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T. Pujol and G. R. North

Abstract

The effects of the nongray absorption (i.e., atmospheric opacity varying with wavelength) on the possible upper bound of the outgoing longwave radiation (OLR) emitted by a planetary atmosphere have been examined. This analysis is based on the semigray approach, which appears to be a reasonable compromise between the complexity of nongray models and the simplicity of the gray assumption (i.e., atmospheric absorption independent of wavelength). Atmospheric gases in semigray atmospheres make use of constant absorption coefficients in finite-width spectral bands. Here, such a semigray absorption is introduced in a one-dimensional (1D) radiative–convective model with a stratosphere in radiative equilibrium and a troposphere fully saturated with water vapor, which is the semigray gas. A single atmospheric window in the infrared spectrum has been assumed.

In contrast to the single absolute limit of OLR found in gray atmospheres, semigray ones may also show a relative limit. This means that both finite and infinite runaway effects may arise in some semigray cases. Of particular importance is the finding of an entirely new branch of stable steady states that does not appear in gray atmospheres. This new multiple equilibrium is a consequence of the nongray absorption only. It is suspected that this new set of stable solutions has not been previously revealed in analyses of radiative–convective models since it does not appear for an atmosphere with nongray parameters similar to those for the earth's current state.

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R. F. Cahalan, D. A. Short, and G. R. North

Abstract

A space-time statistical analysis of total outgoing infrared radiation (derived from the 10.5–12.5 μm window measurements of the NOAA operational satellites) is used to determine the gross features of day-to-day cloudiness fluctuations over the Pacific Ocean in summer and winter. Infrared fluctuations arise from the passage of cloudiness systems through a grid box as well as the creation and destruction of cloudiness in the box. Which process dominates depends upon the size of the box relative to the size, speed and persistence time of a typical cloudiness system. In most regions the statistical analysis yields advection speeds characteristic of 700 mb mean flow with spatial dependence resembling the 300 mb mean flow. Spatial scales less than 2000 km predominate, smaller scales having less persistence. Characteristic time scales are on the order of one or two days, even for a grid box spanning the entire North Pacific storm track. This result is remarkable in view of the much longer time scales commonly associated with atmospheric disturbances. Apparently many cloudiness systems are created and destroyed during the lifetime of a single disturbance.

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H. Salmun, R. F. Cahalan, and G. R. North

Abstract

The steady-state zonally averaged climate is perturbed by adding a latitude-dependent heat source to an energy balance equation of the simplified Budyko-Sellers type. The latitude of the ice edge, which is attached to an isotherm, becomes dependent on the strength of the perturbation. This dependence is given in terms of the well-known iceline-solar constant relation, and the latitude dependence of the perturbed temperature field is then uniquely determined. The exact analytical solution is linearized and expressed in terms of a superposition of line sources at various latitudes. The main features are. 1) The total temperature response is a sum of the direct effect of the perturbation and an indirect ice-albedo effect proportional to the solar ice-edge sensitivity; and 2) the indirect feedback effect produces an enhanced response in polar latitudes.

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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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Bo Li, Aditya Murthi, Kenneth P. Bowman, Gerald R. North, Marc G. Genton, and Michael Sherman

Abstract

The Taylor hypothesis (TH) as applied to rainfall is a proposition about the space–time covariance structure of the rainfall field. Specifically, it supposes that if a spatiotemporal precipitation field with a stationary covariance Cov(r, τ) in both space r and time τ moves with a constant velocity v, then the temporal covariance at time lag τ is equal to the spatial covariance at space lag r = v τ that is, Cov(0, τ) = Cov(v τ, 0). Qualitatively this means that the field evolves slowly in time relative to the advective time scale, which is often referred to as the frozen field hypothesis. Of specific interest is whether there is a cutoff or decorrelation time scale for which the TH holds for a given mean flow velocity v. In this study, the validity of the TH is tested for precipitation fields using high-resolution gridded Next Generation Weather Radar (NEXRAD) reflectivity data produced by the WSI Corporation by employing two different statistical approaches. The first method is based on rigorous hypothesis testing, while the second is based on a simple correlation analysis, which neglects possible dependencies between the correlation estimates. Radar reflectivity values are used from the southeastern United States with an approximate horizontal resolution of 4 km × 4 km and a temporal resolution of 15 min. During the 4-day period from 2 to 5 May 2002, substantial precipitation occurs in the region of interest, and the motion of the precipitation systems is approximately uniform. The results of both statistical methods suggest that the TH might hold for the shortest space and time scales resolved by the data (4 km and 15 min) but that it does not hold for longer periods or larger spatial scales. Also, the simple correlation analysis tends to overestimate the statistical significance through failing to account for correlations between the covariance estimates.

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Hyo-Suk Lim, C. E. Graves, G. R. North, and T. T. Wilheit

Abstract

An algorithm to estimate monthly 5° × 5° area-averaged rain rate over the oceans from January 1973 to December 1976 using single-channel microwave data from the Nimbus-5 satellite has been developed. This study extends the work of Shin et al. by including the full width of scan angles (from −50° to 50°) in order to reduce sampling error. The scan-angle dependence of the estimated rain rate due to variable antenna sidelobe effects, surface emissivity, and propagation pathlength is eliminated using a statistical method. A globally uniform beam-filling correction factor of 2.2 is applied in this study. Comparison with island station rainfall measurements over the Pacific shows a remarkably high correlation between two data in the equatorial dry zone and South Pacific convergence zone (SPCZ) but a low correlation in the extratropics and equatorial western Pacific. It is also proved that the retrieved rain rates are statistically significant.

The rainfall deviations from non-El Niño years April 1973 to December 1975 reveal the temporal and spatial variations produced by the 1972–73 and 1976–77 El Niño episodes. We observe an increase of rainfall over the eastern and central equatorial Pacific Ocean and a decrease over the equatorial western Pacific Ocean and eastern Australia during these events. Consistent with previous work, the rainfall anomaly of the 1972–73 El Niño was much stronger than that of the 1976–77 El Niño.

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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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C. Kummerow, J. Simpson, O. Thiele, W. Barnes, A. T. C. Chang, E. Stocker, R. F. Adler, A. Hou, R. Kakar, F. Wentz, P. Ashcroft, T. Kozu, Y. Hong, K. Okamoto, T. Iguchi, H. Kuroiwa, E. Im, Z. Haddad, G. Huffman, B. Ferrier, W. S. Olson, E. Zipser, E. A. Smith, T. T. Wilheit, G. North, T. Krishnamurti, and K. Nakamura

Abstract

The Tropical Rainfall Measuring Mission (TRMM) satellite was launched on 27 November 1997, and data from all the instruments first became available approximately 30 days after the launch. Since then, much progress has been made in the calibration of the sensors, the improvement of the rainfall algorithms, and applications of these results to areas such as data assimilation and model initialization. The TRMM Microwave Imager (TMI) calibration has been corrected and verified to account for a small source of radiation leaking into the TMI receiver. The precipitation radar calibration has been adjusted upward slightly (by 0.6 dBZ) to match better the ground reference targets; the visible and infrared sensor calibration remains largely unchanged. Two versions of the TRMM rainfall algorithms are discussed. The at-launch (version 4) algorithms showed differences of 40% when averaged over the global Tropics over 30-day periods. The improvements to the rainfall algorithms that were undertaken after launch are presented, and intercomparisons of these products (version 5) show agreement improving to 24% for global tropical monthly averages. The ground-based radar rainfall product generation is discussed. Quality-control issues have delayed the routine production of these products until the summer of 2000, but comparisons of TRMM products with early versions of the ground validation products as well as with rain gauge network data suggest that uncertainties among the TRMM algorithms are of approximately the same magnitude as differences between TRMM products and ground-based rainfall estimates. The TRMM field experiment program is discussed to describe active areas of measurements and plans to use these data for further algorithm improvements. In addition to the many papers in this special issue, results coming from the analysis of TRMM products to study the diurnal cycle, the climatological description of the vertical profile of precipitation, storm types, and the distribution of shallow convection, as well as advances in data assimilation of moisture and model forecast improvements using TRMM data, are discussed in a companion TRMM special issue in the Journal of Climate (1 December 2000, Vol. 13, No. 23).

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