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Leif M. Swenson and Richard Grotjahn

Abstract

Extreme precipitation events have major societal impacts. These events are rare and can have small spatial scale, making statistical analysis difficult; both factors are mitigated by combining events over a region. A methodology is presented to objectively define “coherent” regions wherein data points have matching annual cycles. Regions are found by training self-organizing maps (SOMs) on the annual cycle of precipitation for each grid point across the contiguous United States (CONUS). Using the annual cycle for our intended application minimizes problems caused by consecutive dry periods and localized extreme events. Multiple criteria are applied to identify useful numbers of regions for our future application. Criteria assess these properties for each region: having many more events than experienced by a single grid point, good connectedness and compactness, and robustness to changing the number of regions. Our methodology is applicable across datasets and is tested here on both reanalysis and gridded observational data. Precipitation regions obtained align with large-scale geographical features and are readily interpretable. Useful numbers of regions balance two conflicting preferences: larger regions contain more events and thereby have more robust statistics, but more compact regions allow weather patterns associated with extreme events to be aggregated with confidence. For 6-h precipitation, 12–15 regions over the CONUS optimize our metrics. The regions obtained are compared against two existing region archetypes. For example, a popular set of regions, based on nine groups of states, has less coherent regions than defining the same number of regions with our SOM methodology.

Open access
Yun-Young Lee and Richard Grotjahn

Abstract

California 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 west. The second cluster has the ridge in place for several days prior to extreme CCV heat, but this ridge is located farther north, with heat anomaly over the northwestern United States. This ridge expands south as air parcels at midtropospheric levels descend from the northwest while lower-level parcels over land tend to bring hot air from directions ranging from the hot area to the northeast to the desert areas to the southeast. These two types reveal unexpected dynamical complexity, hint at different remote associations, and expand the assessment needed of climate models’ simulations of these heat waves.

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Richard Grotjahn, Roderick Pedersen, and Joseph Tribbia

Abstract

Normal-mode and nonmodal growth are investigated using initial value models. The initial value problems for the Eady and a generalized Eady model (the G model) are solved with no friction and with both Ekman and interior friction. The nonmodel growth is described as either a superposition of eigenmodes or as a transfer between the “thermal” and relative vorticity parts of quasigeostrophic potential vorticity. When all the eigen-modes are neutral, the growth rate (σH>) of enstrophy is zero, though the growth rate of energy (σE>) and amplitude (σL>) may be positive. For an initial condition having large upstream tilt and constant amplitude, a period of large initial growth in the energy and amplitude is followed by either oscillatory growth and decay (when all eigenmodes are neutral) or asymptotes to a rate given by the most unstable normal mode. In Part I, the authors show that interior friction strongly damps the continuum eigenmodes; however, nonmodal growth can still be significant even when interior friction is present in the Eady model. In the more realistic G model, less overlap between the eigenmodes is found and consequently the nonmodal growth by superposition is reduced compared to the Eady model studied previously by others.

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Richard Grotjahn and James J. O'Brien

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 where the analysis may have to be limited. Only the long waves, i.e., those resolved by many grid points, are represented with any reasonable accuracy.

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Richard Grotjahn, Min Chen, and Joseph Tribbia

Abstract

The eigenvalue problems for the original Eady model and a modified Eady model (the G model) are examined with no friction, Ekman friction only, and both Ekman and interior friction. When both Ekman and interior friction are included in the models, normal modes show little additional change when compared to the case with Ekman friction only, whereas the relevant “continuum modes” have large negative growth rates. Interior friction has a much greater effect on the continuum modes than on the normal modes because inviscid continuum modes have a delta-function vertical profile of potential vorticity q. In contrast, normal modes have much smoother profiles of q in the interior. Streamfunction profiles for the continuum modes are notably different in the two models. The continuum modes in the more realistic G model have sharp peak amplitudes that are not as broad in the vertical as in the Eady model.

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Richard Grotjahn and Robert M. Chervin

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.

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Richard Grotjahn, Daniel Hodyss, and Cris Castello

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.

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Abhishekh Kumar Srivastava, Richard Grotjahn, Paul Aaron Ullrich, and Mojtaba Sadegh

Abstract

Traditional multimodel methods for estimating future changes in precipitation intensity, duration, and frequency (IDF) curves rely on mean or median of models’ IDF estimates. Such multimodel estimates are impaired by large estimation uncertainty, shadowing their efficacy in planning efforts. Here, assuming that each climate model is one representation of the underlying data generating process, i.e., the Earth system, we propose a novel extension of current methods through pooling model data: (i) evaluate performance of climate models in simulating the spatial and temporal variability of the observed annual maximum precipitation (AMP), (ii) bias-correct and pool historical and future AMP data of reasonably performing models, and (iii) compute IDF estimates in a nonstationary framework from pooled historical and future model data. Pooling enhances fitting of the extreme value distribution to the data and assumes that data from reasonably performing models represent samples from the “true” underlying data generating distribution. Through Monte Carlo simulations with synthetic data, we show that return periods derived from pooled data have smaller biases and lesser uncertainty than those derived from ensembles of individual model data. We apply this method to NA-CORDEX models to estimate changes in 24-h precipitation intensity–frequency (PIF) estimates over the Susquehanna watershed and Florida peninsula. Our approach identifies significant future changes at more stations compared to median-based PIF estimates. The analysis suggests that almost all stations over the Susquehanna and at least two-thirds of the stations over the Florida peninsula will observe significant increases in 24-h precipitation for 2–100-yr return periods.

Open access
Gabriele Messori, Rodrigo Caballero, Freddy Bouchet, Davide Faranda, Richard Grotjahn, Nili Harnik, Steve Jewson, Joaquim G. Pinto, Gwendal Rivière, Tim Woollings, and Pascal Yiou
Open access