WATER RESOURCES RESEARCH, VOL. 30, NO. 7, PAGES 2157-2167, JULY 1994 Estimation of mountain front recharge to regional aquifers 1. Development of an analytical hydroclimatic model Adolfo Chavez Facultad de Ingenieria, Universidad Autonoma de Chihuahua, Chihuahua, Mexico Stanley N. Davis and Soroosh Sorooshian Department of Hydrology and Water Resources, University of Arizona, Tucson Abstract. This paper addresses the hydroclimatic modeling of mountain front recharge to regional aquifers. An analytical relationship between the mean seasonal precipitation and runoff is obtained based on a conceptualizationof the hydrologic processes occurring in hard rock mountainousterrain and a derived-distributionapproach where the input variables are consideredto be stochasticand their probability distributions are transformed into the probability distribution of the output variable by using the deterministic physical process. In a first-order approximation a relationship between the seasonalvalues of precipitation and runoff is obtained. An analytical model of the seasonal streamflow is then developed where initial abstraction and the long-term effective subsurfaceoutflow, or mountain front recharge, are viewed as unknown model parameters. In addition, a procedure that combines the water balance equation with a relationship provided by the so-called "vegetal equilibrium hypothesis," and which enables the estimation of effective soil-related parameters jointly with the mean seasonal evapotranspirationand surface runoff, is introduced. This procedure is applied to a mountainous watershed in southern Arizona. Introduction The two main mechanismsof natural recharge to regional aquifers in arid and semiarid areas are channel recharge and mountain front recharge. While mountain front recharge is a vital component of the groundwater system in many of these areas [Feth, 1964], it constitutesonly a minor fraction of the total amount of water delivered to the area by precipitation and therefore cannot be estimated reliably by "gross" water balance calculations. Estimates of mountain front recharge to regional aquifers are required for management purposes,particularly in order to determine the safe yield from wells in groundwater basins where overall recharge is small and development may readily lead to overdraft conditions. Such basins are com- mon in arid and semiarid regions. Estimates of mountain front recharge also provide prescribedflux values for digital models of regional groundwater flow. However, data on groundwater in the mountain and the mountain front region are ordinarily limited to a few widely spacedwells, springs, and base flow streams. This scarcity of data, along with uncertainties inherent in the data and calculations, may lead to errors of up to an order of magnitude in the estimation of mountain front recharge [Belan and Matlock, 1973]. With regardto the inverseproblemin groundwater hydrol- ogy, also known as the groundwater parameter estimation problem, Carrera and Neuman [1986b] found that pre- scribed head conditions at the aquifer boundary resulted in smaller sensitivities than prescribednonzero flux; hence this Copyright 1994 by the American Geophysical Union. Paper number 93WR03369. 0043-1397/94/93 WR-03369505.00 suggests that one should impose the latter condition when- ever possible. Carrera and Neuman [1986a] posed the in- verse problem in the framework of maximum likelihood estimation with prior information about the parameters. In their formulation the prior head errors and the prior param- eter estimation errors were assumed to lack cross correla- tion, and for this reason, they cautioned that head values used for inverse modeling must not be used to derive prior parameter estimates. This rules out the use of flow net analysis to provide prior information about mountain front recharge for inverse modeling purposes, at least within the framework of Carrera and Neuman's approach. Prior estimatesof mountain front recharge can be obtained with the aid of environmental isotopes [Simpson et al., 1970; Gallaher, 1979; Olson, 1982] and hydrochemical mass bal- ance calculations [Thorne, 1982; Adar, 1984]. These meth- ods are associatedwith large uncertainties; hence according to conclusions reached by Carrera and Neuman [1986b] regarding mathematical conditions for well-posedness,esti- mates based on them do little to reduce the degree of ill-posedness of the inverse problem. An alternative approach to estimation of mountain front recharge is the use of hydroclimatic models. Such models are particularly useful in areas where reasonable records of rainfall and streamflow exist but where there is almost no data on groundwater. In paper 1 of this two-part series we develop analytical models of the seasonal surface runoff and streamflow based on a conceptual model of hydrologic processes that should approximate some types of field conditions, in particular, hard rock mountainouswatersheds where deep percolation occurs exclusively through fractures; these models (1) are formulated in terms of parameterswith physical significance, 2157