Abstract
Applying the theory of log-normal-probability distribution, we obtained the theoretical equation showing the relationship between alA and D as listed in Eq. (3), and we referred to this equation as the depth-area-curve equation. We also used Eq. (6), Eq. (7) and Eq. (8) to calculate the values of Dmode, Dmedian and Dmean, respectively. The values calculated by the theoretical equation were compared with the values observed. The results were as follows;
1) The deviation of the theoretical values of Dmode from the observed ones (that were calculated by Eq. (9)) was 41.5% at the maximum value and 1.6% at the minimum one.
2) The theoretical values of a/A at Dmode agreed closely in practice with the values observed.
3) For the values of Dmedian, the theoretical values agreed well with the values observed.
From these results, we concluded that we would be able to use the theoretical equations obtained here to estimate the depth-area curve or the relationship between the water-table depth and its corresponding area, Dmode. Dmedian and Dmean for a given region for a given period. References
