1:3.3.3 Total Rainfall and Duration

The volume of rain is related to rainfall intensity by:

RT=0TidTR_T=\int_0^T i dT 1:3.3.11

where RTR_T is the amount of rain that has fallen at time TT (mm H2_2O) and ii is the rainfall intensity at time TT (mm/hr).

Using the definition for rainfall intensity given in equation 1:3.3.1, equation 1:3.3.11 can be integrated to get:

RT=RTpeakimxδ1(1exp[((TTpeak)δ1)],RTpeak+imxδ2(1exp[(TpeakT)δ2])R_T ={R_{Tpeak}-i_{mx}*\delta_1*(1-exp[(\frac{(T-T_{peak})}{\delta_1})] , {R_{Tpeak}+i_{mx}*\delta_2*(1-exp[\frac{(T_{peak}-T)}{\delta_2}])}} 1:3.3.12

0TTpeak,Tpeak<TTdur0 \le T \le T_{peak} , T_{peak}<T\le T_{dur}

where RTR_T is the cumulative amount of rain that has fallen at time TT(mm H2_2O), RTpeakR_{Tpeak} is the amount of rain that has fallen at time TpeakT_{peak} (mm H2_2O), imxi_{mx} is the maximum or peak rainfall intensity during the storm (mm/hr), δ1\delta_1 is the equation coefficient for rainfall intensity before peak intensity is reached (hr), δ2\delta_2 is the equation coefficient for rainfall intensity after peak intensity is reached (hr), TpeakT_{peak} is the time from the beginning of the storm till the peak rainfall intensity occurs (hr), and TdurT_{dur} is the storm duration (hr). The time to peak intensity is defined as

Tpeak=t^peakTdurT_{peak}=\hat t_{peak}*T_{dur} 1:3.3.13

where TpeakT_{peak} is the time from the beginning of the storm till the peak rainfall intensity occurs (hr), t^peak\hat t_{peak} is the time from the beginning of the storm till the peak intensity expressed as a fraction of the total storm duration (0.0-1.0), and TdurT_{dur} is the storm duration (hr). The cumulative volume of rain that has fallen at TpeakT_{peak} is

RTpeak=t^peakRdayR_{Tpeak}=\hat t_{peak} *R_{day} 1:3.3.14

where RTpeakR_{Tpeak} is the amount of rain that has fallen at time TpeakT_{peak} (mm H2_2O), t^peak\hat t_{peak} is the time from the beginning of the storm till the peak intensity expressed as a fraction of the total storm duration (0.0-1.0), and RdayR_{day} is the total rainfall on a given day (mm H2_2O).

The total rainfall for the day can be defined mathematically by integrating equation 1:3.3.11 and solving for the entire storm duration:

Rday=imx(δ1+δ2)=imxTdur(d1+d2)R_{day}=i_{mx}*(\delta_1+\delta_2)=i_{mx}*T_{dur}*(d1+d2) 1:3.3.15

where RdayR_{day} is the rainfall on a given day (mm H2_2O), imxi_{mx} is the maximum or peak rainfall intensity during the storm (mm/hr), δ1\delta_1 is the equation coefficient for rainfall intensity before peak intensity is reached (hr), δ2\delta_2 is the equation coefficient for rainfall intensity after peak intensity is reached (hr), d1d1 is the normalized equation coefficient for rainfall intensity before peak intensity is reached, d2d2 is the normalized equation coefficient for rainfall intensity after peak intensity is reached, and TdurT_{dur} is the storm duration (hr). This equation can be rearranged to calculate the storm duration:

Tdur=Rdayimx(d1+d2)T_{dur}=\frac{R_{day}}{i_{mx}*(d_1+d_2)} 1:3.3.16

Table 1:3-3: SWAT+ input variables that pertain to generation of maximum half-hour rainfall.

DefinitionInput NameInput File

RdayR_{day}: amount of rain falling on a given day (mm H2_2O)

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