at 4890 m above sea level (asl) on the Antizana Glacier 15 (0.71 km 2 ; 0°28 0 S, 78°09 0 W) in the tropical Andes of Ecuador (inner tropics). These variables were used to compute the annual cycle of the local surface energy balance (SEB). The four radiative fluxes were directly measured, and the turbulent fluxes were calculated using the bulk aerodynamic approach, calibrating the roughness length by direct sublimation measurements. The meteorological conditions are relatively homogeneous throughout the year (air temperature and air humidity). There is a slight seasonality in precipitation with a more humid period between February and June. During June-September, wind velocity shows high values and is responsible for intense turbulent fluxes that cause reduction of melting. Considering the SEB over the whole year, it is dominated by net radiation, and albedo variations govern melting. During the period under consideration the net short-wave radiation S (123 W m À2 ) and the sensible turbulent heat flux H (21 W m À2 ) were energy sources at the glacier surface, whereas the net long-wave radiation L (À39 W m À2 ) and the latent turbulent heat flux LE (À27 W m À2 ) represented heat sinks. Since the O°C isotherm-glacier intersection always oscillates through the ablation zone and considering that the phase of precipitation depends on temperature, temperature indirectly controls the albedo values and thus the melting rates. This control is of major interest in understanding glacier response to climate change in the Ecuadorian Andes, which is related to global warming and ENSO variability.

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A previous study of Fox [Fox, A.N. 1993. Snowline altitude and climate at present and during the Last Pleistocene Glacial Maximum in the Central Andes (5°-28°S). Ph.D. Thesis. Cornell University.] showed that for a fixed 0°C isotherm altitude, the equilibrium-line altitude (ELA) of the Peruvian and Bolivian glaciers from 5 to 20°S can be expressed based on a log-normal expression of local mid-annual rainfall amount (P). In order to extrapolate the function to the whole Andes (10°N to 55°S) a local 0°C isotherm altitude is introduced. Two applications of this generalised function are presented. One concerns the space evolution of mean inter-annual ELA for three decades ) over the whole South American continent. A high-resolution data set (grid data: 10′ for latitude/longitude) of mean monthly air surface temperature and precipitation is used. Mean annual values over the 1961-1990 period were calculated. On each grid element, the mean annual 0°C isotherm altitude is determined from an altitudinal temperature gradient and mean annual temperature (T ) at ground level. The 0°C isotherm altitude is then associated with the annual precipitation amount to compute the ELA. Using computed ELA and the digital terrain elevation model GTOPO30, we determine the extent of the glacierised area in Andean regions under modern climatic conditions. The other application concerns the ELA time evolution on Zongo Glacier (Bolivia), where inter-annual ELA variations are computed from 1995 to 1999. For both applications, the computed values of ELA are in good agreement with those derived from glacier mass balance measurements.

We review the main stages of the evolution of ideas and methods for solving the inverse problem in hydrogeology; i.e., the identification of the transmissivity field in single-phase flow from piezometric data, in mainly steady-state and, occasionally, transient flow conditions. We first define the data needed to solve an inverse problem in hydrogeology, then describe the numerous approaches that have been developed over the past 40 years to solve it, emphasizing the major contributions made by Shlomo P. Neuman. Finally, we briefly discuss fitting processes that start by defining the unknown field as geological images (generated by Boolean or geostatistical methods).The early attempts at solving the inverse problem were direct, i.e., the transmissivity field was directly determined by using stream lines of the flow and inverting the flow equation along these lines. Faced with the poor results obtained in this manner, hydrogeologists have tried many different ways of minimizing the balance error representing an integral of the mass-balance error for each mesh for a given transmissivity field. These attempts were accompanied by constraints imposed on the transmissivity field in order to avoid instabilities.The idea then emerged that the unknown field should reproduce the local observations of the pressure at the measurement points instead of minimizing a balance error. Second, it should also satisfy a condition of plausibility, which means that the transmissivity field obtained through the inverse solution should not deviate too far from an a priori estimate of the real transmissivity field. This a priori notion led to the inclusion of a Bayesian approach resulting in the search for an optimal solution by maximum likelihood, as expounded later.Simultaneously, the existence of locally measured values in the transmissivity field (obtained by pumping tests) allowed geostatistical methods to be used in the formulation of the problem; the result of this innovation was that three major approaches came into being: (1) the definition of the a priori transmissivity field by kriging; (2) the method of cokriging;(3) the pilot point method. Furthermore, geostatistics made it possible to pose the inverse problem in a stochastic framework and to solve an ensemble of possible and equally probable fields, each of them equally acceptable as a solution.

Abstract:The aim of this study was to validate evaporation models that can be used for palaeo-reconstructions of large lake water levels. Lake Titicaca, located in a high-altitude semi-arid tropical area in the northern Andean Altiplano, was the object of this case study. As annual evaporation is about 90% of lake output, the lake water balance depends heavily on the yearly and monthly evaporation flux. At the interannual scale, evaporation estimation presents great variability, ranging from 1350 to 1900 mm year 1 . It has been found that evaporation is closely related to lake rainfall by a decreasing relationship integrating the implicit effect of nebulosity and humidity. At the seasonal scale, two monthly evaporation data sets were used: pan observations and estimations derived from the lake energy budget. Comparison between these data sets shows that (i) there is one maximum per year for pan evaporation and two maxima per year for lake evaporation, and (ii) pan evaporation is greater than lake evaporation by about 100 mm year 1 . These differences, mainly due to a water depth scale factor, have been simulated with a simple thermal model  w h, t of a free-surface water column. This shows that pan evaporation (h D 0Ð20 m) is strongly correlated with direct solar radiation, whereas the additional maximum of lake evaporation (h D 40 m) is related to the heat restitution towards the atmosphere from the water body at the end of summer. Finally, five monthly evaporation models were tested in order to obtain the optimal efficiency/complexity ratio. When the forcing variables are limited to those that are most readily available in the past, i.e. air temperature and solar radiation, the best results are obtained with the radiative Abtew model (r D 0Ð70) and with the Makkink radiative/air temperature model (r D 0Ð67).

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Hydrological and glaciological data were gathered in the watershed (1.37 km 2 ) of the Antizana Glacier 15 (0.7 km 2 ) in the periods 1997-2002 and 1995-2005, respectively. In addition, tracer experiments were carried out to analyse the flow through permeable morainic deposits located between the glacier snout and the runoff gauging station. Over 11 years, the mean specific net balance of the glacier was negative (-627 mm w.e.), despite the occurrence of positive values in the La Niña years (1999)(2000). From the glacier net mass balance between 1997 and 2002, it was found that the mean flow originating from ice melt was significantly higher than the mean discharge measured at the hydrological station. Analyses of tracer experiments and of the different components of the hydrological balance suggest groundwater flow that originates below the glacier accounts for the remaining water. This result is important for regional analyses of available water resources and for the relationship between hydro-cryospheric processes and volcanic activity.

A model was developed for estimating the delay between a change in climatic conditions and the corresponding fall of water level in large lakes. The input data include: rainfall, temperature, extraterrestrial radiation and astronomical mid‐month daylight hours. The model uses two empirical coefficients for computing the potential evaporation and one parameter for the soil capacity. The case studies are two subcatchments of the Altiplano (196 000 km2), in which the central low points are Lake Titicaca and a salar corresponding to the desiccation of the Tauca palaeolake. During the Holocene, the two catchments experienced a 100 m fall in water level corresponding to a decrease in water surface area of 3586 km2 and 55 000 km2, respectively. Under modern climatic conditions with a marked rainy season, the model allows simulation of water levels in good agreement with the observations: 3810 m a.s.l. for Lake Titicaca and lack of permanent wide ponds in the southern subcatchment. Simulations were carried out under different climatic conditions that might explain the Holocene fall in water level. Computed results show quite different behaviour for the two subcatchments. For the northern subcatchment, the time required for the 100 m fall in lake‐level ranges between 200 and 2000 years when, compared with the present conditions, (i) the rainfall is decreased by 15% (640 mm/year), or (ii) the temperature is increased by 5·5 °C, or (iii) rainfall is distributed equally over the year. For the southern subcatchment (Tauca palaeolake), the time required for a 100 m decrease in water level ranges between 50 and 100 years. This decrease requires precipitation values lower than 330 mm/year. Copyright © 2004 John Wiley & Sons, Ltd.