The new generation of weather observatory satellites, namely Global Precipitation Measurement (GPM) constellation satellites, is the lead observatory of the 10 highly advanced earth orbiting weather research satellites. Indeed, GPM is the first satellite that has been designed to measure light rain and snowfall, in addition to heavy tropical rainfall. This work compares the final run of the Integrated Multi-satellitE Retrievals for GPM (IMERG) product, the post real time of TRMM and Multi-satellite Precipitation Analysis (TMPA-3B42) and the Era-Interim product from the European Centre for Medium Range Weather Forecasts (ECMWF) against the Iran Meteorological Organization (IMO) daily precipitation measured by the synoptic rain-gauges over four regions with different topography and climate conditions in Iran. Assessment is implemented for a one-year period from March 2014 to February 2015. Overall, in daily scale the results reveal that all three products lead to underestimation but IMERG performs better than other products and underestimates precipitation slightly in all four regions. Based on monthly and seasonal scale, in Guilan all products, in Bushehr and Kermanshah ERA-Interim and in Tehran IMERG and ERA-Interim tend to underestimate. The correlation coefficient between IMERG and the rain-gauge data in daily scale is far superior to that of Era-Interim and TMPA-3B42. On the basis of daily timescale of bias in comparison with the ground data, the IMERG product far outperforms ERA-Interim and 3B42 products. According to the categorical verification technique in this study, IMERG yields better results for detection of precipitation events on the basis of Probability of Detection (POD), Critical Success Index (CSI) and False Alarm Ratio (FAR) in those areas with stratiform and orographic precipitation, such as Tehran and Kermanshah, compared with other satellite/model data sets. In particular, for heavy precipitation (>15 mm/day), IMERG is superior to the other products in all study areas and could be used in future for meteorological and hydrological models, etc.

Observational errors may have a serious impact on objective analyses. Before conducting an objective analysis, that is, interpolating irregularly spaced observations to a uniform grid, the data should be checked thoroughly for errors. For this procedure a piecewise functional fitting approach is proposed, which is based on a variational algorithm. As for thin-plate splines, an integral of squares of second temporal and/or spatial derivatives is minimized. The second derivatives are obtained from overlapping finite elements using a polynomial approach. In a slightly different mode, the same approach may also be used to interpolate the observational data to a regular grid. The method is formulated for and applied to scalar and vector quantities in a one- and a two-dimensional domain. The basic advantages of the method are on the one hand the fact that no first guess or (prognostic) model field is necessary and on the other hand that no a priori knowledge about structure or weighting functions is re... Abstract Observational errors may have a serious impact on objective analyses. Before conducting an objective analysis, that is, interpolating irregularly spaced observations to a uniform grid, the data should be checked thoroughly for errors. For this procedure a piecewise functional fitting approach is proposed, which is based on a variational algorithm. As for thin-plate splines, an integral of squares of second temporal and/or spatial derivatives is minimized. The second derivatives are obtained from overlapping finite elements using a polynomial approach. In a slightly different mode, the same approach may also be used to interpolate the observational data to a regular grid. The method is formulated for and applied to scalar and vector quantities in a one- and a two-dimensional domain. The basic advantages of the method are on the one hand the fact that no first guess or (prognostic) model field is necessary and on the other hand that no a priori knowledge about structure or weighting functions is re...

Conducting meteorological measurements, one is always confronted with a wide variety of different types of errors and with the decision of how to correct data for further use, if necessary. The selection of an adequate quality control (QC) procedure out of a wide range of methodologies depends on the properties of the observed parameter such as spatial or temporal consistency. But the intended data application (e.g., model-independent data analysis) or the availability of prior knowledge also has to be taken into account. The herein-presented self-consistent and model-independent QC process makes use of the spatial and temporal consistency of meteorological parameters. It is applicable to measurements featuring a high degree of autocorrelation with regard to the resolution of the observational network in space and time. The presented QC procedure can mathematically be expressed as an optimization problem minimizing the curvature of the analyzed field. This results in a matrix equation that can be solved without needing to converge iterations. Based on the resulting deviations and, if applied, on their impacts on the cost function, station values are accepted, corrected, or identified as outliers and hence dismissed. Furthermore, it is pointed out that this method is able to handle complicated station distributions, such as clustered stations or inhomogeneous station densities. This QC method is not only an appropriate tool for case studies but also for model validation and has been proving itself as a preprocessing tool for operational meso- and micrometeorological analyses.

Time series with a significant trend, as is now being the case for the temperature in the course of climate change, need a careful approach for statistical evaluations. Climatological means and moments are usually taken from past data which means that the statistics does not fit to actual data anymore. Therefore, we need to determine the long-term trend before comparing actual data with the actual climate. This is not an easy task, because the determination of the signal—a climatic trend—is influenced by the random scatter of observed data. Different filter methods are tested upon their quality to obtain realistic smoothed trends of observed time series. A new method is proposed, which is based on a variational principle. It outperforms other conventional methods of smoothing, especially if periodic time series are processed. This new methodology is used to test, how extreme the temperature of 2018 in Vienna actually was. It is shown that the new annual temperature record of 2018 is not too extreme, if we consider the positive trend of the last decades. Also, the daily mean temperatures of 2018 are not found to be really extreme according to the present climate. The real extreme of the temperature record of Vienna—and many other places around the world—is the strongly increased positive temperature trend over the last years.

A new approach of splines to examine climatological time series is introduced and different applications are shown. Instead of the classical spline‐procedure to find polynomials which fit given values at certain points (knots), a variational formulation is used here, where a cost function is minimized to obtain smooth interpolated values at arbitrary points. The innovation of the method consists in the selection of the constraint, namely the conservation of mean values within certain smoothing intervals. The methodology allows a sound derivation of the past and present climate conditions in times of climate change. It allows a refined computation of extreme values and of the probability of certain temperature thresholds. The methodology furthermore allows to detect break points in climatological time series. Finally the method leads to a consistent interpolation of time series, which are only given by mean values. Several applications of the method, using climatological time series of Vienna are shown and discussed.

A determination of the generalized CAPE (GCAPE) is suggested where instead of an adiabatic reversible vertical redistribution of air in a conditionally unstable atmosphere, irreversible processes with regard to the water cycle are taken into account. Irreversible processes like entrainment or atmospheric dissipation due to precipitation generally reduce the generation of kinetic energy. Irreversible pseudoadiabatic processes, in contrast, increase the availability of convective potential energy considerably. It is further increased significantly when an irreversible redistribution of water in the atmosphere due to precipitation and its corresponding evaporation is considered. Finally, the contributions of the ice phase in clouds and solid precipitation evaporation to GCAPE are investigated. The second aim of this paper is to compare CAPE and GCAPE in an unstable atmosphere. As an important result, it is shown that CAPE and GCAPE are inequivalent metrics of stability. It is even possible that an atmospheric profile with a considerable GCAPE shows a zero CAPE value. With the aid of different models with increasing complexity of thermodynamic processes, comparisons of numerical values of CAPE and GCAPE for an idealized and a real atmospheric profile are carried out. Although the mechanism and fraction of realization of convective available potential energy may be very different in individual weather systems, the pseudoadiabatic GCAPE arguably seems to be the better quantity than CAPE to compare or calibrate energy conversions in the atmosphere during organized deep convection with precipitation, because convection requires GCAPE but not necessarily CAPE. Evaluations have shown that on all days with thunderstorms in Vienna during a 9-yr period, GCAPE was positive, while a considerable fraction of these days showed zero CAPE.