Table 1 Absolute frequency 2-D contingency table for rainfall (R in mm) and depth to water table (WT, m, bgl) at well W 42 (village: Tishkhora) located in the flood plain of a morphodynamic system in a part of the Ganga basin of Northern India.
WT (m, bgl) | Rainfall (R) in mm | i = 1 | i = 2 | i = 3 | i = 4 | Total | Pj | Log Pj | Pj log Pj | H (WT) | |
|---|---|---|---|---|---|---|---|---|---|---|---|
Rainfall(mm) | 0–100 | 100–200 | 200–300 | 300–410 | |||||||
Marginal entropy | j = 1 | 0–2 | 11 | 3 | 2 | 0 | 16 | 0.615 | −0.700 | −0.431 | 0.961 bits Obtained From the Eq. (5) |
j = 2 | 2–4 | 7 | 2 | 0 | 1 | 10 | 0.385 | −1.379 | −0.530 | ||
j = 3 | 4–6 | 0 | 0 | 0 | 0 | 0 | 0.000 | ||||
j = 4 | 6–8 | 0 | 0 | 0 | 0 | 0 | 0.000 | ||||
j = 5 | 8–10 | 0 | 0 | 0 | 0 | 0 | 0.000 | ||||
Total | 18 | 5 | 2 | 1 | 26 | ||||||
Pi | 0.692 | 0.192 | 0.077 | 0.038 | |||||||
Log Pi | −0.531 | −2.379 | −3.700 | −4.700 | |||||||
Pi*Log Pi | −0.367 | −0.457 | −0.285 | −0.181 | |||||||
H (R) | 1.290 bits obtained from the Eq. (4) | ||||||||||
Pi,j | 0.423 | 0.115 | 0.077 | 0.000 | |||||||
0.269 | 0.077 | 0.000 | 0.038 | ||||||||
0.000 | 0.000 | 0.000 | 0.000 | ||||||||
0.000 | 0.000 | 0.000 | 0.000 | ||||||||
0.000 | 0.000 | 0.000 | 0.000 | ||||||||
Pi,j *Log Pi,j | −0.525 | −0.359 | −0.285 | 0.000 | |||||||
−0.510 | −0.285 | 0.000 | −0.181 | ||||||||
0.000 | 0.000 | 0.000 | 0.000 | ||||||||
0.000 | 0.000 | 0.000 | 0.000 | ||||||||
0.000 | 0.000 | 0.000 | 0.000 | ||||||||
Joint entropy | H (R, WT) = | 2.144 bits obtained from the Eq. (6) | |||||||||
Transformation | T (R, WT) = | 0.107 bits obtained from the Eq. (7) | |||||||||
Natural recharge (%) | R (%) = | 8.30 obtained from the Eq. (8) |
