Assessing the Performance of Different Time of Concentration Equations in Urban Ungauged Watersheds: Case Study of Cartagena de Indias, Colombia

Álvaro González-Álvarez,Kibrewossen Tesfagiorgis,Orlando M Viloria-Marimón,Javier A Mouthón-Bello,Brandon Meza-Zúñiga,José Molina-Pérez

doi:10.3390/hydrology7030047

Álvaro González-Álvarez, Kibrewossen Tesfagiorgis + Show 4 more

Open Access

https://doi.org/10.3390/hydrology7030047

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Abstract

In ungauged watersheds, the estimation of the time of concentration (Tc) is always a challenging task due to the intrinsic uncertainty involved when making assumptions. Given that Tc is one of the main inputs in a hydrological analysis for the design of hydraulic structures for stormwater management, ten equations (including one proposed in several local studies) and two Tc methodologies (overland flow time plus channel flow time) were used to compute the Tc in fifteen urban ungauged watersheds, located in Cartagena de Indias (Colombia), with different area sizes and slopes to statistically assess their performance against the value obtained via the Natural Resources Conservation Service (NRCS) velocity method (assumed to be the true value). According to the Nash–Sutcliffe efficiency index, none of the equations proved to be reliable in all watersheds as only four equations predicted the Tc value in 53% of the cases. In addition, based on the percent bias, all equations tended to significantly over- or underestimate the Tc, which affects the quantification of the runoff volume necessary for, among others, the implementation of best management practices for watershed management (e.g., conventional and/or sustainable drainage system design), flood-prone area delineation and flood risk analyses, urban planning, and stream restoration.

Highlights

Hydrological analysis in ungauged watersheds might be challenging as several assumptions have to be made that could introduce uncertainties into the estimation of the design runoff via rainfall-runoff models, in which rainfall is one of the main inputs
All time of concentration (Tc) equations evaluated in this study showed setbacks, including those recommended by the Colombian drainage manuals MinVivienda [42] and Invías [41]
Estimating the design rainfall and its associated runoff values for a given return period in ungauged watersheds can become daunting as it depends on various assumptions, such as the Tc computation among a large array of available empirical equations with different results

Summary

Introduction

Hydrological analysis in ungauged watersheds might be challenging as several assumptions have to be made that could introduce uncertainties into the estimation of the design runoff via rainfall-runoff models, in which rainfall is one of the main inputs. Hydrology 2020, 7, 47 in different types of stormwater management and design of drainage structure manuals/guidelines [3, 11,12,13,14], embedded in software programs for hydrologic-hydraulic modeling such as Win TR-20 [15], Win TR-55 [16], HydroCAD® [17], Autodesk® [18], Storm Water Management Model (SWMM) [19], Hydrologic Engineering Center-Hydrologic Modeling System HEC-HMS [20], SewerCAD® [21], and StormCAD® [22], in freely available Tc online calculators such as Vlab [23], or as an input in rainfall-runoff models such as the rational method These equations have considered different variables that range from rainfall and surface direct runoff to watershed morphological parameters (e.g., area, slope, length of flow path, and outlet elevation), land use/land cover (LULC) conditions, and channel characteristics.

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