OR/17/068 Lumped models

Collins, S. 2017. Incorporating groundwater flow in land surface models: literature review and recommendations for further work. British Geological Survey. (OR/17/068).

Lateral groundwater flow is not included in the majority of global hydrological models and LSMs. If the goal of modelling is to study groundwater depletion, a volume-based approach is sufficient and lateral flow not essential (Döll et al., 2009, 2012, 2014; Wada et al., 2010; Pokhrel et al, 2012). This section will compare lumped models in the literature by considering how water table dynamics, base flow generation and the groundwater–surface water interaction are simulated. Table 1 details a selection of lumped models used in either LSMs or global hydrological models.

Water table dynamics

The earliest LSMs, as well as most global-scale LSMs, apply a free gravity drainage boundary condition to the bottom of a fixed-depth soil column. This approach assumes that upward flux from the groundwater table is negligible, an assumption that breaks down when the water table is shallow. Including water table dynamics has been shown to improve river discharge simulations (Yeh and Eltahir, 2005; Koirala et al., 2014) and including capillary flux from groundwater increases evapotranspiration, with the global mean simulated to rise by up to 16% (Niu et al., 2007; Anayah et al., 2008; Yeh and Famiglietti, 2009; Koirala et al., 2014).

Gedney and Cox (2003) added an unconfined aquifer layer (12 m thick) under the lowest soil layer of an LSM, but assumed the aquifer to be in equilibrium with the lowest soil layer when the layer was not saturated (i.e. water table depth >3 m). Their model does not allow for the upward movement of water from the groundwater table, but achieved a better simulation of base flow and wetlands. Niu et al. (2007) developed a simple groundwater model comprising a single unconfined aquifer layer underneath the soil column, which exchanges recharge and capillary flux with the soil column. It explicitly solves the water table depth and then uses it as the lower boundary condition of the model. The model was incorporated into the National Center for Atmospheric Research Community Land Model (Bonan et al., 2002; Niu et al., 2007) and later into the Noah LSM (Niu et al., 2011). Other studies (Liang et al., 2003; Maxwell and Miller, 2005; Yeh and Eltahir, 2005a) incorporated a more realistic representation by explicitly coupling the saturated and unsaturated zones in order to explicitly determine the water table depth. To allow for a deeper water table, they added more nodes or layers to the bottom of the soil column: Yeh and Eltahir (2005a) used 50 soil layers. However, despite the extra layers, the maximum water table depth was still relatively shallow (<5 m).

More recently, Koirala et al. (2014) incorporated the groundwater representation developed by Yeh and Elathir (2005a) into the MATSIRO (Minimal Advanced Treatments of Surface Integration and Runoff, Takata et al., 2003) LSM. To account for deeper water tables in arid and semi-arid regions, they extended the bottom soil layer to a thickness of 30 m (total model thickness 40 m). That is, the saturated and unsaturated zones become decoupled only when the water table depth is below 40 m. Pokhrel et al. (2015) increased the thickness of the bottom layer of the same model to 90 m to allow for deep water tables resulting from abstraction.

Most lumped groundwater models in LSMs fail to consider groundwater abstraction. Two exceptions are the models developed by Döll et al. (2012, 2014) (WaterGAP, see below for more details) and Pokhrel et al. (2015). Döll et al. (2012, 2014) did not simulate groundwater table dynamics, but abstractions were removed from groundwater storage. Pokhrel et al. (2015) were able to simulate changes in the water table depth caused by pumping. This was undertaken by adding in flows at a 1° x 1° scale. Groundwater withdrawal was estimated as the water demand in excess of surface water availability, with water demand being a combination of consumptive agricultural, domestic and industrial use. Irrigation water demand was calculated with the model’s irrigation module and domestic and industrial use were obtained from the AQUASTAT database (http://www.fao.org/nr/water/aquastat/main/index.stm). Pokhrel et al. (2010) evaluated the model’s simulated groundwater withdrawal against global-scale groundwater withdrawal data (country based) from Wada et al. (2010), who compiled data from the International Groundwater Resources Assessment Center (https://ggis.un-igrac.org/ggis-viewer/viewer/exploreall/public/default).

Base flow generation and parameterisation

In the WaterGAP global hydrological model used by Döll et al. (2012, 2014), groundwater is represented as a linear reservoir, in which the constant is fixed globally (Müller Schmied et al., 2014). Yeh and Eltahir (2005a) represent groundwater as a non-linear reservoir, having derived a relationship between water table depth and base flow from regression analysis with streamflow as a surrogate for base flow. In a second paper, Yeh and Eltahir (2005b) adapted their model to derive base flow using a statistical-dynamical approach, which they claim accounts for sub-grid heterogeneity in water table depth. Their equation includes the gamma function, which has two parameters, and two other conceptual parameters that cannot be measured and must be calibrated against observed streamflow and inferred base flow information. Yeh and Eltahir (2005b) parameterised the model for locations in Illinois, USA. Koirala et al. (2014) used the same method to study 20 different river basins across the globe. They derived an equation for one parameter based on precipitation and its seasonal variation in Illinois, which was found to be accurate also for uncalibrated basins across the globe. The second parameter was deemed insensitive and fixed (Koirala et al., 2014). In the authors’ global model (Pokhrel et al., 2015), the method was simplified to a linear relationship between water table depth and base flow, containing the same two parameters as the previous equation: an outflow constant and a water table depth threshold at which base flow is generated. Pokhrel et al. (2015) used the same values for these parameters as Koirala et al. (2014). Yeh and Eltahir (2005b) and Koirala et al. (2014) found their models to have low sensitivity to specific yield. Yeh and Eltahir (2005a) fixed specific yield to a value typical of the area they studied, and Niu et al. (2007) and Pokhrel et al. (2015) set it to be globally constant.

Many authors base their derivation of subsurface runoff on the TOPMODEL approach (Beven and Kirkby, 1976), with flow decreasing exponentially as depth to the water table increases (e.g. Gedney and Cox, 2003; Maxwell and Miller, 2005; Niu et al., 2007, 2011). The TOPMODEL-based equation for base flow of Niu et al. (2007, 2011) contains two parameters, which they calibrated globally to runoff data in sensitivity analyses. Maxwell and Miller (2005) had only a single calibration parameter, the saturated hydraulic conductivity at the bottom soil layer.

Groundwater–surface water interaction

One obvious disadvantage of lumped models is their inability to represent groundwater–surface water interactions. All models mentioned in this section have a scheme for generating base flow from the groundwater store, but the model of Döll et al. (2014) is the only one that can simulate recharge from surface water bodies. Their method is, however, very simplified: in areas where precipitation is <50% of potential evapotranspiration, there is a constant recharge rate per unit area of the surface water body. The rate of recharge varies temporally because the surface water bodies change size with the amount of stored water.

Table 1    Selection of lumped models used in global hydrological models or land surface models.

Author	Model	Year	Capillary rise from water table	Water table dynamics	Base flow run off scheme	Groundwater abstraction	Recharge from surface water bodies	Irrigation return flow
Döll et al.	WaterGAP Global Hydrological Model (resolution 0.5˚ x 0.5˚, roughly 55 km x 55 km)	2009			Linear reservoir			×
		2012			Linear reservoir	×		×
		2014			Linear reservoir	×	×	×
Niu et al.	NOAH-MP (part of WRF model)	2007	×	×	TOPMODEL-based, exponential with WTD
		2011	×	×	TOPMODEL-based, exponential with WTD
Yeh and Eltahir	Land Surface Transfer Scheme Groundwater (LSXGW)	2005a	×	×	Non-linear reservoir
Gedney and Cox	Hadley Centre Atmospheric Climate Model (HadAM3) with the Met Office Surface Exchange Scheme (MOSES)	2003		×	TOPMODEL-based, exponential with WTD
Pokhrel et al.	MATSIRO	2015	×	×	Linear relationship between WTD and base flow	×		×
Maxwell and Miller	Common Land Model (LSM) coupled to ParFLow (groundwater model)	2005	×	×	Simplified TOPMODEL approach, exponential with WTD
Koirala et al.	MATSIRO	2014	×	×	Statistical-dynamical approach said to account for sub-grid heterogeneity (see Yeh and Eltahir, 2005b)

WTD – water table depth