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Hye-Kyung Cho
,
Kenneth P. Bowman
, and
Gerald R. North

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.

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J. Craig Collier
,
Kenneth P. Bowman
, and
Gerald R. North

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.

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Dong-Bin Shin
,
Gerald R. North
, and
Kenneth P. Bowman

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.

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Kyung-Sup Shin
,
Phil E. Riba
, and
Gerald R. North

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.

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Shoichiro Nakamoto
,
Juan B. Valdés
, and
Gerald R. North

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.

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Ilya Polyak
,
Gerald R. North
, and
Juan B. Valdes

Abstract

This paper presents the methodologies and results of the multivariate modeling and two-dimensional spectral and correlation analysis of PRE-STORM rainfall gauge data. Estimated parameters of the models for the specific spatial averages clearly indicate the eastward and southeastward wave propagation of rainfall fluctuations. A relationship between the coefficients of the diffusion equation and the parameters of the stochastic model of rainfall fluctuations is derived that leads directly to the exclusive use of rainfall data to estimate advection speed (about 12 m s−1) as well as other coefficients of the diffusion equation of the corresponding fields.

The statistical methodology developed here can be used for confirmation of physical models by comparison of the corresponding second-moment statistics of the observed and simulated data, for generating multiple samples of any size, for solving the inverse problem of the hydrodynamic equations, and for application in some other areas of meteorological and climatological data analysis and modeling.

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Vishwas V. Soman
,
Juan B. Valdés
, and
Gerald R. North

Abstract

This paper presents an analysis of rainfall data based on the radar echoes collected in the vicinity of Darwin, Australia, during the special observation periods in 1988. The Darwin rainfall data are available in the form of hourly averaged grids of size 141 × 141 with an areal resolution of 2 km × 2 km. The data are available for approximately 19 days in the first subset and for 22 days in the second. Since the rainfall data were taken over both the land and the ocean, separate analyses were performed for land and ocean surfaces; thus, three univariate time series (for land, ocean, and combination) are presented for each set. Time series analysis was performed in both time and frequency domains, and both the correlogram and periodogram showed the presence of a strong diurnal cycle in all the time series. Considerable variations can be seen in the diurnal cycles of these time series. To analyze the effect of the diurnal cycle on the sampling errors, flush visits of idealized satellites were simulated. The root-mean-square (rms) errors were especially large for satellites with sampling intervals of 6 and 12 h (about 20% of the mean for the box size of 280 km × 280 km, for 20 days). The rms errors were very large (∼65%) for a sampling interval of 24 h, which is a possibility for the Defense Military Satellite Program satellites. The sampling errors were only 5%–10% for non-sun-synchronous orbiters. This result should be considered for satellite mission planning purposes.

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Gerald R. North
,
Samuel S. P. Shen
, and
Robert Upson

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.

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Hye-Kyung Cho
,
Kenneth P. Bowman
, and
Gerald R. North

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.

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Gerald R. North
,
Fanthune J. Moeng
,
Thomas L. Bell
, and
Robert F. Cahalan

Abstract

Zonally averaged meteorological fields can have large variances in polar regions due to purely geometrical effects, because fewer statistically independent areas contribute to zonal means near the poles than near the equator. A model of a stochastic field with homogeneous statistics on the sphere is presented as an idealized example of the phenomenon. We suggest a quantitative method for isolating the geometrical effect and use it in examining the variance of the zonally averaged 500 mb geopotential height field.

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