GRADEX-based Curve Number calibration for HEC-HMS: an open-source R framework with bootstrap uncertainty and influence diagnostics

Statistical validation, uncertainty quantification, and automated HEC-HMS refinement for data-scarce and ungauged catchments

Abstract

Estimating design floods in ungauged or data-scarce catchments remains a central challenge in applied hydrology. The SCS Curve Number (CN) used in HEC-HMS is routinely assigned from land-use tables, offering no guarantee of statistical coherence between simulated peak discharges and regional extreme-precipitation estimates. The GRADEX equal-slopes criterion (Guillot & Duband, 1967; Naghettini, 1995) resolves this inconsistency by requiring the chord slope of the simulated discharge frequency curve (the runoff GRADEX α_Q) to match the precipitation GRADEX α_P, but a standardized computational implementation has been lacking.

This paper presents gcm_scs_gradex_calib v1.0.0, an open-source R module that fully operationalizes the GRADEX equal-slopes CN calibration pipeline. The module integrates: (i) grid-search optimization with continuous CN refinement via natural cubic spline interpolation and Brent minimization; (ii) formal validation of five statistical assumptions including OLS Gumbel-linearity (R² ≥ 0.95), Shapiro-Wilk normality, Durbin-Watson independence tests, and leave-one-out cross-validation stability; (iii) non-parametric bootstrap uncertainty quantification (n = 2,000 replicates); (iv) sensitivity analysis of CN* to α_P perturbations with local elasticity estimation; (v) LOO-based influence diagnostics per HEC-HMS simulation; and (vi) automated HEC-HMS refinement workflow when calibration error exceeds the prescribed tolerance.

Applied to a ten-simulation HEC-HMS dataset (CN ∈ [50, 95], step = 5; α_P = 20.397 mm), the module yields CN* = 71.289 (E = 11.33%). The calibration is confirmed stable (LOO-CV SD = 1.581; 95% CI = [70.0, 73.9]), with a bootstrap 95% CI of [65.0, 75.0] and sensitivity range of [65.2, 76.5] over ±30% GRADEX uncertainty. The module is particularly valuable in data-scarce and ungauged catchments where regionalized extreme-precipitation GRADEX is available but streamflow records are absent or insufficient for direct flood frequency analysis.