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R. Atlas
,
M. Ghil
, and
M. Halem

Abstract

An experiment was performed to study the effect of increased model resolution on satellite sounding data impact. Assimilation cycles were carried out with data from 0000 GMT 29 January to 0300 GMT 21 February 1976, using coarse- and fine-resolution versions of the GLAS second-order general circulation model (GCM). For each model resolution, an assimilation cycle was performed using both conventional and experimental data, which included temperature soundings from the NOAA-4 and Nimbus-6 satellites. A second cycle was run using the same data but excluding the satellite-derived temperature soundings.

The objective analyses produced by the assimilation cycles were used as initial states for a series of evenly spaced 72 h numerical weather forecasts. Eleven forecasts with the same resolution in the forecast model as in the data assimilation were performed at 48 h intervals for each assimilation. Additional forecasts were made with the higher resolution forecast model from the lower resolution assimilation cycle and vice versa. Initial state differences were evaluated in terms of the magnitude, location and structure of large-scale differences between meteorological fields. Numerical prediction differences were evaluated by means of objective scores and subjective comparisons.

Objective scores show a substantially larger beneficial impact of the sounding data at 48 and 60 h with the higher resolution version of the model. Subjective evaluation also revealed a larger positive impact of satellite sounding data with the higher resolution model.

This study has two important limitations: it was carried out with two versions of one model, the GLAS GCM, and the number of forecast cases analyzed is small. Within these limitations, our results indicate that model improvement enhances the impact of satellite data.

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R. Atlas
,
M. Ghil
, and
M. Halem

Abstract

No abstract available.

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M. Ghil, M. Halem
and
R. Atlas

Abstract

Methods are derived for the time-continuous four-dimensional assimilation of satellite sounding temperatures. The methods presented include time-continuous versions of direct insertion, successive correction and statistical linear regression. They are applied to temperature sounding data obtained from radiance measurements taken by instruments aboard the polar-orbiting satellites NOAA 4 and Nimbus 6. The data were collected during the U.S. Data System Test in January-March 1976.

A comprehensive series of experiments was performed to study the effects of using various amounts of satellite data and differing methods of assimilation. The experiments included the assimilation of data from the NOAA 4 satellite only, from Nimbus 6 only, and of data from both satellites combined. Other experiments involved variations in the application of our time-continuous statistical assimilation methods and of asynoptic successive correction methods. Intermittent assimilation of the sounding data was also tested, and its results compared with those of time-continuous assimilation.

Atmospheric states determined in the assimilation experiments served as initial states for a sequence of evenly spaced 3-day numerical weather forecasts corresponding to each experiment. The effects of the satellite data were evaluated according to the following criteria: 1) differences between the initial states produced with and without utilization of satellite data, 2) differences between numerical predictions made from these initial states, and. 3) differences in local weather forecasts resulting from the large-scale numerical predictions.

Initial-state differences were evaluated in terms of magnitude and location of large-scale differences between meteorological fields. Numerical prediction differences were evaluated in terms of SI skill scores and rms errors, as well as by synoptic case studies. An automated forecasting model (AFM) based on quasi-geostrophic theory and on subjective forecasting principles was developed to facilitate the objective evaluation of differences produced in local weather forecasts, especially precipitation forecasts.

These studies suggest the following conclusions: 1) satellite-derived temperature data can have a modest, but statistically significant positive impact on numerical weather prediction in the 2-3 day range; 2) the impact is highly sensitive to the quantity of data available, and increases with data quantity; and 3) the method used to assimilate the satellite data can influence appreciably the magnitude of the impact obtained for the same data.

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R. Balgovind
,
A. Dalcher
,
M. Ghil
, and
E. Kalnay

Abstract

A simple model that yields the spatial correlation structure of global atmospheric mass-field forecast errors is derived. The model states that the relative potential vorticity of the forecast error is forced by spatially multi-dimensional white noise. The forecast error equation contains a nondimensional parameter c 0, which depends on the Rossby radius of deformation. From this stochastic-dynamic equation, a deterministic equation for the spatial covariance function of the 500 mb geopotential error field is obtained.

Three methods of solution are examined: 1) an analytic method based on spherical harmonics, 2) a numerical method based on stratified sampling of Monte-Carlo realizations of the stochastic-dynamic equation, and 3) a combined analytic-numerical method based on two successive applications of a fast Poisson solver to the deterministic covariance equation. The three methods are compared for accuracy and efficiency, and the third (combined) method is found to be clearly superior.

The model's covariance function is compared with global correlation data of forecast-minus-observed geopoteniial fields for the DST-6 period February–March 1976. The data are based on the GLAS forecast-assimilation system in use at that lime (Ghil et al., 1979).

The model correlations agree well with the latitude dependence of the data correlations. The fit between model and data confirms that the forecast error between 24 and 36 h is largely random, rather than systematic; the value of the parameter c 0 which gives the best fit suggests that much of this error can be attributed to baroclinic, rather than barotropic effects. Deterministic influences not included in the model appear at 12 and 48 h. They suggest possibilities of improving the forecast system by a better objective analysis and initialization procedure, and a better treatment of planetary-wave propagation, respectively.

An analytic formula is obtained which locally approximates well the model's global correlations. This formula is convenient to use in the calculation of weighting coefficients for analysis and assimilation schemes. It shows that Gaussian functions are a poor approximation for the forecast error correlations of the mass field, and their derivatives an even poorer approximation to wind field correlations.

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T. M. Chin
,
M. J. Turmon
,
J. B. Jewell
, and
M. Ghil

Abstract

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

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