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Hydrological modeling is an essential tool to evaluate water resources in hydrological basins. The time invested in it depends on the structure of the hydrological model chosen, the amount and quality of information required and the efforts invested in calibration. CEQUEAU is a distributed hydrological model developed at the INRS-ETE, Quebec, Canada. The basin is divided into cells and the rainfall-runoff process is simulated cell by cell until the outlet. Recent advances in geomatics make it possible to develop modules integrated in geographic information systems (GIS) to facilitate the processing of information required by hydrological models. The objective of the present investigation is to implement the CEQUEAU model in Idrisi GIS for the hydrological modeling of basins, thereby reducing information processing time and improving limitations in the original version, such as the number of discretization cells and methods to calculate evapotranspiration. This document presents the results from the implementation of the CEQUEAU model, including evapotranspiration, water levels (in reservoirs, soil and aquifers) and hydrographs. These results show that these new changes provide more hydrology options to the user and with better results.

Surface hydrology has developed considerably as a science primarily because of systematic knowledge of the land phase of the hydrological cycle, its complexity and the difficulty of obtaining exact and detailed meteorological and hydrometric observations for large areas of drainage basins.

Hydrological models have emerged from the need to calculate the magnitudes of the variables involved in the water cycle. A model is useful to solve a significant number of hydrological studies, such as: reconstitution and generation of long series of data, detection of observation errors, forecasting of extreme events, calculation of flows at ungauged sites, operation of reservoirs and conducting environmental studies, among others. With multidisciplinary approaches, hydrological models are useful to simulate water quality, for example, models that simulate transport of pollutants and those that simulate aquifer levels in agricultural areas, among others [

Since the 1970s, the development of computing has stimulated the generation of distributed hydrological mo- dels (DHM). Investigations using DHM for large areas are based on the hydrological investigation of processes [

DHM have been used to evaluate hydrological conditions (runoff, infiltration, aquifer recharge), the state of vegetation (density, quality) and climate change over large regions. In fact, distributed models can be applied to any type of hydrological problem, including forecasting in basins with no instrumentation.

The use of GIS in hydrological modeling has become more widespread over recent decades. For example, in 1998, the Center for Research in Water Resources (CRWR) at the University of Texas created CRWR-PrePro, a pre-processor in ArcView which extracts information from digital spatial data and makes it available for use by the hydrological program HEC-HMS, which calculates flows [

Molnar and Julien [

It is evident that significant developments have occurred in hydrological models over the past three decades. Three primary factors are involved in these developments: 1) technological advances in geographic information systems (GIS); 2) availability of digital elevation models (DEM) used in GIS; and 3) availability of various digital databases (climatological and hydrometric). This has gradually made it possible to more quickly and accurately obtain the parameters required by hydrological models [

The overall objective of this investigation is to implement the CEQUEAU distributed model in the Idrisi geographic information system and apply that model to the study of a hydrological basin to analyze the efficiency and speed of this new tool to simulate flows.

The specific objectives are: implement the CEQUEAU distributed model in a geomatics framework as an additional application of the Idrisi geographic information system; analyze the land use and hydrometeorological information available in a study basin to organize and generate geodatabases; apply the hydrological model implemented in Idrisi to a basin and analyze the results.

This model was developed at the National Institute for Water-Scientific Research (formerly INRS-EAU, now INRS-ETE, French acronyms) at the University of Quebec, Canada to reproduce runoff in a basin [

The production function refers to the modeling of vertical water flow (rainfall, evapotranspiration, infiltration, etc.). This function is aimed at obtaining the water volume for each one of the three recipients included in the model: lakes-marshes, soil and aquifer. The water volume is calculated for each partial element by multiplying

the water depth produced in the entire square by the area of the partial element under consideration. The transfer function analyzes the way in which the flow is transferred through the drainage network, taking into account lakes, marshes, dams and bypasses, among other factors. The model examines each parcel for defined time intervals, which can be one day or even one hour.

Evapotranspiration is calculated based on the modified Thornthwaite formula [

Two types of input data are required by the model, physiographic and hydrometeorological. The physiographic data are processed for each of the parcels into which the basin is discretized. The use of two-thirds of the hydrometric data is recommended to calibrate the model (estimation of parameters) and the remaining one-third is recommended to validate it.

The model has an application to optimize the model’s parameters. The algorithm is based on the Powell method, whose objective function is the Nash coefficient or the correlation coefficient (r). The equations for these calculations are shown by Equations (1) and (2), respectively.

where the Nash coefficient is dimensionless; ^{3}/s); ^{3}/s) and; ^{3}/s). The Nash coefficient ranges from −∞ to 1, where the value 1 corresponds to perfect simulation.

To implement the CEQUEAU model in Idrisi, the method proposed by Quentin et al. [

1) The hydrological model was conceptualized for its incorporation in a GIS environment. This primarily involves considering the spatial variability of the information (rain, temperature, land use).

2) Based on the conceptual model, the geomatic model was developed taking into account the structures and types of operations available in the GIS. Since different geomatics models can be constructed with the same conceptual model, it was necessary to identify the one most useful for the proposed objectives and requirements.

3) The model was implemented as a GIS geomatics model, that is, the algorithm was implemented in programming language.

4) Lastly, the implemented hydrological model was tested with various applications to correct the algorithm and validate the results.

The hydrological CEQUEAU model was written in Fortran and the applications in Idrisi were implemented in Delphi frameworks base on Pascal language. To this end, the algorithms for the hydrological model needed to be analyzed in order to facilitate the implementation in Delphi.

The number of squares (parcels) into which a basin can be discretized increased, given that the CEQUEAU hydrological model is limited to a maximum of 1000 squares. Nevertheless, since a basin can now be discretized up to the size of the cell (pixel), the dimensions of the square would be defined by the resolution of the matrix file (size of the pixel).

The limit of weather stations increased since previously it was only possible to interpolate information for up to 100 stations, which was not convenient when a larger amount existed. Nevertheless, it is now possible to process information from however many stations are available. Also, estimated meteorological data from radar or satellite can now be used.

The transfer function of the CEQUEAU model takes into account the effect of land use (forest, lakes and marshes) in a constant manner, that is, based on only one physiographic file for the entire simulation period. Thus, the forest, lake and marsh areas are assumed to remain unchanged over time. In the CEQUEAU model implemented in Idrisi more than one physiographic file can be used.

The modified Thornthwaite formula [

To develop any tool used to perform different applications, the extraction sources for the input information must be defined, since its use is not possible without these data. The present investigation proposes and uses four sources from which input information for the CEQUEAU implemented in the Idrisi GIS can be obtained: CLICOM, BANDAS, USGS and CONABIO.

Precipitation and maximum and minimum daily temperatures were obtained from the CLICOM database, which can be acquired from the National Weather Service (SMN, Spanish acronym). CLICOM is the database from which the ERIC (Spanish acronym) database is obtained (Rapid Extractor of Climate Information, Extractor Rápido de Información Climatológica) which was also used by this study.

The hydrometric data were taken from the National Surface Water Data Bank (BANDAS, Spanish acronym). This database was obtained from the Mexican Institute for Water Technology (IMTA, Spanish acronym).

The topography of the study area is represented by an image from the Digital Elevation Model (DEM) generated by the US Geological Survey (USGS) based on radar images. The information is raster (matricial) with a resolution of 90 m × 90 m. The DEM image was downloaded from the USGS site (http://earthexplorer.usgs.gov/), introducing the geographic coordinates of the polygon representing the study.

The land use image for Mexico was obtained from the National Commission for Knowledge and Use of Biodiversity (CONABIO, Spanish acronym) and are vector images at a scale of 1:250,000. The commission developed them by digitalizing topographic maps of the Mexican Republic at that scale. CONABIO developed an interactive download site from which the information can be obtained (http://www.conabio.gob.mx/informacion/gis/).

The similarity between the observed and measured (Vo) values and those that are simulated (Vc) using the hydrological model can be measured or estimated using an objective function or numerical criterion. In general, flow is the variable of greatest interest to calculate using a hydrological model. Nevertheless, depending on the results and the conception of the model, other comparisons can be performed (for example, soil moisture content and evapotranspiration, among others).

After implementing the CEQUEAU hydrological model in Idrisi, tests were performed to verify its accuracy. These consisted of comparing the results obtained using the developped application with those from the original model for the same set of input data. Figures 3-6 present evapotranspiration, water levels in the soil (HS) & aquifer (HN) and flow, respectively, calculated with the CEQUEAU model and the model implemented in Idrisi. In all cases, determination coefficients (R^{2}) and Nash coefficients very close to one were obtained, confirming the correct implementation of the hydrological model.

The CEQUEAU hydrological model implemented in Idrisi was used to simulate daily flows for the La Sierra River basin (

Determination Coefficient | Relative Mean Square Error | Nash Coefficient | Coefficient of Variation Error |
---|---|---|---|

Optimal Value: R^{2} = 1 | ERCM = 0 | NASH = 1 | CVE = 0 |

Range: [0, 1] | [0, ¥) | (−¥, 1] | [0, ¥) |

Vo_{i} : nth observed value, Vc_{i} : nth calculated value,

of 0.96%, anditis located between coordinates 97˚40'50"N, 16˚40'47"W and 92˚3'22"N, 17˚51'38"W. This basin is long and exorheic (5 order) with high reliefs upstream and flat at the outlet. Its area is 4800 km^{2} and its perimeter measures 686 km. It is located in hydrological region No.30 Grijalva-Usumacinta where the annual regional precipitation is 4000 mm.

The results from the simulation of inter-annual daily flows and monthly mean flows using the Thornthwaite method to calculate reference evapotranspiration for the La Sierra River basin are shown in Figures 9-10, respectively. The result of the simulation was satisfactory since for the case of inter-annual daily flows a Nash coefficient of 0.88 was obtained for the entire period and for monthly mean flows a Nash coefficient of 0.89 was obtained.

The results of the simulation of the inter-annual daily flows and monthly mean flows using the Penman- Monteith FAO 56 method to calculate evapotranspiration are shown in Figures 11-12, respectively. The simulation was satisfactory since for the case of inter-annual daily flows a Nash coefficient of 0.83 was obtained for the entire period and for monthly mean flows a Nash coefficient of 0.84 was obtained.

Although these results are lower than those from the simulation using the Thornthwaite method, the model was calibrated only evapotranspiration method and not for the Penman-Monteith FAO 56. In addition, the latter has been shown to be more applicable than the Thornthwaite method for different climates and latitudes [

The CEQUEAU hydrological model was implemented in the Idrisi GIS software, taking into account the need to use information from all the weather stations with data available, discretization of the basin into more than 1000 squares if necessary, use of other evapotranspiration methods and the analysis of the effect of the physiographic variability.

To calculate evapotranspiration, it was possible to implement several calculation methods with a minimal amount of information needed for the analysis, such as maximum and minimum temperatures and the geographic location of the study area. In addition to performing the Thornthwaite method which is used with the CEQUEAU

Year | Thornthwaite | Penman-Monteith FAO 56 | ||||||
---|---|---|---|---|---|---|---|---|

R^{2} | Nash | RMSE^{*} | CVE^{**} | R^{2} | Nash | RMSE^{*} | CVE^{**} | |

1968 | 0.88 | 0.84 | 0.04 | 1.26 | 0.81 | 0.76 | 0.07 | 0.88 |

1969 | 0.98 | 0.95 | 0.04 | 1.04 | 0.93 | 0.93 | 0.14 | 0.69 |

1970 | 0.93 | 0.92 | 0.03 | 1.01 | 0.9 | 0.9 | 0.05 | 0.85 |

1971 | 0.91 | 0.9 | 0.03 | 1.05 | 0.91 | 0.91 | 0.03 | 1.03 |

1972 | 0.89 | 0.88 | 0.02 | 1.24 | 0.76 | 0.76 | 0.05 | 0.93 |

1973 | 0.92 | 0.85 | 0.04 | 1.4 | 0.9 | 0.84 | 0.07 | 1.15 |

1974 | 0.95 | 0.9 | 0.03 | 0.9 | 0.93 | 0.9 | 0.05 | 1.1 |

1975 | 0.98 | 0.98 | 0.04 | 0.98 | 0.96 | 0.96 | 0.12 | 0.75 |

1976 | 0.95 | 0.94 | 0.02 | 0.97 | 0.9 | 0.88 | 0.04 | 0.7 |

1977 | 0.94 | 0.91 | 0.03 | 1 | 0.87 | 0.84 | 0.03 | 0.83 |

1978 | 0.95 | 0.94 | 0.01 | 0.84 | 0.96 | 0.93 | 0.02 | 0.87 |

1979 | 0.97 | 0.86 | 0.05 | 0.79 | 0.93 | 0.84 | 0.09 | 0.8 |

1980 | 0.97 | 0.93 | 0.03 | 0.65 | 0.93 | 0.9 | 0.04 | 0.68 |

1981 | 0.94 | 0.91 | 0.03 | 0.97 | 0.94 | 0.91 | 0.02 | 1.01 |

1982 | 0.94 | 0.91 | 0.04 | 0.66 | 0.97 | 0.91 | 0.03 | 0.92 |

1983 | 0.95 | 0.95 | 0.02 | 0.92 | 0.91 | 0.9 | 0.03 | 0.94 |

1984 | 0.98 | 0.94 | 0.02 | 0.85 | 0.97 | 0.9 | 0.05 | 0.68 |

1985 | 0.82 | 0.71 | 0.06 | 0.65 | 0.73 | 0.5 | 0.09 | 0.54 |

1986 | 0.69 | 0.36 | 0.13 | 0.75 | 0.6 | 0.2 | 0.12 | 0.89 |

1987 | 0.58 | 0.46 | 0.21 | 0.77 | 0.48 | 0.32 | 0.28 | 0.81 |

1988 | 0.95 | 0.95 | 0.04 | 0.84 | 0.93 | 0.91 | 0.07 | 1.02 |

1989 | 0.96 | 0.78 | 0.09 | 0.94 | 0.94 | 0.69 | 0.09 | 1.05 |

1990 | 0.94 | 0.71 | 0.09 | 0.84 | 0.9 | 0.57 | 0.1 | 0.94 |

1991 | 0.86 | 0.63 | 0.08 | 1 | 0.74 | 0.46 | 0.1 | 1.01 |

1992 | 0.86 | 0.71 | 0.1 | 0.62 | 0.85 | 0.63 | 0.11 | 0.68 |

1993 | 0.84 | 0.7 | 0.08 | 0.81 | 0.82 | 0.6 | 0.11 | 0.8 |

1994 | 0.73 | 0.59 | 0.08 | 1 | 0.61 | 0.34 | 0.11 | 1.17 |

1995 | 0.91 | 0.81 | 0.06 | 1.04 | 0.9 | 0.7 | 0.1 | 0.96 |

1996 | 0.86 | 0.24 | 0.13 | 0.75 | 0.78 | −0.02 | 0.17 | 0.78 |

1997 | 0.77 | 0.26 | 0.17 | 0.91 | 0.72 | 0.11 | 0.18 | 0.95 |

1998 | 0.71 | 0.69 | 0.47 | 0.94 | 0.53 | 0.51 | 0.68 | 1.02 |

1999 | 0.96 | 0.88 | 0.08 | 0.81 | 0.93 | 0.79 | 0.1 | 0.82 |

^{*}RMSE: relative mean square error; ^{**}CVE: coefficient of variation error.

hydrological model, methods that better adapt to Mexico’s climatic characteristics were selected: Penman-Mon- teith FAO 56, Hargreaves-Samani, Turc and Makkink.

The availability of spatially distributed information, hydrometeorological data and the radar-generated Digital Elevation Model (DEM) helped to create the geodatabase required by the study, which enabled developing and applying the CEQUEAU hydrological model implemented in Idrisi.

The main objective was met, which was to implement the CEQUEAU distributed model in Idrisi and apply this model to the study of a hydrological basin under different scenarios. In addition, the efficiency of this new tool to simulate flows was analyzed and satisfactory results were obtained (Nash coefficients of 0.83 to 0.88 for inter-annual daily flows).

The authors thank the National Council on Science and Technology (Consejo Nacional de Ciencia y Tecnología (CONACyT, Spanish acronym)) for the scholarship to graduate studies. In addition, this work was financed by the CONACyT research project 90637 and UEAM projects 3459/2013CH and 2752/2009, the latter provided by the Juarez Autonomous University of Tabasco. The authors would like to thank the anonymous reviewers for their constructive comments, which helped to improve the manuscript.