We take the simplest model to show the effects of paving over areas, which increase the total flood heights. A 1992-2010 survey showed that 30% of the Harris County area had been covered by development that cut off the soil reservoir below. I don’t know what the total is including before 1992 and after 2010. So 30% is just a starting point.
We take an ancient area A which could uniformly absorb rain to a depth D. A storm of volume V would then cover the ground to a height “h”, where
V = h A + D A.
Now let the available ground that can absorb water be reduced 30% to an area 0.7 x A. The storm of the same volume V would now cover the same total area to a height H, where
V = H A + D (0.7 A).
We equate the two V’s, and cancel out A, which is in all terms, giving:
h + D = H + 0.7 D.
Or,
H = h + 0.3 D. We then divide all terms by D to form the ratio relationship:
H/D = h/D + 0.3.
This is our result. Lets evaluate this for certain h/D ancient ratios:
h/D H/D
0 0.3
0.5 0.8
1.0 1.3
1.5 1.8
2.0 2.3
In all cases, there is a significant increase in flood height proportional to D.
