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## Agrociencia

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*versión On-line* ISSN 2521-9766*versión impresa* ISSN 1405-3195

### Agrociencia vol.45 no.2 Texcoco feb./mar. 2011

Agua–Suelo–Clima

**Modeling the observed hydrograph recession of a small semiarid watershed**

**Modelación de las curvas de recesión de hidrogramas observados en una cuenca semiárida pequeña **

**Gerardo Núñez–González ^{*}, Miguel A. Domínguez–Cortázar, Eusebio Jr. Ventura–Ramos, Aldo I. Ramírez**

*División de Investigación y Posgrado, Facultad de Ingeniería, Universidad Autónoma de Querétaro, Centro Universitario. 76010. Cerro de las Campanas s/n, Querétaro, Querétaro, México. * Author for correspondence:* (gerardo.nunez@uaq.mx).

Received: August, 2010.

Approved: February, 2011.

**Abstract**

The recession curve of observed hydrographs was modeled based on the concept of linear reservoirs. Each of the recession limbs was fitted using a non–linear curve fitting procedure based on Levenberg–Marquardt algorithm. The results showed that in general the response of this watershed is primarily non–linear. Besides, the recession of the observed hydrographs showed a good fit by means of a two linear reservoirs model with parallel discharge. The mean residence time for this watershed varied between 0.1 and 6 h for direct runoff, while it ranged between 0.7 and 18.5 h for subsurface flow. Finally, it was founded that subsurface flow is an important component of the hydrographs. From these results it can be concluded that hydrograph recession analysis technique could be useful in order to obtain a better insight about the runoff components as well as the recession process in watersheds of semiarid zones.

**Key words: **hydrograph analysis, surface flow, subsurface flow.

**Resumen**

La curva de recesión de hidrogramas observados se modeló con base en el concepto del reservorio lineal. Cada una de las curvas de recesión se ajustó usando un procedimiento de ajuste de curvas no lineal, basado en el algoritmo de Levenberg–Marquardt. Los resultados mostraron que en general la respuesta de la cuenca es principalmente no lineal. Además, la recesión de los hidrogramas observados mostró un buen ajuste por medio del modelo de dos reservorios lineales con descarga paralela. El tiempo medio de residencia en la cuenca varió entre 0.1 y 6 h para el escurrimiento directo, y entre 0.7 y 18.5 h para el flujo subsuperficial. Por último, se encontró que el flujo subsuperficial es un componente importante de los hidrogramas. Con estos resultados se puede concluir que la técnica de análisis de la recesión de hidrogramas podría ser útil para tener una mejor comprensión acerca de los componentes del escurrimiento, así como del proceso de recesión en las cuencas de zonas semiáridas.

**Palabras clave: **análisis de hidrogramas, flujo superficial, flujo subsuperficial.

**Introduction**

The understanding of hydrological processes at watershed scale is an important task in order to optimize management of the available surface water and groundwater resources, as well as for the development of hydrological models (Maldonado–de León *et al., *2001; Torres–Benites *et al., *2005; Paz–Pellat, 2009). Ephemeral streams, which flow only in rainy season, are the predominant fluvial environments in arid and semiarid zones (Shaw and Cooper, 2008). Mechanisms of streamflow generation in ephemeral streams are dominated by throughflow, overland flow, and perched zones of saturated soil and regolith water (Rassam *et al., *2006).

Hydrograph separation is used in order to understand hydrological processes both in humid and temperate basins as well as in semiarid areas (Bohté *et al., *2010). This process is often carried out by considering a storm hydrograph as consisting of two components; basefiow, which represents the part of the discharge which enters into a stream mainly from groundwater, and direct runoff. In a natural watershed, streamflow is sustained after a precipitation event because of drainage from a number of different types of water storages usually located both above and below ground level (Griffiths and Clausen, 1997). In humid and temperate watersheds, groundwater discharge from the shallow unconfined aquifer is commonly assumed to be the main contributor to baseflow (Wittenberg and Sivapalan, 1999). However, groundwater contribution is rarely present in small upland catchments (Hewlett and Hibbert, 1963) as well as in arid zones (Rassam *et al., *2006) where the components of the hydrograph are considered to be subsurface flow (proportion of precipitation which has not passed down to the water table) and direct runoff. The main objective of this study was to modeling the recession of observed hydrographs of a small semiarid watershed in order to obtain a better insight about the runoff components and the recession process of this watershed.

**MATERIALS AND METHODS**

**Theory**

Tallaksen (1995) points out that hydrological research has focused mostly on the baseflow recession for which the exponential function seen in equation 1 is widely used to describe its behavior:

where *Q _{t }* is the discharge at time

*t,*Q

_{0}the initial discharge, and α a recession constant expressed in inverse time. When the assumption that the recession curve of the hydrograph is the result of more than a single reservoir is made, it could be conceptually modeled as the sum of

*n*linear reservoirs. For example, in the case of two linear reservoirs as (Moore, 1997):

where the subindex 1 and 2 make reference to the first and the second reservoir.

**Data**

Measurements of streamflow were made at the small watershed known as La Barreta which is part of Santa Catarina basin (Germán and Domínguez, 2000) in the state of Querétaro, México located at 20° 30' and 20° 54' N, and 100° 17' and 100° 36' W. The watershed has an area of 4.32 km^{2} and its altitude is between 2100 and 2600 m. The time of concentration (Tc) according to the U.S. Corps of Engineers formulae (Campos–Aranda, 2010) for this watershed is around 42 min. Streamflow measurements were made at the outlet of the watershed during two runoff seasons (2005–2006) with a V–shape weir equipped with a water–level sensor. During the period of observation, 17 runoff events were recorded with a time resolution of 10 min each. A summary of the observed runoff events is shown in Table 1 and examples of the hydrograph recorded are presented in Figure 1.

**Methods**

The first stage of this research consisted in the analysis of the semi–logarithmic graph of the recession curves in order to identify the linearity of those curves. Afterward, the data of recession curves were used to fit a model according to equations 1 and 2. In this investigation, in order to establish a conceptual relationship between the direct runoff and subsurface flow, and the components of the models, equation 2 was favored. The fitting process was carried out through an iterative nonlinear curve fitting procedure based on nonlinear least squares using the Levenberg–Marquardt algorithm (Moré, 1978). In order to test the goodness of fit of the equations the coefficient of determination (R^{2}) and the root mean square error (RMSE) were calculated. Finally, assuming that each reservoir identified within the fitting process could represent a runoff component conceptually, the 17 hydrographs recorded were separated into subsurface flow and direct runoff in order to determine the volume coming from each runoff component for comparison purposes, it under the assumption that there was not baseflow.

**RESULTS AND DISCUSSION**

**Graphical interpretation of the hydrograph recession**

The results of the graphical analysis indicate that only 3 of the 17 hydrograph recession analyzed (events 3, 9 and 17 in Table 2) could be considered as linear reservoirs which suggest that this watershed behaves mainly like a multi–reservoir system; in other words, the recession in this watershed corresponds to a nonlinear process. Therefore, the modeling of the recessions of these hydrographs could be done in a more effective way by using equation 2. The aforementioned results are product of the complex interactions of different runoff sources which include overland flow and interflow; this kind of behavior has already been recognized for semiarid watersheds (Peters and Havstad, 2006).

**Equations fitting**

Equations were fitted for all the recessions listed above, obtaining 14 fittings with equation 2 and 3 with equation 1. Details of the fitted equations are shown in Table 2 where sub–index 1 refers to the first reservoir and sub–index 2 to the second reservoir. In the same Table α values for each reservoir are presented. These values were used to obtain the mean residence time as 1/α. It was noted that for the first reservoir the mean time of residence varied between 0.1 y 5–7 h, while in the second reservoir the variation of 1/αwas between 0.65 and 18.5 h. The average of the mean time of residence was 1.1 h for the first reservoir and 4.0 h for the second. The mean residence times obtained show a very rapid response of the watershed which is characteristic of hillslopes and watersheds with steep slopes (Weiler and McDonnell, 2004).

**Direct runoff and subsurface flow volumes**

In Table 3 it is shown a comparison between the direct runoff and subsurface flow drained volumes for the 17 hydrographs. Subsurface flow index ranged from 0 for events number 9 and 17, to 81 % for event 13 with a mean value of 38.5 %. Direct runoff oscillated between 19 and 100 %, for events number 9 and 17 of the total runoff recorded (Table 3). Mean values show that approximately 61.5 % of the runoff is due to a rapid response and the 38.5 % occurs more slowly. These results show that most of the total water flowing at the watershed outlet comes from direct runoff although it is noteworthy that the subsurface flow is a very important component of the drainage.

In Table 4 a comparison between the main statistics of the runoff components is presented for the two runoff seasons monitored in the study area; no significant differences were found between the statistics. However, the coefficient of variation shows that during 2006 the runoff behavior was more heterogeneous.

**CONCLUSIONS**

In this study, 17 hydrographs recorded in a small semiarid watershed in the state of Querétaro, México were used to analyze its recession curves. The results showed that for this watershed the hydrograph recession was in general non–linear and can be well represented with a model of two linear reservoirs. Obtained mean residence times for each of the runoff components showed clear differences between them. In the case of direct runoff, an oscillation of between 0.1 and 6 hours was noted, while the subsurface flow, it ranged between 0.65 and 18.5 hours. The variability in this parameter could be attributed to differences in the pre–event soil moisture content and the magnitude of the rainfall generating runoff. Finally, from the hydrograph separation it could be concluded that in this watershed subsurface flow represents an important amount of the runoff hydrograph which can contribute with a small portion of the following hydrographs, especially in the case of runoff events which are separated by few hours or less than a day.

**ACKNOWLEDGEMENTS**

The first author acknowledges the financial support provided by the Consejo Nacional de Ciencia y Tecnología (CONACyT) for his doctorate studies at the Universidad Autónoma de Querétaro. The authors would also like to acknowledge Silvia C. Stroet of the Engineering Faculty for editing the English in this document.

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