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J. Charney

Abstract

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J. Charney

Abstract

The analysis of Conditional Instability of the Second Kind (CISK) for a resting atmosphere leads to a maximum growth rate at zero width of the rain area. However, if the process takes place in a uniform current moving relative to the ground with a velocity ū, and the width of the rain area is 2a, an Ekman boundary layer cannot be established in the rain area when 2a<ū/f, where f is the Coriolis parameter. It is shown that the incomplete development of the frictional boundary layer in this area leads to a maximum growth rate at a ≈300 km, and this seems to be a reasonable value for the half-width of a cloud cluster in a tropical depression or of the Intertropical Convergence Zone itself. The efolding time is of the order of half the spin- up time f −1E−½ where E is the Ekman number, i.e., about 2 days at 10°.

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J. G. Charney

Abstract

Previous studies of the long-wave perturbations of the free atmosphere have been based on mathematical models which either fail to take properly into account the continuous vertical shear in the zonal current or else neglect the variations of the vertical component of the earth's angular velocity. The present treatment attempts to supply both these elements and thereby to lead to a solution more nearly in accord with the observed behavior of the atmosphere.

By eliminating from consideration at the outset the meteorologically unimportant acoustic and shearing-gravitational oscillations, the perturbation equations are reduced to a system whose solution is readily obtained.

Exact stability criteria are deduced, and it is shown that the instability increases with shear, lapse rate, and latitude, and decreases with wave length. Application of the criteria to the seasonal averages of zonal wind suggests that the westerlies of middle latitudes are a seat of constant dynamic instability.

The unstable waves are similar in many respects to the observed perturbations: The speed of propagation is generally toward the east and is approximately equal to the speed of the surface zonal current. The waves exhibit thermal asymmetry and a westward tilt of the wave pattern with height. In the lower troposphere the maximum positive vertical velocities occur between the trough and the nodal line to the east in the pressure field.

The distribution of the horizontal mass divergence is calculated, and it is shown that the notion of a fixed level of nondivergence must be replaced by that of a sloping surface of nondivergence.

The Rossby formula for the speed of propagation of the barotropic wave is generalized to a baroclinic atmosphere. It is shown that the barotropic formula holds if the constant value used for the zonal wind is that observed in the neighborhood of 600 mb.

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J. G. Charney

Abstract

The small-scale “noise” disturbances of the atmosphere create difficulties for the numerical integration of the equations of motion. For example, their existence demands that very small time differences be used in the integration of the finite-difference equations. To eliminate the noise, a filtering method is devised which consists essentially in replacing the primitive hydrodynamical equations by combining the geostrophic and hydrostatic equations with the conservation equations for potential temperature and potential vorticity. In this way a single equation in the pressure is obtained for the motion of the large-scale systems. A method is suggested for its numerical integration.

The spread of data required for a short-period forecast is discussed in terms of the rate of spread of influences or “signal velocity” in the atmosphere. It is shown that a small disturbance is propagated both horizontally and vertically at a finite rate. Estimates are obtained for the maximum signal-velocity components in order to establish bounds for the influence region. It is found that numerical forecasts for periods of one or perhaps two days are now possible for certain areas of the earth but that forecasts for longer periods require a greater spread of observation stations than is available.

A method is given for reducing the three-dimensional forecast problem to a two-dimensional one by construction of an “equivalent-barotropic” atmosphere. The method is applied to the calculation of the 5OO-mb height tendency, and the results are compared with observation. A rule is derived for determining the positions of the isallohyptic centers from the field of the absolute-vorticity advection.

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Joseph J. Charney
and
J. Michael Fritsch

Abstract

Surface discrete frontal propagation in a wintertime, nonconvective environment is documented using conventional surface and upper-air data and simulated using the PSU–NCAR mesoscale model.

Synoptic and mesoscale surface analyses show a cold front associated with a synoptic-scale low-pressure system propagating from northwest to southeast across the central United States. Apparently discrete frontal propagation occurs when the surface front dissipates and a new front forms approximately 500 km ahead of the original front, with no compelling evidence of frontal passage in the intervening space. Upper-air analyses indicate the infusion of three different airstreams into the frontal region, resulting in the formation of a ribbon of low static stability air parallel to and several hundred kilometers in advance of the original front. This static stability structure appears to be involved in the observed evolution of the front. The development of precipitation over the intervening zone between the old and new frontal positions suggests that precipitation-induced diabatic processes also played a role in the discrete frontal propagation.

The numerical simulation captures the essential surface, upper-air, and precipitation features associated with the discrete propagation. Cross-section analyses of the simulated atmospheric fields indicate that the front propagated discretely only at the surface and in the lowest 200 hPa of the atmosphere, while the midtropospheric trough associated with the surface front propagated continuously though the region. The cross sections also indicate that the vertical winds associated with the frontal system adjust very quickly to the new frontal location while the horizontal winds and mass fields adjust more slowly. Analysis of frontogenetical forcing verifies that the new surface front forms at the expense of the original front. A careful examination of the temperature budgets within the simulation shows that the mass field redistribution associated with the discrete frontal propagation occurred as a result of the lifting of a strong temperature inversion in the prefrontal environment combined with precipitation induced diabatic cooling.

Based on the results of the model simulation, a conceptual model of discrete frontal propagation is presented that incorporates the observed and simulated sequence of events.

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J. G. Charney
and
M. E. Stern

Abstract

We consider the quasi-geostrophic instability of a circumpolar vortex in which there is available kinetic energy of lateral shear as well as available potential energy due to meridional temperature gradients. Stability criteria are developed for the case of an internal jet, i.e., where the meridional temperature gradients at the ground vanish. The internal jet is stable if the gradient of potential vorticity in isentropic surfaces does not vanish. If it vanishes at a closed isopleth of constant mean zonal vorticity, the jet is unstable.

The special role played by the kinematic and thermodynamic boundary conditions in the theory of baroclinic stability is clarified by re-examining earlier theories in the light of an analogy to two-dimensional shear flow. Simple baroclinic flow with rigid horizontal boundaries is isomorphic to Couette flow with free boundaries. The presence of meridional temperature gradients at boundaries relaxes the constraints on the boundary pressure perturbations and makes possible the release of available potential energy, just as the freeing of the boundary in Couette flow makes possible the release of shear kinetic energy.

The mid-winter breakdown of the polar-night jet may be an example of an instability, but we cannot say whether the concomitant disturbance releases mean kinetic, mean potential energy, or both, of the internal jet type, since the possibility of all of these conversions exists. The apparent downward propagation of the unstable disturbances in the polar-night jet below 30 km may be explained by the prior onset of instability at higher levels.

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J. G. Charney
and
N. A. Phillips

Abstract

An n-level generalization of the 2½-dimensional model is derived by specialization of the complete three-dimensional quasi-geostrophic equations. In the case n = 1, it reduces to the two-dimensional single-layer barometric model. In the case N = 2, it reduces to the double-layer barotropic model, or — what is shown to be mathematically equivalent —the 2½-dimensional model. Methods of numerical integration of the 2- and 2½-dimensional equations, and the machine requirements for such integrations, are discussed.

The results of a series of six two-dimensional and six 2½-dimensional forecasts for 12 and 24 hours are presented. Although the 2½-dimensional forecasts are noticeably superior to the two-dimensional forecasts, it is apparent that considerable improvement will be possible with models in which there are fewer artificial constraints. A method of integration is therefore proposed for the n-level generalization of the 2½-dimensional model, and computation schemes are outlined for the general three-dimensional quasi-geostrophic equations. The semi-Lagrangian coordinate system with potential temperature as vertical coordinate is shown to exhibit favorable properties for machine integration.

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J. Charney
,
M. Halem
, and
R. Jastrow

Abstract

No abstract available.

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Michael J. Erickson
,
Brian A. Colle
, and
Joseph J. Charney

Abstract

The performance of a multimodel ensemble over the northeast United States is evaluated before and after applying bias correction and Bayesian model averaging (BMA). The 13-member Stony Brook University (SBU) ensemble at 0000 UTC is combined with the 21-member National Centers for Environmental Prediction (NCEP) Short-Range Ensemble Forecast (SREF) system at 2100 UTC. The ensemble is verified using 2-m temperature and 10-m wind speed for the 2007–09 warm seasons, and for subsets of days with high ozone and high fire threat. The impacts of training period, bias-correction method, and BMA are explored for these potentially hazardous weather events using the most recent consecutive (sequential training) and most recent similar days (conditional training). BMA sensitivity to the selection of ensemble members is explored. A running mean difference between forecasts and observations using the last 14 days is better at removing temperature bias than is a cumulative distribution function (CDF) or linear regression approach. Wind speed bias is better removed by adjusting the modeled CDF to the observation. High fire threat and ozone days exhibit a larger cool bias and a greater negative wind speed bias than the warm-season average. Conditional bias correction is generally better at removing temperature and wind speed biases than sequential training. Greater probabilistic skill is found for temperature using both conditional bias correction and BMA compared to sequential bias correction with or without BMA. Conditional and sequential BMA results are similar for 10-m wind speed, although BMA typically improves probabilistic skill regardless of training.

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Michael J. Erickson
,
Brian A. Colle
, and
Joseph J. Charney

Abstract

The Short-Range Ensemble Forecast (SREF) system is verified and bias corrected for fire weather days (FWDs) defined as having an elevated probability of wildfire occurrence using a statistical Fire Weather Index (FWI) over a subdomain of the northeastern United States (NEUS) between 2007 and 2014. The SREF is compared to the Rapid Update Cycle and Rapid Refresh analyses for temperature, relative humidity, specific humidity, and the FWI. An additive bias correction is employed using the most recent previous 14 days [sequential bias correction (SBC)] and the most recent previous 14 FWDs [conditional bias correction (CBC)]. Synoptic weather regimes on FWDs are established using cluster analysis (CA) on North American Regional Reanalysis sea level pressure, 850-hPa temperature, 500-hPa temperature, and 500-hPa geopotential height. SREF severely underpredicts FWI (by two indices at FWI = 3) on FWDs, which is partially corrected using SBC and largely corrected with CBC. FWI underprediction is associated with a cool (ensemble mean error of −1.8 K) and wet near-surface model bias (ensemble mean error of 0.46 g kg−1) that decreases to near zero above 800 hPa. Although CBC improves reliability and Brier skill scores on FWDs, ensemble FWI values exhibit underdispersion. CA reveals three synoptic weather regimes on FWDs, with the largest cool and wet biases associated with a departing surface low pressure system. These results suggest the potential benefit of an operational analog bias correction on FWDs. Furthermore, CA may help elucidate model error during certain synoptic weather regimes.

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