Tresaproximaciones

Investigaciones Geográficas, Boletín del Instituto de Geografía, UNAM

ISSN 0188-4611, Núm. 76, 2011, pp. 34-55

Three approaches to the assessment of spatio-temporal

distribution of the water balance: the case of the Cuitzeo basin,

Michoacán, Mexico

Received: 20 September 2010. Final version accepted: 23 March 2011

Alfredo Amador García *

Erna Granados López**

Manuel E. Mendoza***

Abstract. Spatial distribution of the energy and flows of

the hydrologic cycle in the form of evapotranspiration,

runoff and infiltration within a region is a function of the

climate (precipitation, temperature and evaporation) and

landscape (relief, soil, land cover) of the area, and constitutes

the hydrological cycle. The general model evaluating each

of these sections and flows is the water balance. Methods

for calculating the water balance in a region are based on

either mass transference or energy transference. The aim of

the present work was to calculate the spatially distributed

regional water balance in a poorly gauged basin by each of

three methods, and to evaluate these methods by comparing

the results. Spatial modelling of the hydrometeorological

variables used the ArcView 3.2 geographic information

system; hydrological modelling made using HEC system

version 3.1.0. The first approach was based on analysis of

the information recorded at the available meteorological

stations, point estimation of the monthly water balance

according to the Thornthwaite and Mather method, and the

use of Thiessen polygons. The second approach was based

on the calculation and distribution of the parameters for the

Thornthwaite and Mather method. The third approach used

the FAO–Penman equation. The models were applied to the

Lake Cuitzeo basin. The result obtained by the third method

indicated a mean annual volume of runoff of 229.05 hm3.

This volume is only 8.5 hm3 less than that estimated as necessary

for maintaining a depth of 1 m throughout the Lake

Cuitzeo water body. This difference represents a possible

fluctuation of 2 cm in the mean level of the surface of the

lake. The HEC model represents an alternative for modelling

the basin since it requires relatively few inputs, of which the

main ones (temperature, precipitation, potential evapotranspiration,

evapotranspiration) are obtainable or deducible by

means of one or other of the approaches presented here.

Key words: Spatial modelling, water balance, poorly gauged

basins, watershed management.

* Facultad de Biología, Universidad Michoacana de San Nicolás de Hidalgo, Ciudad Universitaria, Edif. R, 58030, Morelia,

Michoacán, Mexico. E-mail: aamador@umich.mx

* Departamento de Geología y Mineralogía, Instituto de Investigaciones Metalúrgicas, Universidad Michoacana de San

Nicolás de Hidalgo, Ciudad Universitaria, Edif. U, 58030, Morelia, Michoacán, México. E-mail: ernalopez2004@yahoo.

com.mx

*** Centro de Investigaciones en Geografía Ambiental (CIGA), Universidad Nacional Autónoma de México, Antigua

Carretera a Pátzcuaro No. 8701, Col. Ex Hacienda de San José de la Huerta, 58190, Morelia, Michoacán, Mexico. E-mail:

mmendoza@ciga.unam.mx

Investigaciones Geográficas, Boletín 76, 2011 ][ 35

Three approaches to the assessment of spatio-temporal distribution of the water balance: the case of the Cuitzeo basin...

INTRODUCTION

The spatial distribution of the energy and the

flows of the hydrologic cycle in the form of vapour

(evapotranspiration), runoff and infiltration in a

region are a function of its climate (precipitation,

temperature and evaporation) and landscape (relief,

soil and land cover) (He et al., 2000; Mendoza et

al., 2002). Measurement, estimation and modelling

of changes in the values of these flows can

reveal critical areas of a basin and can influence

decisions appropriate for water management.

One of the key components of the water balance

is evapotranspiration. This is a concept coined in

1948 by C.W. Thornthwaite, who was the first to

devise a method for the regional estimation of this

parameter (Hewlett, 1982). According to Ward and

Trimble (2003), evapotranspiration is so important

that it can represent a magnitude and proportion

equivalent to the quantity of water that occurs in

the form of runoff or infiltration at the global level

and in the balance of many basins.

In general, it is considered that evapotranspiration

under more or less natural conditions

shows less annual variation than parameters such

as precipitation or runoff. However, thinning of

vegetation and change in land use can significantly

reduce this parameter, so that consideration of the

water balance has revealed consequent increases of

up to 70% in the annual runoff (Hewlett, 1982).

The combination of methods for determining

evapotranspiration (ET) and the execution of a

spatially distributed hydrologic model based on

evaluation of morphometric, climatic and biophysics

characteristics of the study area represents

an opportunity to model the runoff (Q). In its turn,

this allows evaluation of the optimal scenarios for

ET, and hence is a useful method in supporting

decision-making in water management for the

basin. This is because it can group spatio-temporal

units of hydrologic response (SCS, 1972; Hay et al.,

1993; Neitsch et al., 2001) that can be incorporated

into simulations of runoff and periods of retention

of moisture in the basin, either under present conditions

or in projections of possible trends or bestcase

projections of land-use change in the basin.

With regard to the Cuitzeo basin in Michoacán,

Mexico, some studies have focused on a review of

Tres aproximaciones para estimación y distribución

espacio-temporal del balance hídrico: el caso de la cuenca

de Cuitzeo, Michoacán, México

Resumen. La distribución espacial de la energía y los flujos

de ciclo hidrológico en forma de vapor (evapotranspiración),

escurrimiento e infiltración en una región, son una función

de las características climáticas (precipitación, temperatura y

evaporación) y del paisaje (relieve, suelo y cobertura) de un

área y constituyen el llamado ciclo hidrológico. El modelo

general de evaluación de cada uno de los compartimentos y

flujos es el balance hídrico. Los métodos desarrollados para

calcular el balance hídrico de una región toman como base

el enfoque de transferencia de masa o el de transferencia

de energía. Este trabajo se planteó como objetivo calcular,

comparar y evaluar tres aproximaciones en la estimación

del balance hídrico regional espacialmente distribuido en

cuencas sin datos de aforos. El modelamiento espacial de las

variables hidrometeorológicas se efectuó en el sistema de información

geográfica ArcView 3.2, y el modelamiento de

los del escurrimiento se realizó con el sistema HEC versión

3.1.0. La primera aproximación está basada en el análisis

de la información registrada en las estaciones meteorológicas

disponibles, estimación puntual del balance hídrico

mensual conforme al método de Thornthwaite y Mather y

de polígonos de Thiessen; la segunda, en el cálculo y distribución

de los parámetros para la aplicación del Método de

Thornthwaite y Mather; finalmente la tercera aproximación

se basó en el uso de la ecuación de FAO – Penman. Se escogió

a la cuenca del lago de Cuitzeo como área de aplicación de los

modelos. Destaca que mediante el resultado de la 3ª aproximación

el volumen anual promedio de escurrimientos corresponde

a 229.05 hm3. Dicho volumen es apenas 8.5 hm3

inferior al estimado como necesario para mantener 1 m de

profundidad en la extensión del cuerpo de agua del lago de

Cuitzeo. Esta diferencia representa en esa misma extensión

una eventual fluctuación de 3 cm en el nivel medio del espejo

del lago. El modelo HEC representa una alternativa para el

modelamiento de la cuenca ya que demanda relativamente

de pocos insumos, los principales (T, PP, PET, ET) obtenibles

o espacializables mediante alguna de las aproximaciones

presentadas aquí.

Palabras clave: Modelamiento espacial, balance hídrico,

cuencas sin aforo, manejo de recursos hídricos.

36 ][ Investigaciones Geográficas, Boletín 76, 2011

Alfredo Amador García, Erna Granados López and Manuel E. Mendoza

environmental characteristics of the water body and

the sources of its contamination (Alvarado et al.,

1994), while another branch of study has focused

on description and analysis of the land cover and

its changes (López et al., 2001 and 2006).

Studies specific to the hydrology of this basin

include those by Mendoza et al. (2010) and Carlón

et al. (2009). The former records the water balance

...