Event-Specific Time of Concentration and Hydrological Signature from IBER Hydrographs: A Proof-of-Concept Framework with Uncertainty Quantification

Integrating GLUE, Bootstrap BCa, synthetic unit hydrographs, and flow-duration curve analysis

Abstract

Background. The time of concentration (Tc) is a fundamental parameter in hydrological design, yet conventional practice treats it as an intrinsic watershed property estimated via empirical formulas. This assumption introduces large uncertainties, particularly in large basins where storage, attenuation, and nonlinear flow effects dominate.

Objective. This paper presents IBER_TcEstimator v1.0, an open-source R framework that extracts event-specific Tc estimates—with formal uncertainty quantification—from IBER hydrographs, and characterises each event through a hydrological signature analysis.

Methods. The framework integrates five analytical modules: (A) uncertainty quantification via GLUE (N = 5,000) and Bootstrap BCa (R = 2,000); (B) baseflow separation with three recursive digital filters (Eckhardt, Chapman, Lyne–Hollick); (C) effective precipitation via the CN-NRCS method; (D) generation of SCS, Clark, and GIUH synthetic unit hydrographs plus Tikhonov deconvolution; and (E) advanced diagnostics including KGE, NSE, PBIAS, Durbin-Watson and Ljung-Box tests, Tc→Qp elasticity, and hydrological event signature analysis (flow-duration curve, Richards-Baker flashiness index, recession slope).

Results. On a synthetic 150.5 km² watershed (CN = 82, Lc = 28.36 km, S = 0.0073), the SCS Lag method yields Tc = 17.85 h—2.1 to 7.1 times larger than six empirical formulas—with a 95 % BCa confidence interval of [13.02, 22.59] h. GLUE produces a posterior median of 16.20 h (95 % CI: [12.71, 19.75] h) with 31.6 % behavioural realisations (KGE ≥ 0.50). Performance metrics indicate good shape fit (KGE = 0.667, NSE = 0.808) with quantified volumetric bias (PBIAS = 26.64 %). Residual autocorrelation (DW ≈ 0, LB = 27,553, p < 0.001) is explicitly characterised. The event flow-duration curve reveals a highly attenuated response (R-B flashiness index = 0.0009) with very slow recession (slope = 0.0179 decades per percentage point). Three baseflow filters yield a narrow BFI range of 0.82–0.85 (CV < 2 %).

Limitations. As a proof-of-concept, results are based on a synthetic watershed. Validation against real gauged catchments, multi-event analysis, and global sensitivity analysis are the primary next steps.