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- Author or Editor: Gerald R. North x
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Abstract
This paper presents a new simple retrieval algorithm for estimating area-time averaged rain rates over tropical oceans by using single channel microwave measurements from satellites. The algorithm was tested by using the Nimbus-5 Electrically Scanning Microwave Radiometer (ESMR-5) and a simple microwave radiative transfer model to retrieve seasonal 5° × 5° area averaged rainrate over the tropical Atlantic and Pacific from December 1973 to November 1974.
The brightness temperatures were collected and analyzed into histograms for each season and in each grid box from December 1973 to November 1974. The histograms suggest a normal distribution of background noise plus a skewed rain distribution at the higher brightness temperatures. By using a statistical estimation procedure based upon normally distributed background noise, the rain distribution was separated from the raw histogram. The radiative transfer model was applied to the rain-only distribution to retrieve area-time averaged rainrates throughout the tropics. An adjustment for the beam filling error was incorporated in the procedure.
Despite limitations of single channel information, the retrieved seasonal rain rates agree well in the open ocean with expectations based upon previous estimates of tropical rainfall over the oceans. We suggest that the beam filling correction factor is the most important, but least understood parameter in the retrieval process.
Abstract
This paper presents a new simple retrieval algorithm for estimating area-time averaged rain rates over tropical oceans by using single channel microwave measurements from satellites. The algorithm was tested by using the Nimbus-5 Electrically Scanning Microwave Radiometer (ESMR-5) and a simple microwave radiative transfer model to retrieve seasonal 5° × 5° area averaged rainrate over the tropical Atlantic and Pacific from December 1973 to November 1974.
The brightness temperatures were collected and analyzed into histograms for each season and in each grid box from December 1973 to November 1974. The histograms suggest a normal distribution of background noise plus a skewed rain distribution at the higher brightness temperatures. By using a statistical estimation procedure based upon normally distributed background noise, the rain distribution was separated from the raw histogram. The radiative transfer model was applied to the rain-only distribution to retrieve area-time averaged rainrates throughout the tropics. An adjustment for the beam filling error was incorporated in the procedure.
Despite limitations of single channel information, the retrieved seasonal rain rates agree well in the open ocean with expectations based upon previous estimates of tropical rainfall over the oceans. We suggest that the beam filling correction factor is the most important, but least understood parameter in the retrieval process.
Abstract
The Moderate Resolution Imaging Spectroradiometer (MODIS) observations provide an unprecedented opportunity for studying cloud macrophysical (cloud-top pressure, temperature, height, and phase), microphysical (effective particle size), and optical (optical thickness) properties. Given the length of time these MODIS products have been available, it is found that the cloud products can provide a wealth of information about equatorial wave systems. In this study, more than six years of the MODIS cloud-top properties inferred from the Aqua MODIS observations are used to investigate equatorial waves. It is shown that the high-resolution daily gridded cloud-top temperature product can be used to quantitatively study convective clouds. Various modes of convectively coupled equatorial waves including Kelvin, n = 1 equatorial Rossby, mixed Rossby–gravity, n = 0 eastward inertial-gravity waves, and the Madden–Julian oscillation are identified on the basis of space–time spectral analysis. The application of spectral analysis to cirrus cloud optical thickness, retrieved from MODIS cirrus reflectance, confirms the convective signals at high altitudes. A cluster of Kelvin pulses is found to propagate eastward around the globe at a phase speed approximately 15 m s−1. The Madden–Julian oscillation propagates at a slower speed and is most prominent over the Indian–Pacific Oceans region. The consistency between the present results with those of previous studies demonstrates that the MODIS cloud-top property products are valuable for studying phenomena associated with atmospheric dynamics.
Abstract
The Moderate Resolution Imaging Spectroradiometer (MODIS) observations provide an unprecedented opportunity for studying cloud macrophysical (cloud-top pressure, temperature, height, and phase), microphysical (effective particle size), and optical (optical thickness) properties. Given the length of time these MODIS products have been available, it is found that the cloud products can provide a wealth of information about equatorial wave systems. In this study, more than six years of the MODIS cloud-top properties inferred from the Aqua MODIS observations are used to investigate equatorial waves. It is shown that the high-resolution daily gridded cloud-top temperature product can be used to quantitatively study convective clouds. Various modes of convectively coupled equatorial waves including Kelvin, n = 1 equatorial Rossby, mixed Rossby–gravity, n = 0 eastward inertial-gravity waves, and the Madden–Julian oscillation are identified on the basis of space–time spectral analysis. The application of spectral analysis to cirrus cloud optical thickness, retrieved from MODIS cirrus reflectance, confirms the convective signals at high altitudes. A cluster of Kelvin pulses is found to propagate eastward around the globe at a phase speed approximately 15 m s−1. The Madden–Julian oscillation propagates at a slower speed and is most prominent over the Indian–Pacific Oceans region. The consistency between the present results with those of previous studies demonstrates that the MODIS cloud-top property products are valuable for studying phenomena associated with atmospheric dynamics.
Abstract
The oceanic rainfall frequency-wavenumber spectrum and its associated space-time correlation have been evaluated from subsets of GATE Phase 1 data. The records, of a duration of 4 days, were sampled at 15 minute intervals in 4 × 4 km grid boxes ova a 400 km diameter hexagon.
In the low frequencies-low wavenumber region the results coincide with those obtained by using the stochastic model proposed by North and Nakamoto. From the derived spectrum the inherent time and space scales of the stochastic model were determined to be approximately 13 hours and 36 km. The space-time correlation function evaluated from the function-wavenumber spectrum and that obtained directly from GATE Phase I records agreed.
The formalism proposed by North and Nakamoto was taken together with the derived spectrum to compute the mean square sampling error due to intermittent visits of a spaceborne sensor. The sampling error was estimated to be on the order of 10%, for monthly mean rainfall averaged over 500 × 500 km boxes which meets the scientific requirements of the TRMM mission. This result is consistent with those previously reported in the literature.
Abstract
The oceanic rainfall frequency-wavenumber spectrum and its associated space-time correlation have been evaluated from subsets of GATE Phase 1 data. The records, of a duration of 4 days, were sampled at 15 minute intervals in 4 × 4 km grid boxes ova a 400 km diameter hexagon.
In the low frequencies-low wavenumber region the results coincide with those obtained by using the stochastic model proposed by North and Nakamoto. From the derived spectrum the inherent time and space scales of the stochastic model were determined to be approximately 13 hours and 36 km. The space-time correlation function evaluated from the function-wavenumber spectrum and that obtained directly from GATE Phase I records agreed.
The formalism proposed by North and Nakamoto was taken together with the derived spectrum to compute the mean square sampling error due to intermittent visits of a spaceborne sensor. The sampling error was estimated to be on the order of 10%, for monthly mean rainfall averaged over 500 × 500 km boxes which meets the scientific requirements of the TRMM mission. This result is consistent with those previously reported in the literature.
Abstract
This study investigates the spatial characteristics of nonzero rain rates to develop a probability density function (PDF) model of precipitation using rainfall data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The minimum χ 2 method is used to find a good estimator for the rain-rate distribution between the gamma and lognormal distributions, which are popularly used in the simulation of the rain-rate PDF. Results are sensitive to the choice of dynamic range, but both the gamma and lognormal distributions match well with the PDF of rainfall data. Comparison with sample means shows that the parametric mean from the lognormal distribution overestimates the sample mean, whereas the gamma distribution underestimates it. These differences are caused by the inflated tail in the lognormal distribution and the small shape parameter in the gamma distribution. If shape constraint is given, the difference between the sample mean and the parametric mean from the fitted gamma distribution decreases significantly, although the resulting χ 2 values slightly increase. Of interest is that a consistent regional preference between two test functions is found. The gamma fits outperform the lognormal fits in wet regions, whereas the lognormal fits are better than the gamma fits for dry regions. Results can be improved with a specific model assumption depending on mean rain rates, but the results presented in this study can be easily applied to develop the rainfall retrieval algorithm and to find the proper statistics in the rainfall data.
Abstract
This study investigates the spatial characteristics of nonzero rain rates to develop a probability density function (PDF) model of precipitation using rainfall data from the Tropical Rainfall Measuring Mission (TRMM) satellite. The minimum χ 2 method is used to find a good estimator for the rain-rate distribution between the gamma and lognormal distributions, which are popularly used in the simulation of the rain-rate PDF. Results are sensitive to the choice of dynamic range, but both the gamma and lognormal distributions match well with the PDF of rainfall data. Comparison with sample means shows that the parametric mean from the lognormal distribution overestimates the sample mean, whereas the gamma distribution underestimates it. These differences are caused by the inflated tail in the lognormal distribution and the small shape parameter in the gamma distribution. If shape constraint is given, the difference between the sample mean and the parametric mean from the fitted gamma distribution decreases significantly, although the resulting χ 2 values slightly increase. Of interest is that a consistent regional preference between two test functions is found. The gamma fits outperform the lognormal fits in wet regions, whereas the lognormal fits are better than the gamma fits for dry regions. Results can be improved with a specific model assumption depending on mean rain rates, but the results presented in this study can be easily applied to develop the rainfall retrieval algorithm and to find the proper statistics in the rainfall data.
Abstract
The fixed anvil temperature (FAT) hypothesis is examined based on the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS)-based cloud-top temperature (CTT) in conjunction with the tropical atmospheric profiles and sea surface temperature (SST) from the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Reanalysis. Consistent with the physical governing mechanism of the FAT hypothesis, the peak clear-sky diabatic subsidence and convergence profiles are located at roughly the same level (200 hPa) as the peak in the cloud profile, which is fundamentally determined by the rapid decrease of water vapor concentration above this level. The geographical maxima of cloud fraction agree well with those of water vapor, clear-sky cooling rates, and diabatic convergence at 200 hPa. The use of direct CTT measurements suggests the CTT in specific Pacific basins exhibit different characteristics as the frequency distribution of the tropical SST varies from boreal winter to summer. When averaging over the tropics as a whole, the CTT distributions are approximately unchanged primarily because of cancellation by the variations associated with individual regions. An analysis of the response of the tropical mean CTT anomaly time series to the SST indicates that a possible negative relationship is present, whereas the relationship tends to be positive over the tropical western Pacific and Indian Oceans. In addition, it is suggested to interpret the FAT hypothesis, and the more recent proportionately higher anvil temperature (PHAT) hypothesis, by using the temperature at the maximum cloud detrainment level instead of the CTT.
Abstract
The fixed anvil temperature (FAT) hypothesis is examined based on the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS)-based cloud-top temperature (CTT) in conjunction with the tropical atmospheric profiles and sea surface temperature (SST) from the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Reanalysis. Consistent with the physical governing mechanism of the FAT hypothesis, the peak clear-sky diabatic subsidence and convergence profiles are located at roughly the same level (200 hPa) as the peak in the cloud profile, which is fundamentally determined by the rapid decrease of water vapor concentration above this level. The geographical maxima of cloud fraction agree well with those of water vapor, clear-sky cooling rates, and diabatic convergence at 200 hPa. The use of direct CTT measurements suggests the CTT in specific Pacific basins exhibit different characteristics as the frequency distribution of the tropical SST varies from boreal winter to summer. When averaging over the tropics as a whole, the CTT distributions are approximately unchanged primarily because of cancellation by the variations associated with individual regions. An analysis of the response of the tropical mean CTT anomaly time series to the SST indicates that a possible negative relationship is present, whereas the relationship tends to be positive over the tropical western Pacific and Indian Oceans. In addition, it is suggested to interpret the FAT hypothesis, and the more recent proportionately higher anvil temperature (PHAT) hypothesis, by using the temperature at the maximum cloud detrainment level instead of the CTT.
Abstract
This study evaluates the simulation of tropical precipitation by the Community Climate Model, version 3, (CCM3) developed at the National Center for Atmospheric Research. Monthly mean precipitation rates from an ensemble of CCM3 simulations are compared to those computed from observations of the Tropical Rainfall Measuring Mission (TRMM) satellite over a 44-month period. On regional and subregional scales, the comparison fares well over much of the Eastern Hemisphere south of 10°S and over South America. However, model– satellite differences are large in portions of Central America and the Caribbean, the southern tropical Atlantic, the northern Indian Ocean, and the western equatorial and southern tropical Pacific. Since precipitation in the Tropics is the primary source of latent energy to the general circulation, such large model–satellite differences imply large differences in the amount of latent energy released. Differences tend to be seasonally dependent north of 10°N, where model wet biases occur in realistic wet seasons or model-generated artificial wet seasons. South of 10°N, the model wet biases exist throughout the year or have no recognizable pattern.
Abstract
This study evaluates the simulation of tropical precipitation by the Community Climate Model, version 3, (CCM3) developed at the National Center for Atmospheric Research. Monthly mean precipitation rates from an ensemble of CCM3 simulations are compared to those computed from observations of the Tropical Rainfall Measuring Mission (TRMM) satellite over a 44-month period. On regional and subregional scales, the comparison fares well over much of the Eastern Hemisphere south of 10°S and over South America. However, model– satellite differences are large in portions of Central America and the Caribbean, the southern tropical Atlantic, the northern Indian Ocean, and the western equatorial and southern tropical Pacific. Since precipitation in the Tropics is the primary source of latent energy to the general circulation, such large model–satellite differences imply large differences in the amount of latent energy released. Differences tend to be seasonally dependent north of 10°N, where model wet biases occur in realistic wet seasons or model-generated artificial wet seasons. South of 10°N, the model wet biases exist throughout the year or have no recognizable pattern.
Abstract
Four years of outgoing longwave radiation (OLR) and rainfall data from the Tropical Rainfall Measuring Mission (TRMM) are investigated to find the dominant large-scale wave modes in the Tropics. By using space– time cross-section analysis and spectral analysis, the longitudinal and latitudinal behaviors of the overall waves and the dominant waves are observed. Despite the noisy nature of precipitation data and the limited sampling by the TRMM satellite, pronounced peaks are found for Kelvin waves, n = 1 equatorial Rossby waves (ER), and mixed Rossby–gravity waves (MRG). Madden–Julian oscillation (MJO) and tropical depression (TD)-type disturbances are also detected. The seasonal evolution of these waves is investigated.
An appendix includes a study of sampling and aliasing errors due to the peculiar space–time sampling pattern of TRMM. It is shown that the waves detected in this study are not artifacts of these sampling features.
The results presented here are compared with previous studies. Consistency with their results gives confidence in the TRMM data for wave studies. The results from this study can be utilized for modeling and testing theories. Also, it may be useful for the future users of the TRMM data to understand the nature of the TRMM satellite sampling.
Abstract
Four years of outgoing longwave radiation (OLR) and rainfall data from the Tropical Rainfall Measuring Mission (TRMM) are investigated to find the dominant large-scale wave modes in the Tropics. By using space– time cross-section analysis and spectral analysis, the longitudinal and latitudinal behaviors of the overall waves and the dominant waves are observed. Despite the noisy nature of precipitation data and the limited sampling by the TRMM satellite, pronounced peaks are found for Kelvin waves, n = 1 equatorial Rossby waves (ER), and mixed Rossby–gravity waves (MRG). Madden–Julian oscillation (MJO) and tropical depression (TD)-type disturbances are also detected. The seasonal evolution of these waves is investigated.
An appendix includes a study of sampling and aliasing errors due to the peculiar space–time sampling pattern of TRMM. It is shown that the waves detected in this study are not artifacts of these sampling features.
The results presented here are compared with previous studies. Consistency with their results gives confidence in the TRMM data for wave studies. The results from this study can be utilized for modeling and testing theories. Also, it may be useful for the future users of the TRMM data to understand the nature of the TRMM satellite sampling.
Abstract
A preliminary climatology of reflectivity profiles derived from the first spaceborne precipitation radar (PR), which is on board the Tropical Rainfall Measuring Mission (TRMM) satellite, is described using the data from January 1998 to February 1999. This study focuses on the behavior of the melting-layer (bright band) altitude in stratiform precipitation. This analysis will be useful for improving passive microwave radiometric estimations of rain rates because it provides information about otherwise unknown parameters in the estimation models (the depth of the rain column). The monthly means of the melting-layer altitude estimated over 10° × 10° latitude–longitude grid boxes show that high melting layers (>4.5 km) tend to appear during extreme events such as El Niño and the Asian summer monsoon, and lower melting layers are usually observed in the winter hemisphere, which suggests a close relationship between surface temperature and the melting-layer altitude. Detailed climatologies of the profiles are provided for eight selected regions. For each region the seasonal variation of the meting-layer altitude and the mean and variation of the reflectivity profiles are discussed. The diurnal cycle of the melting-layer altitude and second-moment products, such as the spatial correlation along the satellite track, illustrate the irregular characteristics of the melting-layer altitude.
Abstract
A preliminary climatology of reflectivity profiles derived from the first spaceborne precipitation radar (PR), which is on board the Tropical Rainfall Measuring Mission (TRMM) satellite, is described using the data from January 1998 to February 1999. This study focuses on the behavior of the melting-layer (bright band) altitude in stratiform precipitation. This analysis will be useful for improving passive microwave radiometric estimations of rain rates because it provides information about otherwise unknown parameters in the estimation models (the depth of the rain column). The monthly means of the melting-layer altitude estimated over 10° × 10° latitude–longitude grid boxes show that high melting layers (>4.5 km) tend to appear during extreme events such as El Niño and the Asian summer monsoon, and lower melting layers are usually observed in the winter hemisphere, which suggests a close relationship between surface temperature and the melting-layer altitude. Detailed climatologies of the profiles are provided for eight selected regions. For each region the seasonal variation of the meting-layer altitude and the mean and variation of the reflectivity profiles are discussed. The diurnal cycle of the melting-layer altitude and second-moment products, such as the spatial correlation along the satellite track, illustrate the irregular characteristics of the melting-layer altitude.
Abstract
This paper presents derivations of some analytical forms for spatial correlations of evolving random fields governed by a white-noise-driven damped diffusion equation that is the analog of autoregressive order 1 in time and autoregressive order 2 in space. The study considers the two-dimensional plane and the surface of a sphere, both of which have been studied before, but here time is introduced to the problem. Such models have a finite characteristic length (roughly the separation at which the autocorrelation falls to 1/e) and a relaxation time scale. In particular, the characteristic length of a particular temporal Fourier component of the field increases to a finite value as the frequency of the particular component decreases. Some near-analytical formulas are provided for the results. A potential application is to the correlation structure of surface temperature fields and to the estimation of large area averages, depending on how the original datastream is filtered into a distribution of Fourier frequencies (e.g., moving average, low pass, or narrow band). The form of the governing equation is just that of the simple energy balance climate models, which have a long history in climate studies. The physical motivation provided by the derivation from a climate model provides some heuristic appeal to the approach and suggests extensions of the work to nonuniform cases.
Abstract
This paper presents derivations of some analytical forms for spatial correlations of evolving random fields governed by a white-noise-driven damped diffusion equation that is the analog of autoregressive order 1 in time and autoregressive order 2 in space. The study considers the two-dimensional plane and the surface of a sphere, both of which have been studied before, but here time is introduced to the problem. Such models have a finite characteristic length (roughly the separation at which the autocorrelation falls to 1/e) and a relaxation time scale. In particular, the characteristic length of a particular temporal Fourier component of the field increases to a finite value as the frequency of the particular component decreases. Some near-analytical formulas are provided for the results. A potential application is to the correlation structure of surface temperature fields and to the estimation of large area averages, depending on how the original datastream is filtered into a distribution of Fourier frequencies (e.g., moving average, low pass, or narrow band). The form of the governing equation is just that of the simple energy balance climate models, which have a long history in climate studies. The physical motivation provided by the derivation from a climate model provides some heuristic appeal to the approach and suggests extensions of the work to nonuniform cases.
Abstract
This paper examines the sampling characteristics of combining data collected by several low-orbiting satellites attempting to estimate the space–time average of rain rates. The several satellites can have different orbital and swath-width parameters. The satellite overpasses are allowed to make partial coverage snapshots of the grid box with each overpass. Such partial visits are considered in an approximate way, letting each intersection area fraction of the grid box by a particular satellite swath be a random variable with mean and variance parameters computed from exact orbit calculations. The derivation procedure is based upon the spectral minimum mean-square error formalism introduced by North and Nakamoto. By using a simple parametric form for the space–time spectral density, simple formulas are derived for a large number of examples, including the combination of the Tropical Rainfall Measuring Mission with an operational sun-synchronous orbiter. The approximations and results are discussed and directions for future research are summarized.
Abstract
This paper examines the sampling characteristics of combining data collected by several low-orbiting satellites attempting to estimate the space–time average of rain rates. The several satellites can have different orbital and swath-width parameters. The satellite overpasses are allowed to make partial coverage snapshots of the grid box with each overpass. Such partial visits are considered in an approximate way, letting each intersection area fraction of the grid box by a particular satellite swath be a random variable with mean and variance parameters computed from exact orbit calculations. The derivation procedure is based upon the spectral minimum mean-square error formalism introduced by North and Nakamoto. By using a simple parametric form for the space–time spectral density, simple formulas are derived for a large number of examples, including the combination of the Tropical Rainfall Measuring Mission with an operational sun-synchronous orbiter. The approximations and results are discussed and directions for future research are summarized.
