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A Significance Test for Principal Components Applied to a Cyclone Climatology
Abstract
A technique is presented for selection of principal components for which the geophysical signal is greater than the level of noise. By contrasting the application of principal components based upon the covariance matrix and correlation matrix for a given data set of cyclone frequencies, it is shown that the former is more suitable to fitting data and locating the individual variables that represent large variance in the record, while the latter is more suitable for resolving spatial oscillations such as the movement of primary storm tracks.-from Authors
... To distinguish statistically significant patterns from random noise, the significant singular value was tested by the Monte Carlo test. Experiments with Gaussian-distributed random data were repeated 100 times and the singular values at a significance level of 99% were obtained using the method developed by Overland and Preisendorfer [25,26]. The cumulative percentages of variance (Figure 4b) showed that most of the variance was about 80% in the first three modes but that, in the summertime, it was relatively lower, about 60%. ...
... Figure 13. Spatial patterns of the (a-c) FGOALS-f2 and (d-f) pentad DSDM forecasts from the third to fifth pentads of July 2021 (the initial pentad was the last pentad of June 2021 (26)(27)(28)(29)(30). The dotted areas indicate that the TCC passed the 95% significance test. ...
... The Z500 anomalies (Appendix A, Figure A1b) prove that the Z500 anomalies were consistent with the first pattern, although the fourth pattern with a Figure 13. Spatial patterns of the (a-c) FGOALS-f2 and (d-f) pentad DSDM forecasts from the third to fifth pentads of July 2021 (the initial pentad was the last pentad of June 2021 (26)(27)(28)(29)(30). The dotted areas indicate that the TCC passed the 95% significance test. ...
In order to focus on pentad-scale precipitation forecasts, we investigated the coupling relationship between 500 hPa geopotential height (Z500) anomalies and precipitation anomalies using the China Meteorological Administration Global Land Surface ReAnalysis Interim (CRA40/Land) gridded precipitation dataset from 1999 to 2018 and the National Centers for Environmental Prediction 1 reanalysis dataset for Z500. We obtained a dynamical–statistical downscaling model (DSDM) on the pentad scale and used the daily Z500 forecast product for sub-seasonal to seasonal forecasts (15–60 days) of the FGOALS-f2 model as the predictor. Our results showed that pentad-scale prediction of precipitation is the key to bridging the current deficiencies in sub-seasonal forecasts. Compared with the FGOALS-f2 model, the pentad DSDM had a higher skill for prediction of precipitation in China at lead times longer than four pentads throughout the year and of two pentads in the summer months. FGOALS-f2 had excellent precipitation predictability at lead times less than three pentads (15 days), so the proposed pentad DSDM could not perform better than FGOALS-f2 in this period. However, at lead times greater than four pentads, the precipitation prediction scores (such as the anomaly correlation coefficient (ACC), the temporal correlation coefficient (TCC) and the mean square skill score (MSSS)) of the pentad DSDM for the whole of China were higher than those of the FGOALS-f2 model. With the rate of increase ranging from 76% to 520%, the mean ACC scores of pentad DSDM were basically greater than 0.04 after a lead time of five pentads, whereas those of the FGOALS-f2 were less than 0.04. An analysis of the Zhengzhou “720” super heavy rainstorm event showed that the pentad DSDM also had better predictability for the distribution of precipitation at lead times of three pentads than the FGOALS-f2 model for the extreme precipitation event.
... The Earth's magnetic field has been decreasing in strength over the past centuries, being reduced by 10 % over the last 150 years (Olson and Amit, 2006). The geomagnetic field is primarily generated by convective processes within Earth's iron-rich liquid outer core, which act like a dynamo (the geodynamo). ...
... The statistical significance of the obtained modes is assessed by comparing the eigenvalues with those obtained from surrogate data sets with the same properties as the original data sets (Overland and Preisendorfer, 1982). Following Delforge et al. (2022), the surrogates are randomly generated as autoregressive processes of order p, where p is determined independently for each time series to minimize the Bayesian information criterion (BIC) and the coefficient fit on the time series. ...
The motions of the liquid within the Earth's outer core lead to magnetic field variations together with mass distribution changes. As the core is not accessible for direct observation, our knowledge of the Earth’s liquid core dynamics only relies on indirect information sources. Mainly generated by the core dynamics, the surface geomagnetic field provides information about the variations of the fluid motion at the top of the core. The dynamic of the fluid core is also associated with mass distribution changes inside the core and produces gravitational field time fluctuations. By applying several statistical blind source separation methods to both the gravity and magnetic field time series, we investigate the common space–time variabilities. We report several robust interannual oscillations shared by the two observation sets. Among those, a common mode of around 7 years looks very significant. Whereas the nature of the driving mechanism of the coupled variability remains unclear, the spatial and temporal properties of the common signal are compatible with a core origin.
... Furthermore, we only considered observations from pixels offshore of the 2,000 m isobath, so that we could identify offshore areas characterized by large anomalies. Statistically significant EOF modes were identified following Overland and Preisendorfer (1982). ...
The Amazon River is a large source of terrigenous dissolved organic carbon (tDOC) to the Atlantic Ocean. The fate of this tDOC in the ocean remains unclear despite its importance to the global carbon cycle. Here, we used two decades of satellite ocean color to describe variability in tDOC in the Amazon River plume. Our analyses showed that tDOC distribution has a distinct seasonal pattern, reaching northwest toward the Caribbean during high discharge periods, and moving eastward entrained in the North Brazil Current retroflection during low discharge periods. Elevated tDOC content extended beyond the shelfbreak in all months of the year, suggesting that cross‐shelf carbon transport occurs year‐round. Maximum variability was found at the plume core, where seasonality accounted for 40% of the total variance, while interannual variability accounted for 15% of the variance. Our results revealed a seasonal pattern in tDOC removal over the shelf with increased consumption in May when river discharge is high. Anomalies in tDOC removal over the shelf with respect to the seasonal cycle were significantly correlated with anomalies in tDOC concentration offshore of the shelfbreak with a lag of 30–40 days, so that anomalously high inshore tDOC removal was associated with anomalously low tDOC content offshore. This suggests that variability in the offshore transport of tDOC in the Amazon River plume is modulated by interannual changes in tDOC removal over the shelf.
... The eigenvectors of that matrix were considered to be the spatial modes of a sort of "mean" atmospheric pressure disturbance representative of all meteotsunami events. The statistical significance of the modes was estimated using the Monte Carlo method proposed by Overland and Preisendorfer (1982). ...
The high‐frequency sea level oscillations (SLO) associated with meteotsunamis can have hazardous consequences for coastal populations. They are triggered by high‐frequency atmospheric disturbances generating an oceanic response that is amplified mainly by Proudman and harbor resonance. So far, the lack of high‐resolution data had prevented a comprehensive characterization of these atmospheric disturbances, even in an extensively studied “hot spot” as Ciutadella (Balearic Islands). Here, we analyze atmospheric disturbances triggering meteotsunamis in Ciutadella during 2021 using data from an ultra‐dense meteorological network (BalearsMeteo). Atmospheric pressure time series with a sampling rate ≤1 min are used to estimate propagation speed and direction, spectral energy content, and the spatial homogeneity of atmospheric disturbances linked to meteotsunami events. We find that the spatial structure of the disturbances are rather heterogeneous, but the inferred propagation velocities are consistent with the occurrence of Proudman resonance on the continental shelves located upstream of Ciutadella (speeds between 24 and 36 m/s and directions from 210° to 260°). Although during meteotsunami events these velocity estimates undergo some changes both in time and in space, they show two key characteristics: (a) the atmospheric pressure disturbances are mostly non‐dispersive; and (b) the largest SLO are observed when the speed and direction of propagation velocities are more homogeneous in space and time. Nevertheless, an empirical relationship between the analyzed atmospheric features and the SLO amplitudes could not be established. That is, the prediction of meteotsunami amplitudes remains challenging due to the intricate interplay of atmospheric and oceanic processes.
... Hence, pattern values can be viewed as regression coefficients of standardized rainfall on the temporal coefficients (36). On the basis of the Monte Carlo technique (69) and North test (70), the leading modes obtained from the MCA and EOF methods in this study are both well separated from the second mode at a 95% confidence interval. ...
In July to August 2022, Pakistan suffered historic flooding while record-breaking heatwaves swept southern China, causing severe socioeconomic impacts. Similar extreme events have frequently coincided between two regions during the past 44 years, but the underlying mechanisms remain unclear. Using observations and a suite of model experiments, here, we show that the upper-tropospheric divergent wind induced by convective heating over Pakistan excites a barotropic anomalous anticyclone over eastern China, which further leads to persistent heatwaves. Atmospheric model ensemble simulation indicates that this dynamic pathway linking Pakistan flooding and East Asian heatwaves is intrinsic to the climate system, largely independent of global sea surface temperature forcing. This dynamic connection is most active during July to August when convective variability is large over Pakistan and the associated divergent flow excites barotropic Rossby waves that propagate eastward along the upper troposphere westerly waveguide. This robust waveguide and the time delay offer hopes for improved subseasonal prediction of extreme events in East Asia.
... PCA was performed using covariance data matrices to reduce dimensionality. We examined the variance of each mode using several selection criteria, including the scree test (Cattell 1966), Kaiser's criterion, and rule N (Overland and Preisendorfer 1982;Termonia 2001), and chose the subspace dimension (m) (Jassby 2000). The loading factors were rotated using varimax rotation after PCA (Everitt, 2006). ...
... Each of the 10,000 random map scores consisted of 42 soil observation values summed from the score matrix. The 95th percentile of these data was then selected as a significance threshold, an approach commonly used in related statistical tests to distinguish signal from noise via data resampling (Overland & Preisendorfer, 1982). This threshold and the observed map score were then used to test the null hypothesis. ...
A soil‐landscape conceptual model developed in the Rhode River subestuary of Maryland was applied to create a soil survey for the adjacent West River subestuary. The survey for the West River subestuary was completed before samples were collected there to evaluate the soil‐landscape conceptual model used to generate the soil survey. The West River subestuary was then sampled along transects that crossed soil map units to compare observed soil taxa with predicted soil taxa. Observed transect samples were classified and scored based on their similarity to predicted taxa in soil map units. These data were resampled via a bootstrapping method to determine if the predictions of the West River subestuary soil survey were significantly different from random predictions. Significant information was provided by the survey, and therefore by the soil‐landscape conceptual model used to generate it.
... EOFs are computed using the 3-month running mean anomaly time series in the 1° latitude boxes. To determine the statistically significant EOF modes for each data set, we used the N-rule approach outlined by Overland and Preisendorfer (1982) to estimate those eigenvalues for which the geophysical signal exceeds the level of noise within the data. In both the Northern and Southern Hemisphere domains, the first seven modes of SST frontal probability and the first two modes of SLA were significant. ...
Along the west coasts of North, Central, and South America, sea surface temperature (SST) fronts are important for circulation dynamics and promoting biological activity. Prevailing equatorward winds during summer results in offshore Ekman transport and upwelling along the coast, where fronts often form between cold, upwelled water and warmer offshore waters. The interannual variability in winds, coastal upwelling, sea level anomalies, and SST in these regions have been linked to the El Niño‐Southern Oscillation (ENSO), however SST fronts have received less attention. Here, we investigate the interannual variability of SST fronts off North, Central, and South America using satellite SST data spanning 1982–2018. Anomalies of fronts within 0–300 km offshore indicate interannual variability that coincides with ENSO events in most regions. Frontal activity generally decreases during El Niño events and increases during La Niña events. The decrease in fronts off Peru and Chile during El Niño coincides with the seasonal peak in frontal activity, while off the United States the decrease occurs when frontal activity is at a seasonal minimum. We also utilized satellite measurements of wind stress and sea level anomaly to investigate how ENSO oceanic and atmospheric forcing mechanisms affect frontal activity. Decreases in frontal activity during El Niño events are largely due to oceanic forcing (i.e., coastal Kelvin waves) off Central and South America and to both oceanic forcing and atmospheric teleconnections off the United States. This study furthers our understanding of the influence of ENSO on coastal upwelling regions in the eastern Pacific Ocean.
... To make sure the EOF modes of PW and SVP are distinguished from the noise signal, the Monte Carlo technique [56] is used to test the significance of the first three modes. ...
Water vapor (WV) is a vital basis of water and energy cycles and varies with space and time. When researching the variations of moisture in the atmosphere, it is intuitive to think about the total WV of the atmosphere column, precipitable water (PW). It is an element that needs high-altitude observations. A surface quantity, surface WV pressure (SVP), has a close relationship to PW because of the internal physical linkage between them. The stability of their linkage at climatic scales is verified using monthly mean data from 1979 to 2021, while studies before mainly focused on daily and annual cycles in local areas. The consistency of their variations is checked with three reanalysis datasets from three angles, the interannual variations, the long-term trends, and the empirical orthogonal function (EOF) modes. Results show that the interannual correlation of SVP and PW can reach a level that is quite high and are significant in most areas, and the weak correlation mainly exists over low-latitude oceans. The long-term trends, as well as the first EOF modes of these two quantities, also show that their variations are consistent, with spatial correlation coefficients between the long-term trends of two variables that are generally over 0.6, but specific differences appearing in some regions including the Tropical Indian Ocean and Middle Africa. With the correspondence of PW and SVP, the variations of total column WV can be indicated by surface elements. The correspondence is also meaningful for the analysis of the co-variation in total column vapor and temperature. For example, we could research the relations between SVP and air temperature, and they can reflect the co-variance of total column vapor and near-surface air temperature, which can avoid analyzing the relation between column-integrated moisture content and surface air temperature directly.
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