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Kwano-Y. Kim
,
Gerald R. North
, and
Gabriele C. Hegerl

Abstract

In this study the magnitude and the temporal and spatial correlation scales of background fluctuations generated by three climate models, two different coupled ocean-atmosphere general circulation models and one energy balance model, were examined. These second-moment statistics of the models were compared with each other and with those of the observation data in several frequency bands. This exercise shows some discordance between the models and the observations and also significant discrepancy among different numerical models. The authors also calculated the empirical orthogonal functions and eigenvalues because these am important ingredients for formulating estimation and detection algorithms. There are significant model to model variations both in the shape of eigenfunctions and in the spectrum of eigenvalues. Also, consistency between the modeled eigenfunctions and eigenvalues and those of the observations are rather poor, especially in the low-frequency bands.

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Samuel S. P. Shen
,
Gerald R. North
, and
Kwang-Y. Kim

Abstract

Making use of EOF analysis and statistical optimal averaging techniques, the problem of random sampling error in estimating the global average temperature by a network of surface stations has been investigated. The EOF representation makes it unnecessary to use simplified empirical models of the correlation structure of temperature anomalies. If an adjustable weight is assigned to each station according to the criterion of minimum mean-square error, a formula for this error can be derived that consists of a sum of contributions from successive EOF modes. The EOFs were calculated from both observed data and a noise-forced EBM for the problem of one-year and five-year averages. The mean square statistical sampling error depends on the spatial distribution of the stations, length of the averaging interval, and the choice of the weight for each station data stream. Examples used here include four symmetric configurations of 4 × 4, 6 × 4, 9 × 7, and 20 × 10 stations and the Angell-Korshover configuration. Comparisons with the 100-yr U.K. dataset show that correlations for the time series of the global temperature anomaly average between the full dataset and this study's sparse configurations are rather high. For example, the 63-station Angell-Korshover network with uniform weighting explains 92.7% of the total variance, whereas the same network with optimal weighting can lead to 97.8% explained total variance of the U.K. dataset.

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Gerald R. North
,
Jue Wang
, and
Marc G. Genton

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.

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Eunho Ha
,
Gerald R. North
,
Chulsang Yoo
, and
Kyung-Ja Ha

Abstract

In this paper point gauge measurements are analyzed as part of a ground truth design to validate satellite retrieval algorithms at the field-of-view spatial level (typically about 20 km). Even in the ideal case the ground and satellite measurements are fundamentally different, since the gauge can sample continuously in time but at a discrete point, while a satellite samples an area average but a snapshot in time. The design consists of comparing a sequence of pairs of measurements taken from the ground and from space. Since real rain is patchy, that is, its probability distribution has large nonzero contributions at zero rain rate, the following ground truth designs are proposed. Design 1 uses all pairs. Design 2 uses the pairs only when the field-of-view satellite average has rain. Design 3 uses the pairs only when the gauge has rain. For the nonwhite noise random field having a mixed distribution, the authors evaluate each design theoretically by deriving the ensemble mean and the mean-square error of differences between the two systems. It is found that design 3 has serious disadvantage as a ground truth design due to its large design bias. It is also shown that there is a relationship between the mean-square error of design 1 and design 2. These results generalize those presented recently by Ha and North for the Bernoulli white noise random field. The strategy developed in this study is applied to a real rain rate field. For the Global Atmospheric Program (GARP) Atlantic Tropical Experiment (GATE) data, it is found that by combining 50 data pairs (containing rain) of the satellite to the ground site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the system alone. For the less realistic case of a white noise random field, the number of data pairs is about 100. Hence, the use of more realistic fields means that only about half as many pairs are needed to detect a 10% bias.

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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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Joanne Simpson
,
Robert F. Adler
, and
Gerald R. North

The Tropical Rainfall Measuring Mission (TRMM) satellite is planned for an operational duration of at least three years, beginning in the mid-1990's. The main scientific goals for it are to determine the distribution and variability of precipitation and latent-heat release on a monthly average over areas of about 105 km2, for use in improving short-term climate models, global circulation models and in understanding the hydrological cycle, particularly as it is affected by tropical oceanic rainfall and its variability.

The TRMM satellite's instrumentation will consist of the first quantitative spaceborne weather radar, a multichannel passive microwave radiometer and an AVHRR (Advanced Very High Resolution Radiometer). The satellite's orbit will be low altitude (about 320 km) for high resolution and low inclination (30° to 35°) in order to visit each sampling area in the tropics about twice daily at a different hour of the day. A strong validation effort is planned with several key ground sites to be instrumented with calibrated multiparameter rain radars.

Mission goals and science issues are summarized. Research progress on rain retrieval algorithms is described. Radar and passive microwave algorithms are discussed and the use of radiative models in conjunction with cloud dynamical-microphysical models is emphasized especially. Algorithms are being and will continue to be tested and improved using microwave instruments on high-altitude aircraft overflying precipitating convective systems, located in the range of well-calibrated radars.

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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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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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