Water Resource Associates

HYDROLOGY

The catchment being simulated can be divided into any number of sub-catchments. The sub-catchment can be divided into up to three hydrological zones, each of which should be reasonably homogeneous with respect to soil type and meteorology.

The five types of input data which the model can use are :

i) Precipitation. This is given as catchment areal average.
ii) Potential evapotranspiration rate. Estimates based on an empirical relationship.
ii) Potential melt rate. This can be based on the degree day method or a more complex one.
iv) Sewage flow/direct abstractions. The net figure for these is used .
v) Groundwater abstractions.

None of the types of data is compulsory. The data can be given in a monthly, daily or any shorter time increment, provided there is an integral number of data items per day.

Snow storage. Any precipitation falling as snow is held in snow storage from where it is released into interception storage. The rate of release is equal to the potential melt rate.

Interception storage. This represents the storage of moisture on the leaves of trees, grasses etc. Moisture is added to this storage from rainfall or snowmelt. The first call on this storage is for evaporation which, experiments have shown, can take place at more than the potential rate. This can be allowed for in the model. Any moisture in excess of the storage limit is passed on to the next stage.

Impermeable area. A proportion of the moisture in excess of the interception storage limit is diverted to minor channel storage to allow for the impermeable proportion of the catchment.

Upper Soil Horizon. This reservoir represents moisture held in the upper (A) soil horizon, i.e. top-soil. It has a finite capacity equal to the depth of this horizon multiplied by its porosity.

A limit on the rate at which moisture can enter this horizon is applied, based on the potential infiltration rate. This rate is assumed to have a triangular areal distribution, as in the models of Crawford and Linsley, and Porter and McMahon.The potential infiltration rate is based on Philips equation, i.e.

x = F t^0.5 + c t^1.0 + w t^1.5 + ......

Where x is the distance travelled downwards by the wetting front, t is time since x = 0 and f, c and w are functions of soil type and condition. It has been shown by Manley that this relationship can be closely approximated to :

x = (2k Pt)^0.5 + kt

where P is the capillary suction (mm. of water) and k the saturated permeability of the medium (mm/hr). This allows determination of the potential infiltration rate.

Brooks and Corey have shown that P can be expressed as :

where Pb is the bubbling pressure (mm of water), g is a parameter (called the pore size distribution index) and Se is the effective saturation defined as :

S_e = (m - S_r)/(1.0 - S_r)

where m is the saturation and S_r is the residual saturation, i.e. the minimum saturation that can be attained by dewatering the soil under increasing suction. By simulating the moisture content in the upper horizon the forces causing movement of the water can therefore be simulated. The first loss from the upper horizon is evapotranspiration which, if the capillary suction is less than 15 atmospheres, takes place at the potential rate (after allowing for any loss from interception storage). If capillary suction is greater than 15 atmospheres no evapotranspiration takes place. The next transfer of moisture that is considered is interflow (i.e. lateral flow). The rate at which this occurs is obviously a very complex function of the effective horizontal permeability, gradient of the layer and distance to a channel or land drain. Brooks and Corey have also shown that the effective permeability of porous media is given by :

k_e = k (S_e)^{(2+3g )/g}

where ke is the effective permeability (mm/hr) and the other terms are as defined previously. Because of its complexity no attempt is made to separate the individual parameters for interflow and it is given as :

Interflow = Rfac1(S_e) ^{(2+3g )/g}

Where Rfac1 is defined as the interflow run-off from the upper soil horizon at saturation. The final transfer from the upper horizon is percolation to the lower horizon and is given by :

Percolation = k_b(S_e) ^{(2+3g )/g}

where k_b is the saturated permeability at the horizon boundary and S_e is the effective saturation in the upper horizon. By combining the above equations the rate of increase in storage is given by :

ds = i - (Rfac₁+k_b) S_e^{(2+3g )/g}
dt

where i is the rate of inflow and S and t are moisture storage and time respectively. Unfortunately this equation cannot be solved explicitly so it has been assumed that the total change in storage in any time increment is small compared to the initial storage. In this case the equation can be simplified and an approximate solution obtained. As a check for extreme situations the change in storage is constrained to lie within an upper and lower limit. The upper limit is defined by the level of storage at which the rate of outflow is equal to the rate of inflow. The lower limit results from setting i equal to zero in the above equation, in which case an explicit solution is possible.

Lower Soil Horizon. This reservoir represents moisture below the upper horizon but still in the zone of rooting (i.e. the B and C horizons). Any unsatisfied potential evapotranspiration is subtracted from the storage at the potential rate, subject to the same limitation as for the upper horizon (i.e. capillary suction less than 15 atmospheres). Similar equations to those in the upper horizon are employed for interflow runoff and percolation to groundwater.

Transitional Groundwater. This is an infinite linear reservoir and represents the first stage of groundwater storage. Particularly in karstic limestone or chalk catchments many of the fissures holding moisture may communicate with a stream rather than deeper groundwater and the transitional groundwater represents this effect. Its operation is defined by two parameters : the discharge coefficient and the proportion of the moisture leaving storage that enters the channels. Being a linear reservoir the relationship between storage and time can be calculated explicitly.

Groundwater. This is also an infinite linear reservoir, assumed to have a constant discharge coefficient. It is from this reservoir that groundwater abstractions are made. As in the above case the rate of runoff can be calculated explicitly.

Minor Channels. This component represents the routing of flows in minor streams, ditches and, if the catchment is saturated, ephemeral channels. It uses an instantaneous unit hydrograph, triangular in shape, with a time base equal to 2.5 times the time to peak.