Table 1 Deduced functional relationships using basin attributes to estimate process sensitivities.

Process	Pred.	Pred.	Estimated functional relationship	Adj. Coeff. of Determ.
	x	y	\({\widetilde{ST}}_{i}^{w}=f(x,y)\)	\({R}_{adj}^{2}({\widetilde{ST}}_{i}^{w},S{T}_{i}^{w})\)
Infiltration	f_S	–	0.2985 − 0.8113x + 1.0443x² − 0.5203x³	0.905
Quickflow	f_S	ΣP	0.9044 − 3.4122x² + 2.6596x³ − 4.771 × 10⁻⁵y − 0.001153xy + 0.001870x²y	0.953
Evaporation	f_S	–	0.3835 − 0.7713x + 0.1945x² + 0.3964x³	0.915
Snow Balance	f_S	–	− 0.009051 + 0.4161x + 1.3796x² − 2.0661x³	0.926
Convolution (srfc runoff)	\(\overline{T}\)	f_cold	0.06531 − 0.00639x + 1.645 × 10⁻⁴x² − 0.0008165y + 4.104 × 10⁻⁵xy + 2.6508 × 10⁻⁶y²	0.657
Potential Melt	f_S	–	− 0.01494 + 0.8236x + 2.4265x² − 3.1523x³	0.950
Percolation	f_S	–	0.2829 − 0.7275x + 0.8276x² − 0.3582x³	0.909
Rain-Snow Partitioning	f_S	f_cold	− 0.001715 + 3.7710x − 0.002150y − 0.03638xy + 1.302 × 10⁻⁵y² + 8.753 × 10⁻⁵xy²	0.815
Precipitation Correction	f_S	I_m,r	0.07343 + 0.5829x² − 1.0106x³ + 0.01122y³ − 0.1677xy² + 0.5264x²y	0.809

Note. Results of the regression analysis identifying the functional relationships between predictors and the variance-weighted total Sobol’ sensitivities \(S{T}_{i}^{w}\) based on the results of the 3316 basins analyzed by xSSA. The regression is performed using polynomials with one predictor (up to degree three with at most six coefficients) and polynomials with two predictors (up to degree three with at most five coefficients). The one-predictor polynomial is used unless the use of a pair of predictors led to an improvement of the adjusted coefficients of determination \({R}_{adj}^{2}\) by at least 0.05. The basin characteristics used as predictors are derived from geophysical attributes and the meteorology available for each basin (1950 to 2010). The adjusted coefficients of determination \({R}_{adj}^{2}\) between the xSSA-derived sensitivities \(S{T}_{i}^{w}\) and the predicted sensitivities \({\widetilde{ST}}_{i}^{w}\) are given in the last column. Description of predictors: f_S is the fraction of precipitation that is snow [mm/mm], ΣP is the annual sum of precipitation [mm], \(\overline{T}\) is the annual average temperature in [°C], f_cold is the average annual number of days below 0 °C, I_m,r is the measure of seasonality ranging between [0,2].

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