River#

River storage and related fluxes are calculated based on section 4.7 of Müller Schmied et al 2021 [1].

river.river_water_balance(x, y, river_storage, river_inflow, outflow_constant, stat_corr_fact, accumulated_unsatisfied_potential_netabs_sw, minstorage_volume)[source]#

Compute River water balance including storages and fluxes.

Parameters:
xint

Latitude index of cell

yint

Longitude index of cell

river_storagefloat

Daily river storage, Unit: [km^3]

river_inflowfloat

Daily river inflow, Unit: [km^3/day]

outflow_constantfloat

River outflow constant (river_velocity / river_length), Unit: [1/day]

stat_corr_factTYPE

Station correction factor to correct streamflow values, Unit: [-]

accumulated_unsatisfied_potential_netabs_sw: float

Accumulated unsatisfied potential net abstraction from surface water, Unit: [km^3/day].

minstorage_volume: float

Volumes at which storage is set to zero, units: [km3]

Returns:
river_storagefloat

Daily river storage, Unit: [km^3]

streamflowfloat

Daily streamflow, Unit: [km^3/day]

accumulated_unsatisfied_potential_netabs_sw: float

Accumulated unsatisfied potential net abstraction after satisfaction from river, Unit: [km^3/day].

actual_use_sw: float

Actual netabstraction from river storage, Unit: [km^3/day].

Water balance#

River storage \(S_r\) \([m^3]\) is computated as

\[\frac{dS_r}{d_t} = {Q}_{r,in} − {Q}_{r,out} − {NA}_{s,r}\]

where \({Q}_{r,in}\) is inflow into the river compartment [\({m}^{3} {d}^{-1}\)], \({Q}_{r,out}\) is the streamflow [\({m}^{3} {d}^{-1}\)], and \({NA}_{s,r}\) is the net abstractions of surface water from the river [\({m}^{3} {d}^{-1}\)].

Inflows#

The inflow \({Q}_{r,in}\) into the river compartment (if there are no surface water bodies) is the sum of soil surface runoff \(({R}_{s})\), groundwater discharge \(({Q}_{g})\), and upstream streamflow. Otherwise fraction of \({R}_{s}\) and \({Q}_{g}\) (in humid cells) is routed through the surface water bodies (See: Model Schematic). The outflow from the surface water body preceding the river compartment then becomes part of \({Q}_{r,in}\). In addition, negative net abstractions \(({NA}_{s})\) values due to high return flows from irrigation with groundwater lead to a net increase in storage. Thus, if no surface water bodies exist in the cell, negative \({NA}_{s}\) is added to \({Q}_{r,in}\).

Outflows#

river.river_velocity(x, y, river_storage, river_length, river_bottom_width, roughness, roughness_multiplier, river_slope)[source]#

Compute river velocity for grid cells.

Parameters:
xint

Latitude index of cell

yint

Longitude index of cell

river_storagefloat

Daily river storage, Unit: [km^3]

river_lengthfloat

River length, Unit: [km]

river_bottom_widthfloat

River bottom width, Unit: [km]

roughnessfloat

Roughness of river bed, Unit: [-]

roughness_multiplierTYPE

Roughness of river bed multiplier, Unit: [-]

river_slopeTYPE

River slope, Unit: [-]

Returns:
river_velocityfloat

River velocity, Unit: [km/day]

outflow_constantfloat

River outflow constant (river_velocity / river_length), Unit: [1/day]

\({Q}_{r,out}\) is defined as the streamflow or river discharge that leaves a cell and is transported to the next cell downstream.

This is calculated as:

\[{Q}_{r,out} = \frac{v}{l} * {S}_{r}\]

where \({v}\) \([m/s]\) is the velocity of the river flow, and \({l}\) is the river length \([m]\). \({l}\) is calculated as the product of the cell’s river segment length, derived from the HydroSHEDS drainage direction map [2], and a meandering ratio specific to that cell described in Verzano et al., 2012 [3].

The velocity \({v}\) is calculated using the Manning–Strickler equation:

\[{v} = {n}^{-1} * {R}_{h}^{\frac{3}{2}} * {s}^{\frac{1}{2}}\]

where \({n}\) is river bed roughness \([–]\), \({R}_{h}\) is the hydraulic radius of the river channel \([m]\) and \({s}\) is river bed slope \([{m}*{m}^{-1}]\) [1] .

Daily varying \({R}_{h}\) is calculated assuming a trapezoidal river cross section with a slope of 0.5. \({R}_{h}\) then can be calculated as a function of daily varying river depth \({D}_{r}\) and temporally constant bottom width \({W}_{r,bottom}\) [3]. WaterGAP implements a consistent method for determining daily width and depth as a function of river water storage. Bankfull flow conditions are assumed to occur at the initial time step and the initial volume of water stored in the river is calculated as:

\[{S}_{r,max} = {\frac{1}{2}} * {l} * {D}_{r,bf} * ({W}_{r,bottom} + {W}_{r,bf})\]

where \({S}_{r,max}\) is the maximum volume of water that can be stored in the river at bankfull depth \([{m}^3]\), \({D}_{r,bf}\) \([{m}]\) and \({W}_{r,bf}\) \([{m}]\) are river depth and top width at bankfull conditions, respectively, and \({W}_{r,bottom}\) is river bottom width \([{m}]\). River water depth \({D}_{r}\) \([{m}]\) is simulated to change at each time step with actual \({S}_{r}\) as:

\[{D}_{r} = - {\frac{{W}_{r,bottom}}{4}} + {\sqrt{{{W}_{r,bottom}} * {\frac{{W}_{r,bottom}}{16}} + {0.5} * {\frac{{S}_{r}}{l}}}}\]

WaterGap also computes net cell runoff \({R}_{n,c}\) \([{m}*{m*d}^{-1}]\), which is the part of the cell precipitation that has neither been evapotranspirated nor stored. It is calculated as:

\[{R}_{n,c} = {\frac{{Q}_{r,in}-{Q}_{r,out}}{{A}_{cont}}} * {10}^{9}\]

where \({A}_{cont}\) is the continental area (0.5° times 0.5° grid cell area minus ocean area) of the grid cell (\([m^2]\)). Renewable water resources are calculated as long-term annual mean \({R}_{nc}\) under naturalized conditions (without human impact). It is possible for renewable water resources to be negative if evapotranspiration in a grid cell is higher than precipitation due to evapotranspiration from global lakes, reservoirs or wetlands that receive water from upstream cells.

References#