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

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.

Figure 1 Methodological process of the HIDRAS model. 

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 km²), 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.

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 m³ 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 m³ 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.

Figure 2 Simulated hydrographs compared with measured hydrographs. 

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.

Figure 3 Model validation hydrographs. 

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.