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  • Author or Editor: Gerald R. North x
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Kyung-Sup Shin
and
Gerald R. North

Abstract

A parameter study of satellite orbits was performed to estimate sampling errors of area-time averaged rain rate due to temporal sampling by satellites. The sampling characteristics were investigated by accounting for varying visiting intervals and varying fractions of averaging area on each visit as a function of the latitude of the grid box for a range of satellite orbital parameters. The sampling errors were estimated by a simple model based on the first-order Markov process of the time series of area averaged rain rates.

For a satellite of nominal TRMM orbit (30° inclination and 300 km altitude) carrying an ideal scanning microwave radiometer for direct precipitation measurements, sampling error would be about 8 to 12% of estimated monthly mean rain rates over a grid box of 5° × 5°. The effect of uneven sampling intervals with latitude tend to be offset by increasing sampling areas with latitude, therefore, the latitude dependence of sampling error was not important. Nomograms for sampling errors are presented for a range of orbital parameters centered at nominal TRMM orbit. An observation system based upon the low inclination satellite combined with a sunsynchronous satellite simultaneously would be especially promising for precipitation measurements from space. Sampling errors well below 10% can be achieved for this idealized system case for the monthly rain rate estimates for 5° × 5° boxes.

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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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Yue Li
,
Gerald R. North
,
Ping Yang
, and
Bryan A. Baum

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.

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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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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
,
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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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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David A. Short
,
Gerald R. North
,
T. Dale Bess
, and
G. Louis Smith

Abstract

Empirical studies of total outgoing infrared radiation IR and surface temperature T have shown them to be well correlated for large time and space scales. An analysis of one year of Nimbus-6 data shows that the simple form IR = A + BT (with A = 204 W m−2, B = 1.93 W m−2K−1) explains 90% of the area-weighted variance in the annual mean and annual cycle of the zonally averaged IR field. The geographical distribution of the annual cycle in IR shows a large amplitude over the continental interiors, as is found in the observed temperature field, and the ratio of the large amplitudes (Blocal ) is approximately 2 W m−2K−1. This helps to explain our recent success in modeling the geographical distribution of the annual cycle in T with a two-dimensional, time-dependent energy balance climate model (EBCM) which makes use of the A + BT rule. The parameterization works well in regions where the thermal inertia is small and the annual cycles of T and IR are large and in phase. Those regions where Blocal differs markedly from 2 W m−2K−1 are where the IR is strongly affected by the cloudiness of seasonal precipitation regimes. This effect is especially evident over the tropical oceans where the parameterization fails; but that is where the thermal inertia is large, the seasonal cycle in T is small, and even large errors in the radiative cooling approximation will have little impact on seasonal cycle simulations by simple climate models.

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Xiaodong Liu
,
Libin Yan
,
Ping Yang
,
Zhi-Yong Yin
, and
Gerald R. North

Abstract

The spatial and temporal variations of aerosol loading over eastern Asia specified in terms of the aerosol optical depth (AOD) at the 550-nm wavelength during July are examined in conjunction with the intensity of the Indian summer monsoon. AOD derived from Moderate Resolution Imaging Spectroradiometer (MODIS) observations, gridded reanalyses, and ground-based measurements are used in the analysis. Two contrasting years, 2002 and 2003, which represent weak and active Indian summer monsoon events, respectively, are selected for the study, with a focus on an eastern Asian southern subregion (SR; 23°–32°N, 105°–120°E) and an eastern Asian northern subregion (NR; 35°–44°N, 115°–130°E). It is shown that the interannual variation of July mean wind intensity is a major factor in regulating the midsummer spatial pattern of aerosols over eastern Asia when the Indian monsoon index is anomalously large. The AOD anomalies in the NR and SR are positive and negative, respectively, during an active monsoon year, whereas the opposite is observed during a weak monsoon year. The variation patterns of less cloudy-day visibility, observed at four meteorological stations in the SR and NR subregions, also show spatial–temporal aerosol variability evident in the MODIS AOD data. Relative to the case of a weak monsoon year, meridional winds and convection are stronger and more clouds and precipitation are observed in the NR subregion during the active monsoon year. The opposite pattern is observed in the SR subregion. The spatial–temporal variation pattern of aerosols over eastern Asia illustrates the nonnegligible role of transport and dispersal mechanisms associated with the Indian summer monsoon in the region.

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