Problem 7.3. A rainstorm of duration t = 8 hr and rainfall intensity P= 30 mm hr occurs over an area with an initial soil saturation of 50% and the following soil properties: 0 -0.35; 4 = -50 cm; K - 11 mm hr": b- 1; These conditions will form the baseline" case for the sensitivity tests described below. Here you can use the time compression approximation (TCA) with the Philip solution. a) What is the physical meaning of the ponding time in infiltration? Under what storm intensity condition relative to soil parameters) will ponding never occur? Write out the equation for the ponding time and use it to compute the ponding time in hours for the baseline case. What is the meaning of the case where the ponding time is greater than the duration of the storm? b) Compute and plot the ponding time for a range of storm intensities consisting of the baseline case, 50% of the baseline case (i.e. 15 mm/hr) and 200% of the baseline case (i.e. 60 mm/hr). Explain the trend seen in ponding time as a function of precipitation rate. c) Compute and plot the ponding time for a range of initial conditions consisting of the baseline case, and 25%, and 75% relative saturation. Explain the trend seen in ponding time as a function of initial condition. d) Write out the equations for concentration time, actual cumulative infiltration, and infiltration excess runoff using the TCA. Use these equations to compute the expected actual cumulative infiltration and infiltration excess runoff (in mm) for the baseline storm case. e) What fraction of the total rainfall is converted to runoff for the baseline case? f) Qualitatively, how would your answers to parts d) and e) change if the precipitation intensity was higher than the baseline case? g) Qualitatively, how would your answers to parts d) and e) change if the initial condition in soil moisture was lower than the baseline case? h) Qualitatively, how would your answers to parts d) and e) differ between sand and clay soil types?