Michael B. Richman

On the Application of Cluster Analysis to Growing Season Precipitation Data in North America East of the Rockies

Abstract Cluster analysis (CA) has been applied to geophysical research for over two decades although its popularity has increased dramatically over the past few years. To date, systematic methodological reviews have not appeared in geophysical literature. In this paper, after a review of a large number of applications on cluster analysis, an intercomparison of various cluster techniques was carried out on a well-studied dataset (7-day precipitation data from 1949 to 1987 in central and eastern North America). The cluster methods tested were single linkage, complete linkage, average linkage between groups, average linkage within a new group, Wards method, k means, the nucleated agglomerative method, and the rotated principal component analysis. Three different dissimilarity measures (Euclidean distance, inverse correlation, and theta angle) and three initial partition methods were also tested on the hierarchical and nonhierarchical methods, respectively. Twenty-two of the 23 cluster algorithms yielded na...

Climatic Pattern Analysis of Three- and Seven-Day Summer Rainfall in the Central United States: Some Methodological Considerations and a Regionalization

Abstract This paper presents the results of climatic pattern analyses of three- and seven-day summer (May–August) rainfall totals for the central United States. A range of eigenvectorial methods is applied to 1949–80 data for a regularly spaced network of 402 stations that extends from the Rocky to the Appalachian Mountains and from the Gulf Coast to the Canadian border. The major objectives are to quantitatively assess the sensitivity of eigenvectorial results to several parameters that have hitherto been the subject of considerable qualitative concern, and to identify the potential applications of those results. The entire domain variance fractions cumulatively explained by a) the first 10 correlation-based unrotated Principal Components (PCs) and b) the 10 orthogonally rotated (VARIMAX criterion) PCs derived from them are identical for the same data. They vary between 35–47 percent depending on the data time scale and form, being higher for seven- than three-day totals and further enhanced when those t...

Observed Nonlinearities of Monthly Teleconnections between Tropical Pacific Sea Surface Temperature Anomalies and Central and Eastern North American Precipitation

Abstract Most investigations of relationships between tropical Pacific sea surface temperature anomaly (SSTA) events and regional climate patterns have assumed the teleconnections to be linear, whereby the climate patterns associated with cold SSTA events are considered to be similar in structure and morphology but opposite in sign to those linked to warm SSTA events. In contrast, and motivated by early evidence of nonlinearity in the above regard, this study identifies characteristic (i.e., composite) calendar monthly central and eastern North American precipitation patterns separately for warm and cold SSTA events in different regions of the tropical Pacific (central, eastern, west-central“horseshoe,” far western) identified through principal component analysis. The precipitation anomaly patterns are computed from an approximately 1° lat–long set of monthly station data for 1950–92. Their robustness and nonlinearity are established using local, regional, and field statistical significance tests and a va...

Spatial Coherence of Monthly Precipitation in the United States

Abstract Factor analysis and an orthogonal rotation to the varimax criterion are used to identify the synoptic-scale regions of the United States over which monthly precipitation amounts show the greatest spatial coherence. The regions are consistent with previously documented cyclone trajectories. The seasonal continuity of the patterns is seriously disrupted only in summer. Regional values of the Palmer Drought Index correlate most highly with the precipitation pattern amplitudes averaged over 13–18 months in the central United States and over 7–9 months along the East and West Coasts. Associations between the regional precipitation and local 700 mb height parameters are strongest with the geostrophic wind components in the Ohio Valley and Great Lakes regions, and with geopotential height and vorticity in the Northern Plains. Sea level pressure anomalies over broad areas of the Atlantic and Pacific Oceans are associated with regional precipitation in the central and eastern United States, while the corr...

Interannual Variability of Tropical Cyclones in the Australian Region: Role of Large-Scale Environment

Abstract This study investigates the role of large-scale environmental factors, notably sea surface temperature (SST), low-level relative vorticity, and deep-tropospheric vertical wind shear, in the interannual variability of November–April tropical cyclone (TC) activity in the Australian region. Extensive correlation analyses were carried out between TC frequency and intensity and the aforementioned large-scale parameters, using TC data for 1970–2006 from the official Australian TC dataset. Large correlations were found between the seasonal number of TCs and SST in the Nino-3.4 and Nino-4 regions. These correlations were greatest (−0.73) during August–October, immediately preceding the Australian TC season. The correlations remain almost unchanged for the July–September period and therefore can be viewed as potential seasonal predictors of the forthcoming TC season. In contrast, only weak correlations (<+0.37) were found with the local SST in the region north of Australia where many TCs originate; these ...

An Observational Study of Derecho-Producing Convective Systems

Abstract This study identifies the common large-scale environments associated with the development of derecho- producing convective systems (DCSs) from a large number of events. Patterns are identified using statistical clustering of the 500-mb geopotential heights as guidance. The majority of the events (72%) fall into three main patterns that include a well-defined upstream trough (40%), a ridge (20%), and a zonal, low-amplitude flow (12%), which is identified as an additional warm-season pattern. Consequently, the environmental large-scale patterns idealized in past studies only depict a portion of the full spectrum of the possibilities associated with the development of DCSs. In addition, statistics of derecho proximity-sounding parameters are presented relative to the derecho life cycle as well as relative to the forcing for upward motion. It is found that the environments ahead of maturing derechos tend to moisten at low levels while remaining relatively dry aloft. In addition, derechos tend to deca...

Seasonality in the Associations between Surface Temperatures over the United States and the North Pacific Ocean

Abstract Thirty-one years of monthly data are used to evaluate the seasonal dependence of the associations between large-scale temperature anomalies over the United States and the North Pacific Ocean. Both station (grid-point) values and empirical orthogonal functions of temperature are used in the correlative analysis. The North Pacific sea surface temperature (SST) anomalies correlate most highly with temperature fluctuations over the southeastern and the far western states. Correlations with the SST anomalies have opposite signs in the two portions of the United States. The associations with the SST anomalies are independent of season only in the western states. The association involving the southeastern states is strongest during the winter and insignificant during the summer. The pattern of North Pacific SST that correlates most highly with the United States temperature is an east-west SST gradient between the West Coast and 35°N, 160°W. Statistically significant fractions of temperature variance ove...

Euclidean Distance as a Similarity Metric for Principal Component Analysis

Abstract Eigentechniques, in particular principal component analysis (PCA), have been widely used in meteorological analyses since the early 1950s. Traditionally, choices for the parent similarity matrix, which are diagonalized, have been limited to correlation, covariance, or, rarely, cross products. Whereas each matrix has unique characteristic benefits, all essentially identify parameters that vary together. Depending on what underlying structure the analyst wishes to reveal, similarity matrices can be employed, other than the aforementioned, to yield different results. In this work, a similarity matrix based upon Euclidean distance, commonly used in cluster analysis, is developed as a viable alternative. For PCA, Euclidean distance is converted into Euclidean similarity. Unlike the variance-based similarity matrices, a PCA performed using Euclidean similarity identifies parameters that are close to each other in a Euclidean distance sense. Rather than identifying parameters that change together, the r...

Relationships between the Definition of the Hyperplane Width to the Fidelity of Principal Component Loading Patterns

Abstract When applying eigenanalysis, one decision analysts make is the determination of what magnitude an eigenvector coefficient (e.g., principal component (PC) loading) must achieve to be considered as physically important. Such coefficients can be displayed on maps or in a time series or tables to gain a fuller understanding of a large array of multivariate data. Previously, such a decision on what value of loading designates a useful signal (hereafter called the loading “cutoff”) for each eigenvector has been purely subjective. The importance of selecting such a cutoff is apparent since those loading elements in the range of zero to the cutoff are ignored in the interpretation and naming of PCs since only the absolute values of loadings greater than the cutoff are physically analyzed. This research sets out to objectify the problem of best identifying the cutoff by application of matching between known correlation/covariance structures and their corresponding eigenpatterns, as this cutoff point (know...

Pattern analysis of growing season precipitation in Southern Canada

Abstract This paper presents the results of climatic pattern analyses of three‐ and seven‐day summer (May‐August) precipitation totals for southern Canada. A range of eigenvectorial methods is applied to 1949–80 data for a fairly uniform network of 170 stations that extends to the east of the Rockies, to the north of the Great Lakes, and through the St Lawrence Valley. The major objectives are to identify the characteristic spatial patterns of the precipitation (including any dependence on the eigenvectorial model) and to suggest some potential applications of the results. The entire domain variance fraction cumulatively explained by the first eight unrotated Principal Components (PCs), and also the eight orthogonally‐rotated (varimax criterion) PCs derived from them, is approximately 55% for square‐root transformations of both the three‐ and seven‐day totals. The unrotated PC spatial loading patterns possess moderately strong large‐scale (e.g. one‐third to one‐half domain) anomaly features through root 3...