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Alan J. Thorpe

Abstract

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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Hongyan Zhu
and
Alan Thorpe

Abstract

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 Thorpe
and
David Rogers

Abstract

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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Alan Thorpe
and
David Rogers
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Alan J. Thorpe
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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

Abstract

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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Meral Demirtas
and
Alan J. Thorpe

Abstract

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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Hannah R. Pomroy
and
Alan J. Thorpe

Abstract

The existence and production of reduced upper-tropospheric potential vorticity (RUPV) by heating is considered. An objective technique is used that identifies anomalies of PV arising from a particular physical process (here latent heat release). The evolution of two RUPV anomalies and a related diabatically increased lower-tropospheric PV (ILPV) anomaly occurring during Intensive Observing Period One of the cyclones from the Fronts and Atlantic Storm Track Experiment (FASTEX) is examined using model analyses, sounding data, and trajectory calculations. Three distinct airflows are identified emanating from the ILPV anomaly each with a different evolution. Results show that RUPV anomalies exist in the atmosphere and, in a weaker form, in numerical models.

The dynamical role of RUPV anomalies is examined using a nonlinear balance PV inversion and reruns of the U.K. Meteorological Office Limited Area Model. This shows that instantaneously the flow and temperature perturbations associated with RUPV anomalies are of at least comparable magnitude and extent to those induced by a similar positive anomaly. Over time one RUPV anomaly is seen to have a significant effect upon the development of its parent low. This low is more compact and more rapidly developing in the absence of the anomaly. The effect of the positive anomaly is also significant, but removing it has only a short-term effect as the anomaly quickly reforms. These results show that it is important to consider the role of RUPV in the PV model of a midlatitude cyclone.

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Douglas J. Parker
and
Alan J. Thorpe

Abstract

It is shown here that there exists a regime of balanced frontogenesis that is forced almost entirely by the diabatic hating due to convection at a front. This theory is explored in the context of the two-dimensional semigeostrophic equations with an Eady basic state: convection is parameterized to be dependent on the low-level moisture convergence of the cross-frontal ageostrophic flow, in accordance with recent diagnostic studies. The significant result is that the growth rate of the convective frontal system becomes independent of the total wavelength of the domain once the diabatic heating exceeds a relatively large threshold magnitude. In this regime the frontal zone has a width and structure dependent on the heating magnitude but not on the wavelength. The system is described as “solitary” or “isolated” since the dynamics are self-contained and independent of the far field.

The energetics of the system have a diabatic conversion that is an order of magnitude greater than that due to the large-scale alongfront temperature gradient. The large-scale forcing is, however, necessary as a catalyst in maintaining a weak ageostrophic convergence that allows the convective heating to be triggered. The constraint of alongfront geostrophic balance means that convective forcing alone cannot maintain frontogenesis. It is suggested that the dynamics exhibited by the convectively dominated front may also be important in the study of midlatitude squall lines.

The propagation and dynamics of the front are interpreted in terms of the notion of a “diabatic Rossby wave.”

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