Garden with Insight v1.0 Help: Hydrology - Percolation & Lateral Subsurface Flow

The EPIC percolation component uses a storage routing technique to simulate flow through soil layers. Flow from a soil layer occurs when soil water content exceeds field capacity. Water drains from the layer until the storage returns to field capacity. The reduction in soil water is simulated with the following equation

SW(l) = (SW(0l) - FC(l)) * exp(-24 / TT(l)) + FC(l) (Equation 39)

where SW and SW(0) are the soil water contents at the end and the start of time interval delta-t (24 hr) and TT is travel time through layer l in hr.

Thus, daily percolation can be computed by taking the difference between SW and SW(0)

O(l) = (SW(0l) - FC(l)) * (1.0 - exp(-24 / TT(l))) (Equation 40)

where O is the percolation rate for layer l in mm/day.

Percolation travel time through a layer is computed with the linear storage equation [Equation 41] where PO is the porosity in mm, FC is field capacity in mm, and SC is saturated conductivity in mm/hr.

Equation 41:

TT = (PO - FC) / SC
Code:
same
Variables:
TT = PercolationTravelTimeForLayer_hr
PO = porosity_mm
FC = fieldCapacity_mm
SC = saturatedConductivity_mmPhr

Equations 42 and 43 are discussed later (after equation 48).

Lateral Subsurface Flow is calculated simultaneously with percolation. The lateral flow function (similar to equation 40) is expressed in the equation

QH(l) = (SW(0l) - FC(l)) * (1.0 - exp(-24 / TT(Hl))) (Equation 44)

where QH is the lateral flow rate for soil layer l in mm/day and TT(Hl) is the lateral flow travel time in days.

The lateral flow travel time is estimated for each soil layer using the equation [Equation 45] where S is the land surface slope in m/m.

Equation 45:

TT(H) = TT / S
Code:
TT(H) = (po-fc) / (SC * S)
unless the layer has a drainage system, when TT(H) is
(po-fc) / ((po-wp) / (24 * timeForDrainageSystemToReducePlantStress_days))
TT = (po-fc) / SC
TT(H) = TT / S
Variables:
TT(H) = lateralFlowTravelTime_hr
TT = percolationTravelTime_hr
S = slopeSteepness_mPm

Equations 40 and 44 must be solved simultaneously to avoid one process dominating the other, simply because the solution occurs first. Thus, an equation for the sum of percolation and lateral flow is written as [Equation 46].

Equation 46:

O + QH = (SW - FC) * (1.0 - exp(-24 / TT) * exp(-24 / TT(H)))
Code:
if 24 / TT + 24 / TT(H) > 20.0
O + QH = SW - FC
else
O + QH = (SW - FC) * (1.0 - exp(-(24 / TT + 24 / TT(H))))
Variables:
O + QH = PercolationAndLatFlowForLayer_mm
SW(0) = waterContent_mm
FC = fieldCapacity_mm
TT = percolationTravelTime_hr
TT(H) = lateralFlowTravelTime_hr

Taking the ratio of QH/O and substituting the resulting QH into equation 46 leads to the equation

O + O * (1.0 - exp(-24/TT(Hl))/(1.0 - exp(-deltat-t/TT(l)))) =
(SW(0l) - FC(l)) * (1.0 - exp(-24/TT(l) * exp(-24/TT(Hl)))) (Equation 47)

Solving for O gives the final percolation equation [Equation 48].

Equation 48:

O = ((SW - FC) * (1.0 - exp(-24 / TT) * exp(-24 / TT(H))))
/ (1.0 + (1.0 - exp(-24 / TT(H))) / (1.0 - exp(-24 / TT)))
Code:
O + QH = (SW - FC) * (1.0 - exp(-(24 / TT + 24 / TT(H))))
O = (O + QH) / (1.0 + (24 / TT(H)) / (24 / TT))
Variables:
O = PercolationForLayer_mm
SW(0) = waterContent_mm
FC = fieldCapacity_mm
TT = percolationTravelTime_hr
TT(H) = lateralFlowTravelTime_hr

The calculated O value is substituted into [Equation 46] to obtain the final estimate of QH.

Equation 46:

O + QH = (SW - FC) * (1.0 - exp(-(24 / TT + 24 / TT(H)))
QH = (SW - FC) * (1.0 - exp(-(24 / TT + 24 / TT(H))) - O
QH = (O + QH) - O
Code:
same
Variables:
QH = LateralFlowForLayer_mm
O + QH = percolationAndLatFlowForLayer_mm
O = percolationForLayer_mm

Going back to equations 42 and 43...

There is also a provision for upward movement when a lower layer exceeds field capacity. Movement from a lower layer to an adjoining layer is regulated by soil water to field capacity ratios using the equation [Equation 42].

Equation 42:

UF = (SW - FC) * (1.0 - exp(0.05 * (SW(l-1) / FC(l-1) - SW / FC)))
Code:
same
Variables:
UF = UpwardMovementOverFieldCapacityForLayer_mm
SW = waterContent_mm
SW(l-1) = soilWaterContentHigherLayer_mm
FC = fieldCapacity_mm
FC(l-1) = fieldCapacityHigherLayer_mm

Saturated conductivity may be input or estimated for each soil layer by using the equation [Equation 43] where CLA is the percentage of clay in soil layer l and SS is the soil strength factor (described in the Growth Constraints section of this section).

Equation 43:

SC = 12.7 * (100 - CLA) * SS / ((100 - CLA) + (11.45 - 0.097 * (100 - CLA)))
Code:
SC = 1.0 + 12.7 * (100 - CLA) * SS / ((100 - CLA) + exp(11.45 - 0.097 * (100 - CLA)))
Variables:
SC = SaturatedConductivityForLayer_mmPhr
CLA = clayContent_pct
SS = soilStrengthFactorForSatCond

Now skipping forward to equation 49...

Equations 46 and 48 are used to partition flow between vertical and lateral components. The lateral flow component is estimated by considering subsurface flow from a hillside. This is generally adequate for small areas composed of a hillside landscape. However, for larger more complex areas, there is need to lag lateral flow to simulate return flow. EPIC uses an additional routing equation to accomplish the proper lag: [Equation 49] where QE is the return flow volume in mm and TT(R) is the return flow travel time in days (input to EPIC).

Equation 49:

QR = (1.0 - exp(-1.0 / TT(R))) * (sum from 1 to M of) QH
Code:
QR = (1.0 - exp(-1.0 / TT(R))) * QH
same except QH is for layer
Variables:
QR = LatFlowAdjForReturnFlow_mm
TT(R) = returnFlowTravelTime_days
QH = unadjLateralFlow_mm