569.21The asymptotic properties of least-squares estimates of almost periodic signals under random noise are investigated. The consistency and strong consistency of the estimates are proved.One of the most important problems of the modern theory of risk is predicting situations that may cause technotronic catastrophes or natural cataclysms with disastrous (catastrophic) human and material losses. Simulation and prediction of disastrous flood and assessment of material resources for mitigation of their consequences are especially topical in recent years. One of the most popular approaches to solving such problems is analyzing stochastic information, processing time series of hydrological observations, adequate modeling of disastrous flood, and estimating its parameters.Svanidze [1] justified a flood model described by a harmonic signal whose observations are noisy due to a stationary random process or a field. For example, in the case of a one-dimensional argument, the flood model has the formwhere A k and w k are the amplitudes and frequencies of periodic components, j k is the phase, which is a random variable. As a rule, y t ( ) are observed in a mixture with a random noise x( ) t , i.e., the observation model has the form x t y t t ( ) ( ) ( ) = +x .It is necessary to use the observations x t ( )on the interval [0, T] to estimate the unknown parameters A k and w k . Such models were considered in [2,3], where so-called periodogram estimates of unknown parameters were studied and statements on their strong consistency and asymptotic normality were proved. More complicated is the problem where a signal y t ( ) is represented as an infinite series of unknown harmonics. In this case, it is necessary to estimate optimally, in some sense, the proper function y t ( ) in a certain function space. Such problems pertain to problems of nonparametric statistics, i.e., the parameter being estimated is an element of a function space. Of the studies of functions of one variable, [4] is noteworthy. Here, we consider functions of two arguments.The problem is formulated as follows. Let a real random field { } x( , ), ( , ) s t s t ÎR 2 be given in a probabilistic space ( , , ) W F P . It is necessary to use the observation of the random fieldx s t a s t s t s t D T T T