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lateral flux

Source: R/RcppExports.R
lateral.Rd

In hydrological modeling, lateral flow refers to the process by which water flows horizontally through the soil or aquifer, rather than vertically. It is typically represented by a loss term in the water balance equation, so it also named as groundwater exchange (e.g. GR4J (Perrin et al. 2003) ). The flux of lateral exchange is always calculated (only) by the water in the ground layer \(W_{grnd}\). Unlike other fluxes, the lateral exchange can be positive or negative, with positive indicating a supply from other regions and negative indicating distribution to other regions.

This process is so flexible that we must carefully use it, because it can easily destroy the waster balance in the research catchment.

\[F_{ltrl} = f_{lateral}(D_{grnd})\]

to:

\[F_{ltrl} = f_{lateral}(W_{grnd}, C_{grnd}, ...)\]

where

  • \(W_{grnd}\) is ground_water_mm

  • \(C_{grnd}\) is ground_capacity_mm, but not all the methods need the \(C_{grnd}\)

The output density distribution from 6 methods:

Usage

lateral_SupplyPow(
  ground_water_mm,
  ground_capacity_mm,
  param_lateral_sup_k,
  param_lateral_sup_gamma
)

lateral_SupplyRatio(ground_water_mm, param_lateral_sur_k)

lateral_GR4J(ground_water_mm, ground_capacity_mm, ground_potentialLateral_mm)

lateral_GR4Jfix(
  ground_water_mm,
  ground_capacity_mm,
  ground_potentialLateral_mm,
  param_lateral_grf_gamma
)

lateral_ThreshPow(
  ground_water_mm,
  ground_capacity_mm,
  ground_potentialLateral_mm,
  param_lateral_thp_thresh,
  param_lateral_thp_gamma
)

lateral_Arno(
  ground_water_mm,
  ground_capacity_mm,
  ground_potentialLateral_mm,
  param_lateral_arn_thresh,
  param_lateral_arn_k
)

Arguments

ground_water_mm

(mm/m2/TS) water volume in groundLy

ground_capacity_mm

(mm/m2) water storage capacity in groundLy

param_lateral_sup_k

<-1, 1> coefficient parameter for lateral_SupplyPow()

param_lateral_sup_gamma

<0.01, 5> parameters for lateral_SupplyPow()

param_lateral_sur_k

<-2, 1> coefficient parameter for lateral_SupplyRatio()

ground_potentialLateral_mm

<-7, 7> (mm/m2/TS) potential lateral flow

param_lateral_grf_gamma

<0.01, 5> parameter for lateral_GR4Jfix()

param_lateral_thp_thresh

<0.1, 0.9> coefficient parameter for lateral_ThreshPow()

param_lateral_thp_gamma

<0.1, 5> exponential parameter for lateral_ThreshPow()

param_lateral_arn_thresh

<0.1, 0.9> coefficient parameter for lateral_ThreshPow()

param_lateral_arn_k

<0.1, 1> exponential parameter for lateral_ThreshPow()

Value

lateral_mm (mm/m2)

_SupplyPow:

\[F_{ltrl} = k \left( \frac{W_{grnd}}{C_{grnd}} \right)^\gamma W_{grnd}\] where

  • \(k\) is param_lateral_sup_k

  • \(\gamma\) is param_lateral_sup_gamma

_SupplyRatio:

\[F_{ltrl} = k * W_{grnd}\] where

  • \(k\) is param_lateral_sur_k

_GR4J (Perrin et al. 2003) :

\[F_{ltrl} = M_{ltrl} \left( \frac{W_{grnd}}{C_{grnd}} \right)^{7/2} \] where

  • \(M_{ltrl}\) is ground_potentialLateral_mm

_GR4Jfix (Perrin et al. 2003)

based on _GR4J use a new parameter to replace the numer 4: \[F_{ltrl} = M_{ltrl} \left( \frac{W_{grnd}}{C_{grnd}} \right)^\gamma \] where

  • \(\gamma\) is param_lateral_grf_gamma

_ThreshPow

based on the _GR4Jfix and add the one threshold \(\phi_b\): \[F_{ltrl} = 0, \quad \frac{W_{grnd}}{C_{grnd}} < \phi_b\] \[F_{ltrl} = M_{ltrl} \left(\frac{\frac{W_{grnd}}{C_{grnd}} - \phi_b}{1-\phi_b} \right)^\gamma, \quad \frac{W_{grnd}}{C_{grnd}} \geq \phi_b\] where

  • \(\phi_b\) is param_lateral_thp_thresh

  • \(\gamma\) is param_lateral_thp_gamma

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

has also in two cases divided by a threshold water content \(\phi_b\): \[F_{ltrl} = k M_{ltrl} \frac{W_{grnd}}{C_{grnd}}, \quad \frac{W_{grnd}}{C_{grnd}} < \phi_b\] \[F_{ltrl} = k M_{ltrl} \frac{W_{grnd}}{C_{grnd}} + (1-k) M_{ltrl} \left(\frac{W_{grnd} - W_s}{C_{grnd} - W_s} \right)^2, \quad \frac{W_{grnd}}{C_{grnd}} \geq \phi_b\] \[W_s = k C_{grnd}\] where

  • \(\phi_b\) is param_lateral_arn_thresh

  • \(k\) is param_lateral_arn_k

References

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 .