A storm with $10$ cm precipitation produced a direct surface runoff of $5\mathrm{.}3$ cm in the equivalent depth unit. The time distribution of the storm is given in the table.

$($a$)$ Estimate the $\backslash (\backslash$emptyset $\backslash )-$index of the storm and the excess rainfall hyetogrph.

$($b$)$ Calculate the runoff coefficient.

$($c$)$ If the $\backslash (\backslash$emptyset $\backslash )-$index method is not good enough, we want to use Green$-$Ampt method for correction. The field survey shows the soil parameters as: $\backslash (\backslash$mathrm$\{$K$\}=0\mathrm{.}34\backslash$mathrm$\{$~cm$\}/\backslash$mathrm$\{$h$\},\backslash$psi$=\backslash )\backslash (9\mathrm{.}98\backslash$mathrm$\{$~cm$\},\backslash$theta e$=0\mathrm{.}34\backslash ),$ and $\backslash ($ S e$=0\mathrm{.}2\backslash ).$ What kind of soil you think it is$?$

$($d$)$ Use Green$-$Ampt method to calculate the abstraction and excess rainfall.

$($e$)$ Calculate the runoff coefficient

$($f$)$ Now we still want use $\backslash (\backslash$emptyset $\backslash )-$index method to simplify this problem. Any suggestion to adjust the $\backslash (\backslash$varnothing $\backslash )-$index? Just let me know higher or lower will be fine.

$($g$)$ Assume the $\backslash (\backslash$emptyset $\backslash )-$index is more accurate and we know the value of hydraulic conductivity is not certain. Do you think we overestimate or underestimate K $,$ how you calibrate the value? Why? $($Please give a brief answer. Do not try to calculate the correct K value.$)$

$($h$)$ A senior engineering told you try to calibrate the suction head instead of conductivity. What's your opinion of $\backslash (\backslash$psi $\backslash )?$ Did we overestimate or underestimate it$?$ Why? $($Same$,$ please give a brief answer. Do not try to calculate the correct $\backslash (\backslash$psi $\backslash )$ value.$)$