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 H2Omm\space H_2O) and ii is the rainfall intensity at time TT (mm/hr{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 TTTT (mm H2Omm\space H_2O), RTpeakR_{Tpeak} is the amount of rain that has fallen at time TpeakT_{peak} (mm H2Omm\space H_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 (hrhr), δ2\delta_2 is the equation coefficient for rainfall intensity after peak intensity is reached (hrhr), TpeakT_{peak} is the time from the beginning of the storm till the peak rainfall intensity occurs (hrhr), and TdurT_{dur} is the storm duration (hrhr). 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 (hrhr), 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 (hrhr). 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 H2Omm\space H_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 H2Omm\space H_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}*(d_1+d_2) 1:3.3.15

where RdayR_{day} is the rainfall on a given day (mm H2Omm\space H_2O), imxi_{mx} is the maximum or peak rainfall intensity during the storm (mm/hr{mm}/{hr}), δ1\delta_1 is the equation coefficient for rainfall intensity before peak intensity is reached (hrhr), δ2\delta_2 is the equation coefficient for rainfall intensity after peak intensity is reached (hrhr), d1d_1 is the normalized equation coefficient for rainfall intensity before peak intensity is reached, d2d_2 is the normalized equation coefficient for rainfall intensity after peak intensity is reached, and TdurT_{dur} is the storm duration (hrhr). 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.

Definition
Input Name
Input File

RdayR_{day}: amount of rain falling on a given day (mm H2Omm\space H_2O)

pcp

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