Options for Modelling of Rainfall Excess from Pervious Areas

The rainfall excess corresponding to different surfaces (i.e. directly connected impervious areas, supplementary areas and pervious areas) are modelled differently in ILSAX because of their different processes. Since there are two methods available for modelling rainfall excess from pervious areas, they are discussed in this section. These methods are studied in detail in Section 6.5. The details of modelling rainfall excess for directly connected impervious areas and supplementary area are described in O’Loughlin (1993).

The pervious area losses are modelled in the ILSAX model through an initial and continuous loss model. The initial loss model is represented by pervious area depression storage, which accounts for the processes of interception, depression storage and evaporation. The continuing loss allows for infiltration and estimated from the Horton infiltration equation. Since the ILSAX model is an event model, the conditions at the start of the event must be established by defining a value of the antecedent moisture conditions (AMC) for the soil underlying the pervious area. The ILSAX model defines four soil classifications designated as A, B, C and D, as shown in Figure 4.3. These soil

classifications are also called the Curve Numbers (CN) in ILSAX, and given values 1, 2, 3 and 4 respectively. Other soil types can be generated by interpolation between these four classifications. These soil types are used in conjunction with antecedent moisture conditions (AMC’s), which fix the points on the infiltration curves at which calculations commence (Figure 4.3).

Figure 4.3: Infiltration Curves for Soil Types Used in ILSAX (O’Loughlin, 1993)

The soil type CN in ILSAX is described by the Horton infiltration equation, as follows.

kt c c

p f f f e

f = +( ₀− ) − (4.1) where fp is the infiltration capacity of soil (m/s),

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fc is the minimum or ultimate value of fp(m/s),

f0 is the maximum or initial value of fp (m/s),

t is the time from beginning of storm (s), and

k is the decay coefficient (s-1).

To define the soil type of a catchment, the user can specify CN in the range 1 to 4 (non- integer numbers are possible) according to soil type of the catchment and AMC value considering the rainfall occurred prior to the storm event. Then the four soil curves (or intermediate curve if CN is non-integer value) are used in conjunction with AMC which fix the points on the infiltration curves at which calculations commence. The second option is to define a curve with characteristics provided by the user. In this option, the user has to enter f0, fc, k and four AMC values (altogether 7 parameters) to define the curve for

catchment soil type.

AMCs immediately prior to the storm event obviously play a very significant role in determining the actual pervious area runoff contribution. The effect is more significant, as the magnitude of the storm event increases because of the potential for increased pervious area runoff. Table 4.2, which is reproduced from the ILSAX manual (O’Loghlin, 1993), provides some guidance for selecting the AMC immediately prior to the storm event by considering the total 5-day rainfall depths prior to the event.

As can be seen from Table 4.2, the AMC does not consider the temporal distribution of the rainfall during the previous five days. In reality, the AMC condition of a catchment that receives 25 mm of rainfall on the first day of the 5-day period prior to the storm event is not the same as the catchment receiving 25 mm of rainfall on the fifth day. However, Table 4.2 is the best information currently available to compute the initial AMC.

As stated earlier, there are two options in ILSAX to compute the rainfall excess from pervious areas. In the first method, the losses are subtracted from rainfall, while in the second method, losses are subtracted from supply rate (i.e. after rainfall is routed using the time-area method). These methods are explained below.

(O’Loughlin, 1993) AMC

condition

Description Total Rainfall in 5 days Preceding the Storm (mm) 1 Completely dry 0

2 Rather dry 0 to 12.5 3 Rather wet 12.5 to 25.0

4 Saturated Over 25.0

Losses subtracted from rainfall

In this method, the losses (i.e. both initial and continuous) are subtracted from the rainfall to compute rainfall excess. The rainfall excess is then routed using the time-area method. During the hydrograph event, although rainfall stops at the end of storm, flows may still travel across pervious surfaces to the catchment outlet, which will have extra continuing losses. Therefore, this method does not allow for the possible continuing losses after rainfall stops.

Losses subtracted from supply rate

In this method, the hyetograph is convolved with the time-area diagram without considering losses to obtain the supply rate. Then, both initial and continuing losses are subtracted from this supply rate. This method is preferred since it allows for possible losses even after rainfall stops.

Time-Area Method

Both methods above use the time-area method to generate hydrographs for each subcatchment area. In this method, the rainfall hyetograph (whether the original rainfall or the rainfall excess) is combined with the time-area diagram in a similar manner to unit hydrograph calculations. Figure 4.4 illustrates the time-area procedure. The following paragraphs explain the basic theory of this procedure, as described in O’Loughlin (1993).

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Figure 4.4: Construction of Hydrograph by the Time-Area Method (O’Loughlin, 1993)

The rainfall hyetograph is divided into computational time steps of ∆t. ∆t is a user-defined value and is a fraction of the time of concentration (or the time of entry) for a subcatchment area. The time of concentration is determined from the methods described in Section 4.2.2.

The time-area diagram (i.e. a plot of the catchment area contributing to runoff at the inlet pit versus time from the start of the storm) is also divided into time steps of ∆t. This diagram can be visualised by drawing isochrones, or lines of equal time of travel to the catchment outlet. For times greater than the time of concentration, the area contributing equals the total area of the catchment. ILSAX assumes a linear relationship between contributing area and time of concentration, as shown in Figure 4.4(a).

When a storm commences in a catchment which has a time of entry of 3∆t (Figure 4.4), the initial flow Q0 is zero. After one time step ∆t, only sub-area A1 contributes to the flow at

the outlet. Any runoff from other sub-areas is still in transit to the outlet. Thus the flow rate at the end of the first time step can be approximated using the formula of Q1 = C.A1.I1,

where C represents the conversion factor from mm/h to m3/s units (If A is in ha, C = 1/360), and I1 is the average rainfall intensity (mm/h) during the first time step.

At the end of the second time step, there are two contributions to the outlet flow, Q2, due to

the first and second blocks of rainfall. First contribution is from subarea A1 due to second

block of rainfall (=C.A1.I2) and the second contribution is from subarea A2 due to first

block of rainfall (=C.A2.I1). Therefore, Q2 = C.(A1.I2 + A2.I1). At the end of the third time

step, there are three contributions, Q3 = C.(A1.I3 + A2.I2 + A3.I1), and so on, as shown in

Figure 4.4. The hydrograph builds up to a peak and then recedes once rainfall stops and catchment drains.