different algorithms and the ET results may vary strongly in some areas (Glenn et al. 2011). This product was chosen as it is widely used and readily available at 1-km resolution for the global vegetated land areas (Hu et al. 2015; Velpuri et al. 2013).
Model setup
WAVES solves the Richards equation to derive time-varying soil moisture distribution and requires grid discretisation for the unsaturated zone. In this study, the depth of each model was 4 m similar to previous studies (Xie et al. 2018; Crosbie et al. 2010a; McCallum et al. 2010). Because the average water table depth is 10–15 m, the recharge estimated in this study should be considered to be potential recharge, which will occur at some time in the future, providing that there are no impermeable layers between the 4 m depth and the water table. Note, however, that the model depth of 4 m assumes that vegetation rooting depth is not greater than 4 m. This is reasonable for annual and perennial pasture as their maximum rooting depth is expected to be less than 1.5 m (Table 1). However, this model depth might not be reasonable for trees whose rooting depth could exceed 4 m. Given limited information about tree rooting depth in the study area and because forested areas only account for approximately 15% of the catchment area, the model depth of 4 m has been used throughout this study for consistency. It is acknowledged, though, that estimated recharge rates beneath trees might overestimate true recharge rates.
The elemental size of the model increased gradually from 0.001 m near the top to 0.05 m at the depth of 0.4 m gradually. A constant elemental size of 0.1 m was used for the depth range between 0.4 and 4 m. The model discretisation resulted in a total of 58 elements. The top 0.3 m and the bottom 3.7 m were assumed to be the topsoil and subsoil, respectively. The top of the model represents the land surface with intensive interactions with the atmosphere, whereas the bottom of the model was assigned a free drainage boundary condition.
The initial head and the initial root carbon mass of the model were −100 m and 0.002 kg/m2, respectively, across the soil column, whereas the initial leaf carbon and stream carbon were set at 0.05 kg/m2 and 0.5 km/m2, respectively. Because the exact initial conditions were not known a priori, these specified initial conditions were rather arbitrary and so the model required time to spin-up to the equilibrium state. Similar to Xie et al. (2018), the spin-up time was examined for the leaf area index (LAI) in several selected model realisations (i.e., use the time for LAI to reach long-term trends to indicate if a model has reached equilibrium). The assessment indicates a spin-up time of less than 5 years in those selected model realisations. As simulations were performed for 127 years starting from 1889, the long-term average groundwater recharge was calculated between 2003 and 2013. Any model realisation should be able to reach equilibrium state before 2003.
Recharge rates are estimated for three rainfall regimes, four vegetation types, and two soil types, giving a theoretical 24 recharge zones. In practice, however, only 13 zones were modelled, as some zones were too small to be considered significant. Recharge zones are designated by three letter codes. The first letter refers to the precipitation regime (H: high, M: medium; L: low); the second letter refers to the vegetation type (A: annual pasture, P: perennial pasture; T: trees), and the third letter refers to the soil type (L: loam, C: clay loam). These recharge zones are also summarised in Table 3.
Uncertainty assessment
There are three steps for assessing recharge uncertainty for an individual recharge zone: (1) performing Monte Carlo simulations; (2) identifying acceptable model realisations; and (3) quantifying the uncertainty of long-term average potential recharge R.
As a first step, Monte Carlo simulations were conducted. Before model simulations, R was defined as the annual deep drainage averaged between 2003 and 2013 (11 years). This timeframe is consistent with the MODIS ET that was used for model calibration. R (mm/y) is given as
where q(t) is time-varying daily deep drainage (mm/day), to is the length of the simulation period (4,017 days) and 11 represents the number of years for the simulation period.
The Latin Hypercube sampling technique was used to enhance the Monte Carlo simulations. It performs stratified sampling of all parameters to permit a reasonable distribution of parameter values over parameter ranges. This technique has been used in previous studies to examine the uncertainty of long-term average recharge (Xie et al. 2018) and the uncertainty of long-term cumulative river–aquifer exchanges (Xie and Batlle-Aguilar 2017). As in Xie et al. (2018) and for consistency, 40,000 realisations were generated for each combination of climate, vegetation and soil to examine the recharge uncertainty.
After simulations were run, acceptable model realisations were determined by examining the goodness of fit of modelled ET to actual ET (MODIS ET) in the form of Root Mean Squared Error (RMSE). RMSE is given as
where Pi and Oi are predicted and observed ET, respectively. Smaller RMSE indicates better prediction of a model realisation. A quantitative and consistent criterion must be used to determine acceptable models. Different criteria have been used before, including a measurement-based cut-off value (Xie et al. 2016; Xie and Batlle-Aguilar 2017) or an arbitrary fraction of results ranked by RMSE (e.g., Blasone et al. 2008; Ward et al. 2013). In this study, the criteria were defined as 30% of the lowest RMSE. That is, for each recharge zone, the minimum RMSE (RMSEmin) was first determined and then the model realisations were accepted if their RMSE is lower than RMSEmin plus additional 30% of RMSEmin. This 30% also considers the likely error of remotely sensed ET as reported by Kalma et al. (2008) and Glenn et al. (2011). Clearly, the choice of a cut-off criterion is subjective. It is believed that this acceptance criterion is more reasonable than others (Blasone et al. 2008; Ward et al. 2013), as it is based on potential ET estimation error.
The uncertainty of R was quantified by examining all the accepted model realisations. Each acceptable model realisation produces an acceptable R and the R values produced from all the acceptable models allow for the calculation of recharge statistics.
Results
Uncertainty assessment for a representative recharge zone
Zone HAL is used as an example to illustrate the derivation of groundwater recharge uncertainty. This zone accounts for 13.5% of the catchment and is located in the upland of the catchment with an average precipitation of 746 mm/y, annual pasture, loamy topsoil and sandy clayey subsoil (Table 3). A total of 40,000 simulations were performed and assessed by comparing simulated ET to MODIS ET. As shown in Fig. 4, the observed ET varied between 20 and 105 mm/month between 2003 and 2013. ET was generally high between October and December when soil was still damp and solar radiation was sufficient. The best model realisation (model 3 in Fig. 4) reproduced ET reasonably well with RMSE of 9.3 mm/month.
The 40,000 model realisations produced RMSE ranging from 9.3 to 41.3 mm/month (ET fitting errors) and groundwater recharge varying from 0.0 to 409.3 mm/y (Fig. 5). The uncertainty range of recharge was determined using the acceptance criterion (1.3 times RMSEmin). As a result, the criterion used to accept models is 12.1 mm/month (dashed line in Fig. 5). The acceptance criterion resulted in the uncertainty range of groundwater recharge between 1.1 and 251.9 mm/y (Fig. 5). Like the models shown in Fig. 4, all the accepted models were able to fit the observed ET time series reasonably well. The large recharge uncertainty range is likely attributed to two factors, including the large estimation error associated with remotely sensed ET (30%) and the lack of information on other water balance components (overland flow and storage change). Note that overland flow in WAVES is generated when rainfall exceeds infiltration capacity and is treated as a sink.
The recharge of the accepted model realisations for zone HAL follows a normal distribution (Fig. 6). The 90% confidence range (5–95%) of the groundwater recharge is between 40.8 and 210.9 mm/y. This large uncertainty range indicates that the recharge uncertainty cannot be substantially reduced by ET time series alone and additional work (e.g., reducing ET estimation error and collecting other types of data) should be performed to further reduce the recharge uncertainty. Because the recharge follows a normal distribution, the recharge from the best-fit model realisation is close to the median value of the recharge range (Fig. 6).
Recharge mapping with uncertainty assessment
The same procedure for assessing the recharge uncertainty of zone HAL above was applied to the remaining recharge zones. In this study, recharge estimates mostly follow lognormal distributions (due to zero being the lower limit of possible recharge), and sometimes follow normal distributions when there is sufficient water input (Fig. 7).
Recharge uncertainty seems to be more correlated to water input, as larger water input tends to result in larger uncertainty (Fig. 8), consistent with Keese et al. (2005)—for example, mean recharge of 133, 93, 112, and 234 mm/y for zones HAL, HAC, HPL and LIC, respectively, are higher than that for the other zones. For the same climatic and soil conditions, annual pasture is more likely to cause larger recharge than perennial pasture and trees (compare mean recharge for zones HAL, HPL and HTL with annual pasture, perennial pasture and trees, respectively). This is because annual pasture only grows for about half a year and recharge is greater through bare soil than vegetated land. For the same climate and vegetation, recharge under soil type L is larger than that under soil type C (compare MAL and MAC, also compare LTL and LTC) due to relatively higher saturated hydraulic conductivity.
Recharge statistics were used to produce recharge maps. Because the simulations involved only three precipitation zones (Fig. 2a), the recharge maps were dominated by precipitation zones. Hence, the recharge maps were smoothed by building correlations between recharge and precipitation and using the long-term annual mean precipitation map. Overall, if irrigation is not present, mean recharge generally decreases from south to north (from bottom to top on the map), following the climatic and soil patterns (compare Figs. 9a and 2). Once the irrigation is included, the maximum mean recharge in the catchment almost doubles (i.e., maximum mean recharge changed from zone HAL to LIC as seen in Fig. 8), although the soil in the irrigated areas is less permeable. This significant increase in recharge is due to flood irrigation that is clearly not water-efficient. The irrigation effect on recharge is consistent with Tan et al. (2014) who found recharge increased from 21.2 to 101.7 mm/y after adding irrigation. The 90% confidence interval map shows that the absolute uncertainty decreases from south to north, consistent with the mean recharge trend without irrigation (Fig. 9b). Interestingly, in comparison to the upland area, the irrigated area has lower relative recharge uncertainty, despite larger mean recharge (Fig. 9c). This is because all irrigation water infiltrates within a short period and only a small portion of irrigated water is evapotranspired before passing through the root zone.
Discussion
This study examined spatial recharge uncertainty using an unsaturated flow model. As is common practice, the study catchment was divided into a number of recharge zones based on the classification of the soil, climate and land cover. The classification resulted in 13 recharge zones for uncertainty analysis. The Monte Carlo approach enhanced by the Latin Hypercube sampling technique was employed to perform uncertainty analysis for each recharge zone.
Role of uncertainty analysis
Spatial recharge mapping using unsaturated flow modelling is usually conducted by choosing one set of parameters for each area or representative site (Anuraga et al. 2006; Batelaan and De Smedt 2001; Jyrkama et al. 2002; Crosbie et al. 2010a, 2013; Keese et al. 2005). It is therefore a deterministic assessment without quantification of uncertainty in recharge. The choice of parameters is highly dependent upon expert knowledge possessed by the assessor within the uncertainty ranges of the parameters. The validity of the resulting recharge estimate is often assessed by comparing it to recharge estimates derived from prior experience in similar systems and using other methods. Without uncertainty analysis (e.g., Crosbie et al. 2010a, 2013; Keese et al. 2005; Anuraga et al. 2006; Jyrkama et al. 2002), various recharge maps could be produced (Fig. 10), each using a different set of parameters.
As can be seen in Fig. 10, a similar pattern (generally high, then low and then high recharge from south to north) can be observed across all the three recharge maps, consistent with the spatial mean recharge pattern (Fig. 9a). This pattern mirrors the clear precipitation pattern in this catchment. This indicates that a spatial recharge pattern could be identified through a common recharge mapping approach, provided that there is a clear precipitation pattern. When there is no clear climatic pattern, it becomes difficult to identify spatial recharge patterns (e.g., compare recharge estimates within southern and middle parts of the catchment in Fig. 10). Despite the similar pattern, there is still a factor of six variation in annual volumetric recharge among these three recharge distribution scenarios (obtained by integrating recharge across the study area). The strong variability in the annual volumetric recharge indicates the difficulty in obtaining meaningful groundwater recharge and the potential risk of overestimating or underestimating recharge for water resources management.
In comparison, an uncertainty assessment not only provides a spatial pattern of groundwater recharge across the region similar to recharge mapping without uncertainty, but provides the variance or confidence levels of the different areas. This information is valuable for water resources management. It allows the water resource to be managed within a risk and uncertainty framework. For example, in the southern part, both the mean recharge and the absolute uncertainty range are quite large because of large precipitation (Fig. 9a,b). However, the largest relative uncertainty did not occur in the areas with the large absolute uncertainty (Fig. 9c). This implies that focus of any future data collection should be placed on the area with the largest relative uncertainty in order to improve the accuracy of groundwater recharge.
Major controls on groundwater recharge
This study affirms that climate plays a significant role in affecting mean groundwater recharge as shown in Fig. 11a, because climate directly determines the availability of water for maximum potential recharge. This finding is consistent with previous studies (Crosbie et al. 2010a; Keese et al. 2005), although no uncertainty assessments were performed in those previous studies. Keese et al. (2005) found that climate explains 80% of the recharge variability in Texas.
The next important control is flood irrigation. Figure 9 clearly suggests mean recharge with flood irrigation is approximately double of that in the upland area. Tan et al. (2014) reported a factor of five increase in groundwater recharge when irrigation was introduced in the North China Plain. Despite the fact that the additional water input from irrigation has a clear impact on mean recharge, its impact on recharge uncertainty cannot be easily differentiated if the difference in annual precipitation is not sufficiently large (see 517 and 440 mm/y areas in Fig. 11a) because soil and vegetation may play opposing roles in affecting recharge.
Both vegetation types and soil textures affect mean recharge (Crosbie et al. 2010b; Kim and Jackson 2012; Scanlon et al. 2006). Annual pasture tends to have largest recharge, as it only grows for part of a year and percolation becomes fast for bare soil (Zhang and Schilling 2006). In comparison, trees often result in lower mean recharge than pastures due to greater rooting depth (Keese et al. 2005). Similarly, it is expected that loamy soil allows more water to infiltrate through the root zone and hence cause larger recharge rates compared to clay loamy soil; however, no clear trends of the effects of vegetation and soil texture on mean recharge could be observed in this study (Fig. 11b,c), likely because different combinations of vegetation and soil texture could produce similar recharge (e.g. trees + sandy soil compared to annual pasture + clayey soil).
Model calibration
Model calibration using observations plays an important role in reducing recharge uncertainty ranges; however, this has rarely been performed for regional-scale recharge assessment, partly due to computational limitations in the past. Model calibration has been conducted only in relatively simple conditions such as homogeneous land cover (e.g. Cheng et al. 2014), bucket type models used (e.g. Batelaan and De Smedt 2001; Dripps and Bradbury 2010; Hartmann et al. 2015; Westenbroek et al. 2010). In this study, MODIS ET was used as model calibration data as the data set is readily available. Other data such as water table observations could also be used where they are also available; however, using water-table observations would also need to consider other factors such as groundwater pumping and regional groundwater flow. It would also require that the model simulated the entire unsaturated thickness, so that the time delay between infiltration and recharge could be correctly simulated. This would greatly increase the complexity of the study.
Recharge uncertainty ranges are wider without model calibration than with model calibration. Wider uncertainty ranges increases the difficulty of applying the data for water resources management—for example, the 5–95 percentile range for zone LIC is between 0 and approximately 180 mm/y without performing calibration (Fig. 8), but it is between 200 and 270 mm/y after performing calibration (Fig. 12). Hence, although model calibration using MODIS ET cannot reduce recharge uncertainty to a small range, it still helps to lower recharge uncertainty in comparison to without such a process (compare Figs. 8 and 12). Xie et al. (2018) examined the recharge uncertainty for a combination of low precipitation, annual pasture and clay loam soil in lower Campaspe Catchment (approximately zone LAC in this study). Despite the difference in the methods to derive soil hydraulic parameters, the recharge uncertainty estimated for zone LAC in this study (0–190 mm/y) is consistent with that reported by Xie et al. (2018) (7–236 mm/y).
This study clearly shows that it is very difficult to reliably determine groundwater recharge using MODIS ET alone to constrain the model. In a semi-arid area (usually water-limited), recharge is often smaller than the error of actual ET (de Vries and Simmers 2002); hence, it is reasonable to expect a large uncertainty in groundwater recharge estimation with a large estimation error. In this study, 30% error in MODIS ET was assumed. Xie et al. (2018) examined the effect of ET error on recharge uncertainty. They found that the reduction of the ET estimation error can greatly reduce the recharge uncertainty; however, the MODIS ET could be useful in humid areas (usually energy-limited), as recharge will be greater than the ET error. Westerhoff et al. (2018) estimated recharge for New Zealand by treating MODIS ET as a model input and found the recharge estimates compared well to lysimeter recharge estimates. To reduce recharge uncertainty for semi-arid areas, multiple data sets should be used including soil moisture and actual evapotranspiration and also the estimation error of the actual evapotranspiration should be reduced (Mathias et al. 2017; Xie et al. 2018). However, further research is required to better understand the usefulness of different datasets and their spatiotemporal resolution for regional-scale recharge estimation.
Limitations
This study is a modelling exercise to examine potential groundwater recharge at the regional scale. A fixed model thickness (4 m) was chosen for all the scenarios considered, as used in previous studies (Crosbie et al. 2010a, 2013; Xie et al. 2018). Potential groundwater recharge was estimated as the free drainage through the bottom boundary. Where interest is in short-term temporal patterns of recharge (months to years), the model thickness could play a significant role because of potentially significant lag times between precipitation and actual recharge in semi-arid regions (Cook et al. 2003; Crosbie et al. 2013). In comparison, the model thickness should not strongly affect mean recharge estimated for 11 years; however, the potential recharge in forested areas could be affected by the model thickness regardless of temporal scales. Where water-table depth exceeds 4 m, which is the case over much of the Campaspe catchment, tree rooting depth could exceed 4 m and hence potential recharge could be overestimated. As this study already shows quite small mean recharge in the forested areas (Fig. 8) and the total forested area accounts for only about 15% of the catchment, the potential recharge overestimation should not significantly affect the recharge pattern at the regional scale. It is recommended that the effect of model thickness on potential recharge be examined carefully in future studies.
This study used multiple maps with different spatial resolutions to estimate spatial scale potential recharge. As the highest spatial resolution is 50 m from the soil and vegetation maps, each unsaturated flow model represents a spatial resolution of 50 m. In comparison, the spatial resolution of any MODIS ET map is approximately 1 km. It is clear that there is a mismatch in the spatial scale of the MODIS ET maps and the spatial scale represented by unsaturated flow models. Although the simulation results could be interpreted at the spatial scale that was simulated (50 m), the accuracy would not be as good as the coarsest scale of the data used (1 km). However, it is believed that the recharge pattern at the regional scale which is the focus of this study should not be affected by the mismatch in the spatial resolution.
Conclusions
Groundwater recharge has been mapped for many areas around the world. In comparison to the number of recharge mapping studies, there have been no studies on recharge uncertainty at the catchment scale using unsaturated flow modelling. As a first systematic and quantitative study, an attempt was made to examine the importance of uncertainty analysis for recharge assessment.
This study suggests that the common one-estimate-per-site approach can still identify the spatial pattern of groundwater recharge in the study site due to the presence of a precipitation pattern. However, uncertainty analysis not only identifies the spatial pattern, but also provides confidence levels in groundwater recharge critical for water resources management. This study also shows that large recharge absolute uncertainty occurs in areas with large water inputs but large relative uncertainty happens in areas with small recharge. Uncertainty analysis plays an important role in assessing different uncertainties and allows for prioritising future work.
In addition, this study found that measurements for model calibration are important for reducing recharge uncertainty. MODIS ET is a valuable data set as it is at the commensurate scale as the scale of recharge estimation. MODIS ET can reduce recharge uncertainty but cannot reduce it down to a plausible range reported for semi-arid regions. Future studies should attempt to reduce ET estimation error and collect data that can reflect on other water components (e.g., overland flow and storage change) in order to further reduce the recharge uncertainty.
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Acknowledgements
This study benefitted from discussions with Dr. John Hutson and Associate Professor Murk Bottema from Flinders University, and Professor Derek Eamus from the University of Technology Sydney.
Funding
The authors are grateful to the Murray-Darling Basin Authority for the financial support for this project.
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Xie, Y., Crosbie, R., Simmons, C.T. et al. Uncertainty assessment of spatial-scale groundwater recharge estimated from unsaturated flow modelling. Hydrogeol J 27, 379–393 (2019). https://doi.org/10.1007/s10040-018-1840-0
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DOI: https://doi.org/10.1007/s10040-018-1840-0