The use of personal weather station observations to improve precipitation estimation and interpolation

The number of personal weather stations (PWSs) with data available through the internet is increasing gradually in many parts of the world. The purpose of this study is to investigate the applicability of these data for the spatial interpolation of precipitation using a novel approach based on indicator correlations and rank statistics. Due to unknown errors and biases of the observations, rainfall amounts from the PWS network are not considered directly. Instead, it is assumed that the temporal order of the ranking of these data is correct. The crucial step is to find the stations which fulfil this condition. This is done in two steps – first, by selecting the locations using the time series of indicators of high precipitation amounts. Then, the remaining stations are then checked for whether they fit into the spatial pattern of the other stations. Thus, it is assumed that the quantiles of the empirical distribution functions are accurate. These quantiles are then transformed to precipitation amounts by a quantile mapping using the distribution functions which were interpolated from the information from the German National Weather Service (Deutscher Wetterdienst – DWD) data only. The suggested procedure was tested for the state of Baden-Württemberg in Germany. A detailed cross validation of the interpolation was carried out for aggregated precipitation amount of 1, 3, 6, 12 and 24 h. For each of these temporal aggregations, nearly 200 intense events were evaluated, and the improvement of the interpolation was quantified. The results show that the filtering of observations from PWSs is necessary as the interpolation error after the filtering and data transformation decreases significantly. The biggest improvement is achieved for the shortest temporal aggregations.

The Reliability of Numerical Modeling in Remote Sensing Data Analysis

The article deals with the problem of calculating reliable estimates of empirical distribution functions under conditions of small sample and data uncertainty. To study these issues, we develope computational probabilistic analysis as a new area in computational statistics. We propose a new approach based on random interpolation polynomials and order statistics. Arithmetic operations on probability density functions and procedures for constructing the probabilistic extensions are used.

Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures

This paper develops readily applicable methods for estimating the intrinsic dimension of multivariate datasets. The proposed methods, which make use of theoretical properties of the empirical distribution functions of (pairwise or pointwise) distances, build on the existing concepts of (i) correlation dimensions and (ii) charting manifolds that are contrasted with (iii) a maximum likelihood technique and (iv) other recently proposed geometric methods including MiND and IDEA. This comparison relies on application studies involving simulated examples, a recorded dataset from a glucose processing facility, as well as several benchmark datasets available from the literature. The performance of the proposed techniques is generally in line with other dimension estimators, specifically noting that the correlation dimension variants perform favorably to the maximum likelihood method in terms of accuracy and computational efficiency.

HEURISTIC METHODS FOR THE DESIGN OF CRYPTOGRAPHIC BOOLEAN FUNCTIONS

In this article, heuristic methods of hill climbing for cryptographic Boolean functions satisfying the required properties of balance, nonlinearity, autocorrelation, and other stability indicators are considered. A technique for estimating the computational efficiency of gradient search methods, based on the construction of selective (empirical) distribution functions characterizing the probability of the formation of Boolean functions with indices of stability not lower than required, is proposed. As an indicator of computational efficiency, an average number of attempts is proposed to be performed using a heuristic method to form a cryptographic Boolean function with the required properties. Comparative assessments of the effectiveness of the heuristic methods are considered. The results of investigations of the cryptographic properties of the formed Boolean functions in comparison with the best known assessments are given. On the basis of the conducted research, it can be concluded that the functions constructed in accordance with the developed method have high persistence indexes and exceed the known functions by these indicators.

Detection of changes in flow regime of rivers in Poland

The aim of this study is to detect changes in flow regime of rivers in Poland. On the basis of daily discharges recorded in 1951-2010 at 159 gauging stations located on 94 rivers regularities in the variability of the river flow characteristics in the multi-year period and in the annual cycle were identified and also their spatial uniformity was examined. In order to identify changes in the characteristics of river regime, similarities of empirical distribution functions of the 5-day sets (pentads) of discharges were analyzed and the percent shares of similar and dissimilar distributions of the 5-day discharge frequencies in the successive 20-year sub-periods were compared with the average values of discharges recorded in 1951-2010. Three alternative methods of river classification were employed and in the classification procedure use was made of the Ward’s hierarchical clustering method. This resulted in identification of groups of rivers different in terms of the degree of transformation of their hydrological regimes in the multi-year and annual patterns.