Groundwater

Groundwater storage and related fluxes are calculated based on section 4.5 of Müller Schmied et al 2021 [1].

Water balance

Groundwater storage \(S_g\) \([m^3]\) is computed as

\[\frac{dS_g}{d_t} = {R}_{g} − {R}_{gl,res,w}− {Q}_{g} - {NA}_{g}\]

where \({R}_{g}\) is diffuse groundwater recharge from soil [\(m^3 {d}^{-1}\)]. \({R}_{gl,res,w}\) is point groundwater recharge from surface water bodies (lakes, reservoirs and wetlands) in (semi)arid areas [\(m^3 {d}^{-1}\)], \({Q}_{g}\) is groundwater discharge [\(m^3 {d}^{-1}\)] and \({NA}_{g}\) is net abstraction from groundwater [\(m^3 {d}^{-1}\)].

Inflows

Diffuse groundwater recharge from soil \([m^3 {d}^{-1}]\) is the main inflow in humid cells and point groundwater recharge from surface water bodies (lakes, reservoirs and wetlands) \({R}_{gl,res,w}\) \([m^3 {d}^{-1}]\) is the main inflow in (semi)arid grid cells. \({R}_{gl,res,w}\) varies temporally with the area of the surface water body, which depends on the respective water storage.

Outflows

Groundwater discharge, \(Q_g [m^3 {d}^{-1}]\) to surface waterbodies is an outflow which is computed as:

\[{Q}_{g} = {k}_{g} \times {S}_{g}\]

WaterGAP computes actual net abstraction from groundwater, \(NA_g [m^3 {d}^{-1}]\) from the potential net groundwater abstraction. The potential net abstraction from groundwater is computed from the Groundwater-Surface Water Use (GWSWUSE) model (see section 2 of Müller Schmied et al 2021 [1]). Details on the computation of the actual net abstaction groundwater can be found in the water abstractions section. net_abstractions:

Note

Groundwater storage is solved analytically for each timestep of one day to prevent numerical inaccuracies. This avoids the use of very small timesteps which will be computaionally expensive and hence lead to numerical problems.

Since \(R_g\) , \({R}_{gl,res,w}\) and \(NA_g\) are constant per each time step, they are grouped as one constant called Net recharge \((NR={R}_{g} − {R}_{gl,res,w} − {NA}_{g})\). The final balance euqation to solve is then:

\[\frac{dS_g}{d_t} = NR − {Q}_{g}\]

Analytical solution is given as:

\[S_g(t) = S_g(t-1) \times {exp}^{-k_g} + \frac{NR}{k_g} \times (1-{exp}^{-k_g})\]

References

[1] (1,2)

Müller Schmied, H., Cáceres, D., Eisner, S., Flörke, M., Herbert, C., Niemann, C., Peiris, T. A., Popat, E., Portmann, F. T., Reinecke, R., Schumacher, M., Shadkam, S., Telteu, C.E., Trautmann, T., & Döll, P. (2021). The global water resources and use model WaterGAP v2.2d: model description and evaluation. Geoscientific Model Development, 14(2), 1037–1079. https://doi.org/10.5194/gmd-14-1037-2021