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Richard Grotjahn

Abstract

A new form of the linear, quasi-geostrophic model is derived on a sphere. The new feature is the use of empirically defined orthogonal basis functions (OBFs) to represent the vertical structure of the perturbation solutions. The prescribed basic state is expressed using a third vertical structure function. Spherical harmonics are used for the horizontal structure. The nonseparablc eigenvalue problem is derived. Solutions are presented using various vertical OBFs, basic flows (both zonally varying and zonally uniform) and horizontal truncations(both rhomboidal and triangular). One OBF (labeled "MOBF') is patterned after the structure found in the most unusable solution of a simpler problem. Another OBF (labeled "2-L") is intended to simulate a two-layer model.

Increasing the horizontal resolution from RI5 (rhomboidal truncation at zonal wavenumber 15) to R30 is found to decrease the growth rates in nearly all cas. (One exception is solid body rotation.) Surprisingly high resolution is needed to properly represent the instability of most of the basic flow jets studied herein. For some of these flows, R30 may not be high-enough resolution. In none of the flows examined did we conclude that RI 5 was adequate. The phase speeds in the "MOBF" cases are frequently much faster.than the most unstable modes in the "2-L" cases. In a few instances, the "2-U" version of the model obtains nearly stationary, rapidlygrowing modes whose counterpart is not found in the "MOBF" model.

Initially, our results suggested that much higher resolution may be needed than suggested by a previous researcher. This contradiction was seemingly resolved by our obse~vatlon that the convergence to the correct solution was faster when the basic jet was centered at a lower latitude. Some implications for low-resolution general circulaton models are made.

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Richard Grotjahn

At least six waterspouts occurred at a large alpine lake in the western United States over several hours during 26 September 1998. Photographs showing the conditions as well as representative examples of this extremely rare event are presented. Some mechanisms are discussed that may explain the persistence of the convection and the low-level vorticity that gave rise to the waterspouts.

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Richard Grotjahn

Abstract

All terms of the frictionless, nonlinear, vorticity equation are examined. Traditional scale analysis provides one of several justifications for using the quasigeostrophic (QG) system of equations to model extratropical cyclones. Analysts of observations have long known that some of the other terms (non-QG) are individually comparable to terms kept in quasigeostrophy. While the non-QG terms are not small, they are assumed to have a large degree of cancellation and so are still neglected in sum. The distributions, magnitudes, and possible cancellations of vorticity equation terms are examined. Analyzed data composites for 15 cases of mature, developing, extratropical cyclones are used.

These results lead us to conclude that several commonly neglected terms are neither especially small nor do they cancel. The way each term contributes to the redistribution, advection, of amplification of vorticity is discussed. In sum, cyclone growth is greater at all levels, especially at low levels, in the full set of terms compared to the QG terms.

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Richard Grotjahn

Abstract

A preliminary investigation into the dynamical effects produced by the tropopause upon a mid-latitude wave cyclone is described. This article describes linear effects since the various structures of a fixed tropopause are examined. In general, the solutions are sensitive to changes in tropopause structure only when they have large amplitude in the tropopause vicinity or the forcing for the problem is significantly altered by the tropopause structure. The forcing is greatest at the bottom boundary and interior tropopause interface. The basic current contains an internal jet. Many characteristic properties of this jet were found in a less sophisticated antecedent study where the velocity maximum occurred at the top boundary. This research forms the basis for future inquiry into nonlinear tropopause dynamics.

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Richard Grotjahn

Abstract

The properties of wavelike eddies imbedded in zonal flows containing vertical and horizontal shear are examined via an analytical model of a midlatitude cyclone. The model combines and extends some work by several previous investigators. Perturbation methods are used to formulate and solve this model. A transformation to geostrophic coordinates is employed that includes some ageostrophic effects and additional ageostrophic terms are retained after scaling the primitive equations. The zonal flows are chosen to model conditions observed in the atmosphere during incipient wave-cyclone development. Solutions grow due to barotropic and (primarily) baroclinic instability of the zonal flow.

The stability, structure and energetics of some solutions are discussed. The lowest order solutions are in basic agreement with several previous studies. The effects of the intensity and vertical structure of the prescribed model thermal front are examined in a consistent fashion. As. the intensity of the front increases, the growth rate increases for most wavenumbers. As the meridional width of the east-west aligned frontal zone diminishes, 1) the most unstable wavelength shifts to shorter wavelengths, 2) the fastest moving wave shifts to longer wavelengths and 3) the meridional scale of the eddy decreases proportionally. The amplitude is increased in the vicinity of the front. The phase of the eddy pressure field is changed by the front in two ways: 1) barotropically unstable horizontal tilts are introduced and 2) the westward tilt with height is decreased in the upper region and increased in the lowest part by the horizontal shear. The energy conversions in these experiments reveal that the two instability mechanisms inhibit each other. This occurs because the two mechanisms are not independent. The ageostrophic terms 1) introduce meridional asymmetry into the solution, 2) reduce the growth rate and phase, speed and 3) tend to form a jet in a mean zonal flow that is initially only a function of height. Like the ageostrophic terms, the nonlinear distortion caused by the coordinate transformation improves the comparison between the model solutions and observed cyclones.

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Richard Grotjahn

Abstract

The observed vertical structures of the trough axes for 27 extratropical cyclones are presented. This study is motivated by results from a simple theoretical model. Two observing times during the cyclone life cycle are shown: prior to development and during the “mature” but still amplifying stage. Prior to development, upper and lower troughs are present and separate, each has little or no tilt, the upper one is typically prominent down to 4-km elevation, and the separation between the lower and the upper features varies depending on where the approaching upper trough happens to be at the observing time. At the mature stage, upper and lower features are connected, a uniform tilt typically develops through the entire troposphere, the tilt is typically due west with height, and the tilt may have a preferred slope. An empirical orthogonal function (EOF) analysis finds that two modes account for more than 97% of the variance. The equivalent barotropic EOF has the most variance by far, though the fractional amount diminishes over time as this EOF also extends further downward. The first baroclinic EOF increases fractional amplitude in compensation.

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Richard Grotjahn and Ghislain Faure

Abstract

Extraordinary weather events in the Sacramento, California, region are examined using a simple compositing technique. The extraordinary events identified are uncommon and the worst of their kind, but not necessarily severe. While the criteria outlined herein are drawn from Sacramento weather station data, the identified events are extraordinary elsewhere over much, if not all, of California’s Central Valley. Several types of extraordinary events are highlighted, including the hardest freezes, heaviest prolonged rain events, longest-duration fog, and worst heat waves (onset and end) in a 21-yr period. Bootstrap resampling establishes the statistical significance of features on the composite maps. The composite maps with statistically significant features highlighted allow a forecaster to search for key features in forecast maps that coexist with or that precede an extraordinary weather event. Local- and regional-scale extraordinary events have larger-scale signatures that can be traced back in time. Many of these features are intuitive and known to local forecasters (and that provides a check upon the methodology used here). However, some features appear to be unexpected. For example, a ridge (in height and thermal fields) over the southeastern United States generally occurs prior to the worst heat waves and hardest freezes. Some features appear to exhibit the theoretical concept of downstream development. Several extraordinary weather types are preceded by a ridge either over Alaska (hardest freezes and heaviest prolonged rain) or just west of Alaska (worst heat waves). While the Alaskan ridge passes a significance test, the presence of other features (such as the southeastern ridge) determines what, if any, extraordinary event occurs near Sacramento. However, a feature that passes the significance test for the composite might not occur in every member of a given extraordinary event. The height and thermal patterns over the West Coast and North Pacific are similar for summer’s worst heat waves and winter’s longest-duration fog: both types of events are preceded by a trough in the eastern mid-Pacific.

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Richard Grotjahn and Rui Zhang

Abstract

How does extreme cold air reach the California Central Valley (CCV) and most of the U.S. west coast? This question is answered using composite patterns for the 10 coldest cold air outbreaks (CAOs) to reach the CCV during 1979–2013. While unusually cold air over California occurs in all events by design, how it arrives there is complicated and varies. The only other feature present in all events for several days prior to CAO onset is unusually strong surface high pressure in and south of the Gulf of Alaska. This high has low-level cold air on its west side and a deep layer of cold air moving southward on its east side. Cold air aloft flows parallel to the North American west coast and sinks as it approaches the CCV. Farther west, warm advection builds a ridge aloft. The large-scale meteorological pattern (LSMP) is equivalent barotropic. The LSMP’s ridge over Alaska, trough near California, and ridge over the southeastern United States appear in all cases by onset and resemble the Pacific–North American teleconnection pattern. Cross sections show cold air flowing from the continental interior consistent with a strong pressure gradient created by extreme cold in the continental interior. Where and when the interior cold and surface flow occurs varies between events. A geopotential height trough associated with that cold air aloft passes over the CCV before onset fostering sinking behind that is reinforced by the cold air advection below. Although sinking, as a locally defined anomaly, the cold intensifies as it migrates from the polar region to the climatologically warmer CCV.

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Richard Grotjahn and Cris Castello

Abstract

An earlier article deduced a doubling of the scale of the sea level pressure pattern for lows as they developed in the North Pacific. Scale here refers to horizontal extent of the low. This study uses a different technique to estimate scale change in the upper troposphere. The prior study used wavelets; here circular averaging is used on several fields, with primary emphasis on the geostrophic kinetic energy (gKE) field.

The technique herein confirms the earlier result that sea level pressure (SLP) scale increases. When applied to the 300-hPa level, the trough extent does not change scale significantly. The average scale has radius of about 1200 km at sea level and 1700 km at 300 hPa. During development the average radius of maximum gKE changes little at the surface but decreases at upper levels. The maximum gKE is typically located 600–1100 km from the 300-hPa low center, 450–650 km from the SLP low center. Composite maps of gKE are shown during different stages in cyclone development at both levels. Consistency between the results presented here and the conventional view of jet streak migration around an upper low is mentioned. Some implications for theoretical work are mentioned.

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Richard Grotjahn and Ching-Hua Wang

Abstract

The linear instability of a zonal flow passing over a large-scale mountain, having one of two orientations and two shapes, is considered via an eigenvalue/eigenvector problem using spherical coordinates in a quasi-geostrophic model. Topography enters only as slope flow in the bottom boundary condition. All variables are expressed using orthogonal functions in three dimensions. Realistic (variable) static stability is applied in the study.

The topography reduces the growth rates primarily by reducing the baroclinic energy conversion. For the two mountain orientations investigated here, when the ridge is oriented east–west the growth rates are reduced more than when the orientation is north-south. The highs and lows (at the surface) are deflected northward by the topography which places them where the basic flow vertical shear is less for a longer time when the ridge is oriented east–west. The deflection effects the eddy heat fluxes by increasing the meridional velocity on the southeastern side of each eddy. This increases the meridional heat fluxes, making the baroclinic conversion (from zonal mean to eddy available potential energy) largest on the upslope side. The eddy vertical velocities are also enhanced on the upslope (west) side of the ridge. This means that the conversion from eddy available potential to eddy kinetic energy is also larger there. On the downslope side the heat fluxes are usually reduced. In most cases the topography deflects the storm track more in the lower troposphere than in the upper troposphere. In a few cases, the topography causes the upper and lower level eddies to move at different rates and to be deflected in different directions; the phase relationship between temperature and pressure is altered such that negative baroclinic conversion occurs on the downslope side of the mountain.

Accurate solutions require even higher horizontal resolution than anticipated by earlier studies. But, much economy is gained by adopting a “parallelogramic” truncation, which uses more meridional than zonal wave-numbers.

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