Rudolf O. Weber

Spectra and correlations of climate data from days to decades

The correlations of several daily surface meteorological parameters such as maximum, minimum, and mean temperature, diurnal temperature range, pressure, precipitation, and relative air humidity are analyzed by partly complementary methods being effective on different timescales: power spectral analysis, second- and higher-degree detrended fluctuation analysis, Hurst analysis, and the direct estimation of the autocorrelation in the time domain. Data from American continental and maritime and European low-elevation and mountain stations are used to see possible site dependencies. For all station types and locations, all meteorological parameters show correlations from the shortest to the longest statistically reliable timescales of about three decades. The correlations partly show a clear power law scaling with site-dependent exponents. Mainly, the short-time behavior of the correlations depends on the station type and differs considerably among the various meteorological parameters. In particular, the detrended fluctuation and the Hurst analyses reveal a possible power low behavior for long timescales which is less well resolved or even may remain unrecognized by the classical power spectral analysis and from the autocorrelation. The long-time behavior of the American temperatures is governed by power laws. The corresponding exponents coincide for all temperatures except for the daily temperature range with different values for the maritime and the continental stations. From the European temperatures those from low-elevation stations also scale quite well, whereas temperatures from mountain stations do not.

TRENDS OF MAXIMUM AND MINIMUM DAILY TEMPERATURES IN CENTRAL AND SOUTHEASTERN EUROPE

Changes in maximum and minimum daily temperatures (TMAX and TMIN, respectively) in nine selected regions of central Europe and in Bulgaria during 1951–1990 are investigated. Average series for central Europe are compiled and analyzed by linear trend analysis and the kernel smoothing. The increase in the annual TMAX in central Europe was, during 1951–1990, slightly lower than that of TMIN (0ċ52°C and 0ċ60°C, respectively). This results in a small decrease in the daily temperature range (DTR) by −0ċ08°C. With the exception of the spring TMIN other linear trends are insignificant. The observed insignificant trends in DTR in the central European region are related to small cloudiness changes. Long-term fluctuations of annual TMAX, TMIN, and DTR for eight selected series during the twentieth century are also investigated.

20Th-Century Changes of Temperature in the Mountain Regions of Central Europe

Daily maximum and minimum temperatures from 29 low-lying and mountain stations of 7 countries in Central Europe were analyzed. The analysis of the annual variation of diurnal temperature range helps to distinguish unique climatic characteristics of high and low altitude stations. A comparison of the time series of extreme daily temperatures as well as mean temperature shows a good agreement between the low-lying stations and the mountain stations. Many of the pronounced warm and cold periods are present in all time series and are therefore representative for the whole region. A linear trend analysis of the station data for the period 1901–1990 (19 stations) and 1951–1990 (all 29 stations) shows spatial patterns of similar changes in maximum and minimum daily temperatures and diurnal temperature range. Mountain stations show only small changes of the diurnal temperature range over the 1901–1990 period, whereas the low-lying stations in the western part of the Alps show a significant decrease of diurnal temperature range, caused by strong increase of the minimum temperature. For the shorter period 1951–1990, the diurnal temperature range decreases at the western low-lying stations, mainly in spring, whereas it remains roughly constant at the mountain stations. The decrease of diurnal temperature range is stronger in the western part than in the eastern part of the Alps.

Remarks on the definition and estimation of friction velocity

One of the mainscaling parameters in similarity theory of the atmospheric boundary layer is friction velocity. Unfortunately, several definitions of friction velocity exist in the literature. Some authors use the component of the horizontal Reynolds stress vector in the direction of the mean wind vector to define friction velocity. Others define the friction velocity by means of the absolute value of the horizontal Reynolds stress vector. The two definitions coincide only if the direction of the mean wind vector is parallel to the horizontal Reynolds stress vector. In general, the second definition gives larger values for the friction velocity. Over complex terrain the situation is further complicated by the fact that the terrain following flow is not necessarily horizontal. Thus, several authors have proposed to use terrain following coordinate systems for the definition of friction velocity. By means of a large dataset of fast-response wind measurements with an ultrasonic anemometer the friction velocities resulting from the different definitions are compared. Furthermore, it is shown that friction velocity can be well estimated from horizontal wind speed, and even better from simple horizontal or vertical turbulence parameters.

Asymmetric diurnal temperature change in the Alpine Region

By now there is general agreement that the annual mean temperature of earths surface has increased during the last century. Recently, it has become obvious that this warming is quite inhomogeneous in various respects. Besides the spatial and seasonal variability of the temperature trend a diurnal asymmetry of increase has been observed. In large continental regions the annual mean of the daily minimum temperature has increased noticeably faster than the annual mean of the daily maximum. The same behaviour is found in the present study for low-lying stations in Central Europe. However, data from mountain top stations show a similar increase for both minimum and maximum of daily temperatures. No diurnal asymmetry was observed for these stations. The good agreement of the time series from different mountain stations leads us to believe that the observed trends of minimum and maximum temperature are not caused by particular local influences or observation errors. An analysis of monthly and seasonal means shows that most of the warming took place in fall.

Some Remarks on Spatial Correlation Function Models

Abstract The method of optimal interpolation, which is widely used in meteorological data assimilation, relies very much on good approximations of spatial correlation functions. Therefore, many models for such functions have been developed. These models should fulfill certain mathematical constraints; particularly, they should be positive-definite functions. For the classes of homogeneous and isotropic processes, the positivity property and its consequences are reviewed. A special class of correlation models based on so-called spatial autoregressive processes is critically examined. It is shown that models of this type are not positive definite on the meteorological relevant spaces. Some other models taken from the literature are shown to lack this property also. Three strategies to obtain models that have the appropriate mathematical properties are outlined.

Classification of Mesoscale Wind Fields in the MISTRAL Field Experiment

Abstract A two-stage classification scheme with outlier detection is proposed to find groups of wind fields. A hierarchical cluster analysis according to the complete linkage method is combined with a k-means procedure with detection and exclusion of outliers. The classification method is applied to a 1-yr dataset of 1-h mean wind observations from the MISTRAL field experiment. A small number of typical regional flow patterns is identified. An analysis of temperature observations shows that some of the 12 regional flow patterns have thermally forced wind systems. The main spatial forcing patterns are revealed by a principal component analysis of temperature observations. A comparison of the regional flow patterns and the synoptic-scale weather types of the Alpine region shows that only weak connections between the local flow and the synoptic-scale weather type exist.

Automated Classification Scheme for Wind Fields

Abstract In earlier works of several authors, wind fields or flow patterns were grouped by means of trajectory calculations or by use of a principal component analysis. A new automated classification method is proposed that makes use only of wind observations and does not require predefined circulation patterns, a priori rules, or spatial or temporal interpolation. A distance measure is defined between pairs of wind fields, represented by a set of observations. Based on the resulting distance matrix, a hierarchical cluster analysis is performed that also provides an indication for the choice of an appropriate number of clusters. The classification method is applied to a monthly record of 1-h averages of wind measurements in the region of Basel, Switzerland. Different clustering schemes are tested, and the complete linkage method is chosen as most appropriate. For the test case a relatively small number of classes (12) provides a sufficient description of the different flow patterns in this complex topogra...

Estimators for the Standard Deviation of Horizontal Wind Direction

The standard deviation of horizontal wind direction is a central quantity in the description of atmospheric turbulence and of great practical use in dispersion models. As horizontal wind direction is a circular variable, its standard deviation cannot be directly estimated by on-line methods. For a mathematically strict determination of the angular standard deviation, it is necessary to store all observations and perform off-line calculations. A more practical approach is to calculate on-line moments of linear variables and to parameterize angular standard deviation in terms of these moments. A variety of such estimators is compared by means of a large dataset from an ultrasonic anemometer. The paper systematically investigates which types of linear variables lead to the best estimators and which parameterizations are best within each group of linear variables. Estimators based on moments of the sine and cosine of the wind direction turned out to be most robust. The parameterizations based on an isotropic Gaussian model of turbulence gave the estimators with smallest error within the different groups.

Estimator for the Standard Deviation of Wind Direction Based on Moments of the Cartesian Components

Abstract Mean and variance of horizontal wind direction are defined in a minimal variance sense. Starting from a theoretical model, termed anisotropic Gaussian model, of the probability density functions of the Cartesian wind components, the standard deviation of wind direction is calculated. This angular standard deviation is expressed as a function of the means and variances of the Cartesian wind components alone. These latter moments can be obtained by single-pass methods from measured data. Additionally, a parameterization of the angular standard deviation as a function of persistence of wind direction is given. A comparison with other estimation methods is made and some applications to experimental data are given.