Soil#

This module computes soil storage and related fluxes for all grid cells based on section 4.4 of Müller Schmied et al 2021 [1].

Note

The computation order for the soil storage module is as follows: First, immediate runoff (R1) is calculated. After, effective precipitation is reduced by the immediate runoff. Then, runoff from soil water overflow (R2) is computed. After, daily runoff (R3) is calculated followed by actual evapotranspiration. Soil storage is updated. Afterwards, ground water recharge is calculated based on daily runoff. Then, total daily runoff from land (RL) is computed as daily runoff (R3) + immediate runoff (R1) + soil water overflow (R2).

Note: Total daily runoff from land is corrected with an areal correction factor (CFA) (if gamma is insufficient to fit simulated discharge). To conserve water balance, actual evapotranspiration is also corrected with CFA. After evapotranspiration correction, soil storage, total daily runoff from land and groundwater recharge are adjusted as well. Finally, Surface runoff \(({R}_{s})\) is calculated as total daily runoff from land minus groundwater recharge.

Water balance#

Soil storage \(S_s\) \([mm]\) is calculated as:

\[\frac{dS_s}{d_t} = {P}_{eff} − {R}_{l}− {E}_{s}\]

where \({P}_{eff}\) is effective precipitation \([mm/d]\), \({R}_{l}\) is total runoff from land \([mm/d]\) and \({E}_{s}\) is the actual evapotranspiration from soil \([mm/d]\).

Inflows#

Effective precipitation \({P}_{eff}\) is calculated as:

\[{P}_{eff} = {P}_{t} − {P}_{sn} + {M}\]

where \({P}_{t}\) is throughfall \([mm/d]\), \({P}_{sn}\) is snowfall \([mm/d]\) and \({M}\) is snow melt \([mm/d]\).

Actual evapotranspiration \({E}_{s}\) from soil \([mm/d]\) is calculated as:

\[{E}_{s} = min\biggl(({E}_{pot} - E_c) , ({E}_{pot,max} - E_c) \times \frac{S_s}{S_s,max} \biggr)\]

where \({E}_{pot}\) is potential evapotranspiration \([mm/d]\), \({E}_{c}\) is canopy evaporation \([mm/d]\) and \({S}_{s,max}\) is the maximum soil water content \([mm]\) derived as a product of total available water capacity in the upper meter of the soil [2] and land-cover-specific rooting depth (Table C2 [1]). The maximum potential evapotranspiration \({E}_{pot,max}\) is set to \(15 {mm}/{d}\) globally.

Total daily runoff from land (RL) is calculated as:

\[RL = R1 + R3 + R2\]

where immediate runoff from urban areas (R1) is computed as:

\[{immediate \: runoff} = 0.5 \times {P}_{eff} \times fraction \: of \: build \: up \: area\]

and where soil water overflow (R2) is calculated as:

\[\begin{split}{P}_{eff} = \begin{cases} {P}_{eff} +{S}_{s,p} - {S_s,max}, & \text{if } ({P}_{eff} + {S}_{s,p})>{S_s}_{,max} \\ 0, & \text{otherwise} \end{cases}\end{split}\]

where \({P}_{eff}\) is effective precipitation, \({S}_{s,p}\) and \({S}_{s,max}\) is soil storage of the previous day and maximum soil storage respectively.

Daily runoff from soil (\({R3}\)) \([mm/day]\) is calculated following Bergström (1995) [3] as:

\[R3 = {P}_{eff} \biggl(\frac{S_s}{S_s,max}\biggr)^\Gamma\]

where Gamma is the runoff coefficient \([–]\). This parameter, which varies between :math`0.1` and \(5.0\), is used for calibration. Together with soil saturation, it determines the fraction of \({P}_{eff}\) that becomes \({R3}\).

Note

If the sum of \({P}_{eff}\) and \({S}_{s}\) of the previous day exceed \({S}_{s,max}\), the overflow \({R2}\) is added to daily runoff \({R3}\) and immediate runoff \({R1}\) to total daily runoff from land \({R}_{L}\).

\({R3}\) is partitioned into fast surface and subsurface runoff \({R}_{s}\) and diffuse groundwater recharge \({R}_{g}\) according to the heuristic scheme.

\[{R}_{g} = min\biggl({R}_{gmax} , ({f}_{g} \times {R3} \biggr)\]

where \({R}_{gmax}\) is soil-texture-specific maximum groundwater recharge with values of 7, 4.5 and 2.5 \([mm/d]\) for sandy, loamy and clayey soils, respectively, and \({f}_{g}\) is the groundwater recharge factor ranging between 0 and 1. \({f}_{g}\) is determined based on relief, soil texture, aquifer type, and the existence of permafrost or glaciers [4].

Note

If a grid cell is defined as (semi)arid and has coarse (sandy) soil, groundwater recharge will only occur if precipitation exceeds a critical value of 12.5 \([mm/d]\), otherwise the water remains in the soil. The fraction of \({R}_{3}\) that does not recharge the groundwater becomes \({R}_{s}\), which recharges surface water bodies and the river compartment.

If the gamma parameter is not enough to match the observed discharge, the total daily runoff from land is adjusted by multiplying it with a real correction factor (CFA). To conserve mass balance actual total evaporation from land (\({E}_{s}\)) is corrected such that when a real correction factor is increased or reduced to increase runoff, actual total evaporation will also be reduced or increased respectively.

\[\begin{split}RL &= P - E_s - \frac{dS}{dt}, (dt=1), eqn.1, \\ RL \times CFA &= P - {E}_{s,corr} - dS,eqn2,\end{split}\]

substituting \(RL\) from equation 2 into equation 1:

\[\begin{split}P - {E}_{s,corr} - ds &= CFA (P - E_s - ds), \\ {E}_{s,corr} &= dS(CFA-1) - P(CFA-1) + E_s(CFA)\end{split}\]

where \({P}\) is precipitation \([mm/day]\).

Note

Surface runoff \(({R}_{s})\) is finally calculated as total daily runoff from land minus groundwater recharge.

References#