Table 2 Regression parameters (a, b, c, d) from nonlinear regression models of S_R on the basis of mean monthly values

S_R = a × S_T^b × S_M^c

2.015 × S_T^−0.001 × S_M^0.757;

R² = 0.83; AIC = 4.91

0.51 × S_T^−1.131 × S_M^0.776;

R² = 0.94; AIC = − 5.77

1.026 × S_T^0.19 × S_M^0.906;

R² = 0.73; AIC = 7.25

0.039 × S_T^1.005 × S_M^1.224;

R² = 0.87; AIC = 4.35

S_R = a × exp^bST × cS_M

2.047 × exp^0ST × S_M^0.759;

R² = 0.83; AIC = 4.91

0.604 × exp^0.046ST × S_M^0.787;

R² = 0.94; AIC = − 6.02

1.631 × exp^0.007ST × S_M^0.898;

R² = 0.73; AIC = 14.61

0.039 × exp^0.037ST × S_M^1.208;

R² = 0.86; AIC = 5.33

S_R = a × exp^bST × cS_M × dS_MA

1.364 × exp^−0.003ST × S_M^0.722 × S_MA^0.24;

R² = 0.84; AIC = 3.5

0.12 × exp^0.04ST × S_M^0.732 × S_MA^0.855;

R² = 0.95; AIC = − 8.96

1.134 × exp^−0.017ST S_M^0.016 × S_MA^−0.728;

R² = 0.85; AIC = 6

0.461 × exp^−0.036ST × S_M^0.852 × S_MA^0.326;

R² = 0.91; AIC = − 0.98

S_R = a × S_T^b × S_M^c × S_MA^d

1.552 × S_T^−0.063 × S_M^0.721 × S_MA^0.24;

R² = 0.84; AIC = 3.5

0.014 × S_T^0.973× S_M^0.723 × S_MA^0.853;

R² = 0.95; AIC = − 8.8

2.807 × S_T^−0.409 × S_M^0.45 × S_MA^1.171;

R² = 0.85; AIC = 6.25

0.049 × S_T^0.972 × S_M^0.909 × S_MA^.295;

R² = 0.91; AIC = − 2.9

S_R = a + bS_T + cS_M + dS_MA

0.601 − 0.018S_T + 1.195S_M + 0.096S_MA

R² = 0.85; AIC = 2.86

− 2.024 + 0.037S_T + 1.252S_M + 0.217S_MA

R² = 0.93; AIC = − 6.58

0.786 − 0.006S_T + 1.134S_M + 0.787S_MA;

R² = 0.82; AIC = 8.64

− 7.955 + 0.207S_T + 1.72S_M + 0.464S_MA;

R² = 0.92; AIC = − 1.72