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percolation

Source: R/RcppExports.R
percola.Rd

In hydrological modeling, percolation refers to the process by which water from the soil moves downward through the pores and cracks in the soil or rock. This process is physically driven by a moisture gradient, but this is often simplified in conceptual percolation models (Craig and Tea 2022) . It can be calculated by the water in the soil layer \(W_{soil}\), it can also be tread as the part of the \(W_{soil}\).

So we can give the function from:

\[F_{prcl} = f_{percola}(D_{grnd}, D_{soil})\]

to:

\[F_{prcl} = f_{percola}(W_{soil}, C_{soil}, W_{grnd}, C_{grnd}, ...) = k^* W_{soil}\] \[F_{prcl} \leq W_{soil}\] \[F_{prcl} \leq C_{grnd} - W_{grnd}\]

where

  • \(F_{prcl}\) is soil_percola_mm

  • \(W_{soil}\) is water_soil_mm

  • \(C_{soil}\) is capacity_soil_mm

  • \(W_{grnd}\) is ground_water_mm

  • \(C_{grnd}\) is capacity_water_mm

  • \(k^*\) is estimated ratio

The output density distribution from 8 methods:

Usage

percola_GR4J(soil_water_mm, soil_capacity_mm)

percola_GR4Jfix(soil_water_mm, soil_capacity_mm, param_percola_grf_k)

percola_MaxPow(
  soil_water_mm,
  soil_capacity_mm,
  soil_potentialPercola_mm,
  param_percola_map_gamma
)

percola_ThreshPow(
  soil_water_mm,
  soil_capacity_mm,
  soil_potentialPercola_mm,
  param_percola_thp_thresh,
  param_percola_thp_gamma
)

percola_Arno(
  soil_water_mm,
  soil_capacity_mm,
  soil_potentialPercola_mm,
  param_percola_arn_thresh,
  param_percola_arn_k
)

percola_BevenWood(
  soil_water_mm,
  soil_capacity_mm,
  soil_fieldCapacityPerc_1,
  soil_potentialPercola_mm
)

percola_SupplyPow(
  soil_water_mm,
  soil_capacity_mm,
  param_percola_sup_k,
  param_percola_sup_gamma
)

percola_SupplyRatio(soil_water_mm, param_percola_sur_k)

Arguments

soil_water_mm

(mm/m2) water volume in soilLy

soil_capacity_mm

(mm/m2) average soil Capacity (maximal storage capacity)

param_percola_grf_k

<0.01, 1> coefficient parameter for percola_GR4Jfix()

soil_potentialPercola_mm

<0.01, 7> (mm/m2/TS) potential percolation

param_percola_map_gamma

<0.1, 5> exponential parameter for percola_MaxPow()

param_percola_thp_thresh

<0.1, 0.9> coefficient parameter for percola_ThreshPow()

param_percola_thp_gamma

<0.1, 5> exponential parameter for percola_ThreshPow()

param_percola_arn_thresh

<0.1, 0.9> coefficient parameter for percola_ThreshPow()

param_percola_arn_k

<0.1, 1> exponential parameter for percola_ThreshPow()

soil_fieldCapacityPerc_1

<0, 1> the relative ratio (\(\theta_fc / \theta^*\)) that the water content can drainage by gravity

param_percola_sup_k

<0.01, 1> coefficient parameter for percola_SupplyPow()

param_percola_sup_gamma

<0, 7> parameter for percola_SupplyPow()

param_percola_sur_k

<0.01, 1> coefficient parameter for percola_SupplyRatio()

Value

percola_mm (mm/m2)

_GR4J (Perrin et al. 2003) :

\[k^* = 1 - \left[ 1 + \left(\frac{4}{9} \frac{W_{soil}}{C_{soil}} \right)^4 \right]^{-1/4}\] where

  • \(k^*\) is estimated ratio

_GR4Jfix (Perrin et al. 2003) :

\[k^* = 1 - \left[ 1 + \left(k \frac{W_{soil}}{C_{soil}} \right)^4 \right]^{-1/4}\] where

  • \(k\) is param_percola_grf_k

_MaxPow:

\[F_{prcl} = M_{prcl} \left(\frac{W_{soil}}{C_{soil}} \right)^\gamma\] where

  • \(M_{prcl}\) is soil_potentialPercola_mm

  • \(\gamma\) is param_baseflow_map_gamma

_ThreshPow

based on the _MaxPow and add the one threshold \(\phi_b\): \[F_{prcl} = 0, \quad \frac{W_{soil}}{C_{soil}} < \phi_b\] \[F_{prcl} = M_{prcl} \left(\frac{\frac{W_{soil}}{C_{soil}} - \phi_b}{1-\phi_b} \right)^\gamma, \quad \frac{W_{soil}}{C_{soil}} \geq \phi_b\] where

  • \(\phi_b\) is param_percola_thp_thresh

  • \(\gamma\) is param_percola_thp_gamma

_Arno (Franchini and Pacciani 1991; Liang et al. 1994)

has also in two cases divided by a threshold water content \(\phi_b\): (This method is actually not the original method, but an analogy with baseflow_Arno) \[F_{prcl} = k M_{prcl} \frac{W_{soil}}{C_{soil}}, \quad \frac{W_{soil}}{C_{soil}} < \phi_b\] \[F_{prcl} = k M_{prcl} \frac{W_{soil}}{C_{soil}} + (1-k) M_{prcl} \left(\frac{W_{soil} - W_s}{C_{soil} - W_s} \right)^2, \quad \frac{W_{soil}}{C_{soil}} \geq \phi_b\] \[W_s = k C_{soil}\] where

  • \(\phi_b\) is param_percola_arn_thresh

  • \(k\) is param_percola_arn_k

_BevenWood (Beven and Wood 1983; Beven et al. 1995) :

\[k = \frac{W_{soil}}{C_{soil} - W_{soil}} \quad {\rm and} \quad k \leq 1\] \[F_{prcl} = k M_{prcl}\] where

  • \(k_{fc}\) is soil_fieldCapacityPerc_1

  • \(\gamma\) is param_percola_sup_gamma

_SupplyPow:

\[k^* = k \left(\frac{W_{soil}}{C_{soil}} \right)^\gamma\] where

  • \(k\) is param_percola_sup_k

  • \(\gamma\) is param_percola_sup_gamma

_SupplyRatio:

\[k^* = k\] where

  • \(k\) is param_percola_sur_k

References

Beven K, Lamb R, Quinn P, Romanowicz R, Freer J (1995). “TOPMODEL.” Computer models of watershed hydrology., 627--668.

Beven K, Wood EF (1983). “Catchment Geomorphology and the Dynamics of Runoff Contributing Areas.” Journal of Hydrology, 65(1), 139--158. ISSN 0022-1694, doi: 10.1016/0022-1694(83)90214-7 .

Craig JR, Tea RD (2022). “Raven User's and Developer's Manual (Version 3.5).”

Franchini M, Pacciani M (1991). “Comparative Analysis of Several Conceptual Rainfall-Runoff Models.” Journal of Hydrology, 122(1), 161--219. ISSN 0022-1694, doi: 10.1016/0022-1694(91)90178-K .

Liang X, Lettenmaier D, Wood E, Burges S (1994). “A Simple Hydrologically Based Model of Land Surface Water and Energy Fluxes for GSMs.” J. Geophys. Res., 99. doi: 10.1029/94JD00483 .

Perrin C, Michel C, Andr攼㸹assian V (2003). “Improvement of a Parsimonious Model for Streamflow Simulation.” Journal of Hydrology, 279(1-4), 275--289. ISSN 00221694, doi: 10.1016/S0022-1694(03)00225-7 .