Lakes and wetlands

Lakes and wetlands storages and related fluxes are calculated based on section 4.6 of Müller Schmied et al 2021 [1]. In WaterGAP, lakes and wetlands are categorized into two types: local and global. Local water bodies receive inflow only from the runoff generated within the grid cell, while global water bodies additionally receive streamflow from upstream grid cells. All local (global) wetlands within a \(0.5° \times 0.5°\) grid cell are simulated as one local (global) wetland that covers a specified fraction of the cell, and all local lakes within a grid cell are aggregated and simulated as one. It is important to note that the water balance of global lakes is computed at the outflow cell. The location, area, and other attributes of these water bodies are defined using the Global Lakes and Wetland Database (GLWD) (Lehner and Döll, 2004). Area fractions of local lakes and wetlands, except for global lake (which have absolute area), are obtained from this database (see appendix D in Müller Schmied et al 2021), and this information is then used for the computation of the maximum capacity of the surface water bodies.

Note

Each grid cell can have a maximum of one local wetland, one global wetland, one local lake, and one global lake compartment. The lateral water flow within the cell follows the sequence shown in the watergap schematic diagram. For example, if there is a local lake compartment in a grid cell, it receives a fraction of the outflow from the groundwater compartment (under a humid climate) and of the fast surface and subsurface outflow. The outflow from the local lake becomes inflow to the local wetland if it exists, otherwise to the global lake

Water balance

Lakes and wetland storage \({S}_{l,w}\) \([m^3]\) is computed as

\[\frac{dS_l,w}{d_t} = {Q}_{in} + A(P − {E}_{pot}) − {R_g}_{l,w} − {NA}_{l} − {Q}_{out}\]

where \({Q}_{in}\) is inflow into the lake or wetland from upstream \([m^3 {d}^{-1}]\), \(A\) is a global (or local) water body surface area \([m^2]\) in the grid cell at time step \(t\), \(P\) is precipitation \([m^3 {d}^{-1}]\), \({E}_{pot}\) is potential evapotranspiration \([m^3 {d}^{-1}]\), \({R_g}_{l,w}\) is point source groundwater recharge from the water body (only in arid/semiarid regions) \([m^3 {d}^{-1}]\), \({NA}_{l}\) is net abstraction from lakes \([m^3 {d}^{-1}]\) and \({Q}_{out}\) is the outflow from the water body to other surface water bodies including river storage \([m^3 {d}^{-1}]\).

The area of these surface water bodies (except global lakes) varies temporally and is computed as:

\[A = r \times {A}_{max}\]

where \(r\) is the reduction factor \([–]\), and \({A}_{max}\) is the maximum extent of the water body \([m^2]\) and is computed as the \({A}_{grid} \times {A}_{fraction,l}\). \({A}_{grid}\) is the area of :math: 0.5° times 0.5° grid cell and \({A}_{fraction,l}\) is the area fraction of the surface waterbody \([m^2]\).

The reduction factor is applied differently for local and global lakes. In the case of local lakes, the reduction factor is used to reduce the lake area, while for global lakes, it is only used for reducing evaporation since the global lake area is assumed not to be dynamic. This would prevent the continuous decline of global lake levels in some cases such as (semi)arid regions. The reduction factor is computed for local and global lakes as:

\[r = 1- \left(\frac{|S_l - Sl,max|}{2({S}_{l,max})}\right)^p, 0 <= r <=1\]

where \(S_l\) is the volume of the water \([m^3]\) stored in the lake at time step t \(days\), \({S}_{l,max}\) is the maximum storage of the lake \([m^3]\). \({S}_{l,max}\) is computed based on \({A}_{max}\) and a maximum storage depth of 5 m, and p is the reduction exponent \([–]\), set to 3.32 [1].

Note

According to the lake reduction factor equation, the area is reduced by \(1 \%\) if \(S_l = 50 \% \times {S}_{l,max}\), by \(10 \%\) if \(S_l = 0\) and by \(100 \%\) if \(S_l=-{S}_{l,max}\).

In the case of local and global wetlands, the reduction factor is used to reduce the area. It is computed as:

\[r = 1- \left(\frac{|S_w - Sw,max|}{{S}_{w,max}}\right)^p, 0 <= r <=1\]

where \(S_w\) is the volume of the water \(m^3\) stored in the wetlands at time step t \(days\), \({S}_{w,max}\) is the maximum storage of the wetland \(m^3\). Reduction exponent p is set to 3.32 [1].

Note

Also by the wetland reduction factor equation, the area is reduced by \(10 \%\) if \(S_w = 50 \% \times {S}_{w,max}\), by \(70 \%\) if \(S_w = 10 \% \times {S}_{w,max}\).

Inflows

Computation of inflow \({Q}_{in}\) differs for local and global water bodies. For local lakes and wetlands, inflow comes only from local runoff within the same grid cell. A fraction \(fswb\) (see fractional routing scheme in section 4 of Müller Schmied et al. (2021) [1]) of the fast surface and subsurface runoff, as well as discharge from groundwater in humid grid cells, is directed to these local water bodies (see watergap schematic). If a grid cell contains both a local lake and a wetland, the outflow from the lake becomes the inflow to the wetland (see watergap schematic). On the other hand, global lakes and wetlands receive inflow from both local runoff and river inflow from upstream grid cells (see watergap schematic).

Outflows

Lakes and wetlands lose water through evaporation (\({E}_{pot}\)), which is assumed to be equal to the potential evapotranspiration computed using the Priestley–Taylor equation with an albedo of 0.08.

In arid and semiarid grid cells, lakes and wetlands are assumed to recharge the groundwater through focused groundwater recharge (\({R}_{{g}_{l,w}}\)). In humid areas, groundwater mostly recharges surface water bodies [2], as explained in Section 4.6.2 [1]. The focussed groundwater recharge \({R}_{{g}_{l,w}}\) is calculated as:

\[{R}_{{g}_{l,w}} = {k}_{{gw}_{l,w}} * {r} * {A}_{max}\]

where \({k}_{{gw}_{l,w}}\) is the groundwater recharge constant below lakes and wetlands \([0.01 {m}*{d}^{-1}]\).

It is assumed that water can be abstracted from lakes but not from wetlands (for more information on how net abrstactions are computed, see Net abstractions).

Outflow from lakes and wetlands is calculated as a function of \({S}_{l,w}\) (lakes and wetlands storage). The principal effect of a lake or wetland is to reduce the variability of streamflow, which can be simulated by computing the outflow \({Q}_{out}\) as:

\[{Q}_{out} = {k} * {S}_{ll, wl} * (\frac{{S}_{ll, wl}}{{S}_{ll, wl, max}})^{a},\]

where \({S}_{ll, wl}\) is the local lake or wetland storage [\({m}^{3}\)], and \({k}\) is the surface water outflow coefficient \([0.01 {d}^{-1}]\). The storage \({S}_{ll, wl}\) is computed based on \({A}_{max}\) and a maximum storage depth of \({5}\) [\({m}\)] for local lakes and \({2}\) [\({m}\)] for local wetlands. The exponent \({a}\) is set to \({1.5}\) for local lakes, based on the theoretical value of outflow over a rectangular weir, while an exponent of \({2.5}\) is used for local wetlands, leading to a slower outflow [3]. The outflow of global lakes and global wetlands is computed as:

\[{Q}_{out} = k * {S}_{lg,wg}\]

References

[1] (1,2,3,4,5)

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

[2]

Döll, P., Müller Schmied, H., Schuh, C., Portmann, F. T., and Eicker, A. (2014). Global-scale assessment of groundwater depletion and related groundwater abstractions: Combining hydrological modeling with information from well observations and GRACE satellites, Water Resour. Res., 50, 5698–5720, https://doi.org/10.1002/2014WR015595

[3]

Döll, P., Kaspar, F., and Lehner, B. (2003). A global hydrological model for deriving water availability indicators: model tuning and validation, J. Hydrol., 270, 105–134, https://doi.org/10.1016/S0022-1694(02)00283-4