Abstract

Abstract
In data-scarce urban regions, the development of Intensity-Duration-Frequency (IDF) curves is constrained by the absence of high-resolution sub-daily rainfall records. This study develops IDF curves for Kaduna City, Nigeria, by fitting the Generalized Extreme Value (GEV) distribution to a 62-year (1955-2016) Annual Maximum Daily (AMD) rainfall series and disaggregating the fitted 24-hour AMD to shorter durations using a simple-scaling model. Prior to frequency analysis, the AMD series was tested for trend, homogeneity, and independence using the Mann-Kendall test, Sen's slope estimator, the Pettitt test, and the Ljung-Box test; none of the tests indicated a significant trend or change-point (p > 0.05), confirming that the stationarity assumption required for at-site GEV fitting is satisfied. Maximum likelihood estimation gave a best fit distribution as Fréchet with fitted parameters of location = 2.475, scale = 0.468 and shape = 0.163, with AIC = 513.325, BIC = 519.706 and AICc =513.739, outperforming the Gumbel model (AIC = 513.865, BIC = 518.119, AICc =514.068). A robust scaling exponent η = 0.758 (95% CI: 0.745 - 0.772) was derived from a regional IDF matrix by log-log regression across six return periods and used to downscale the 24-hour AMD. The resulting IDF values were fitted to a four-parameter Horner model, I=26.66{T }^{0.1892}{left(d+0.00008right) }^{-0.7582} with R2 = 0.9998 and leave-one-out cross-validated R2 = 0.9996. Parameter uncertainty was quantified using 1000-sample parametric and non-parametric bootstrap procedures. The developed curves reproduce the historical Gumbel-based IDF relationships for the study area within acceptable error margins (MAPE 4.7 - 6.8%; mNSE 0.74 - 0.84), supporting their use for stormwater infrastructure design and flood-risk planning in similarly data-scarce sub-Saharan African catchments.

Keywords: GEV distribution, Fréchet, IDF curves, simple scaling, rainfall disaggregation, scaling exponent

Key words: GEV distribution, Fréchet, IDF curves, simple scaling, rainfall disaggregation, scaling exponent