ALBERT

Description: This paper presents a reexamination of the earth radiation budget parameterization of energy balance climate models in light of data collected over the last 12 years. The study consists of three parts: (1) an examination of the infrared terrestrial radiation to space and its relationship to the surface temperature field on time scales from 1 month to 10 years; (2) an examination of the albedo of the earth with special attention to the seasonal cycle of snow and clouds; (3) solutions for the seasonal cycle using the new parameterizations with special attention to changes in sensitivity. While the infrared parameterization is not dramatically different from that used in the past, the albedo in the new data suggest that a stronger latitude dependence be employed. After retuning the diffusion coefficient the simulation results for the present climate generally show only a slight dependence on the new parameters. Also, the sensitivity parameter for the model is still about the same (1.25 C for a 1 percent increase of solar constant) for the linear models and for the nonlinear models that include a seasonal snow line albedo feedback (1.34 C). One interesting feature is that a clear-sky planet with a snow line albedo feedback has a significantly higher sensitivity (2.57 C) due to the absence of smoothing normally occurring in the presence of average cloud cover.

Description: A method for the estimation of the mean area average rain rate from dependent data is developed and applied to the GARP Atlantic Tropical Experiment data. The method consists of fitting a mixed distribution, containing an atom at zero, by minimum chi-square in combination with certain time-space sampling designs. In modeling the continuous component of the mixed distribution, it is shown that the lognormal distribution provides a very close fit for the nonzero area average rainrates. A comparison with the gamma distribution shows that the lognormal distribution is a better choice as expressed by the minimum chi-square criterion. Some of the time-space sampling designs correspond to satellite sampling. The results indicate that a satellite visiting an area of about 350 x 350 sq km in the tropics approximately every 10 hours over a period can provide a rather close estimate for the mean area average rain rate.

Description: Estimates of monthly average rainfall based on satellite observations from a low earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. The size of this error is estimated for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). First, the statistical description of rainfall on scales from 1 to 1000 km is examined in detail, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM-like satellite is flown over a two-dimensional time-evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area-averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10 percent of the mean for rainfall averaged over a 500 x 500 sq km area.

Description: A comparison of rain rates retrieved from the Nimbus 5 electronically scanning microwave radiometer brightness temperatures and observed from shipboard radars during the Global Atlantic Tropical Experiment (GATE) phase I shows that the beam filling error is the major source of discrepancy between the two. When averaged over a large scene (the GATE radar array, 400 km in diameter), the beam filling error is quite stable, being 50 percent of the observed rain rate. This suggests the simple procedure of multiplying retrieved rain rates by 2 (correction factor). A statistical model of the beam filling error is developed by envisioning an idealized instrument field-of-view that encompasses an entire gamma distribution of rain rates. A modeled correction factor near 2 is found for rain rate and temperature characteristics consistent with GATE conditions. The statistical model also suggests that the correction factor varies from 1.5 to 2.5 for suppressed to enhanced tropical convective regimes, and decreases to 1.5 as the freezing level and average depth of the rain column decreases to 2.5 km.

Description: A review of Energy Balance Models is presented. Results from the Outgoing Longwave Radiation parameterization are discussed. The albedo parameterizations and the consequences of the new parameterizations are examined.

Description: Some evidence is presented that the main part of the atmospheric climate system is such that small forcings in the heat balance lead to linear responses in the surface temperature field. By examining first a noise forced energy-balance climate model and then comparing it with a long run of a highly symmetrical general circulation model, one finds a remarkable connection between spatial autocorrelation statistics and the thermal influence function for a point heat source. These findings are brought together to indicate that this particular climatological field may be largely governed by linear processes.

Description: In this paper a scheme is proposed to use a point raingage to compare contemporaneous measurements of rain rate from a single-field-of-view (FOV) estimate based on a satellite remote sensor such as a microwave radiometer. Even in the ideal case the measurements are different because one is at a point and the other is an area average over the field of view. Also the point gage will be located randomly inside the field of view on different overpasses. A space-time spectral formalism is combined with a simple stochastic rain field to find the mean-square deviations between the two systems. It is found that by combining about 60 visits of the satellite to the ground-truth site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the systems alone. This seems to be a useful level of tolerance in terms of isolating and evaluating typical biases that might be contaminating retrieval algorithms.

Description: 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) 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.

Description: The spatial and temporal characteristics of rainfall over Oklahoma and Kansas are analyzed using the raingage data collected during the Preliminary Regional Experiment for STORM-Central (PRE-STORM). The spectra obtained are compared with those obtained from the oceanic precipitation in the GARP and with that obtained from analyzing raingage records in east Texas. In addition, the spectra are used to evaluate the sampling errors that are due to the spatial gaps in measurements. It was found that the temporal spectra from PRE-STORM had a spectral shape similar to that obtained in GARP, except that the tail of the PRE-STORM spectra has a lower slope than in GARP spectra, suggesting that the largest difference between tropical oceanic rainfall and convective land precipitation is at the highest frequencies.

Description: In this paper both a microwave attenuation measurement along a horizontal line and multiple point gauge measurements are analyzed as possible ground-truth designs to validate satellite precipitation retrieval algorithms at the field of view spatial level (typically about 20 km). The design consists of comparing a sequence of pairs of contemporaneous measurements taken from the ground and from space. The authors examine theoretically the variance of expected differences between the two systems. The line average measurement leads to a smaller mean-square error compared to the case of a single point gauge, since some of the small-scale variability of the rain field is smoothed away by the line integration. The multiple point gauge measurements also give smaller mean-square error than that of a single point gauge. The centroid of the line and point gauge configurations are considered to be located randomly inside the field of view for different overpasses. A space-time spectral formalism is used with a noise-forced diffusive rain field to find the mean-square error. By considering instantaneous ground and satellite measurement pairs over about 50 visits when raining, we can reduce the expected error to approximately 10% of the standard deviation of climatological variability. This is considered to be a useful level of tolerance for identifying biases in the retrieval algorithms. It is found that the multiple point gauges (especially two gauges) are the economical ground-truth design compared to the microwave attenuation based on the mean-square error comparison. The major finding of this study is that a significant improvement over the point gauge is obtained by adding a single additional piece of information; adding more gauges or extending the line of attenuation is not an important improvement.