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Measurements of hailstone diameters and kinetic energy, collected by the Swiss network of automatic hail sensors, are available in three regions of Switzerland for the period between September 2018 and August 2023. In this study, we propose the use of double-moment normalization for modeling the hail size number distribution (HSND), which is defined as the number of hailstone impacts measured, for each diameter size, by one instrument during one hail event. This method uses two of the empirical moments of the HSND to compute a normalized distribution. While the HSND is dependent on the duration and intensity of the event and on the detection area of the sensor, we show that the normalized distribution has limited variability across the three geographical regions of deployment of the sensors. Thanks to its invariance in space and time, a generalized gamma function is used to model the normalized distribution, and its parameters have been determined through a fit over approximately 70 % of the events. The fitted model and the previously chosen pair of empirical moments can be used to reconstruct the HSND at any location in Switzerland. The accuracy of the reconstruction has been estimated over the remaining 30 % of the dataset. An additional evaluation has been performed on an independent HSND, made of estimates of hail diameters measured by drone photogrammetry during a single event. This HSND has a much larger number of hailstone impacts (18 000) than those of the hail sensor events (from 30 to 400). The double-moment normalization is able to reproduce well the HSND recorded by the hail sensors and the drone, albeit with an underestimation of the number of impacts at small diameters. These results highlight the invariance of the normalized distribution and the adaptability of the method to different data sources. [ABSTRACT FROM AUTHOR]

Archives of composite weather radar images represent an invaluable resource to study the predictability of precipitation. In this paper, we compare two distinct approaches to construct empirical low-dimensional attractors from radar precipitation fields. In the first approach, the phase space variables of the attractor are defined using the domain-scale statistics of precipitation fields, such as the mean precipitation, fraction of rain, and spatial and temporal correlations. The second type of attractor considers the spatial distribution of precipitation and is built by principal component analysis (PCA). For both attractors, we investigate the density of trajectories in phase space, growth of errors from analogue states, and fractal properties. To represent different scales and climatic and orographic conditions, the analyses are done using multi-year radar archives over the continental United States (≈4000×4000 km 2 , 21 years) and the Swiss Alpine region (≈500×500 km 2 , 6 years). [ABSTRACT FROM AUTHOR]

Archives of composite weather radar images represent an invaluable resource to study the predictability of precipitation. In this paper, we compare two distinct approaches to construct empirical low-dimensional attractors from radar precipitation fields. In the first approach, the phase space dimensions of the attractor are defined using the domain-scale statis5 tics of precipitation fields, such as the mean precipitation, fraction of rain, spatial and temporal correlations. The second type of attractor considers the spatial distribution of precipitation and is built by principal component analysis (PCA). For both attractors, we investigate the density of trajectories in phase space, growth of errors from analogue states, and fractal properties. To represent different scales, climatic and orographic conditions, the analyses are done using multi-year radar archives over the continental United States (≈ 4000 × 4000 km², 21 years) and the Swiss Alpine region (≈ 500 × 500 km², 6 years). [ABSTRACT FROM AUTHOR]

A still wind turbine (WT) observed with a fixed pointing radar antenna shows peculiar polarimetric signatures: during two minutes (from 17:08 to 17:10 UTC) of the first day (March 4, 2020) of the WT MeteoSwiss X-band radar campaign in Schaffhausen, the copolar correlation coefficient between the two orthogonal polarization states was persistently equal to 1. The reflectivity at vertical polarization was bounded between 38.5 and 41.5 dBz; however, the changes between two consecutive 64 ms values (retrieved by means of 128 transmitted pulses) were either 0 dBz or ±0.5 dBz. The 2-min median (mean) value was 40.0 (39.9) dBz over the 1875 echoes of this interval. The reflectivity at horizontal polarization was persistently equal to 56.5 dBz, which means no change exceeding ±0.25 dBz. The standard deviation (1874 degrees of freedom) of the differential phase shift, which in the absence of precipitation was, in fact, coincident with the dispersion of the differential backscattering phase shift, was as small as 3.0°. During two 10-min intervals (17:10-17:20 UTC and 17:30-17:40 UTC) the rotor has moved less than 1 revolution; however, this slow movement together with a change in blade angles and nacelle orientation was sufficient to cause large changes and significant variability in the polarimetric signatures, with two pairs of ZH consecutive values reaching the extreme of 78.5 dBz, which is the absolute reflectivity maximum reached in the whole campaign (March 4-21, 2020). Between 17:20 and 17:30 UTC, the rotor has accomplished 22.5 revolutions: the variability becomes smoother and softer in the central part of the interval (probably thanks to uniform rotor speed and "frozen" blade angles and nacelle orientation). It is desirable and recommended to extend this preliminary (32-minute) analysis (based on thirty thousand polarimetric measurables) to several other 10-min intervals with zero rotor speed. [ABSTRACT FROM AUTHOR]

We show how the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (TPR) can be used to monitor and adjust ground-based radar (GR) data, as a function of the distance from the radar site. Problems caused by the variability of precipitation and differences in sampling volume of the two instruments are reduced to a level that is achievable with, and acceptable for, the present analysis. Throughout the region under surveillance, TPR has poorer spatial resolution than GR. The sampling volume of the GR changes quite remarkably according to the range from the GR site: it increases with the square of the range. TPR, on the other hand, has similar sampling volumes in all the locations. The analysis is based on the average linear radar reflectivity, in circular rings around the GR site, [(Z).sub.2[pi]], as a function of the range from the GR site. The GR/TPR ratio varies, for the Cyprus radar, on average from 2 dB, at 10 km, to -8 dB at 100 km. The average departure at the average range is considered to be mainly caused by the calibration of the GR. The range dependence of the GR/TPR ratio is significant and similar, in all the investigated cases. This is interpreted to be caused by the increasing sampling volume of the GR with range, combined with nonhomogeneous beam filling, e.g., at longer ranges of GR, the lower part of the volume could be in rain, whereas the upper part of the same pulse could be filled with snow, or even be without an echo. After correcting the GR data by using the derived averaged relationship, a significantly better agreement between the GR and TPR is found in all the overpasses analyzed. The agreement between the results of the two instruments is better for both the percentage of echo areas and the rain amount within each area. It is also better for the agreement of the GR with the gauges. In the absence of TPR data, it will be useful to investigate to what extent long-term, climatological data can be used to substitute TPR data. Index Terms--Meteorological radar, meteorology, microwave radio propagation meteorological factors, numerical analysis and verification, rain, spaceborne and ground-based weather radar, Tropical Rainfall Measuring Mission (TRMM).

Through a Fredholm integral equation of the first kind, aerosol kernel functions relate the variations in radiance measured by satellites to the variations in the aerosol extinction profile and thus permit profile retrieval from radiance measurements by inversion of the set of radiative transfer equations for various spectral intervals. Previously [Appl. Opt. 36, 1328 (1997)] the kernel functions were evaluated for the red and near-infrared spectral regions outside molecular absorption bands. Here they are computed within the oxygen A band with 20-cm-1 spectral resolution. It is shown that, even with such a relatively low spectral resolution, the new set of kernels is able to provide better information on and improved accuracy of the retrieved profile.

Although reanalysis products for remote high-mountain regions provide estimates of snow precipitation, this data is inherently uncertain and assessing a potential bias is difficult due to the scarcity of observations, thus also limiting their reliability to evaluate long-term effects of climate change. Here, we compare the winter mass balance of 95 glaciers distributed over the Alps, Western Canada, Central Asia and Scandinavia, with the total precipitation from the ERA-5 and the MERRA-2 reanalysis products during the snow accumulation seasons from 1981 until today. We propose a machine learning model to adjust the precipitation of reanalysis products to the elevation of the glaciers, thus deriving snow water equivalent (SWE) estimates over glaciers uncovered by ground observations and/or filling observational gaps. We use a gradient boosting regressor (GBR), which combines several meteorological variables from the reanalyses (e.g. air temperature, relative humidity) with topographical parameters. These GBR-derived estimates are evaluated against the winter mass balance data by means of a leave-one10 glacier-out cross-validation (site-independent GBR) and a leave-one-season-out cross-validation (season-independent GBR). Both site-independent and season-independent GBRs allowed reducing (increasing) the bias (correlation) between the precipitation of the original reanalyses and the winter mass balance data of the glaciers. Finally, the GBR models are used to derive SWE trends on glaciers between 1981 and 2021. The resulting trends are more pronounced than those obtained from the total precipitation of the original reanalyses. On a regional scale, significant 41-year SWE trends over glaciers are observed in the Alps (MERRA-2 season-independent GBR: +0.4%/year) and in Western Canada (ERA-5 season-independent GBR: +0.2 %/year), while significant positive/negative trends are observed in all the regions for single glaciers or specific elevations. Negative (positive) SWE trends are typically observed at lower (higher) elevations, where the impact of rising temperatures is more (less) dominant. [ABSTRACT FROM AUTHOR]

Scattering from atmospheric aerosols causes blurring of satellite images. A study of this effect suggests that it might be possible to evaluate aerosol properties from these images. We consider an aerosol layer superimposed on a surface with a one-dimensional sinusoidal variation in reflectivity and with a half-plane reflectivity variation. A single scattering approximation is used to show that information about the aerosol layer height and optical depth can be extracted provided the variation in ground reflectivity is known.