# Interpreting the Manning Roughness Coefficient in Overland Flow Simulations with Coupled Hydrological-Hydraulic Distributed Models

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Aggregated Hydrological Modelling

^{2}basin located in Mexico, was firstly analysed with an aggregated hydrological modelling approach through the HEC-HMS software [43]. A standard methodology was applied, based on the local administration guidelines, to discretize the basin. The unit hydrograph (UH) methodology was used for the rainfall-runoff transformation processes, which was obtained from the dimensionless unit hydrograph of the Soil Conservation Service [16,44]. The ${t}_{lag}$ parameter and the value of the time of concentration (${t}_{c}$) were estimated by means of the Kirpich formula. Precipitation losses were accounted for using the SCS-CN method [44,45], also referred to as the NRCS-CN method [46] after the U.S. Soil Conservation Service was renamed as Natural Resources Conservation Service. All parameters of the numerical model are detailed in the Supplementary Material.

#### 2.2. Distributed Hydrological Modelling

## 3. Case Studies

#### 3.1. Case Study 1: Adjustment of the Roughness Coefficient Based on the Time of Concentration

#### 3.2. Case Study 2: Adjustment of the Roughness Coefficient Based on the Peak Time and Discharge from Aggregated Hydrological Models

^{2}and its mean slope is 0.75%. Land uses are characterized by large extensions of secondary vegetation (48.51%) and forested (24.23%) areas. Other areas are covered by rivers (10.70%), pasturelands (10.60%), and rainforest agriculture extents (5.42%). According to the World Reference Base for Soil Resources [67], the basin edaphology is mainly composed of large areas of regosol (71%) and other types of soil such as phaeozem (11.3%) and cambisol (9.6%). From the land uses classification, a Curve Number (CN) of 76.7 was estimated as an area weighted average value in the whole basin.

#### 3.3. Case Study 3: Adjustment of the Roughness Coefficient Based on Observed Storm Events

^{2}and a reservoir at the outlet of 61 hm

^{3}of storage capacity. Weather conditions of the basin are characterized by a wide variability of the rainfall regime, which is influenced by marine conditions with small thermal as well as rain variations [72]. Extreme weather conditions—such as heavy rain events with high precipitation intensities and water accumulations concentrating in a few days or hours, and water scarcity associated to long dry-weather periods—are typical of the area [73,74].

## 4. Results

#### 4.1. Case Study 1

^{1/3}, in intervals of 0.01 s/m

^{1/3}. The purpose was to obtain the best approximation for the minimum, the maximum, and the mean times of concentration (${t}_{c}$) calculated with the empirical formulas (Table 2). The maximum discharge generated with the aforementioned rainfall intensity is, in this case, a constant discharge. For the estimation of ${t}_{c}$, the discharge was considered to be constant when its variation between two consecutive results time steps was lower than 0.1% of the discharge. Results time steps of 60 s were used.

^{1/3}) was needed for the S-curve to fit with the minimum ${t}_{c}$, which, in this case, corresponds to the Kirpich formula. In Trinity (Figure 2c) and Brazos (North Elm Creek) (Figure 2d) basins, it was not possible to reproduce the minimum ${t}_{c}$ without considering any friction since the hydrograph needed more time than the minimum ${t}_{c}$ to stabilize. For this reason, they are not plotted in Figure 2. This induces the thought that the Kirpich formula, the one that provides such minimum values, is quite unrealistic for these basins, as water propagation is slower even with no friction. This is in agreement with the assertion of Michailidi et al. [11] that “the Kirpich formula is a special case of a very general expression that is valid under very limited conditions” and that this formula was obtained for basins where channel flow was predominant.

^{1/3}and between 3 and 5 h for $n$ = 0.14 s/m

^{1/3}) after an initial rapid discharge increase, which can be attributed to the effect of small basins having reached their maximum discharges.

^{1/3}in order to achieve similar responses of the basin to those obtained by common time of concentration formulas and an aggregated model. As expected, a low value of the Manning coefficient provides faster response, while high values in a slower runoff advance. It is worth mentioning that a unique roughness coefficient value was used all over the basin; thus, a more detailed roughness discretisation would result in higher values at hillsides and areas outside of the hydrographic network, and lower ones in rivers and floodplains.

#### 4.2. Case Study 2

^{1/3}, corresponding to urban settlements, to 0.207 s/m

^{1/3}corresponding to forested area. All these values widely exceed the traditionally recommended values for hydraulic computations in artificial or natural channels and floodplains areas [38,39,40,81,82,83].

#### 4.3. Case Study 3

^{1/3}with steps of 0.02 s/m

^{1/3}, resulting in different hydrological responses. The computed water elevation in the reservoir at the basin outlet was compared with the field observations along the events and at the end of each one. Figure 4 shows the simulated water elevation for the four rainfall events analysed.

^{1/3}—one that achieves the best adjustment (0.005% of error). For this event, significant differences on the arrival time of the flood can be observed, with a time gap of around 12 h between the hydrographs corresponding to the minimum and maximum $n$ values. The evolution of the water elevation during the second-half of day 2 clearly shows faster hydrological responses for low values of $n$.

^{1/3}.

^{1/3}, the water elevation at the end of the event shows a good adjustment with relative error being less than 0.16%.

^{1/3}). In general, the hydrological response of the model is more sensible for low values of $n$ than for high ones, especially from the point of view of water resources. As expected, low values of $n$ produce larger overland flow discharges in shorter times.

^{1/3}. The precision of the results is aligned with the assumption of a unique Manning roughness coefficient value for the whole catchment, which in this case, was appropriate for hydrological purposes. On the other hand, for values of $n$ in the lower range, oscillations on the water surface elevation appear.

^{2}). Table 5 summarizes the performance of the model for the four rainfall events in terms of these indicators. A good adjustment is seen for 20130304_3d and 20131115_3d events, with low values of MAE and RMSE, but also with high values of R

^{2}. The performance of 20141128_2d event is, in general, the poorest—the simulated water resources are clearly underestimated during almost all the event. In contrast with the other events, as the hydrological response is slower in comparison with the observations, the indicators show the best adjustments are for low values of $n$. Finally, the 20150320_6d event presents the worst R

^{2}values. A peer-to-peer results analysis (RMSE and MAE) reveals that the model has, in general, a good adjustment, especially for values of $n$ greater than 0.06 s/m

^{1/3}.

## 5. Discussion

**On the roughness coefficient values and their effect on the hydrological response**

**On the role of the domain discretisation in the basin hydrological response**

^{3}/s is observed for calculation meshes with more than 1.9 million elements. This peak discharge increment is probably due to the better representation of the topography, in general, as well as the better definition of the river-channel, in particular, which improve the flow propagation representation. This last domain discretisation (1.9 M elements) represents approximately 19 elements per ha, which is still far from the values of flood studies where more than 1000 elements per ha is quite common [95].

**On the numerical approach**

## 6. Conclusions

^{1/3}, which would correspond to the hydraulic value for very smooth material, much different from those existing in natural basins.

## Supplementary Materials

^{3}/s) for the four basins of the Case Study 1 estimated by the Rational Method for a constant rainfall intensity of 25 mm/h, Table S2: Characteristics of the discretization of the Marquelia basin and parameters of the aggregated numerical approach, Table S3: Spatial characteristics of the land uses of the Marquelia basin and Manning roughness coefficient best fit to the 50-years return period synthetic hydrograph.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Fonseca, A.R.; Santos, M.; Santos, J.A. Hydrological and flood hazard assessment using a coupled modelling approach for a mountainous catchment in Portugal. Stoch. Environ. Res. Risk Assess.
**2018**, 32, 2165–2177. [Google Scholar] [CrossRef] - Kron, W. Flood Risk = Hazard + Values + Vulnerability. Water Int.
**2005**, 30, 58–68. [Google Scholar] [CrossRef] - ISDR Global Assessment Report on Disaster Risk Reduction; United Nations: Geneva, Switzerland, 2009; ISBN 978-92-1-332019-8.
- Fraga, I.; Cea, L.; Puertas, J.; Mosqueira, G.; Quinteiro, B.; Botana, S.; Fernández, L.; Salsón, S.; Fernández-García, G.; Taboada, J. MERLIN: Una nueva herramienta para la predicción del riesgo de inundaciones en la demarcación hidrográfica Galicia-Costa. Ing. Agua
**2021**, 25, 215. [Google Scholar] [CrossRef] - Thiemig, V.; Bisselink, B.; Pappenberger, F.; Thielen, J. A pan-African medium-range ensemble flood forecast system. Hydrol. Earth Syst. Sci.
**2015**, 19, 3365–3385. [Google Scholar] [CrossRef][Green Version] - Mure-Ravaud, M.; Binet, G.; Bracq, M.; Perarnaud, J.-J.; Fradin, A.; Litrico, X. A web based tool for operational real-time flood forecasting using data assimilation to update hydraulic states. Environ. Model. Softw.
**2016**, 84, 35–49. [Google Scholar] [CrossRef] - Alvarez-Garreton, C.; Ryu, D.; Western, A.W.; Su, C.-H.; Crow, W.T.; Robertson, D.E.; Leahy, C. Improving operational flood ensemble prediction by the assimilation of satellite soil moisture: Comparison between lumped and semi-distributed schemes. Hydrol. Earth Syst. Sci.
**2015**, 19, 1659–1676. [Google Scholar] [CrossRef][Green Version] - Beven, K. Rainfall-Runoff Modelling. The Primer; John Wiley & Sons, Ltd.: Chichester, UK, 2012; ISBN 9780470714591. [Google Scholar]
- Paudel, M.; Nelson, E.J.; Downer, C.W.; Hotchkiss, R. Comparing the capability of distributed and lumped hydrologic models for analyzing the effects of land use change. J. Hydroinform.
**2011**, 13, 461–473. [Google Scholar] [CrossRef] - Grimaldi, S.; Petroselli, A.; Tauro, F.; Porfiri, M. Time of concentration: A paradox in modern hydrology. Hydrol. Sci. J.
**2012**, 57, 217–228. [Google Scholar] [CrossRef][Green Version] - Michailidi, E.M.; Antoniadi, S.; Koukouvinos, A.; Bacchi, B.; Efstratiadis, A. Timing the time of concentration: Shedding light on a paradox. Hydrol. Sci. J.
**2018**, 63, 721–740. [Google Scholar] [CrossRef][Green Version] - Beven, K.J. A history of the concept of time of concentration. Hydrol. Earth Syst. Sci.
**2020**, 24, 2655–2670. [Google Scholar] [CrossRef] - Mulvany, T.J. On the use of self-registering rain and flood gauges in making observations of the relations of rainfall and flood discharges in a given catchment. Proc. Inst. Civ. Eng. Irel.
**1851**, 4, 18–33. [Google Scholar] - W.M.O. International Glossary of Hydrology. Report No. 385; World Meteorological Organization (W.M.O.): Geneva, Switzerland, 1974. [Google Scholar]
- NCRS Hydrology. National Engineering Handbook; US Department of Agriculture: Washington, DC, USA, 1972. [Google Scholar]
- Chow, V.T.; Maidment, D.R.; Mays, L.W. Applied Hydrology; MCGRAW-HIL: New York, NY, USA, 1988; ISBN 9780071001748. [Google Scholar]
- Témez, J.R. Cálculo Hidrometeorológico de Caudales Máximos en Pequeñas Cuencas Naturales; Ministerio de Obras Públicas y Urbanismo, Dirección General de Carreteras: Madrid, España, 1978; ISBN 7433-457-8. [Google Scholar]
- Kirpich, Z.P. Time of concentration of small agricultural watersheds. Am. Soc. Civ. Eng.
**1940**, 10, 362. [Google Scholar] - Mijares, A. Fundamentos de Hidrología de Superficie; Editorial Limusa, Grupo Noriega Editores: México D.F., México, 1998; ISBN 9681830148. [Google Scholar]
- CONAGUA. Manual de Agua Potable, Alcantarillado y Saneamiento: Drenaje Pluvial Urbano; Comisión Nacional del Agua. Naturales, Secretaría de Medio Ambiente y Recursos: Ciudad de México, México, 2016; ISBN 9786076260159. [Google Scholar]
- SCT. Estudios Hidráulico-Hidrológicos para Puentes: Manual de Análisis Hidrológicos; Secretaría de Comunicaciones y Transportes, Gobierno de México: Ciudad de México, México, 2000. [Google Scholar]
- Nanía, E.S.; Gomez-Valentín, M. Ingeniería Hidrológica, 2nd ed.; Grupo Editorial Universitario: Granada, España, 2014; ISBN 84-8491-636-7. [Google Scholar]
- Reed, S.; Koren, V.; Smith, M.; Zhang, Z.; Moreda, F.; Seo, D.J. Overall distributed model intercomparison project results. J. Hydrol.
**2004**, 298, 27–60. [Google Scholar] [CrossRef] - Refsgaard, J.C. Parameterisation, calibration and validation of distributed hydrological models. J. Hydrol.
**1997**, 198, 69–97. [Google Scholar] [CrossRef] - Cea, L.; Bladé, E. A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications. Water Resour. Res.
**2015**, 51, 5464–5486. [Google Scholar] [CrossRef][Green Version] - Caro, C.A. Modelación Hidrológica Distribuida Basada en Esquemas de Volúmenes Finitos. Ph.D. Thesis, School of Civil Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain, 2016. [Google Scholar]
- Kim, J.; Warnock, A.; Ivanov, V.Y.; Katopodes, N.D. Coupled modeling of hydrologic and hydrodynamic processes including overland and channel flow. Adv. Water Resour.
**2012**, 37, 104–126. [Google Scholar] [CrossRef] - Cea, L.; Garrido, M.; Puertas, J. Experimental validation of two-dimensional depth-averaged models for forecasting rainfall–runoff from precipitation data in urban areas. J. Hydrol.
**2010**, 382, 88–102. [Google Scholar] [CrossRef] - Viero, D.P.; Peruzzo, P.; Carniello, L.; Defina, A. Integrated mathematical modeling of hydrological and hydrodynamic response to rainfall events in rural lowland catchments. Water Resour. Res.
**2014**, 50, 5941–5957. [Google Scholar] [CrossRef][Green Version] - Yu, C.; Duan, J. Simulation of Surface Runoff Using Hydrodynamic Model. J. Hydrol. Eng.
**2017**, 22, 04017006. [Google Scholar] [CrossRef] - Nguyen, P.; Thorstensen, A.; Sorooshian, S.; Hsu, K.; AghaKouchak, A.; Sanders, B.; Koren, V.; Cui, Z.; Smith, M. A high resolution coupled hydrologic–hydraulic model (HiResFlood-UCI) for flash flood modeling. J. Hydrol.
**2016**, 541, 401–420. [Google Scholar] [CrossRef][Green Version] - Panday, S.; Huyakorn, P.S. A fully coupled physically-based spatially-distributed model for evaluating surface/subsurface flow. Adv. Water Resour.
**2004**, 27, 361–382. [Google Scholar] [CrossRef] - Toro, E.F. Riemann Solvers and Numerical Methods for Fluid Dynamics; Springer: Berlin/Heidelberg, Germany, 2009; Volume 40, ISBN 978-3-540-25202-3. [Google Scholar]
- Beven, K. Changing ideas in hydrology—The case of physically-based models. J. Hydrol.
**1989**, 105, 157–172. [Google Scholar] [CrossRef] - Jakeman, A.J.; Hornberger, G.M. How much complexity is warranted in a rainfall-runoff model? Water Resour. Res.
**1993**, 29, 2637–2649. [Google Scholar] [CrossRef] - Barnes, C.J. The art of catchment modeling: What is a good model? Environ. Int.
**1995**, 21, 747–751. [Google Scholar] [CrossRef] - Beven, K. How far can we go in distributed hydrological modelling? Hydrol. Earth Syst. Sci.
**2001**, 5, 1–12. [Google Scholar] [CrossRef] - Chow, V. Open Channel Hydraulics; McGraw-Hill Education: New York, NY, USA, 2006; ISBN 9780750668576. [Google Scholar]
- Barnes, H.H. Roughness characteristics of natural channels. J. Hydrol.
**1969**, 7, 354. [Google Scholar] - Arcement, G.J.G.J.J.J.; Schneider, V.R. Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains; Paper 2339; 19. Books and Open-File Reports Section; U.S. Geological Survey, Federal Center: Denver, CO, USA, 1989. [Google Scholar]
- Kalyanapu, A.J.; Burian, S.J.; McPherson, T.N. Effect of land use-based surface roughness on hydrologic model output. J. Spat. Hydrol.
**2009**, 9, 51–71. [Google Scholar] - Barnard, T.; Agnaou, M.; Barbis, J. Two Dimensional Modeling to Simulate Stormwater Flows at Photovoltaic Solar Energy Sites. J. Water Manag. Model.
**2017**, 25, 8. [Google Scholar] [CrossRef][Green Version] - USACE. Hydrologic Modeling System HEC-HMS. Technical Reference Manual; US Army Coprs of Engineers, Institute for Water Resources, Hydrologic Engineering Center: Dacis, CA, USA, 2000. [Google Scholar]
- USDA-SCS. SCS National Engineering Handbook, Hydrology, Section 4; US Department of Agriculture, Soil Conservation Service: Washington, DC, USA, 1972. [Google Scholar]
- USDA-SCS. National Engineering Handbook, Supplement A, Section 4, Chapter 10: Hydrology; US Department of Agriculture, Soil Conservation Service: Washington, DC, USA, 1985. [Google Scholar]
- USDA-NRCS. Part 630 Hydrology—Chapter 10. In National Engineering Handbook; US Department of Agriculture, Soil Conservation Service: Washington, DC, USA, 2004; p. 79. [Google Scholar]
- Bladé, E.; Cea, L.; Corestein, G.; Escolano, E.; Puertas, J.; Vázquez-Cendón, E.; Dolz, J.; Coll, A. Iber: Herramienta de simulación numérica del flujo en ríos. Rev. Int. Métodos Numér. Cálc. Diseño Ing.
**2014**, 30, 1–10. [Google Scholar] [CrossRef][Green Version] - Cea, L.; Bladé, E.; Corestein, G.; Fraga, I.; Espinal, M.; Puertas, J. Comparative analysis of several sediment transport formulations applied to dam-break flows over erodible beds. In Proceedings of the EGU General Assembly 2014, Vienna, Austria, 27 April–2 May 2014. [Google Scholar]
- Bladé, E.; Cea, L.; Corestein, G. Numerical modelling of river inundations. Ing. Agua
**2014**, 18, 68. [Google Scholar] [CrossRef] - Anta Álvarez, J.; Bermúdez, M.; Cea, L.; Suárez, J.; Ures, P.; Puertas, J. Modelización de los impactos por DSU en el río Miño (Lugo). Ing. Agua
**2015**, 19, 105. [Google Scholar] [CrossRef] - Cea, L.; Bermudez, M.; Puertas, J.; Blade, E.; Corestein, G.; Escolano, E.; Conde, A.; Bockelmann-Evans, B.; Ahmadian, R. IberWQ: New simulation tool for 2D water quality modelling in rivers and shallow estuaries. J. Hydroinform.
**2016**, 18, 816–830. [Google Scholar] [CrossRef][Green Version] - Ruiz-Villanueva, V.; Bladé, E.; Sánchez-Juny, M.; Marti-Cardona, B.; Díez-Herrero, A.; Bodoque, J.M. Two-dimensional numerical modeling of wood transport. J. Hydroinform.
**2014**, 16, 1077. [Google Scholar] [CrossRef] - Sanz-Ramos, M.; Bladé Castellet, E.; Palau Ibars, A.; Vericat Querol, D.; Ramos-Fuertes, A. IberHABITAT: Evaluación de la Idoneidad del Hábitat Físico y del Hábitat Potencial Útil para peces. Aplicación en el río Eume. Ribagua
**2019**, 6, 158–167. [Google Scholar] [CrossRef][Green Version] - Sanz-Ramos, M.; Bladé, E.; Torralba, A.; Oller, P. Las ecuaciones de Saint Venant para la modelización de avalanchas de nieve densa. Ing. Agua
**2020**, 24, 65–79. [Google Scholar] [CrossRef] - Sanz-Ramos, M.; Andrade, C.A.; Oller, P.; Furdada, G.; Bladé, E.; Martínez-Gomariz, E. Reconstructing the Snow Avalanche of Coll de Pal 2018 (SE Pyrenees). GeoHazards
**2021**, 2, 196–211. [Google Scholar] [CrossRef] - Sañudo, E.; Cea, L.; Puertas, J. Modelling Pluvial Flooding in Urban Areas Coupling the Models Iber and SWMM. Water
**2020**, 12, 2647. [Google Scholar] [CrossRef] - Aranda, J.Á.; Beneyto, C.; Sánchez-Juny, M.; Bladé, E. Efficient Design of Road Drainage Systems. Water
**2021**, 13, 1661. [Google Scholar] [CrossRef] - Sanz-Ramos, M.; Amengual, A.; Bladé, E.; Romero, R.; Roux, H. Flood forecasting using a coupled hydrological and hydraulic model (based on FVM) and highresolution meteorological model. E3S Web Conf.
**2018**, 40, 06028. [Google Scholar] [CrossRef] - Sanz-Ramos, M.; Martí-Cardona, B.; Bladé, E.; Seco, I.; Amengual, A.; Roux, H.; Romero, R. NRCS-CN Estimation from Onsite and Remote Sensing Data for Management of a Reservoir in the Eastern Pyrenees. J. Hydrol. Eng.
**2020**, 25, 05020022. [Google Scholar] [CrossRef] - Roe, P.L. A basis for the upwind differencing of the two-dimensional unsteady Euler equations. Numer. Methods Fluid Dyn. II
**1986**, 55–80. [Google Scholar] - Caro, C.A.A.; Lesmes, C.; Bladé, E. Drying and transport processes in distributed hydrological modelling based on finite volume schemes (IBER model). In Proceedings of the 9th Annual International Symposium on Agricultural Research, Athens, Greece, 11–14 July 2016; p. 33. [Google Scholar]
- Jenson, S.K.; Domingue, J.O. Extracting Topographic Structure from Digital Elevation Data for Geographic Information System Analysis. Photogramm. Eng. Remote Sens.
**1988**, 54, 1593–1600. [Google Scholar] - Bates, P.; De Roo, A.P. A simple raster-based model for flood inundation simulation. J. Hydrol.
**2000**, 236, 54–77. [Google Scholar] [CrossRef] - Johnstone, D.; Cross, W.P. Elements of Applied Hydrology; Civil Engineering Series; Ronald Press Company: New York, NY, USA, 1949; ISBN 978-1124128436. [Google Scholar]
- DPW. California Culvert Practice, 2nd ed.; Department of Public Works, DPW, Division of Highways: Sacramento, CA, USA, 1995. [Google Scholar]
- Viparelli, C. Ricostruzione dell’idrogramma di Piena; Istituto di Idraulica dell’Università di Palermo, Stab. Tip. Genovese: Napoli, Italy, 1961; Volume 6. [Google Scholar]
- WRB-IUSS. World Reference Base for Soil Resources. World Soil Resources Reports 106; Food and Agriculture Organization of the United Nations: Rome, Italy, 2015; ISBN 9789251083697. [Google Scholar]
- Chen, C. Rainfall Intensity-Duration-Frequency Formulas. J. Hydraul. Eng.
**1983**, 109, 1603–1621. [Google Scholar] [CrossRef] - Campos-Aranda, D.F. Introducción a la Hidrología Urbana; San Luis Potosí, México, 2010; ISBN 970-95118-1-5. Available online: https://bibliotecasibe.ecosur.mx/sibe/book/000051798 (accessed on 5 September 2021).
- Weiss, L.L. Ratio of true fixed-interval maximum rainfall. J. Hydraul. Div.
**1964**, 90, 77–82. [Google Scholar] [CrossRef] - Roux, H.; Amengual, A.; Romero, R.; Bladé, E.; Sanz-Ramos, M. Evaluation of two hydrometeorological ensemble strategies for flash-flood forecasting over a catchment of the eastern Pyrenees. Nat. Hazards Earth Syst. Sci.
**2020**, 20, 425–450. [Google Scholar] [CrossRef][Green Version] - ACA. Planificació de l’Espai Fluvial. Estudis d’inundabilitat en l’àmbit del projecte PEFCAT-Memòria Específica Conca de La Muga; Agència Catalana de l’Aigua. Generalitat de Catalunya: Barcelona, España, 2007. [Google Scholar]
- Llasat, M.C.; Rodriguez, R. Extreme rainfall events in Catalonia. The case of 12 November 1988. Nat. Hazards
**1992**, 5, 133–151. [Google Scholar] [CrossRef] - Martín-Vide, J. Geographical Factors in the Pluviometry of Mediterranean Spain: Drought and Torrential Rainfall; The University of Iowa, Iowa Institute of Hydraulic Research: Iowa, IA, USA, 1994. [Google Scholar]
- EEA. CORINE Land Cover 2006 Technical Guidelines; European Enviromental Agency, Technical Report No 17/2007; Office for Official Publications of the European Communities: Luxembourg, Luxembourg, 2007; ISBN 978-92-9167-968-3. [Google Scholar]
- Ramos-Fuertes, A.; Marti-Cardona, B.; Bladé, E.; Dolz, J. Envisat/ASAR Images for the Calibration of Wind Drag Action in the Doñana Wetlands 2D Hydrodynamic Model. Remote Sens.
**2013**, 6, 379–406. [Google Scholar] [CrossRef][Green Version] - Mateo Lázaro, J.; Sánchez Navarro, J.Á.; García Gil, A.; Edo Romero, V. Sensitivity analysis of main variables present in flash flood processes. Application in two Spanish catchments: Arás and Aguilón. Environ. Earth Sci.
**2014**, 71, 2925–2939. [Google Scholar] [CrossRef] - Allison, S.V. Review of Small Basin Runoff Prediction Methods. J. Irrig. Drain. Div.
**1967**, 93, 1–6. [Google Scholar] [CrossRef] - Fuentes, O.; Ravelo, A.; Ávila, A. Método Para Determinar Los Parámetros K, X Y Los Coeficentes De Tránsito Del Método De Muskingum-Cunge. In Proceedings of the XIX Congreso Nacional De Hidráulica; Asociación Mexicana de HIdráulcia: Cuernavaca, Mexico, 2006; p. 6. [Google Scholar]
- INEGI. Contínuo de Elevaciones Mexicano 3.0. Available online: https://www.inegi.org.mx/app/geo2/elevacionesmex/ (accessed on 15 July 2021).
- Sánchez-Juny, M.; Bladé, E.; Dolz, J. Analysis of pressures on a stepped spillway. J. Hydraul. Res.
**2008**, 46, 410–414. [Google Scholar] [CrossRef] - Sanz-Ramos, M.; Bladé, E.; Niñerola, D.; Palau-Ibars, A. Evaluación numérico-experimental del comportamiento histérico del coeficiente de rugosidad de los macrófitos. Ing. Agua
**2018**, 22, 109–124. [Google Scholar] [CrossRef][Green Version] - Bladé, E.; Sanz-Ramos, M.; Dolz, J.; Expósito-Pérez, J.M.; Sánchez-Juny, M. Modelling flood propagation in the service galleries of a nuclear power plant. Nucl. Eng. Des.
**2019**, 352, 110180. [Google Scholar] [CrossRef] - ICGC Descàrregues. Available online: https://www.icgc.cat/Descarregues (accessed on 2 February 2021).
- Demissie, H.K.; Bacopoulos, P. Parameter estimation of anisotropic Manning’s n coefficient for advanced circulation (ADCIRC) modeling of estuarine river currents (lower St. Johns River). J. Mar. Syst.
**2017**, 169, 1–10. [Google Scholar] [CrossRef] - Zhang, S.; Liu, Y. Experimental Study on Anisotropic Attributes of Surface Roughness in Watersheds. J. Hydrol. Eng.
**2017**, 22, 06017005. [Google Scholar] [CrossRef] - Zhang, S.; Liu, Y.; Zhang, J.; Liu, Y. Simulation study of anisotropic flow resistance of farmland vegetation. Soil Water Res.
**2017**, 12, 220–228. [Google Scholar] [CrossRef][Green Version] - Anees, M.T.; Abdullah, K.; Nordin, M.N.M.; Rahman, N.N.N.A.; Syakir, M.I.; Kadir, M.O.A. One- and Two-Dimensional Hydrological Modelling and Their Uncertainties. Flood Risk Manag.
**2017**, 11, 221–244. [Google Scholar] - Aureli, F.; Prost, F.; Vacondio, R.; Dazzi, S.; Ferrari, A. A GPU-accelerated shallow-water scheme for surface runoff simulations. Water
**2020**, 12, 637. [Google Scholar] [CrossRef][Green Version] - Ozcelik, C.; Gorokhovich, Y. An overland flood model for geographical information systems. Water
**2020**, 12, 2397. [Google Scholar] [CrossRef] - Roux, H.; Labat, D.; Garambois, P.-A.; Maubourguet, M.-M.; Chorda, J.; Dartus, D. A physically-based parsimonious hydrological model for flash floods in Mediterranean catchments. Nat. Hazards Earth Syst. Sci.
**2011**, 11, 2567–2582. [Google Scholar] [CrossRef][Green Version] - Echeverribar, I.; Morales-Hernández, M.; Lacasta, A.; Brufrau, P.; García-Navarro, P. Simulación numérica con RiverFlow2D de posibles soluciones de mitigación de avenidas en el tramo medio del río Ebro. Ing. Agua
**2017**, 21, 53. [Google Scholar] [CrossRef][Green Version] - García-Feal, O.; González-Cao, J.; Gómez-Gesteira, M.; Cea, L.; Domínguez, J.M.; Formella, A. An Accelerated Tool for Flood Modelling Based on Iber. Water
**2018**, 10, 1459. [Google Scholar] [CrossRef][Green Version] - Liang, Q.; Xia, X.; Hou, J. Catchment-scale High-resolution Flash Flood Simulation Using the GPU-based Technology. Procedia Eng.
**2016**, 154, 975–981. [Google Scholar] [CrossRef][Green Version] - Sanz-Ramos, M.; Bladé, E.; Escolano, E. Optimización del cálculo de la Vía de Intenso Desagüe con criterios hidráulicos. Ing. Agua
**2020**, 24, 203. [Google Scholar] [CrossRef] - USDA-NRCS. Part 630 Hydrology—Chapter 10. In National Engineering Handbook; US Department of Agriculture, Soil Conservation Service: Washington, DC, USA, 2010; pp. 449–456. [Google Scholar]

**Figure 1.**Location of the three case studies and the analysed basins: four in USA (Case Study 1), one in Mexico (Case Study 2), and one in Spain (Case Study 3).

**Figure 2.**Calculated S-type hydrographs related to the minimum (red line), maximum (blue line), and mean (green line) time of concentration (${t}_{c}$) calculated with empirical formulas, and each corresponding Manning coefficient ($n$): (

**a**) Brazos basin, Cow Bayu; (

**b**) San Antonio basin, Escondido Creek; (

**c**) Trinity basin, North Creek; and (

**d**) Brazos basin, North Elm Creek.

**Figure 3.**Results of Case Study 2: (

**a**) hydrograph resulting from the aggregated approach (dashed line), and from the distributed approach, the best fit of the roughness coefficient resulted (continuous line); (

**b**) first 24 h of the hydrograph from the distributed approach and hydrographs considering ± 20% of the roughness coefficients (dot and dashed lines).

**Figure 4.**Water elevation evolution in the reservoir for the events 20130304_3d (

**a**), 20131115_3d (

**b**), 20141128_3d (

**c**), and 20150320_6d (

**d**). Representation of the observed data (dotted line) and the results of the simulations using different Manning roughness coefficients (coloured lines).

**Figure 5.**Sensitivity analysis in Case Study 2 (Marquelia basin): (

**a**) variation of the peak discharge with the mesh size; (

**b**) variation of the time of concentration with the rainfall intensity.

Characteristic | Brazos Basin (Cow Bayu) | San Antonio Basin (Escondido Creek) | Trinity Basin (North Creek) | Brazos Basin (North Elm Creek) |
---|---|---|---|---|

Area (km^{2}) | 13.08 | 22.80 | 58.96 | 119.46 |

Mean slope (%) | 5.90 | 2.90 | 5.20 | 1.40 |

Main channel length (km) | 7.09 | 8.00 | 18.02 | 33.34 |

Formula | Time of Concentration (h) | |||
---|---|---|---|---|

Brazos Basin (Cow Bayu) | San Antonio Basin (Escondido Creek) | Trinity Basin (North Creek) | Brazos Basin (North Elm Creek) | |

Johnstone and Cross [64] | 1.98 | 3.05 | 3.35 | 9.07 |

DPW [65] | 1.63 | 2.40 | 4.13 | 10.02 |

NCRS [15] | 3.72 | 6.33 | 8.93 | 24.28 |

Giandotti [65] | 4.77 | 8.20 | 9.23 | 17.77 |

Kirpich [18] | 0.92 | 1.35 | 1.95 | 5.40 |

Viparelli [66] | 1.37 | 1.60 | 3.42 | 6.58 |

Témez [17] | 2.28 | 2.85 | 4.73 | 9.70 |

Minimum | 0.92 | 1.35 | 1.95 | 5.40 |

Mean | 2.38 | 3.68 | 5.10 | 11.83 |

Maximum | 4.77 | 8.20 | 9.23 | 24.28 |

Event | Cumulated Rainfall (mm) | Max. Intensity in 5-min (mm/h) | CN |
---|---|---|---|

20130304_3d | 181.3 | 30.0 | 81 |

20131115_3d | 123.2 | 54.0 | 50 |

20141128_2d | 150.9 | 61.2 | 65 |

20150320_6d | 197.4 | 67.2 | 50 |

**Table 4.**Manning roughness coefficient according to the land uses discretisation shown in Figure S3b that provides the best adjustment in the calibration process.

Land Use | $\mathit{n}$ |
---|---|

Rainforest agriculture | 0.138 |

Urban settlements | 0.051 |

Pine and oak forest | 0.207 |

Reservoir | 0.069 |

Pastureland | 0.069 |

River | 0.083 |

Savanna | 0.138 |

**Table 5.**Coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE) for each Manning roughness coefficient ($n$) evaluated.

Event | Statistic | Manning Coefficient (s/m^{1/3}) | |||||||
---|---|---|---|---|---|---|---|---|---|

0.02 | 0.04 | 0.06 | 0.08 | 0.10 | 0.12 | 0.14 | 0.16 | ||

20130304_3d | RMSE | 0.512 | 0.361 | 0.263 | 0.258 | 0.236 | 0.297 | 0.352 | 0.352 |

MAE | 0.262 | 0.130 | 0.069 | 0.067 | 0.056 | 0.088 | 0.124 | 0.124 | |

R2 | 0.953 | 0.982 | 0.990 | 0.993 | 0.993 | 0.991 | 0.988 | 0.984 | |

20131115_3d | RMSE | 0.214 | 0.145 | 0.095 | 0.073 | 0.070 | 0.078 | 0.088 | 0.099 |

MAE | 0.046 | 0.021 | 0.009 | 0.005 | 0.005 | 0.006 | 0.008 | 0.010 | |

R2 | 0.903 | 0.964 | 0.979 | 0.973 | 0.962 | 0.945 | 0.925 | 0.902 | |

20141128_2d | RMSE | 0.485 | 0.521 | 0.580 | 0.630 | 0.669 | 0.703 | 0.732 | 0.758 |

MAE | 0.235 | 0.272 | 0.336 | 0.397 | 0.447 | 0.494 | 0.536 | 0.575 | |

R2 | 0.767 | 0.756 | 0.734 | 0.714 | 0.699 | 0.685 | 0.672 | 0.660 | |

20150320_6d | RMSE | 0.511 | 0.374 | 0.305 | 0.282 | 0.269 | 0.261 | 0.255 | 0.252 |

MAE | 0.261 | 0.140 | 0.093 | 0.080 | 0.072 | 0.068 | 0.065 | 0.063 | |

R2 | 0.255 | 0.282 | 0.298 | 0.303 | 0.306 | 0.309 | 0.311 | 0.314 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sanz-Ramos, M.; Bladé, E.; González-Escalona, F.; Olivares, G.; Aragón-Hernández, J.L. Interpreting the Manning Roughness Coefficient in Overland Flow Simulations with Coupled Hydrological-Hydraulic Distributed Models. *Water* **2021**, *13*, 3433.
https://doi.org/10.3390/w13233433

**AMA Style**

Sanz-Ramos M, Bladé E, González-Escalona F, Olivares G, Aragón-Hernández JL. Interpreting the Manning Roughness Coefficient in Overland Flow Simulations with Coupled Hydrological-Hydraulic Distributed Models. *Water*. 2021; 13(23):3433.
https://doi.org/10.3390/w13233433

**Chicago/Turabian Style**

Sanz-Ramos, Marcos, Ernest Bladé, Fabián González-Escalona, Gonzalo Olivares, and José Luis Aragón-Hernández. 2021. "Interpreting the Manning Roughness Coefficient in Overland Flow Simulations with Coupled Hydrological-Hydraulic Distributed Models" *Water* 13, no. 23: 3433.
https://doi.org/10.3390/w13233433