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- Author or Editor: Efi Foufoula-Georgiou x
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Abstract
In this paper the authors study how zero intermittency in spatial rainfall, as described by the fraction of area covered by rainfall, changes with spatial scale of rainfall measurement or representation. A statistical measure of intermittency that describes the size distribution of “voids” (nonrainy areas imbedded inside rainy areas) as a function of scale is also introduced. Morphological algorithms are proposed for reconstructing rainfall intermittency at fine scales given the intermittency at coarser scales. These algorithms are envisioned to be useful in hydroclimatological studies where the rainfall spatial variability at the subgrid scale needs to be reconstructed from the results of synoptic- or mesoscale meteorological numerical models. The developed methodologies are demonstrated and tested using data from a severe springtime midlatitude squall line and a mild midlatitude winter storm monitored by a meteorological radar in Norman, Oklahoma.
Abstract
In this paper the authors study how zero intermittency in spatial rainfall, as described by the fraction of area covered by rainfall, changes with spatial scale of rainfall measurement or representation. A statistical measure of intermittency that describes the size distribution of “voids” (nonrainy areas imbedded inside rainy areas) as a function of scale is also introduced. Morphological algorithms are proposed for reconstructing rainfall intermittency at fine scales given the intermittency at coarser scales. These algorithms are envisioned to be useful in hydroclimatological studies where the rainfall spatial variability at the subgrid scale needs to be reconstructed from the results of synoptic- or mesoscale meteorological numerical models. The developed methodologies are demonstrated and tested using data from a severe springtime midlatitude squall line and a mild midlatitude winter storm monitored by a meteorological radar in Norman, Oklahoma.
Abstract
It has been observed that the finite-dimensional distribution functions of rainfall cannot obey simple scaling laws due to rainfall intermittency (mixed distribution with an atom at zero) and the probability of rainfall being an increasing function of area. Although rainfall fluctuations do not suffer these limitations, it is interesting to note that very few attempts have been made to study them in terms of their self-similarity characteristics. This is due to the lack of unambiguous definition of fluctuations in multidimensions. This paper shows that wavelet transforms offer a convenient and consistent method for the decomposition of inhomogeneous and anisotropic rainfall fields in two dimensions and that the components of this decomposition can be looked at as fluctuations of the rainfall field. It is also shown that under some mild assumptions, the component fields can be treated as homogeneous and thus are amenable to second-order analysis, which can provide useful insight into the nature of the process. The fact that wavelet transforms are a space-scale method also provides a convenient tool to study scaling characteristics of the process. Orthogonal wavelets are used, and these properties are investigated for a squall-line storm to study the presence of self-similarity.
Abstract
It has been observed that the finite-dimensional distribution functions of rainfall cannot obey simple scaling laws due to rainfall intermittency (mixed distribution with an atom at zero) and the probability of rainfall being an increasing function of area. Although rainfall fluctuations do not suffer these limitations, it is interesting to note that very few attempts have been made to study them in terms of their self-similarity characteristics. This is due to the lack of unambiguous definition of fluctuations in multidimensions. This paper shows that wavelet transforms offer a convenient and consistent method for the decomposition of inhomogeneous and anisotropic rainfall fields in two dimensions and that the components of this decomposition can be looked at as fluctuations of the rainfall field. It is also shown that under some mild assumptions, the component fields can be treated as homogeneous and thus are amenable to second-order analysis, which can provide useful insight into the nature of the process. The fact that wavelet transforms are a space-scale method also provides a convenient tool to study scaling characteristics of the process. Orthogonal wavelets are used, and these properties are investigated for a squall-line storm to study the presence of self-similarity.
Beyond the Pixel: Using Patterns and Multiscale Spatial Information to Improve the Retrieval of Precipitation from Spaceborne Passive Microwave ImagersAbstract
The quantitative estimation of precipitation from orbiting passive microwave imagers has been performed for more than 30 years. The development of retrieval methods consists of establishing physical or statistical relationships between the brightness temperatures (TBs) measured at frequencies between 5 and 200 GHz and precipitation. Until now, these relationships have essentially been established at the “pixel” level, associating the average precipitation rate inside a predefined area (the pixel) to the collocated multispectral radiometric measurement. This approach considers each pixel as an independent realization of a process and ignores the fact that precipitation is a dynamic variable with rich multiscale spatial and temporal organization. Here we propose to look beyond the pixel values of the TBs and show that useful information for precipitation retrieval can be derived from the variations of the observed TBs in a spatial neighborhood around the pixel of interest. We also show that considering neighboring information allows us to better handle the complex observation geometry of conical-scanning microwave imagers, involving frequency-dependent beamwidths, overlapping fields of view, and large Earth incidence angles. Using spatial convolution filters, we compute “nonlocal” radiometric parameters sensitive to spatial patterns and scale-dependent structures of the TB fields, which are the “geometric signatures” of specific precipitation structures such as convective cells. We demonstrate that using nonlocal radiometric parameters to enrich the spectral information associated to each pixel allows for reduced retrieval uncertainty (reduction of 6%–11% of the mean absolute retrieval error) in a simple k-nearest neighbors retrieval scheme.
Abstract
The quantitative estimation of precipitation from orbiting passive microwave imagers has been performed for more than 30 years. The development of retrieval methods consists of establishing physical or statistical relationships between the brightness temperatures (TBs) measured at frequencies between 5 and 200 GHz and precipitation. Until now, these relationships have essentially been established at the “pixel” level, associating the average precipitation rate inside a predefined area (the pixel) to the collocated multispectral radiometric measurement. This approach considers each pixel as an independent realization of a process and ignores the fact that precipitation is a dynamic variable with rich multiscale spatial and temporal organization. Here we propose to look beyond the pixel values of the TBs and show that useful information for precipitation retrieval can be derived from the variations of the observed TBs in a spatial neighborhood around the pixel of interest. We also show that considering neighboring information allows us to better handle the complex observation geometry of conical-scanning microwave imagers, involving frequency-dependent beamwidths, overlapping fields of view, and large Earth incidence angles. Using spatial convolution filters, we compute “nonlocal” radiometric parameters sensitive to spatial patterns and scale-dependent structures of the TB fields, which are the “geometric signatures” of specific precipitation structures such as convective cells. We demonstrate that using nonlocal radiometric parameters to enrich the spectral information associated to each pixel allows for reduced retrieval uncertainty (reduction of 6%–11% of the mean absolute retrieval error) in a simple k-nearest neighbors retrieval scheme.
Abstract
A coupled modeling framework is used in this study to investigate the effect of subgrid-scale rainfall variability on the spatial structure of the evolving storm and on other surface variables and water and energy fluxes. The Fifth-Generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model coupled with the Biosphere–Atmosphere Transfer Scheme is combined with a dynamical/statistical scheme for statistically downscaling rainfall. Model simulations with and without including subgrid-scale rainfall variability are compared at the grid scale to quantify the propagation of small-scale rainfall heterogeneities through the nonlinear land–atmosphere system. It was found that including subgrid-scale rainfall variability (here on the order of 3 km) affects the spatial organization of the storm system itself, surface temperature, soil moisture, and sensible and latent heat fluxes. These effects were found to occur at spatial scales much larger than the scale at which rainfall variability was prescribed, illustrating the pronounced nonlinear spatial dynamics of the land–atmosphere system and its important role on hydrometeorological predictions.
Abstract
A coupled modeling framework is used in this study to investigate the effect of subgrid-scale rainfall variability on the spatial structure of the evolving storm and on other surface variables and water and energy fluxes. The Fifth-Generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model coupled with the Biosphere–Atmosphere Transfer Scheme is combined with a dynamical/statistical scheme for statistically downscaling rainfall. Model simulations with and without including subgrid-scale rainfall variability are compared at the grid scale to quantify the propagation of small-scale rainfall heterogeneities through the nonlinear land–atmosphere system. It was found that including subgrid-scale rainfall variability (here on the order of 3 km) affects the spatial organization of the storm system itself, surface temperature, soil moisture, and sensible and latent heat fluxes. These effects were found to occur at spatial scales much larger than the scale at which rainfall variability was prescribed, illustrating the pronounced nonlinear spatial dynamics of the land–atmosphere system and its important role on hydrometeorological predictions.
Abstract
Using satellite measurements in microwave bands to retrieve precipitation over land requires proper discrimination of the weak rainfall signals from strong and highly variable background Earth surface emissions. Traditionally, land retrieval methods rely on a weak signal of rainfall scattering on high-frequency channels and make use of empirical thresholding and regression-based techniques. Because of the increased surface signal interference, retrievals over radiometrically complex land surfaces—snow-covered lands, deserts, and coastal areas—are particularly challenging for this class of retrieval techniques. This paper evaluates the results by the recently proposed Shrunken Locally Linear Embedding Algorithm for Retrieval of Precipitation (ShARP) using data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The study focuses on a radiometrically complex region, partly covering the Tibetan highlands, Himalayas, and Ganges–Brahmaputra–Meghna River basins, which is unique in terms of its diverse land surface radiation regime and precipitation type, within the TRMM domain. Promising results are presented using ShARP over snow-covered land surfaces and in the vicinity of coastlines, in comparison with the land rainfall retrievals of the standard TRMM 2A12, version 7, product. The results show that ShARP can significantly reduce the rainfall overestimation due to the background snow contamination and markedly improve detection and retrieval of rainfall in the vicinity of coastlines. During the calendar year 2013, compared to TRMM 2A25, it is demonstrated that over the study domain the root-mean-square difference can be reduced up to 38% annually, while the improvement can reach up to 70% during the cold months of the year.
Abstract
Using satellite measurements in microwave bands to retrieve precipitation over land requires proper discrimination of the weak rainfall signals from strong and highly variable background Earth surface emissions. Traditionally, land retrieval methods rely on a weak signal of rainfall scattering on high-frequency channels and make use of empirical thresholding and regression-based techniques. Because of the increased surface signal interference, retrievals over radiometrically complex land surfaces—snow-covered lands, deserts, and coastal areas—are particularly challenging for this class of retrieval techniques. This paper evaluates the results by the recently proposed Shrunken Locally Linear Embedding Algorithm for Retrieval of Precipitation (ShARP) using data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The study focuses on a radiometrically complex region, partly covering the Tibetan highlands, Himalayas, and Ganges–Brahmaputra–Meghna River basins, which is unique in terms of its diverse land surface radiation regime and precipitation type, within the TRMM domain. Promising results are presented using ShARP over snow-covered land surfaces and in the vicinity of coastlines, in comparison with the land rainfall retrievals of the standard TRMM 2A12, version 7, product. The results show that ShARP can significantly reduce the rainfall overestimation due to the background snow contamination and markedly improve detection and retrieval of rainfall in the vicinity of coastlines. During the calendar year 2013, compared to TRMM 2A25, it is demonstrated that over the study domain the root-mean-square difference can be reduced up to 38% annually, while the improvement can reach up to 70% during the cold months of the year.
Abstract
The constellation of spaceborne passive microwave (MW) sensors, coordinated under the framework of the Precipitation Measurement Missions international agreement, continuously produces observations of clouds and precipitation all over the globe. The Goddard profiling algorithm (GPROF) is designed to infer the instantaneous surface precipitation rate from the measured MW radiances. The last version of the algorithm (GPROF-2014)—the product of more than 20 years of algorithmic development, validation, and improvement—is currently used to estimate precipitation rates from the microwave imager GMI on board the GPM core satellite. The previous version of the algorithm (GPROF-2010) was used with the microwave imager TMI on board TRMM. In this paper, TMI-GPROF-2010 estimates and GMI-GPROF-2014 estimates are compared with coincident active measurements from the Precipitation Radar on board TRMM and the Dual-Frequency Precipitation Radar on board GPM, considered as reference products. The objective is to assess the improvement of the GPM-era microwave estimates relative to the TRMM-era estimates and diagnose regions where continuous improvement is needed. The assessment is oriented toward estimating the “effective resolution” of the MW estimates, that is, the finest scale at which the retrieval is able to accurately reproduce the spatial variability of precipitation. A wavelet-based multiscale decomposition of the radar and passive microwave precipitation fields is used to formally define and assess the effective resolution. It is found that the GPM-era MW retrieval can resolve finer-scale spatial variability over oceans than the TRMM-era retrieval. Over land, significant challenges exist, and this analysis provides useful diagnostics and a benchmark against which future retrieval algorithm improvement can be assessed.
Abstract
The constellation of spaceborne passive microwave (MW) sensors, coordinated under the framework of the Precipitation Measurement Missions international agreement, continuously produces observations of clouds and precipitation all over the globe. The Goddard profiling algorithm (GPROF) is designed to infer the instantaneous surface precipitation rate from the measured MW radiances. The last version of the algorithm (GPROF-2014)—the product of more than 20 years of algorithmic development, validation, and improvement—is currently used to estimate precipitation rates from the microwave imager GMI on board the GPM core satellite. The previous version of the algorithm (GPROF-2010) was used with the microwave imager TMI on board TRMM. In this paper, TMI-GPROF-2010 estimates and GMI-GPROF-2014 estimates are compared with coincident active measurements from the Precipitation Radar on board TRMM and the Dual-Frequency Precipitation Radar on board GPM, considered as reference products. The objective is to assess the improvement of the GPM-era microwave estimates relative to the TRMM-era estimates and diagnose regions where continuous improvement is needed. The assessment is oriented toward estimating the “effective resolution” of the MW estimates, that is, the finest scale at which the retrieval is able to accurately reproduce the spatial variability of precipitation. A wavelet-based multiscale decomposition of the radar and passive microwave precipitation fields is used to formally define and assess the effective resolution. It is found that the GPM-era MW retrieval can resolve finer-scale spatial variability over oceans than the TRMM-era retrieval. Over land, significant challenges exist, and this analysis provides useful diagnostics and a benchmark against which future retrieval algorithm improvement can be assessed.
Resolving Surface Rain from GMI High-Frequency Channels: Limits Imposed by the Three-Dimensional Structure of PrecipitationAbstract
The scattering of microwaves at frequencies between 50 and 200 GHz by ice particles in the atmosphere is an essential element in the retrieval of instantaneous surface precipitation from spaceborne passive radiometers. This paper explores how the variable distribution of solid and liquid hydrometeors in the atmospheric column over land surfaces affects the brightness temperature (TB) measured by GMI at 89 GHz through the analysis of Dual-Frequency Precipitation Radar (DPR) reflectivity profiles along the 89-GHz beam. The objective is to refine the statistical relations between observed TBs and surface precipitation over land and to define their limits. As GMI is scanning with a 53° Earth incident angle, the observed atmospheric volume is actually not a vertical column, which may lead to very heterogeneous and seemingly inconsistent distributions of the hydrometeors inside the beam. It is found that the 89-GHz TB is mostly sensitive to the presence of ice hydrometeors several kilometers above the 0°C isotherm, up to 10 km above the 0°C isotherm for the deepest convective systems, but is a modest predictor of the surface precipitation rate. To perform a precise mapping of atmospheric ice, the altitude of the individual ice clusters must be known. Indeed, if variations in the altitude of ice are not accounted for, then the high incident angle of GMI causes a horizontal shift (parallax shift) between the estimated position of the ice clusters and their actual position. We show here that the altitude of ice clusters can be derived from the 89-GHz TB itself, allowing for correction of the parallax shift.
Abstract
The scattering of microwaves at frequencies between 50 and 200 GHz by ice particles in the atmosphere is an essential element in the retrieval of instantaneous surface precipitation from spaceborne passive radiometers. This paper explores how the variable distribution of solid and liquid hydrometeors in the atmospheric column over land surfaces affects the brightness temperature (TB) measured by GMI at 89 GHz through the analysis of Dual-Frequency Precipitation Radar (DPR) reflectivity profiles along the 89-GHz beam. The objective is to refine the statistical relations between observed TBs and surface precipitation over land and to define their limits. As GMI is scanning with a 53° Earth incident angle, the observed atmospheric volume is actually not a vertical column, which may lead to very heterogeneous and seemingly inconsistent distributions of the hydrometeors inside the beam. It is found that the 89-GHz TB is mostly sensitive to the presence of ice hydrometeors several kilometers above the 0°C isotherm, up to 10 km above the 0°C isotherm for the deepest convective systems, but is a modest predictor of the surface precipitation rate. To perform a precise mapping of atmospheric ice, the altitude of the individual ice clusters must be known. Indeed, if variations in the altitude of ice are not accounted for, then the high incident angle of GMI causes a horizontal shift (parallax shift) between the estimated position of the ice clusters and their actual position. We show here that the altitude of ice clusters can be derived from the 89-GHz TB itself, allowing for correction of the parallax shift.
Abstract
Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3–60-day periods) in both GPH and SST and El Niño–Southern Oscillation (ENSO) at low frequencies (2–7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics.
Abstract
Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3–60-day periods) in both GPH and SST and El Niño–Southern Oscillation (ENSO) at low frequencies (2–7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics.
Abstract
Small-scale (less than ∼15 km) precipitation variability significantly affects the hydrologic response of a basin and the accurate estimation of water and energy fluxes through coupled land–atmosphere modeling schemes. It also affects the radiative transfer through precipitating clouds and thus rainfall estimation from microwave sensors. Because both land–atmosphere and cloud–radiation interactions are nonlinear and occur over a broad range of scales (from a few centimeters to several kilometers), it is important that, over these scales, cloud-resolving numerical models realistically reproduce the observed precipitation variability. This issue is examined herein by using a suite of multiscale statistical methods to compare the scale dependence of precipitation variability of a numerically simulated convective storm with that observed by radar. In particular, Fourier spectrum, structure function, and moment-scale analyses are used to show that, although the variability of modeled precipitation agrees with that observed for scales larger than approximately 5 times the model resolution, the model shows a falloff in variability at smaller scales. Thus, depending upon the smallest scale at which variability is considered to be important for a specific application, one has to resort either to very high resolution model runs (resolutions 5 times higher than the scale of interest) or to stochastic methods that can introduce the missing small-scale variability. The latter involve upscaling the model output to a scale approximately 5 times the model resolution and then stochastically downscaling it to smaller scales. The results of multiscale analyses, such as those presented herein, are key to the implementation of such stochastic downscaling methodologies.
Abstract
Small-scale (less than ∼15 km) precipitation variability significantly affects the hydrologic response of a basin and the accurate estimation of water and energy fluxes through coupled land–atmosphere modeling schemes. It also affects the radiative transfer through precipitating clouds and thus rainfall estimation from microwave sensors. Because both land–atmosphere and cloud–radiation interactions are nonlinear and occur over a broad range of scales (from a few centimeters to several kilometers), it is important that, over these scales, cloud-resolving numerical models realistically reproduce the observed precipitation variability. This issue is examined herein by using a suite of multiscale statistical methods to compare the scale dependence of precipitation variability of a numerically simulated convective storm with that observed by radar. In particular, Fourier spectrum, structure function, and moment-scale analyses are used to show that, although the variability of modeled precipitation agrees with that observed for scales larger than approximately 5 times the model resolution, the model shows a falloff in variability at smaller scales. Thus, depending upon the smallest scale at which variability is considered to be important for a specific application, one has to resort either to very high resolution model runs (resolutions 5 times higher than the scale of interest) or to stochastic methods that can introduce the missing small-scale variability. The latter involve upscaling the model output to a scale approximately 5 times the model resolution and then stochastically downscaling it to smaller scales. The results of multiscale analyses, such as those presented herein, are key to the implementation of such stochastic downscaling methodologies.
Abstract
Monitoring changes of precipitation phase from space is important for understanding the mass balance of Earth’s cryosphere in a changing climate. This paper examines a Bayesian nearest neighbor approach for prognostic detection of precipitation and its phase using passive microwave observations from the Global Precipitation Measurement (GPM) satellite. The method uses the weighted Euclidean distance metric to search through an a priori database populated with coincident GPM radiometer and radar observations as well as ancillary snow-cover data. The algorithm performance is evaluated using data from GPM official precipitation products, ground-based radars, and high-fidelity simulations from the Weather Research and Forecasting Model. Using the presented approach, we demonstrate that the hit probability of terrestrial precipitation detection can reach to 0.80, while the probability of false alarm remains below 0.11. The algorithm demonstrates higher skill in detecting snowfall than rainfall, on average by 10%. In particular, the probability of precipitation detection and its solid phase increases by 11% and 8%, over dry snow cover, when compared to other surface types. The main reason is found to be related to the ability of the algorithm in capturing the signal of increased liquid water content in snowy clouds over radiometrically cold snow-covered surfaces.
Abstract
Monitoring changes of precipitation phase from space is important for understanding the mass balance of Earth’s cryosphere in a changing climate. This paper examines a Bayesian nearest neighbor approach for prognostic detection of precipitation and its phase using passive microwave observations from the Global Precipitation Measurement (GPM) satellite. The method uses the weighted Euclidean distance metric to search through an a priori database populated with coincident GPM radiometer and radar observations as well as ancillary snow-cover data. The algorithm performance is evaluated using data from GPM official precipitation products, ground-based radars, and high-fidelity simulations from the Weather Research and Forecasting Model. Using the presented approach, we demonstrate that the hit probability of terrestrial precipitation detection can reach to 0.80, while the probability of false alarm remains below 0.11. The algorithm demonstrates higher skill in detecting snowfall than rainfall, on average by 10%. In particular, the probability of precipitation detection and its solid phase increases by 11% and 8%, over dry snow cover, when compared to other surface types. The main reason is found to be related to the ability of the algorithm in capturing the signal of increased liquid water content in snowy clouds over radiometrically cold snow-covered surfaces.
