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Alan Thorpe and David Rogers
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Alan J. Thorpe
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Hongyan Zhu and Alan Thorpe

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Errors in numerical weather forecasts can be attributed to two causes: deficiencies in the modeling system and inaccurate initial conditions. Understanding of the characteristics of the growth of forecast spread related to model uncertainty is less developed than that for initial condition uncertainty. In this research, the authors aim to construct a theoretical basis for describing such forecast error growth resulting from model uncertainty using mostly an empirical modeling approach. Primitive equation models with different vertical discretization and different horizontal resolutions are used to investigate the impacts of model uncertainties on the predictability of extratropical cyclones. Three sets of initial perturbations related to an upper-level trigger, with slightly different amplitudes, are designed for representing the situation when the initial condition uncertainty leads to significant forecast error growth.

Forecast error growth is here estimated by following the properties of a developing cyclone in the simulations. Generally, there are three phases for forecast error growth in the experiments with initial condition and model uncertainties. For the experiments with the structured initial condition uncertainties, the errors grow rapidly at the earlier transient stage, with the growth rate well above the fastest growing normal mode. Afterward the error grows exponentially at approximately the same growth rate as the cyclone, followed by a saturation period, when the growth rate starts to decline. For the experiments with the model uncertainties, the forecast errors are initially zero and increase as time to a power of μ, which is between 0.5 and 3 depending on the strength of the cyclone at the time the simulation is initiated. After a certain time interval, the exponential growth phase and saturation period start as in the initial error experiments. Starting an integration with a stronger initial cyclone, the forecast error associated with the model uncertainty takes a shorter time to reach the exponential growth period and the forecast error grows more rapidly initially with a smaller value of μ. Also, when the initial cyclone is strong enough, then the exponential growth phase may only last for a very short time.

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Alan J. Thorpe

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Ate balanced flow structure of various classic synopitc-scale disturbances is reviewed using the invertibility principle for isentropic potential vorticity (IPV) distributions. Complete solutions are shown for cold and warm core structures of various types. The basic model imagines the tropopause to be the interface between the lower potential vorticity of the troposphere and the approximately six-fold larger value typical of the lower stratosphere. The sensitivity of the structure of the potential temperature variation along the tropopause and at the surface is described. Results are presented in diagrammatic form to allow easy diagnosis of the vortex structure from synoptic data available at perhaps only a few levels. The point is made that upper air IPV and surface potential temperature distributions are often the most crucial in accounting for the balanced flow structure.

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Alan Thorpe and David Rogers

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The Global Weather Enterprise (GWE) encompasses the scientific research, technology, observations, modeling, forecasting, and forecast products that need to come together to provide accurate and reliable weather information and services that save lives, protect infrastructure, and enhance economic output. It is a value chain from weather observations to, ultimately, the creation of actionable analysis-and-forecast weather information of huge benefit to society. The GWE is a supreme exemplar of the value of international cooperation, public–private engagement, and scientific and technological know-how. It has been a successful enterprise, but one that has ever-increasing requirements for continual improvement as population density increases and climate change takes place so that the impacts of weather hazards can be mitigated as far as possible. However, the GWE is undergoing a period of significant change arising, for example, from the growing need for more accurate and reliable weather information, advances coming from science and technology, and the expansion of private sector capabilities. These changes offer real opportunities for the GWE but also present a number of obstacles and risks that could, if not addressed, stifle this development, adversely impacting the societies it aims to serve. This essay aims to catalyze the GWE to address the issues collectively, by dialogue, engagement, and mutual understanding.

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Walter Fernandez and Alan J. Thorpe

Abstract

Raymond's (1975) wave-CISK model is applied to several tropical convective storms observed in Venezuela, the eastern Atlantic and West Africa to predict their propagation velocity. Similar calculations are carried out with Moncrieff and Miller's (1976) analytical model for tropical cumulonimbus and squall lines. A comparison of the model predictions with the observed values is made. In some cases the models give good predictions, but not in others. In general, Raymond's model underestimates the propagation speed of the storms, while the Moncrieff-Miller model overestimates it. Raymond's model is poor when the cloud bases are very low. This result indicates that over tropical oceans wave-CISK models cannot give good results unless the mass flux due to the plumes, which is equated to the mass flux across cloud base, is treated in a more realistic way. The Moncrieff-Miller model gives better results if the mean wind component along the direction of motion is used rather than the mid-level wind.

The wave-CISK model and steady-state models of storm motion are then considered in conditions of constant wind shear. In particular, their predictions are compared over a wide range of shear values, using realistic thermodynamic soundings. Despite the obvious differences between the models, it is found that, for Richardson number small (R<1) and very large, they give comparable predictions for the storm velocity. It appears that a very good approximation for the wave-CISK model over the entire R range is to put the storm speed proportional to the shear, plus a constant.

An important conclusion is that the ability of storms to propagate relative to the environmental flow can be reproduced in the linear wave-CISK model and thus may not be a fundamentally nonlinear effect. It is therefore crucial to further examine forcing mechanisms of convective overturning and, in particular, to clarify the relationship between CISK and the implicit forcing involved in the steady model.

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Ming Xue and Alan J. Thorpe

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A nonhydrostatic numerical model suitable for simulating mesoscale meteorological phenomena is developed and described here. The model is the first to exploit the nonhydrostatic equation system in σ (normalized pressure) coordinates. In addition to the commonly recognized advantages of σ-coordinate models, this model is potentially advantageous in nesting with large-scale σ-coordinate models. The equation system does not support sound waves but it presents the internal gravity waves accurately. External gravity waves are the fastest wave modes in the system that limit the integration time step. However, since short nonhydrostatic external waves are much slower than the speed of shallow-water waves and because fast hydrostatic long waves imposes less severe restriction on the time step when they are resolved by many grid points, a large time step (compared to that determined by the speed of hydrostatic shallow-water waves) can be used when horizontal grid spacing is on the order of 1 km.

The system is solved in a way analogous to the anelastic system in terrain-following height coordinates. The geopotential height perturbation is diagnosed from an elliptic equation. Conventional finite-differencing techniques are used based on Arakawa C grid, The flux-corrected transport (FCT) scheme is included as an option for scalar advection.

The model has been used to study a variety of problems and here the simulations of dry mountain waves are presented. The resists of simulations of the 11 January 1972 Boulder severe downslope windstorm are reported and the wave development mechanism discussed.

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Alain Joly and Alan J. Thorpe

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A methodology suitable for assessing the stability of any time-dependent basic state is presented. The equivalent of the normal modes for steady basic states are the eigenvectors of the resolvent matrix; this matrix incorporates the evolution of the large-scale flow, and growth rates are replaced by amplification rates. This method is applied to the three-dimensional stability of two-dimensional fronts undergoing frontogenesis in the presence of latent heat release in a semigeostrophic model. Disturbances developing in this flow are therefore geostrophically balanced. The concepts are first illustrated in a dry time-dependent uniform shear and potential vorticity flow. At any time during the evolution of the basic flow the stability can be compared to that obtained by assuming that the frontogenesis has, at that instant, ceased. Although differences between the results from the two methods exist, general conclusions as to the scales and structure of the modes are not altered; only large-scale waves are unstable. The situation in moist baroclinic waves is dramatically different. Growth rates are enhanced compared to the steady state analysis, but the possibility for frontal waves on the 1000-km scale to amplify most rapidly depends on the rate of development of the parent wave. Such waves dominate the spectrum only when that rate is slow and then only when the frontal ascent takes on a small cross-frontal width and the vorticity maximum penetrates over a deep layer. The short-wave growth is mostly due to latent heat release in the wave. This heating is shown, in a simplified case, to modify the necessary conditions for instability. It is concluded that shearing deformation does not intrinsically inhibit frontal instability, but paradoxically it greatly favors two-dimensional growth in the early stages due to the more rapid frontogenesis in the presence of latent heating. The role of stretching deformation may be substantially different but is not considered here.

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Meral Demirtas and Alan J. Thorpe

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A new method is described to interpret satellite water vapor (WV) imagery in dynamical terms using potential vorticity (PV) concepts. The method involves the identification of mismatches between the WV imagery and a numerical weather prediction model description of the upper-level PV distribution at the analysis time. These mismatches are usually associated with horizontal positioning errors in the tropopause location in the oceanic storm-track region in midlatitudes. The PV distribution is locally modified to minimize this mismatch, and PV inversion is carried out to provide dynamically consistent additional initial data with which to reinitialize the numerical forecast.

One of the advantages of using this method is that it is possible to generate wind and temperature data suitable for inclusion as initial data for numerical weather forecasts. By using PV additional data can be inferred that cannot otherwise be simply derived from the WV data. In this way dynamical concepts add considerable value to the WV imagery, which by themselves would probably not have as significant a forecast impact.

Several examples of the use of this method are given here including cases of otherwise poorly forecast North Atlantic cyclones. In cases where the analysis errors occur at upper levels of the troposphere, the method leads to a significant improvement in the short-range forecast skill. In general, it is useful in highlighting where forecast problems are arising.

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Fred Kucharski and Alan J. Thorpe

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The concept of local extended exergy is here applied to an idealized, dry, and reversible-adiabatic cyclone development. The extended exergy as well as the kinetic energy are decomposed into a mean part, defined by a zonal average, and into a perturbation from the mean. The resulting local energy evolution equations provide an extension of the well-known Lorenz-type available energy equations. A term in the baroclinic conversion rate, connected with static stability anomalies, which is not usually considered, is of significance even in this idealized case study and contributes significantly to the nonlinear equilibration of the baroclinic wave.

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