Richard Grotjahn

North American extreme temperature events and related large scale meteorological patterns: A review of statistical methods, dynamics, modeling, and trends

Abstract The objective of this paper is to review statistical methods, dynamics, modeling efforts, and trends related to temperature extremes, with a focus upon extreme events of short duration that affect parts of North America. These events are associated with large scale meteorological patterns (LSMPs). The statistics, dynamics, and modeling sections of this paper are written to be autonomous and so can be read separately. Methods to define extreme events statistics and to identify and connect LSMPs to extreme temperature events are presented. Recent advances in statistical techniques connect LSMPs to extreme temperatures through appropriately defined covariates that supplement more straightforward analyses. Various LSMPs, ranging from synoptic to planetary scale structures, are associated with extreme temperature events. Current knowledge about the synoptics and the dynamical mechanisms leading to the associated LSMPs is incomplete. Systematic studies of: the physics of LSMP life cycles, comprehensive model assessment of LSMP-extreme temperature event linkages, and LSMP properties are needed. Generally, climate models capture observed properties of heat waves and cold air outbreaks with some fidelity. However they overestimate warm wave frequency and underestimate cold air outbreak frequency, and underestimate the collective influence of low-frequency modes on temperature extremes. Modeling studies have identified the impact of large-scale circulation anomalies and land–atmosphere interactions on changes in extreme temperatures. However, few studies have examined changes in LSMPs to more specifically understand the role of LSMPs on past and future extreme temperature changes. Even though LSMPs are resolvable by global and regional climate models, they are not necessarily well simulated. The paper concludes with unresolved issues and research questions.

Some Inaccuracies in Finite Differencing Hyperbolic Equations

Abstract The errors introduced by the use of various numerical schemes for solving mathematical models have generally been only vaguely determined previously by numerical modelers. A method for a more quantitative analysis of the inaccuracies is outlined. The error associated with some simple schemes is analyzed for several linear hyperbolic systems representative of typical problems in meteorology and oceanography. Results of previous studies of phase velocity inaccuracies are confirmed and form a basis for an extension of the analysis to group velocities. Significant angular and magnitude errors are found in the group velocity. Directional errors of 180° are found for some waves. Since the group velocity is the propagation speed of the energy, such errors may have severe consequences in a numerical model. When analysis was made of complex systems of equations, results found for simple systems reappeared. Thus, studies of simple systems may provide useful indications of behavior in more complex problems ...

Animated Graphics in Meteorological Research and Presentations

For the past two years, the authors have been involved in the production of computer-animated movies at the National Center for Atmospheric Research (NCAR). The computer- generated frames are high-quality graphs of two- and three-dimensional variables featuring trajectories, contour lines, shading patterns, or three-dimensional surfaces (viewed in perspective). The original application was for comparing the FGGE dataset motion fields with satellite film loops. Applications have broadened to include model-generated data. Computer animation is particularly useful for efficiently previewing and presenting large quantities of data. Experiments with stereo images have also been made.

Do Frontal Cyclones Change Size? Observed Widths of North Pacific Lows

Abstract Wavelet transforms in the longitudinal and latitudinal directions are applied to sea level pressure data for 12 extratropical cyclones. Each low is tracked over time from a stage of small amplitude to a stage of large amplitude. The wavelet transform provides a quantitative, localized estimate of the size of the low pressure. Separate one-dimensional transforms are taken in the longitudinal and latitudinal directions; these are averaged to reduce scale variations created as circular asymmetries rotate around a low center. On average, the size of the lows increases such that the diameter doubles over a 4-day period. These results pass a standard “f test” with greater than 99% confidence. Some implications for theoretical studies are included.

A Study of Frontal Cyclone Surface and 300-hPa Geostrophic Kinetic Energy Distribution and Scale Change

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 le...

California Central Valley Summer Heat Waves Form Two Ways

AbstractCalifornia Central Valley (CCV) heat waves are grouped into two types based on the temporal and spatial evolution of the large-scale meteorological patterns (LSMPs) prior to onset. The k-means clustering of key features in the anomalous temperature and zonal wind identifies the two groups. Composite analyses show different evolution prior to developing a similar ridge–trough–ridge pattern spanning the North Pacific at the onset of CCV hot spells. Backward trajectories show adiabatic heating of air enhanced by anomalous sinking plus horizontal advection as the main mechanisms to create hot lower-tropospheric air just off the Northern California coast, although the paths differ between clusters.The first cluster develops the ridge at the west coast on the day before onset, consistent with wave activity flux traveling across the North Pacific. Air parcels that arrive at the maximum temperature anomaly (just off the Northern California coast) tend to travel a long distance across the Pacific from the ...

Vorticity Equation Terms for Extratropical Cyclones

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 s...

Linearized Tropopause Dynamics and Cyclone Development

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.

Cyclone Development along Weak Thermal Fronts

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 incre...

Composite Trough Evolution of Selected West Pacific Extratropical Cyclones

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 frac...