Using an ensemble machine learning model to delineate groundwater potential zones in desert fringes of East Esna-Idfu area, Nile valley, Upper Egypt

Geoscience Letters

Official Journal of the Asia Oceania Geosciences Society (AOGS)

Table 2 The equations used to create some effective features (TRI, TWI and SPI) associated with the equations used for random forest model evaluation

The equations used for creating effective features
S. n.	Index	Equation
1	TRI	\(\left(Avg-Min\right)/(Max-Min)\)
2	TWI	\(\mathrm{ln}(\frac{ \mathrm{ Fa } }{\mathrm{tan}\beta })\)
3	SPI	\(\mathrm{Fatan}\beta\)

The equations used for the random forest model validation
	Measure	Equation
4	MSE_OOB	\({n}^{-1}\sum_{i=1}^{n}({\gamma }_{i}-{\Delta }_{i})\)
5	Accuracy	\(\frac{TP+TN}{TP+TN+FP+FN}\)
6	Sensitivity	\(\frac{TP}{TP+FN}\)
7	Precision	\(\frac{TP}{TP+FP}\)
8	F1-score	\(2\times \frac{(Sensitivity \times Precision)}{(Sensitivity+Precision)}\)
9	MCC	\(\frac{(TP\times TN-FP\times FN)}{\sqrt{(TP+FP)\times (TP+FN)\times (TN+FP)\times (TN+FN)}}\)

TRI: terrain ruggedness index; Avg, Max, and Min: averages, highest and lowest elevation values of pixels in nine rectangular neighborhoods of elevation values, respectively; TWI: topographic wetness index; Fa: flow accumulation (m² m⁻¹); \(\beta\): slope angle measured in degrees; SPI: stream power index; MSE: mean square error; OOB: out of bag; TP: true positive; TN: true negative; FP: false positive; FN: false negative; MCC: Matthews correlation coefficient