baseflow

In hydrological modeling, baseflow refers to the flow of water in rivers and streams that is sustained by the release of water from the groundwater. Or baseflow refers to the flow of water from an aquifer or deeper soil horizon to surface water, typically due to a head gradient between fully saturated soil and stream (Craig and Tea 2022) . It may be considered the sum of the contribution of deep groundwater exchange with a river and delayed storage (Craig and Tea 2022) .

It is always calculated (only) by the water in the ground layer \(W_{grnd}\), which can also be treated as part of \(W_{grnd}\). However, the impact of other RUs (response units) on the route to the river will be ignored.

So we can give the function from:

\[F_{base} = f_{baseflow}(D_{grnd})\]

to:

\[F_{base} = f_{baseflow}(W_{grnd}, C_{grnd}, M_{base}, ...)\] \[F_{base} = k^* W_{grnd} \quad {\rm or} \quad F_{base} = k^* M_{base}\] \[0 \leq k^* \leq 1\]

where

• \(W_{grnd}\) is ground_water_mm

• \(M_{base}\) is ground_potentialBaseflow_mm

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

• \(k^*\) is estimated ratio

The output density distribution from 7 methods:

Usage

baseflow_GR4J(ground_water_mm, ground_capacity_mm)

baseflow_GR4Jfix(ground_water_mm, ground_capacity_mm, param_baseflow_grf_gamma)

baseflow_SupplyRatio(ground_water_mm, param_baseflow_sur_k)

baseflow_SupplyPow(
  ground_water_mm,
  param_baseflow_sup_k,
  param_baseflow_sup_gamma
)

baseflow_MaxPow(
  ground_water_mm,
  ground_capacity_mm,
  ground_potentialBaseflow_mm,
  param_baseflow_map_gamma
)

baseflow_ThreshPow(
  ground_water_mm,
  ground_capacity_mm,
  ground_potentialBaseflow_mm,
  param_baseflow_thp_thresh,
  param_baseflow_thp_gamma
)

baseflow_Arno(
  ground_water_mm,
  ground_capacity_mm,
  ground_potentialBaseflow_mm,
  param_baseflow_arn_thresh,
  param_baseflow_arn_k
)

Arguments

ground_water_mm

(mm/m2/TS) water volume in groundLy

ground_capacity_mm

(mm/m2) water storage capacity in groundLy

param_baseflow_grf_gamma

<2, 7> exponential parameter for baseflow_GR4Jfix()

param_baseflow_sur_k

<0.01, 1> coefficient parameter for baseflow_SupplyRatio()

param_baseflow_sup_k

<0.01, 1> coefficient parameter for baseflow_SupplyPow()

param_baseflow_sup_gamma

<0, 1> exponential parameter for baseflow_SupplyPow()

ground_potentialBaseflow_mm

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

param_baseflow_map_gamma

<0.1, 5> exponential parameter for baseflow_MaxPow()

param_baseflow_thp_thresh

<0.1, 0.9> coefficient parameter for baseflow_ThreshPow()

param_baseflow_thp_gamma

<0.1, 5> exponential parameter for baseflow_ThreshPow()

param_baseflow_arn_thresh

<0.1, 0.9> coefficient parameter for baseflow_ThreshPow()

param_baseflow_arn_k

<0.1, 1> exponential parameter for baseflow_ThreshPow()

Value

ground_baseflow_mm (mm/m2/TS)

_GR4J (Perrin et al. 2003) :

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

• \(k^*\) is estimated ratio

_GR4Jfix (Perrin et al. 2003) :

This method based on _GR4J use a new parameter to replace the numer 4: \[F_{base} = k^* W_{grnd}\] \[k^* = 1 - \left[ 1 + \left(\frac{W_{grnd}}{C_{grnd}} \right)^\gamma \right]^{-1/\gamma}\] where

• \(\gamma\) is param_baseflow_grf_gamma

_SupplyRatio:

\[F_{base} = k W_{grnd}\] where

• \(k\) is param_baseflow_sur_k

_SupplyPow:

\[F_{base} = k(W_{grnd})^\gamma\] where

• \(k\) is param_baseflow_sup_k

• \(\gamma\) is param_baseflow_sup_gamma

_MaxPow:

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

• \(M_{base}\) is ground_potentialBaseflow_mm

• \(\gamma\) is param_baseflow_map_gamma

_ThreshPow

This method based on the _MaxPow and add the one threshold \(\phi_b\): \[F_{base} = 0, \quad \frac{W_{grnd}}{C_{grnd}}

• \(\phi_b\) is param_baseflow_thp_thresh

• \(\gamma\) is param_baseflow_thp_gamma

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

This method has also in two cases divided by a threshold water content \(\phi_b\): \[F_{base} = k M_{base} \frac{W_{grnd}}{C_{grnd}}, \quad \frac{W_{grnd}}{C_{grnd}}

• \(\phi_b\) is param_baseflow_arn_thresh

• \(k\) is param_baseflow_arn_k

References

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, Andréassian 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 .