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**On the Modeling of the Surface Energy Exchange Processes by Combined "Fuzzy Sets and Neural
Networks" Approach**

POKROVSKY, Oleg, (pokrov@main.mgo.rssi.ru), Main Geophysical Observatory, Karbyshev Str.7, St.Petersburg, 194021, Russia

Key Words: fuzzy sets, neural network, diurnal cycle modeling

Ecological numerical models depend on many surface energy variables. Principal variables are land/water and air temperatures, moisture, solar downward irradiance, albedo, reflected and emitted radiances, heat fluxes into ground and atmosphere, and latent and eddy heat fluxes. Its values are mainly determined by individual optical, physical, and chemical properties of a given homogeneous land/water pattern. The pattern scale, depending heavily on landscape peculiarities, could variate from several meters to several kilometers (or even to tens or hundreds of km in desert areas). However, there are two weak sides of these data implementation in ecological models. The first side is that all mentioned variables, with the exception of air temperature and moisture, are not synoptically observed, and become available for users with a 1-month delay at least. The second is due to substantial departures between observed and modeled diurnal values of these variables (see: Betts et al., Q.J. Roy, Met. Soc., 119, p.p. 975-1001, 1993). Above mentioned variables are traditionally calculated from solving a full set of parameterized equations for the surface-the atmosphere boundary layer system. Model and observation relative differences are so great that they often exceed the 100 percent level; hence, implementation of low accuracy information in ecological models could not lead to reliable results. A new approach to surface variable diurnal cycle modeling was proposed (Pokrovsky, 1998) in order to overcome this problem. This approach is based on a combination of fuzzy logic and neural network methods.

The joint statistical distribution of principal meteorological variables (temperature of air and soil, humidity of air and soil, atmospheric precipitation, pressure, short-wave radiation, cloudiness) are investigated. Ten-year length time series of 1-hour temporal resolutions are used for several meteorological sites in a northwest region of Russia. The data set of simultaneous observations (for all variables and stations) allows it to reveal main features of joint diurnal distributions by means of a known "min-max" fuzzy set approach. Known and novel interrelationships between various meteorological and connected soil variables are reviewed. The revealed relationships between solar downward radiative fluxes and soil temperature diurnal patterns allow it to simulate all principal elements of a surface energy exchange: longwave outgoing radiative fluxes in the atmosphere, soil heat fluxes, available, turbulent, and latent heat fluxes. It was found out that the most complicated links take place for fuzzy sets, corresponding to fractional cloudiness diurnal patterns. For example, there is an asymmetrical (unknown before) relationship between daily solar radiance sums for half-cloudy days and corresponding mean soil temperature values. This means that two quite different mean soil temperature values could correspond to a pair of SRB partly cloudy patterns, having equal daily radiance sums. This and other documented facts allow consideration of alternative approaches to improve the simulation of surface meteorological, radiation, and heat balance component diurnal cycles in most climate and ecological models.

Introduced stationary and transition modes for main meteorological variable diurnal patterns represent the background for simulation of all known weather phenomena. These modes are used as neural network nodes for hidden layers. Implementation of neural networks (back propagation algorithm) allowed us to perform several modeling experiments. Observed and simulated diurnal pattern departures are explored. Intercomparison results, derived by proposed technique and conventional linear regression methods, show substantial modeling accuracy improvement due to the advantage of fuzzy logic implementation. The problem of optimum network configuration (number of nodes in hidden layers) is discussed. Here, the number of nodes is equal to the number of clusters. Another implementing direction is the diurnal cycle meteorological variable reconstruction. Our investigation shows the ability of 1-hour diurnal pattern reconstruction with sufficient accuracy, based on 3-5 instantaneous meteorological observations. Adapted nonlinear mapping of one group of variables (and its diurnal distributions) on another, allow the investigation of this approach application for diagnostic aims. Potential applications of the developed approach are: parametrization of energy exchange processes of the Earth's surface, downscaling of global models, and spatial field reconstructions in the case of missing observational data (for some variable(s)).