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John M. Lewis

Abstract

The dynamical adjustment scheme of P.D. Thompson (1969) has been adapted to the two-parameter baroclinic model which has potential vorticity as the constraint. In contrast to Thompson's approach, which used a differential-difference form of the constraint in space-time, the governing equations are discretized. Analyses simulated from analytic functions and analyses derived at the National Meteorological Center (NMC) are used to test the adjustment procedure. The reduction in error variance is related to the characteristics of the analysis error and the consequences of discretization, i.e., truncation error in the constraint and associated Euler–Lagrange equations.

The principal results are as follows:

1) Significant reduction in mean square error of vorticity can be accomplished with systematic or random error sources when r = |V| Δts < 1, where |V| is the geostrophic advection speed, Δt is one-half the time interval between maps, and Δs is the spatial resolution along the steering contours.

2) The limit of error reduction is reached as r→0, and the limiting values obtained from experiment compare favorably with the theoretical results of Thompson.

3) Height fields that are post-processed from adjusted vorticities also exhibit reduced error variance.

4) Results from the two-parameter model indicate that the strategy of adjustment will be useful in assimilating a sequence of mean temperature (thickness) fields derived from the VISSR Atmospheric Sounder (VAS) which is to be carded on all GOES satellites during this decade.

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John M. Lewis

Abstract

The interaction between a squall line and its environment is examined by using the model of Ogura and Cho (1973). This model incorporates a continuous spectrum of cumulus clouds that are distinguished by their entrainment rates. Conversion of liquid water droplets into raindrops has been included in the cloud microphysical process, but the ice phase has been neglected. By virtue of the cloud spectrum, convective transport terms in the larger scale heat and moisture equations appear as functions of vertical mass flux within the clouds. Once the larger-scale distributions are determined from observations, the vertical mass flux can be found from the budget equations. The cloud populations, i.e., fractional area covered by each cloud category, and the cumulative rainfall rate are functions of this vertical mass flux.

A squall line observed in the National Severe Storms Laboratory (NSSL) network on 8 June 1966 is used to test the theory. This squall line encompassed approximately 10% of the area used in the budget calculations. Observed heat and moisture distributions in the larger scale environment of the squall line are explained in terms of the cumulus processes. A comparison between the theoretically-derived cloud population and observed population was made possible by the WSR-57 radar at NSSL. Cloud population was estimated using precipitation reflectivity data from hourly tilt sequences of this 10 cm radar. The observed and theoretical distribution of clouds compared favorably on 1) the relative frequency of tall clouds, and 2) total areal coverage by clouds.

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John M. Lewis

Abstract

Inaccuracy in the numerical prediction of the moisture content of return-flow air over the Gulf of Mexico continues to plague operational forecasters. At the Environmental Modeling Center/National Centers for Environmental Prediction in the United States, the prediction errors have exhibited bias—typically too dry in the early 1990s and too moist from the mid-1990s to present. This research explores the possible sources of bias by using a Lagrangian formulation of the classic mixed-layer model. Justification for use of this low-order model rests on careful examination of the upper-air thermodynamic structure in a well-observed event during the Gulf of Mexico Experiment. The mixed-layer constraints are shown to be appropriate for the first phase of return flow, namely, the northerly-flow or outflow phase. The theme of the research is estimation of sensitivity—change in the model output (at termination of outflow) in response to inaccuracies or uncertainties in the elements of the control vector (the initial conditions, the boundary conditions, and the physical and empirical parameters). The first stage of research explores this sensitivity through a known analytic solution to a reduced form of the mixed-layer equations. Numerically calculated sensitivity (via Runge–Kutta integration of the equations) is compared to the exact values and found to be most credible. Further, because the first- and second-order terms in the solution about the base state can be found exactly for the analytic case, the degree of nonlinearity in the dynamical system can be determined. It is found that the system is “weakly nonlinear”; that is, solutions that result from perturbations to the control vector are well approximated by the first-order terms in the Taylor series expansion. This bodes well for the sensitivity analysis. The second stage of research examines sensitivity for the general case that includes moisture and imposed subsidence. Results indicate that uncertainties in the initial conditions are significant, yet they are secondary to uncertainties in the boundary conditions and physical/empirical parameters. The sea surface temperatures and associated parameters, the saturation mixing ratio at the sea surface and the turbulent transfer coefficient, exert the most influence on the moisture forecast. Uncertainty in the surface wind speed is also shown to be a major source of systematic error in the forecast. By assuming errors in the elements of the control vector that reflect observational error and uncertainties in the parameters, the bias error in the moisture forecast is estimated. These bias errors are significantly greater than random errors as explored through Monte Carlo experiments. Bias errors of 1–2 g kg−1 in the moisture forecast are possible through a variety of systematic errors in the control vector. The sensitivity analysis also makes it clear that judiciously chosen incorrect specifications of the elements can offset each other and lead to a good moisture forecast. The paper ends with a discussion of research approaches that hold promise for improved operational forecasts of moisture in return-flow events.

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John M. Lewis

Abstract

The generation of a probabilistic view of dynamical weather prediction is traced back to the early 1950s, to that point in time when deterministic short-range numerical weather prediction (NWP) achieved its earliest success. Eric Eady was the first meteorologist to voice concern over strict determinism—that is, a future determined by the initial state without account for uncertainties in that state. By the end of the decade, Philip Thompson and Edward Lorenz explored the predictability limits of deterministic forecasting and set the stage for an alternate view—a stochastic–dynamic view that was enunciated by Edward Epstein.

The steps in both operational short-range NWP and extended-range forecasting that justified a coupling between probability and dynamical law are followed. A discussion of the bridge from theory to practice follows, and the study ends with a genealogy of ensemble forecasting as an outgrowth of traditions in the history of science.

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JOHN M. LEWIS

Abstract

Sasaki's variational analysis method is used to describe the subsynoptic surface conditions accompanying severe local storms. Observations are extracted from the network of surface stations that routinely report every hour. The variational analysis filters the observations by constraining the meteorological fields to satisfy a set of governing prognostic equations. The filtering is monotonic and is designed to admit space and time scales of the order of 500 km and 10 hr, respectively.

The analysis is applied to a severe storm situation on June 10, 1968. The development of an intense squall line from the incipient to mature stage is depicted by an index coupling vertical motion and surface moisture. The results demonstrate that dynamically consistent time continuity can be achieved by using the variational method.

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John M. Lewis
,
Christopher M. Hayden
, and
Anthony J. Schreiner

Abstract

Comparisons between geopotential analyses derived from rawinsondes (RAOB) and the VISSR Atmospheric Sounder (VAS) generally exhibit differences that are ultimately related to the horizontal density and placement of the respective observations and the vertical resolution inherent in the instruments. In order to overcome some of the inconsistencies that appear, two strategies have been developed which allow the analyses to communicate through the derived variable, geostrophic potential vorticity. The first incorporates the statistics of RAOB derived potential vorticity into the VAS vorticity analysis. This is accomplished by making a least-squares adjustment to VAS while constraining it to have first and second moments identical to the RAOB analysis. The other approach makes mutual least-squares adjustments to RAOB and VAS vorticity analyses subject to the dynamic constraint that forecast and hindcast of potential vorticity to the time midway between analyses are equal. The forecast and hindcast are made from a two-parameter baroclinic model. In both procedures, the heights are recovered from adjusted vorticities by inverting the elliptic operators that relate height to vorticity.

Data from the GOES-East satellite at 1430 GMT 6 March 1982 are used along with rawinsonde data at 1200 GMT to test the schemes. The statistical adjustment approach makes synoptically meaningful adjustments to the VAS analysis over the Gulf of Mexico and Gulf coast region, but fails to correct the obvious discrepancies over the continental United States. The dynamic scheme succeeds in making meaningful adjustments over both the Gulf of Mexico and the continent which result in improved vertical motion fields.

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