Four main processes in Hydro are vegetation interception process, soil process, urban process, and
channel process. Soil process is most complicated process. In this document, I introduce all the physical
functions and parameters involved in soil process simulation.
Soil Process and Parameters
General description: iTree-Hydro uses the TOPMODEL concept. When the rain or throughfall (P) reaches
the soil surface, it will infiltrate into the root zone first. If the rain rate is higher than the infiltration rate,
surface flow (infiltration excess over land flow) will be generated. The infiltrated water (infilQ) will
recharge the root zone. If infilQ is more than the sum of the root zone water deficit and evaporation, the
extra water (rzQ) will flow to the unsaturated zone. If rzQ is larger than the storage deficit of the
unsaturated zone, surface flow (saturated over land flow) will be generated. The water stored in the
unsaturated zone also flows vertically to the saturated zone (uzQ) in a rate Suz/(Si*Td). Suz is unsaturated
zone storage, Si is the water table depth (the distance from the saturated zone surface to land surface),
and Td is a time delay constant. The base flow is generated from the saturated zone. Figure 1 shows the
concept of TOPMODEL.
Figure 1. TOPMODEL Concept, where R is rainfall [L/T], E is evaporation [L/T], S is water storage, q is
water flux between zones or as baseflow. Storage at each location, using pixel cells, in the watershed is
denoted by subscript (i), and S(i) changes depending on topographic weighting. Image is from
community.
a. Infiltration process
According to Beven (1984), the infiltration rate i is given as
∫
(11)
In which I is the cumulated infiltration, Kz (=K0*exp(-fZ)) is the hydraulic conductivity at soil
depth Z and
is the effective wetting front suction.
(The understanding of this equation can be: U/R for electronic circuit.)
The water will infiltrate to the soil in the rain rate or throughfall rate before ponding. At the
ponding time tp, the cumulated infiltration Ip has penetrated to depth Zp: Zp=Ip/∆θ, in which ∆θ is
the saturated soil moisture content minus the initial soil moisture content.
(∆θ is the DWSMI(m), K0 is K0(m/h), and
is the WFS(m) in the param.dat file )
By putting these values to equation (11), the cumulated water and time at ponding can be
obtained. After ponding, at any time t, the cumulated infiltration can also be obtained by
equation (11).
b. Root zone process
The root zone has a maximum storage deficit (MSD(m) in param.dat file). The larger the MSD(m),
the more water can be absorbed by the root zone before generating any flow.
c. Unsaturated zone process and Saturated zone process
The calculation of the water table depth Si (the depth from the surface of saturated zone to the ground
surface) is the key for TOPMODEL. There are three assumptions in TOPMODEL:
1. The subsurface flow from the saturated zone is stable, so in any location in the watershed, the
subsurface flow (qi ) passing through unit length equals to the water from upslope:
qi=R*ai
(1)
in which R is the recharge rate and ai is the accumulation area per unit contour length.
2. The hydraulic gradient for the saturated zone is the local surface topographic slope, so according
to Darcy’s law, the subsurface flow (qi)can also be obtained from:
qi=Ti*tanβi
(2)
in which Ti is the transmissivity of the saturated zone, and tanβi is the local surface topographic
slope.
3. The soil transmissivity Ti of saturated zone is a function of water table depth (exponentially or
powerly):
Ti=T0*exp(-Si/m) or Ti=T0(1-Si/m)n
(3)
In which T0 is the soil transmissivity at saturation (T0 in param.dat), Si is the water table depth, n
(n in param.dat file) is the power number, and m (m in param.dat file) is a scaling parameter. m
can be interpreted as unsaturated zone maximum water storage depth.
Equal the right side of equation (1) and equation (2), and put equation (3) to the right side of equation
(2), then the water table depth at location i can be obtained:
Si=-m(ln(R/T0)+ln(ai/tanβi))
Si=m(1-(R/T0)1/n(ai/tanβi)1/n) (4)
or
From equation (4), we can see the water table depth Si relates to ln(ai/tanβi) or (ai/tanβi)1/n.
ln(a/tanβ) or (a/tanβ)1/n is then defined as Topographic Index (TI). When Si equals to 0, the water table
reaches the land surface.
The average water table depth for the watershed can be obtained by integrating equation (4).
̅
∫
(5)
In which A is the watershed area. The result of equation (5) is
̅
̅̅̅
̅
or
̅̅̅
(6)
In which ̅̅̅ is the average TI for the watershed. Replace the ln (R/T0) term (or (R/T0)1/n) in equation (4)
by equation (6), we can get the local water table depth:
̅
̅̅̅
̅
or
̅̅̅
(7)
The subsurface flow (base flow) for the whole watershed is calculated as function of ̅ and ̅̅̅:
̅
̅̅̅
̅̅̅
or
̅
(8)
The average water table depth ( ̅) of the watershed is updated each time step by equation:
̅
̅
̅̅̅̅̅
̅
(9)
In which ̅̅̅̅̅ represents the average vertical flow from unsaturated zone to saturated zone. ̅̅̅̅̅ is
calculated by
̅̅̅̅̅
∑
(10)
In which n is the total cell number,
is the unsaturated zone storage of cell i at time step t, and Td
(Td in param.dat file) is a time delay constant.
Based on equation (9) and (7), the water table depth (Si) for each cell is then updated for each time step.