capilarise

In hydrological modeling, capillary rise refers to the process by which water is drawn upward from groundwater (table) through the soil due to the force of capillary action. In conceptual watershed models, the capillary rise term often refers to a process that moves water from lower to higher soil water stores, which may also implicitly include lateral groundwater flow processes in a sloping domain.

It can be calculated by the water in the ground layer \(W_{grnd}\), which can also be treated as part of \(W_{grnd}\). There are not many methods to describe this process. Most HMs ignore this process, perhaps because it is not significant in most situations, or because the process of percolation can deal with this process at the same time.

So we can give the function from:

\[F_{capi} = f_{capirise}(D_{grnd}, D_{soil})\]

to:

\[F_{capi} = f_{capirise}(W_{grnd}, W_{soil}, C_{soil}, ...)\] \[F_{capi} \leq W_{grnd}\] \[F_{capi} \leq C_{soil} - W_{soil}\]

where

• \(F_{capi}\) is ground_capirise_mm

• \(W_{grnd}\) is ground_water_mm

• \(W_{soil}\) is water_soil_mm

• \(C_{soil}\) is capacity_soil_mm

The output density distribution from 4 methods:

Usage

capirise_HBV(
  ground_water_mm,
  soil_water_mm,
  soil_capacity_mm,
  soil_potentialCapirise_mm
)

capirise_HBVfix(
  ground_water_mm,
  soil_water_mm,
  soil_capacity_mm,
  soil_fieldCapacityPerc_1,
  soil_potentialCapirise_mm
)

capirise_AcceptRatio(
  ground_water_mm,
  soil_water_mm,
  soil_capacity_mm,
  soil_fieldCapacityPerc_1,
  param_capirise_acr_k
)

capirise_AcceptPow(
  ground_water_mm,
  soil_water_mm,
  soil_capacity_mm,
  soil_fieldCapacityPerc_1,
  param_capirise_acp_k,
  param_capirise_acp_gamma
)

Arguments

ground_water_mm

(mm/m2/TS) water volume in groundLy

soil_water_mm

(mm/m2) water volume in soilLy

soil_capacity_mm

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

soil_potentialCapirise_mm

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

soil_fieldCapacityPerc_1

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

param_capirise_acr_k

<0.01, 1> coefficient parameter capirise_AcceptRatio()

param_capirise_acp_k

<0.01, 1> coefficient parameter for capirise_AcceptPow()

param_capirise_acp_gamma

<0.01, 1> exponential parameter for capirise_AcceptPow()

Value

ground_capirise_mm (mm/m2/TS) capillary rise

_HBV (Lindstroem et al. 1997) :

\[F_{capi} = M_{capi} \left( 1 - \frac{W_{soil}}{C_{soil}} \right)\] where

• \(M_{capi}\) is soil_potentialCapirise_mm

_HBVfix (Lindstroem et al. 1997) :

\[F_{capi} = M_{capi} \left( 1 - \frac{W_{soil}}{k_{fc}C_{soil}} \right), \quad W_{soil}

• \(k_{fc}\) is soil_fieldCapacityPerc_1

_AcceptRatio:

\[F_{capi} = k \left( W_{soil} - k_{fc}C_{soil} \right), \quad W_{soil}

• \(k\) is param_capirise_acr_k

• \(k_{fc}\) is soil_fieldCapacityPerc_1

\[F_{capi} = k \left( W_{soil} - k_{fc}C_{soil} \right)^\gamma, \quad W_{soil}

• \(k\) is param_capirise_acp_k

• \(\gamma\) is param_capirise_acp_gamma

References

Lindstroem G, Johansson B, Persson M, Gardelin M, Bergstroem S (1997). “Development and Test of the Distributed HBV-96 Hydrological Model.” Journal of Hydrology, 201, 272--288. doi:10.1016/S0022-1694(97)00041-3 .