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Agrociencia
versión On-line ISSN 2521-9766versión impresa ISSN 1405-3195
Agrociencia vol.50 no.7 Texcoco oct./nov. 2016
Water-soils-climate
Direct runoff events simulation in small basins with the HIDRAS model
^{1} Facultad Ingeniería, División de Investigación y Posgrado, Universidad Autónoma de Querétaro, Querétaro, 76010, México. (toniokv2@gmail.com), (nabil@uaq.mx), (egs@uaq.mx), (chagcarlos@gmail.com).
^{2} Instituto Mexicano de Tecnología del Agua, Jiutepec, Morelos, 62550, México. (cbfuentesr@gmail.com).
Direct runoff is the integrated effect of rain, interception, evapotranspiration, infiltration and depth of overland flow at a specific point in the watershed. Conversion of precipitation to runoff is a complex process that depends on both spatial and temporal distribution of the rains and the physical characteristics of the watershed. This study had the objective of proposing procedures for simulating direct runoff at the event scale in small watersheds. We selected two experimental watersheds of Mexico with different characteristics in terms of size, location, vegetation type, topography, and rainfall regime: the Mixcoac River watershed in the Valley of Mexico, and the Cerro Blanco runoff unit, in Tabasco. The simulations were conducted with our own hydrological model, which we call HIDRAS, in which the methods proposed by Haan et al. (1994) and Sánchez and Gracia (1997) were implemented to calculate hydrographs using a scheme of unitary response to correct the effects of regulation. Flow routing was done using an integral form of the dynamic advection-diffusion equation. The hydrographs resulting from the simulation were assessed comparing their main elements quantitatively with the measured hydrographs and in terms of the NashSutcliffe index (NS). The results were favorable after applying calibration techniques. NS efficiency indexes of 0.75 and 0.83 were obtained for the first and second study cases, respectively. In the Cerro Blanco runoff unit, for which the database is ample, the model was validated: NS was 0.81 and 0.74 when events previous and posterior to that used for calibration were simulated. This validation allows us to recommend application of the methodology developed in this study to other cases of interest with characteristics similar to those presented here.
Key words: Synthetic hydrographs; HIDRAS; distributed hydrological modelling; hydrograph calibration
El escurrimiento directo es el efecto integrado de la lluvia, intercepción, evapotranspiración, infiltración y el escurrimiento en lámina sobre el terreno, en un punto específico de una cuenca. La conversión de las lluvias a escurrimiento es un proceso complejo que depende tanto de la distribución espacial y temporal de las lluvias como de las características físicas de la cuenca. Este estudio tuvo por objetivo plantear procedimientos para simular el escurrimiento directo a escala de evento en cuencas pequeñas. Como casos de estudio se eligieron dos cuencas experimentales de México con características diferentes en cuanto a tamaño, ubicación, tipo de vegetación, topografía y régimen pluviométrico: río Mixcoac, en el valle de México; y la unidad de escurrimiento Cerro Blanco, en Tabasco. Las simulaciones se realizaron con un modelo hidrológico propio denominado HIDRAS, en el cual se implementaron los métodos propuestos por Haan et al. (1994) y Sánchez y Gracia (1997) para calcular hidrogramas, usando un esquema de respuesta unitaria para corregir los efectos de regulación. El tránsito de avenidas se realizó usando una forma integral de la ecuación dinámica de advección-difusión. Los hidrogramas resultantes de la simulación se valoraron comparando cuantitativamente sus principales elementos con los hidrogramas medidos y en términos del índice Nash Sutcliffe (NS). Los resultados fueron favorables después de aplicar técnicas de calibración; se obtuvieron índices de bondad NS de 0.75 y 0.83 para el primer y segundo caso de estudio, respectivamente. En la unidad de escurrimiento Cerro Blanco, donde la base de datos es amplia, se logró validar el modelo y NS fue 0.81 y 0.74, al simular eventos previos y posteriores al utilizado para realizar la calibración. Esta validación permite recomendar la aplicación de la metodología desarrollada en este estudio a otros casos de interés con características similares a las expuestas.
Palabras clave: Hidrogramas sintéticos; HIDRAS; modelación hidrológica distribuida; calibración de hidrogramas
Introduction
One important aspect of hydrology is determining how much water will flow in a stream after a given rainfall event. When runoff data are not available or not sufficient for reliable interpretation or extrapolation, rainfallrunoff relationships can be very useful for generating information of runoff from records of precipitation (^{OMM, 1994}). An adequate relationship between precipitation and runoff allows good estimation of runoff in a watershed and can be used in the design of flood-control infrastructure or in making timely forecasts. It can also serve to operate existing works and emit warnings to mobilize populations in areas at risk (^{Domínguez et al., 2008}).
Hydrological simulation models tend to integrate different processes that previously were studied separately. Their heavy dependence on spatial data has led to coupling them with geographic information systems (GIS), and even to integrating them under a single platform (^{Domínguez et al., 2008}; ^{Guzmán et al., 2011}; ^{Bhatt et al., 2014}; ^{Fotakis et al., 2014}). Such is the case of distributed parameter physicalhydrological models, whose objective, besides being a tool in forecasting, is to help understand the physical system and provide a method of analysis of the involved phenomena. In this sense, ^{Mobayed and Cruickshank (1998)}, ^{Mobayed and Ortiz (2000)} and ^{Mobayed (2009) }developed the distributed hydrological model HIDRAS, which integrates digital climatological, hydrometric, physiographic and topographic information processing on a single platform to estimate hydrological parameters and implements calculation algorithms of the different stages of the rainfall-runoff process.
The objective of this study was to simulate direct runoff at the event scale in small watersheds implementing procedures based on hydrological methods in the HIDRAS model for calculation of hydrographs applicable to the cases included in this study, after previous calibration and validation of the model.
Materials and methods
The HIDRAS model
The distributed hydrological model HIDRAS utilizes the information of digital elevation models (DEM), not only to define flow directions and accumulation of elements for configuring the drainage network, but also to scale the watershed in geomorphological cells (^{Mobayed and Cruickshank, 1998}), a minimal but sufficient grouping of elements that shape a tributary surface. This grouping corresponds to the minimum area capable of forming an incipient runoff flow (threshold area).
For pluvial runoff, each unit produces an incipient, peculiar hydrograph equivalent to the excess precipitation of each unit. Flow routing is based on an integral form of the dynamic equation of advection-diffusion, which is a simplification of the equations of Saint-Venant for transitory 1D open channel flow (^{Diskin and Ding, 1994}). Given that the shape and size of a geomorphological cell can modify the hydrograph defined only in function of excess rainfall, a convolution scheme is used to characterize the regulatory effect of the tributary area. And to assess the effect produced by the flood areas, the change that celerity and the diffusion coefficient undergo when runoff occurs in the modified section of the flood area (plain) is taken into account. The hydrographs that a flow routing produces without the effect of regulation serves as an element of reference to quantify the retention and return to current volumes by comparison with the hydrographs regulated to estimate both overall retention and that associated with each element of the drainage network.
Excess rainfall, hydrographs and its routing
In the HIDRAS model, effective precipitation (Pe), that is, the part of the total precipitation that participates in runoff, is calculated with the expression proposed by the Soil Conservation Service of the United States (^{SCS, 1993}), in which P is total precipitation and S is the potential retention (both in mm).
To standardize the method, the adimensional number CN is defined, so that 0<CN≤100, being maximum for impervious surfaces and lower for natural terrains. This number and the potential retention S are related by:
The above equations are valid when the initial abstraction (Ia) is lower than the total precipitation (P). Studying the results of many small experimental watersheds, the SCS found the following empirical relationship to estimate the initial abstraction:
To transform effective precipitation (Pe) into direct runoff, in the HIDRAS model we implemented the method of ^{Haan et al. (1994)} and that proposed by ^{Sánchez and Gracia (1997)}, which are presented below.
^{Haan et al. (1994)} proposed the following adimensional relationship to generate the ordinates (q _{ u } ), in time (t), as a function of the peak time (tp), maximum flow (qp) and an adimensional parameter K _{ H } :
According to these authors, the unitary adimensional hydrograph proposed by the SCS is reproduced adequately by equation (4) when K _{ H } ≈3.77.
^{Sánchez and Gracia (1997)} based their method on the following hypothesis: losses, as output, are proportional to storage. Based on this assumption, the continuity equation and the relationships between the runoff coefficient (CE), losses (CP), runoff depth (BE) and lost depth (BP), they deduced the following expression to calculate the variation in depth h of time t at t+1:
where i _{ t } is the precipitation intensity at time t and BC=BE/CE. Since h _{ t+1 } =h _{ t } +Δh, there is a criterion that allows rapid calculation of the depth of rainfall in the watershed if BE is known. Calculation of this coefficient can be obtained by a numerical method, such that when the last time interval is arrived at, the magnitude of the depth h _{ final } is lower than a certain tolerance limit near zero, in which it is verified that:
The output flow, that is, the ordinates of the hydrograph, which involve the area (A) of the watershed, are given by the following expression:
Flow routing is performed using the method proposed by ^{Diskin and Ding (1994)}. The integral solution does not require a subdivision for routing a flow. It is expressed as an impulse response function, that is, it can be applied directly to an input value I to obtain the output Q.
In this case, Q _{ j } is an ordinate of the output curve associated with time jΔt, while I _{ k } refers to the input in time kΔt. The value of u is estimated with equation (9) for time t=(j-k+1)Δt, distance L between hydrographs, and for mean values of the speed and diffusion coefficients, C and D, respectively The methodology for characterization of C and D can be consulted in the study of ^{Mobayed and Ortiz (2000)}.
Parameter calibration
The HIDRAS model uses the method of optimization known as differential evolution (^{Storn and Price, 1997}) to find values of the parameters involved in the methods of hydrological calculation with which the best value of the ^{Nash-Sutcliffe (1970)} index can be obtained and whose expression is the following:
where NS is the Nash-Sutcliff index; NQ is the number of ordinates of the calculated hydrograph; Qc(i) and Qo(i) are the calculated and observed flows, respectively, in the time interval i;
Study cases
There is sufficient information to carry out hydrological modelling of the two experimental watersheds: Mixcoac, in the Valley of Mexico, and Cerro Blanco, on the border between Chiapas and Tabasco, Mexico. The Mixcoac River watershed has an area of 31.5 km^{2}; medium and highly permeable soils predominate; vegetation peculiar to fir (oyamel) forests is dense. The Cerro Blanco runoff unit belongs to the sub-watershed of the Sierra River. It has an area of approximately 0.67 ha. Plant soil cover is cultivated grass, soil has good permeability and land use is agriculture. The pluviometric and hydrometric data used in this study were obtained from ^{Domínguez et al. (2008)} and Granada et al. (2014).
Information processing
In this study, we followed the methodological process shown in the flow chart of Figure 1, which shows how to operate the HIDRAS model. The Digital Elevation Models (DEM) of the Instituto Nacional de Estadística y Geografía (INEGI) were used with a cell resolution of 5 m and a scale of 1:10 000. Also used were vector maps that include descriptive tables of soil cover at a scale of 1:50 000.
For the Mixcoac River watershed, we worked with a distributed parameter model scheme, a threshold of a minimum area of 10 800 cells (0.27 km^{2}), and obtained a network of channels and a total of 92 geomorphological cells with areas (A) in the interval of 0.375≤A≤77.40 ha and assigned a runoff curve number (CN) between 31≤CN≤91. In the case of the runoff unit Cerro Blanco, because of its size, we did not discretize the study area. For this reason, the model used was of a global type with a single channel, and no flow routing; the runoff curve number (CN) assigned was 69.
Results and discussion
To test the reliability of the algorithms formulated by each of the methods of calculating hydrographs, rainfall-runoff events were simulated with the HIDRAS model. The event (E1) selected was that registered on July 28, 1998, in the Mixcoac River watershed, with precipitation (P) of 31.97 mm and duration of 4.5 h. In the Cerro Blanco runoff unit, we selected the storm event registered on October 11, 2011 (E2), with P of 46.4 mm and duration of 9.75 h. Two simulations were performed for each event. For the first, we used initial parameter values and the second was done after executing the parameter calibration process. In each study case, the latter was applied only to the method of formulation of hydrographs that had the best results. Table 1 presents the values of the initial parameters and those resulting from the calibration process. The calibration process was based on the results of the simulation with the initial parameters. During this simulation, the best results in the calculation of direct runoff in the Mixcoac River watershed were obtained by applying the Haan method to rainfall event E1. This resulted in a hydrograph similar in shape and volume to the measured hydrograph, but with differences in the values of base time, which was overestimated, peak time and peak flow. The latter two acquire values lower than the recorded values. Based on this result, the process of calibration involved the shape parameter K _{ H } , which, once calibrated, improved the Nash-Sutcliffe efficiency index (NS) of -0.13 to 0.75 (Table 1). The Sánchez and Gracia method, before calibrating, produced a runoff graph very similar to that recorded in the Cerro Blanco runoff unit on October 11, 2011. The graph coincided with certain time lags and the way the flows occurred, but it did not coincide with volumes since the calibration, which initiated with an NS value of -4.98, mainly affected the parameters that modify the volume, such as the initial abstraction (Ia), which reduced its value to a little more than half (Table 1). Moreover, the curve number (CN), which, by increasing after calibration (Table 1), reflects higher preceding moisture conditions than those assumed. This can be verified by reviewing the rainfall records of the dates previous to the event being analyzed, and thus, it results in a larger volume of direct runoff, which improves the target function NS at a value of 0.83.
Parámetro | Mixcoac | Cerro Blanco | ||
Inicial | Calibrado | Inicial | Calibrado | |
Número de curva | 31 ≤ CN ≤ 91 | - | 69 | 77.5 |
Abstracción inicial (mm) | 5.0 ≤ Ia ≤ 113.0 | - | 22.8 | 10.2 |
Coeficiente de Haan K _{ H } | 3.77 | 3.00 | 3.77 | - |
Nash - Sutcliffe NS | -0.13 | 0.75 | -4.98 | 0.83 |
The results of the simulation with the resulting parameters of the calibration are shown in Figure 2, which presents the total discharge, calculated (Qc) and observed (Qo) together, in the lower part, and the input hyetograph (P), in the upper part, for each of the simulation scenarios. In the case of the Mixcoac River (Figure 2A), the simulated hydrograph was obtained with the method of Haan, resulting in a maximum flow of 14.30 m^{3} s^{-1}, which had a time lag of one interval (15 min) relative to the measured peak time, which, compared with the measured maximum flow of 15.42 m^{3} s^{-1}, represents an error of 7.3 %, obtained with a goodness of fit NS index of 0.75. In the runoff unit Cerro Blanco, the hydrograph shows discharges expressed in L s^{-1} units, which are recorded and estimated every 10 min (Figure 2B). It should be pointed out that in both hydrographs, the base flow was separated from the total discharge by means of a conventional graphic procedure and added to direct runoff since a sub-routine for calculating this runoff component has not yet been implemented.
Because of the ample hydrometric and pluviometric database available at the Cerro Blanco runoff unit, it is feasible to validate the parameters calibrated for the Sánchez and Gracia method. In this case, two events are simulated, one before and the other after that used during the process of calibration (October 11, 2011). Figure 3 shows the results of the validation. Here, it can be seen that the method used with the calibrated parameters adequately simulates the measured hydrographs, in which a goodness of fit NS index of 0.81 is obtained for the event of October 4 (Figure 3A) and an NS of 0.74 for October 16 (Figure 3B). The process of validation could not be carried out for the case of the Mixcoac River watershed because of the lack of other runoff records.
In the analysis of the three hydrographs measured in the runoff unit Cerro Blanco (Figure 2B and 3B), it was observed that runoff occurs almost immediately after precipitation initiated, meaning that the initial abstraction is small or negligible, or that saturation of the soil is elevated. This coincides with the hypothesis of the Sánchez and Gracia method, which defines the losses and the flow volume as proportional to the rate of precipitation, regardless of the effect of initial delay that the anteceding moisture deficit produces, and since the dimensions of the area do not favor regulation of rain volumes, this method produces a runoff graph very similar to the graph of recorded data.
Conclusions
In the Mixcoac River watershed, the Haan method was able to reproduce the hydrograph of the recorded event with an acceptable NS efficiency index (NS=0.75), while in the runoff unit Cerro Blanco, because of its characteristics of homogeneous topography and soil use and type, it responded better to the Sánchez and Gracia method (NS=0.83).
The HIDRAS model, which has different methods of calculating the rainfall-runoff process and a semiopen code, allowed adding the algorithms necessary for finding that which provides the best hydrological response. These results confirm the convenience of using hydrological methods different from traditional methods, particularly when the hypotheses for which they were developed and tested are not met. The lack of sufficient hydrometric data is common in this country, and therefore, it is indispensable to have hydrological models for estimating runoff that a rainfall event can generate.
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Received: July 2015; Accepted: December 2015