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- Author or Editor: Jean-Dominique Creutin x
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Abstract
The vertical variability of reflectivity in the radar beam is one of the main sources of error in estimating rainfall intensity. This vertical variability, which has several origins, is characterized globally by a function called "vertical profile of reflectivity." The impact of this vertical profile of reflectivity on the radar measurement is quantified by incorporating this function in the radar equation. It is then possible to specify the influence of the characteristics of the radar, the distance, and the vertical profile on errors in estimating rain rates at the ground level. A method for determining the vertical profile of reflectivity is then described. This procedure requires the use of radar images from at least two different elevation angles. It is based on the evolution of theratio of reflectivities (reflectivity at high elevation divided by reflectivity at a lower elevation angle) versus distance. The ratio evolution is closely related to the vertical profile of reflectivity and to the conditions of radar operation. An inverse solution method is used to identify the vertical profile of reflectivity corresponding to the observed ratio of reflectivities. The advantages and limitations of the proposed method are discussed.
Abstract
The vertical variability of reflectivity in the radar beam is one of the main sources of error in estimating rainfall intensity. This vertical variability, which has several origins, is characterized globally by a function called "vertical profile of reflectivity." The impact of this vertical profile of reflectivity on the radar measurement is quantified by incorporating this function in the radar equation. It is then possible to specify the influence of the characteristics of the radar, the distance, and the vertical profile on errors in estimating rain rates at the ground level. A method for determining the vertical profile of reflectivity is then described. This procedure requires the use of radar images from at least two different elevation angles. It is based on the evolution of theratio of reflectivities (reflectivity at high elevation divided by reflectivity at a lower elevation angle) versus distance. The ratio evolution is closely related to the vertical profile of reflectivity and to the conditions of radar operation. An inverse solution method is used to identify the vertical profile of reflectivity corresponding to the observed ratio of reflectivities. The advantages and limitations of the proposed method are discussed.
Abstract
A method of identification of the vertical profile of reflectivity, formulated by the authors in an accompanying paper, is tested through a sensitivity analysis. Two simulated but realistic profiles (with and without brightband effects) are used. The radar features and the statistical parameters involved in this method are allowed to varyaround standard values in order to understand their influence on the results. The main conclusion is that, for a given radar configuration, results of acceptable quality can be obtained with a single adjustment ofthe method for the two types of profiles, which suggests the approach is operationally applicable. To complement this theoretical analysis, actual profiles of reflectivities are studied for two rainfall eventsobserved in the Cevennes region of France. The efficiency of the proposed method is appreciated from a hydrological point of view. A comparison is performed at the basin scale between hourly rainfall intensities, measured with a dense network of rain gauges and radar data. The analysis shows that the introduction of the identification and the correction of the influence of vertical profiles of reflectivity improve the accuracy of rainfall estimates from radar data.
Abstract
A method of identification of the vertical profile of reflectivity, formulated by the authors in an accompanying paper, is tested through a sensitivity analysis. Two simulated but realistic profiles (with and without brightband effects) are used. The radar features and the statistical parameters involved in this method are allowed to varyaround standard values in order to understand their influence on the results. The main conclusion is that, for a given radar configuration, results of acceptable quality can be obtained with a single adjustment ofthe method for the two types of profiles, which suggests the approach is operationally applicable. To complement this theoretical analysis, actual profiles of reflectivities are studied for two rainfall eventsobserved in the Cevennes region of France. The efficiency of the proposed method is appreciated from a hydrological point of view. A comparison is performed at the basin scale between hourly rainfall intensities, measured with a dense network of rain gauges and radar data. The analysis shows that the introduction of the identification and the correction of the influence of vertical profiles of reflectivity improve the accuracy of rainfall estimates from radar data.
Abstract
We propose a new approach to explain multiday rainfall accumulation over a French Alpine watershed using large-scale atmospheric predictors based on analogy. The classical analogy framework associates a rainfall cumulative distribution function (CDF) with a given atmospheric situation from the precipitation accumulations yielded by the closest situations. The analogy may apply to single-day or multiday sequences of pressure fields. The proposed approach represents a paradigm shift in analogy. It relies on the similarity of the local topology mapping the pressure field sequences, somehow forgetting the pressure fields per se. This topology is summarized by the way the sequences of pressure fields resemble their neighbors (dimensional predictors) and how fast they evolve in time (dynamical predictors). Although some information—and hence predictability—is expected to be lost when compared with classical analogy, this approach provides new insight on the atmospheric features generating rainfall CDFs. We apply both approaches to geopotential heights over western Europe in view of assessing 3-day rainfall accumulations over the Isère River catchment at Grenoble, France. Results show that dimensional predictors are the most skillful features for predicting 3-day rainfall—bringing alone 60% of the predictability of the classical analogy approach—whereas the dynamical predictors are less explicative. These results open new directions of research that the classical analogy approach cannot handle. They show, for instance, that both dry sequences and strong rainfall sequences are associated with singular 500-hPa geopotential shapes acting as local attractors—a way of explaining the change in rainfall CDFs in a changing climate.
Abstract
We propose a new approach to explain multiday rainfall accumulation over a French Alpine watershed using large-scale atmospheric predictors based on analogy. The classical analogy framework associates a rainfall cumulative distribution function (CDF) with a given atmospheric situation from the precipitation accumulations yielded by the closest situations. The analogy may apply to single-day or multiday sequences of pressure fields. The proposed approach represents a paradigm shift in analogy. It relies on the similarity of the local topology mapping the pressure field sequences, somehow forgetting the pressure fields per se. This topology is summarized by the way the sequences of pressure fields resemble their neighbors (dimensional predictors) and how fast they evolve in time (dynamical predictors). Although some information—and hence predictability—is expected to be lost when compared with classical analogy, this approach provides new insight on the atmospheric features generating rainfall CDFs. We apply both approaches to geopotential heights over western Europe in view of assessing 3-day rainfall accumulations over the Isère River catchment at Grenoble, France. Results show that dimensional predictors are the most skillful features for predicting 3-day rainfall—bringing alone 60% of the predictability of the classical analogy approach—whereas the dynamical predictors are less explicative. These results open new directions of research that the classical analogy approach cannot handle. They show, for instance, that both dry sequences and strong rainfall sequences are associated with singular 500-hPa geopotential shapes acting as local attractors—a way of explaining the change in rainfall CDFs in a changing climate.
Abstract
This study demonstrates the sensitivity of reflectivity–rainfall rate (Z–R) relationships, which were derived from disdrometer-based drop size distribution measurements, to the fall velocity of the drops. The dataset used comes from the simultaneous observation of a series of five moderate rainfall events with a Joss and Waldvogel disdrometer and an optical spectropluviometer. The signal-processing software of the latter was able to measure the residence time of the drops in its sampling volume, enabling computation of the volumetric drop concentration without any assumption on the fall velocity of the drops. The Z–R relationships derived from the two instruments are significantly different. This difference is shown to essentially arise from the drop fall velocities in a twofold manner. First, it comes from the use of a theoretical terminal fall velocity in still air to compute the drop concentration from the drop flux. Second, it comes from the principle of drop size measurement by the impact-type disdrometer that relies on the “energy” of the drop, and thus on its size and fall velocity.
Abstract
This study demonstrates the sensitivity of reflectivity–rainfall rate (Z–R) relationships, which were derived from disdrometer-based drop size distribution measurements, to the fall velocity of the drops. The dataset used comes from the simultaneous observation of a series of five moderate rainfall events with a Joss and Waldvogel disdrometer and an optical spectropluviometer. The signal-processing software of the latter was able to measure the residence time of the drops in its sampling volume, enabling computation of the volumetric drop concentration without any assumption on the fall velocity of the drops. The Z–R relationships derived from the two instruments are significantly different. This difference is shown to essentially arise from the drop fall velocities in a twofold manner. First, it comes from the use of a theoretical terminal fall velocity in still air to compute the drop concentration from the drop flux. Second, it comes from the principle of drop size measurement by the impact-type disdrometer that relies on the “energy” of the drop, and thus on its size and fall velocity.
Abstract
This paper is devoted to a sensitivity study of the equation describing attenuation effects in rain for ground-based weather radar systems operating at X- or C-band wavelengths. First, the so-called attenuation equation, also termed the HB solution or HB algorithm in reference to the well-known paper by , is recalled. A procedure aimed at obtaining consistent relations between average values of the equivalent reflectivity factor Z e , the attenuation coefficient k, and the rain rate R as function of two parameters of the drop size distribution (DSD) is also presented. Then, a numerical simulation framework based on a simple description of rainfall characteristics and accounting for some of the radar measurement features is proposed to test the ability of the HB algorithm to perform attenuation correction of hypothetical rain-rate profiles. In a first step, the well-known instability of the solution is illustrated. For instance, it is shown that, even in the absence of radar calibration error and with perfect knowledge of the DSD, the algorithm is not able to correct profiles with path-integrated attenuation (PIA) greater than about 20 dB when typical values are considered for the radar parameters. Owing to this inherent instability, the sensitivity study with respect to the DSD parameters is therefore limited to profiles with PIAs less than 15 dB. The two following results are obtained: 1) a PIA of about 10 dB should be considered as the upper limit that the algorithm is able to correct and 2) given the choice of the (Z e , k, R) relations, optimization of one parameter is necessary and sufficient to obtain improvement over the standard ZR method for this range of PIAs. This parameter plays the role of a correction term for the radar calibration error, the uncertainty in the knowledge of the DSD, and other sources of bias. These results are confirmed by an X-band radar–rain gauge comparison with a dataset collected during the Marseilles Hydrometeorological Experiment.
Abstract
This paper is devoted to a sensitivity study of the equation describing attenuation effects in rain for ground-based weather radar systems operating at X- or C-band wavelengths. First, the so-called attenuation equation, also termed the HB solution or HB algorithm in reference to the well-known paper by , is recalled. A procedure aimed at obtaining consistent relations between average values of the equivalent reflectivity factor Z e , the attenuation coefficient k, and the rain rate R as function of two parameters of the drop size distribution (DSD) is also presented. Then, a numerical simulation framework based on a simple description of rainfall characteristics and accounting for some of the radar measurement features is proposed to test the ability of the HB algorithm to perform attenuation correction of hypothetical rain-rate profiles. In a first step, the well-known instability of the solution is illustrated. For instance, it is shown that, even in the absence of radar calibration error and with perfect knowledge of the DSD, the algorithm is not able to correct profiles with path-integrated attenuation (PIA) greater than about 20 dB when typical values are considered for the radar parameters. Owing to this inherent instability, the sensitivity study with respect to the DSD parameters is therefore limited to profiles with PIAs less than 15 dB. The two following results are obtained: 1) a PIA of about 10 dB should be considered as the upper limit that the algorithm is able to correct and 2) given the choice of the (Z e , k, R) relations, optimization of one parameter is necessary and sufficient to obtain improvement over the standard ZR method for this range of PIAs. This parameter plays the role of a correction term for the radar calibration error, the uncertainty in the knowledge of the DSD, and other sources of bias. These results are confirmed by an X-band radar–rain gauge comparison with a dataset collected during the Marseilles Hydrometeorological Experiment.
Abstract
Based on weather radar detection, orographic rainbands parallel to wind direction may persist for several hours over a Mediterranean mountainous region prone to stable wind and humidity conditions. A statistical analysis shows that orographic rainbands are more active and more stable over the mountains than over the lower hills. By the mean of the range–time indicator technique, the northward advection velocity of the rain cells is deduced (60 km h−1) and is slightly lower than the wind velocity (85 km h−1) measured at the high-altitude weather station (Mont Aigoual, 1565 m above mean sea level). The detailed analysis highlights that the positioning of individual orographic cells in relation to the relief is not random: they are triggered by relief shoulders on their southeast flank. Their regular spacing (typically 15 km) is responsible for the general organization of the rainbands. Rain accumulations vary from 20 to over 100 mm day−1 from the outside to the center of the rainbands.
Abstract
Based on weather radar detection, orographic rainbands parallel to wind direction may persist for several hours over a Mediterranean mountainous region prone to stable wind and humidity conditions. A statistical analysis shows that orographic rainbands are more active and more stable over the mountains than over the lower hills. By the mean of the range–time indicator technique, the northward advection velocity of the rain cells is deduced (60 km h−1) and is slightly lower than the wind velocity (85 km h−1) measured at the high-altitude weather station (Mont Aigoual, 1565 m above mean sea level). The detailed analysis highlights that the positioning of individual orographic cells in relation to the relief is not random: they are triggered by relief shoulders on their southeast flank. Their regular spacing (typically 15 km) is responsible for the general organization of the rainbands. Rain accumulations vary from 20 to over 100 mm day−1 from the outside to the center of the rainbands.
Abstract
This paper investigates the internal spatial distribution of rain rates inside the rain areas. Moving trend functions are defined for different thresholds τ. They are obtained as conditional mathematical expectations of the rain rates above τ, and depend on the distance between the considered point with rain rate higher than τ and the boundary of the τ-thresholded area, which is the area where the intensity is above τ. These functions are linked to the dynamics of rainfall patterns and are thus named moving trend functions. Such functions are calculated on a dataset of hourly rainfall fields recorded in 1989 and 1990 in the framework of the Epsat-Niger project. The study area is about 12 000 km2 and is instrumented with a dense gauge network. The shape of the moving trend functions show that, on average, the rain intensity increases from the edge to the center of the τ-thresholded areas. Thus, the spatial distribution of the rain rates depends on the shape of the τ-thresholded areas.
An estimation algorithm for mean areal rainfall is then proposed using the moving trend functions. This estimation implicitly depends on the shape of the τ-thresholded area. The algorithm is applied to two subareas of 400 and 3600 km2 of the Niger dataset. The method is also compared with the threshold method on these two subareas. The two techniques give equivalent results on the 3600-km2 area and some small improvements can be observed on the 400-km2 area, especially for low thresholds. However, problems encountered in the estimation of the moving trend functions discussed in the paper and due to the finite size of the study area prevent the moving trend function technique to demonstrate its potentiality clearly.
Abstract
This paper investigates the internal spatial distribution of rain rates inside the rain areas. Moving trend functions are defined for different thresholds τ. They are obtained as conditional mathematical expectations of the rain rates above τ, and depend on the distance between the considered point with rain rate higher than τ and the boundary of the τ-thresholded area, which is the area where the intensity is above τ. These functions are linked to the dynamics of rainfall patterns and are thus named moving trend functions. Such functions are calculated on a dataset of hourly rainfall fields recorded in 1989 and 1990 in the framework of the Epsat-Niger project. The study area is about 12 000 km2 and is instrumented with a dense gauge network. The shape of the moving trend functions show that, on average, the rain intensity increases from the edge to the center of the τ-thresholded areas. Thus, the spatial distribution of the rain rates depends on the shape of the τ-thresholded areas.
An estimation algorithm for mean areal rainfall is then proposed using the moving trend functions. This estimation implicitly depends on the shape of the τ-thresholded area. The algorithm is applied to two subareas of 400 and 3600 km2 of the Niger dataset. The method is also compared with the threshold method on these two subareas. The two techniques give equivalent results on the 3600-km2 area and some small improvements can be observed on the 400-km2 area, especially for low thresholds. However, problems encountered in the estimation of the moving trend functions discussed in the paper and due to the finite size of the study area prevent the moving trend function technique to demonstrate its potentiality clearly.
Abstract
The aim of the present study is to characterize mountain returns measured with a ground-based weather radar operating in a mountainous region. A computation code based on the use of a digitized terrain model is developed for calculating the areas illuminated by the radar beam. Partial and total screening effects am accounted for in the calculation. The angular and range weighting functions of the radar measurement am modeled using Gaussian approximations to give the so-called weighted illuminated areas for various sizes of the radar resolution volume. Radar measurements are compared to the computed illuminated areas in order to determine the average backscattering coefficient of partly grass-covered, partly forested mountains: 87% of the measured time-averaged mountain return variance is explained by the computed values when the 15-dB resolution volume is considered. Additional geometrical information, provided by the calculated angles of incidence, is accounted for to yield a linear σ(dB) 0(α) model relevant for the so-called near-grazing region since most of the angles of incidence are in the 70°–900° range. Here 92% of the measurement variance is explained when the σ(dB) 0(α) model is used.
Abstract
The aim of the present study is to characterize mountain returns measured with a ground-based weather radar operating in a mountainous region. A computation code based on the use of a digitized terrain model is developed for calculating the areas illuminated by the radar beam. Partial and total screening effects am accounted for in the calculation. The angular and range weighting functions of the radar measurement am modeled using Gaussian approximations to give the so-called weighted illuminated areas for various sizes of the radar resolution volume. Radar measurements are compared to the computed illuminated areas in order to determine the average backscattering coefficient of partly grass-covered, partly forested mountains: 87% of the measured time-averaged mountain return variance is explained by the computed values when the 15-dB resolution volume is considered. Additional geometrical information, provided by the calculated angles of incidence, is accounted for to yield a linear σ(dB) 0(α) model relevant for the so-called near-grazing region since most of the angles of incidence are in the 70°–900° range. Here 92% of the measurement variance is explained when the σ(dB) 0(α) model is used.
Abstract
The optical spectropluviometer is a shadowgraph instrument able to measure independently the equivalent diameter and the fall speed of raindrops at ground level. Hardware and software modifications are proposed and tested. A modern digital signal processing system allows for the simultaneous sampling and analyzing of the signal delivered by the sensor. The IR light transmission is pulsed to avoid interference with natural radiation and the protection of the optics is improved. The validation procedure consists of comparing the rain rates derived from the measured drop size distributions with rain rates delivered by nearby rain gauges. The results obtained during 65 storm events show that the proposed improvements reduce the bias of the rain-rate estimation from 34% to 16%. Suggestions are given to further improve the performance of this instrument.
Abstract
The optical spectropluviometer is a shadowgraph instrument able to measure independently the equivalent diameter and the fall speed of raindrops at ground level. Hardware and software modifications are proposed and tested. A modern digital signal processing system allows for the simultaneous sampling and analyzing of the signal delivered by the sensor. The IR light transmission is pulsed to avoid interference with natural radiation and the protection of the optics is improved. The validation procedure consists of comparing the rain rates derived from the measured drop size distributions with rain rates delivered by nearby rain gauges. The results obtained during 65 storm events show that the proposed improvements reduce the bias of the rain-rate estimation from 34% to 16%. Suggestions are given to further improve the performance of this instrument.
Abstract
The aim of the current study is to quantify attenuation effects that X- and C-band weather radar systems may experience in heavy rainfall. Part of this information can be obtained from power-law relationships between the attenuation coefficient k (dB km−1) and the rain rate R (mm h−1). These relations exhibit a strong dependence on the wavelength used and a significant influence of the raindrop size and temperature distributions. Here the purpose is to go one step further by providing estimates of the path-integrated attenuations (PIAs) that could be observed as a function of range for a given wavelength. Obviously, these values depend on the space and time structure of rainfall and, therefore, refer to a given climatological context. The methodology used consists of using k–R relations to downgrade carefully processed S-band radar data to the corresponding X- and C-band signals. The data were collected in the Cévennes region, a Mediterranean region in France subject to intense and long-lasting rain events during the autumn season. A refined data processing procedure was applied to the available reflectivity measurements, including ground-clutter removal and correction for the effects of the vertical profile of reflectivity as well as a final bias adjustment using rain gauge data. For three rain events, 75 h of instantaneous rain-rate fields thus were available with total rain amounts that exceeded 300 mm over most of the area of interest. Examples of attenuated profiles are presented, and PIA-range-frequency curves are established for the two wavelengths considered under various hypotheses that concern the raindrop size distribution. One of the results is that, at C band, a PIA of 3 dB is exceeded for 5% of the rain-rate profiles at a range of 50 km. Another finding is that a multiplicative factor of about 6 exists between C- and X-band attenuation effects. Implications for rain-rate estimation at X- and C band are discussed.
Abstract
The aim of the current study is to quantify attenuation effects that X- and C-band weather radar systems may experience in heavy rainfall. Part of this information can be obtained from power-law relationships between the attenuation coefficient k (dB km−1) and the rain rate R (mm h−1). These relations exhibit a strong dependence on the wavelength used and a significant influence of the raindrop size and temperature distributions. Here the purpose is to go one step further by providing estimates of the path-integrated attenuations (PIAs) that could be observed as a function of range for a given wavelength. Obviously, these values depend on the space and time structure of rainfall and, therefore, refer to a given climatological context. The methodology used consists of using k–R relations to downgrade carefully processed S-band radar data to the corresponding X- and C-band signals. The data were collected in the Cévennes region, a Mediterranean region in France subject to intense and long-lasting rain events during the autumn season. A refined data processing procedure was applied to the available reflectivity measurements, including ground-clutter removal and correction for the effects of the vertical profile of reflectivity as well as a final bias adjustment using rain gauge data. For three rain events, 75 h of instantaneous rain-rate fields thus were available with total rain amounts that exceeded 300 mm over most of the area of interest. Examples of attenuated profiles are presented, and PIA-range-frequency curves are established for the two wavelengths considered under various hypotheses that concern the raindrop size distribution. One of the results is that, at C band, a PIA of 3 dB is exceeded for 5% of the rain-rate profiles at a range of 50 km. Another finding is that a multiplicative factor of about 6 exists between C- and X-band attenuation effects. Implications for rain-rate estimation at X- and C band are discussed.
