Problem $7\mathrm{.}3.$ A rainstorm of duration $t_r=8hr$ and rainfall

intensity $P=30mmh{r}^{-1}$ occurs over an area with an initial

soil saturation of $50\%$ and the following soil properties:

${}_s=0\mathrm{.}35$;${}_s=-50cm$;$K_s=11mmh{r}^{-1}$;$b=1$

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$.15m\frac{m}{h}r)$ and $200\%$ of the baseline case $($i$.$e$.60$

$m\frac{m}{h}r).$ 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 actualcumulative 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?

Problem $7\mathrm{.}3.$ A rainstorm of duration $t_r=8hr$ and rainfall

intensity $P=30mmh{r}^{-1}$ occurs over an area with an initial

soil saturation of $50\%$ and the following soil properties:

${}_s=0\mathrm{.}35$;${}_s=-50cm$;$K_s=11mmh{r}^{-1}$;$b=1$

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$.15m\frac{m}{h}r)$ and $200\%$ of the baseline case $($i$.$e$.60$

$m\frac{m}{h}r).$ 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?