A flow of random events generates actions, which may either accelerate the future events, or slow then down in a time-proportional way. Costs are assigned to each action, and with each occurrence of an event. We describe the nature of the rate proportional models and their possible use in environmental studies. Some feasible general cost models related to proportional rate actions with random nature are analyzed. Further, a particular rate (extreme- value type process) illustrates the behavior of the expected costs as functions of some controlled parameters.

STEFANKA S. CHUKOVA
Department of Mathematics and Science
Kettering University
1700 W.Third Avenue
Flint, Michigan 48504-4898, USA
schukova@kettering.edu
 
 

The underground water-reservoirs are supplied by the infiltrating water from the precipitation. Consequently, in order to explain the changes of the underground water supply the process of infiltration has to be known better. Infiltrating water can carry various contaminations, an other reason why to know infiltration is so important. There is, however, a very complicated relationship between the natural random fluctuation in groundwater levels, and the amount of the infiltrating water supply. It is especially so in karstic areas, specifically in the Balaton Highland in Western Hungary, which is the subject of our study. Infiltration itself is a very complex process, because the amount of the infiltrating water depends on the geomorphology, the water conductivity of the superficial soil and rocks, the air temperature, the amount, duration and the physical state of the precipitation, and also the vegetation and many other factors. This is the reason why there is no unique procedure to compute infiltration. There are, however, different empirically tested methods, weighting the actual precipitation according to the various circumstances of its fall. We show, that these methods result in an unstructured, white noise type process, whereas the water fluctuations in undisturbed wells resemble rather an ARMA type process. An appropriate ARMA process, generated from the computed infiltrations will describe the process by satisfactory precision. The geological interpretation of such a process can also be given. The structure of the process is very important, when one wishes to estimate the effect of infiltration by applying dynamic factor analysis. The spatial and spatiotemporal behaviour of infiltration remains the subject of further investigations.

JOZSEF KOVACS
Department of Applied and Environmental Geology
Eotvos Lorand University
Muzeum krt. 4/a
Budapest, H-1088, Hungary
kevesolt@iris.geobio.elte.hu
 
 

The problem, to maintain the quality of drinking water resources reserved in such natural underground reservoirs like the karst, will in no way pass away with the passing century. It will give a lot of future work for researchers and aquifer vulnerability will remain a key issue in those investigations. Aquifer vulnerability is strictly connected to the speed and amount of infiltrating water from precipitation. Being a very complex process however, infiltration is very difficult to determine, especially, when human interference distorts the natural course of hydrogeological processes. Usually it is calculated by weighting the amount of precipitation according to the circumstances of its fall and subtracting evapotranspiration. An other option is to start from the observed groundwater level fluctuation, resulted from different cumulative effects, among which infiltration is one of the most dominating. Since it is practically impossible to measure these effects directly, they need to be estimated. The conventional tool to determine latent effects governing variability or fluctuations is factor analysis. It has been elaborated for independent observations, while the observed karstwater levels at a certain location represent realisations of time series. Hence the latent factors, governing the fluctuations, can be revealed by applying dynamic factor analysis to the hydrographs of monitoring wells. One of the obtained dynamic factors can be corresponded to the infiltration. The intensity of infiltration at a given observation site is then given by the loadings of this dynamic factor. To extend this information to arbitrary locations universal kriging is used and analysed for the spatial process of the estimated loadings. Being simply structured processes the factors are easy to forecast in time, and by the help of the intensities a spatiotemporal prediction can be given for the water level, and compared to the one, obtained by spatiotemporal Bayesian kriging.

LASZLO MARKUS
Department of Probability Theory and Statistics
Eotvos Lorand University
Rakoczi u. 5
Budapest, H-1088, Hungary
markus@cs.elte.hu