Propagating Annular Modes: Empirical Orthogonal Functions, Principal Oscillation Patterns, and Time Scales

Results from a control integration and time-dependent greenhouse warming experiments performed with a coupled ocean-atmosphere model are analysed in terms of their signal-to-noise properties. The aim is to illustrate techniques for efficient description of the space-time evolution of signals and noise and to identify potentially useful components of a multivariate greenhouse-gas “fingerprint”. The three 100-year experiments analysed here simulate the response of the climate system to a step-function doubling of CO2 and to the time-dependent greenhouse-gas increases specified in Scenarios A (“Business as Usual”) and D (“Draconian Measures”) of the Intergovernmental Panel on Climate Change (IPCC). If signal and noise patterns are highly similar, the separation of the signal from the natural variability noise is difficult. We use the pattern correlation between the dominant Empirical Orthogonal Functions (EOFs) of the control run and the Scenario A experiment as a measure of the similarity of signal and noise patterns. The EOF 1 patterns of signal and noise are least similar for near-surface temperature and the vertical structure of zonal winds, and are most similar for sea level pressure (SLP). The dominant signal and noise modes of precipitable water and stratospheric/tropospheric temperature contrasts show considerable pattern similarity. Despite the differences in forcing history, a highly similar EOF 1 surface temperature response pattern is found in all three greenhouse warming experiments. A large part of this similarity is due to a common land-sea contrast component of the signal. To determine the degree to which the signal is contaminated by the natural variability (and/or drift) of the control run, we project the Scenario A data onto EOFs 1 and 2 of the control. Signal contamination by the EOF 1 and 2 modes of the noise is lowest for near-surface temperature, a situation favorable for detection. The signals for precipitable water, SLP, and the vertical structure of zonal temperature and zonal winds are significantly contaminated by the dominant noise modes. We use cumulative explained spatial variance, principal component time series, and projections onto EOFs in order to investigate the time evolution of the dominant signal and noise modes. In the case of near-surface temperature, a single pattern emerges as the dominant signal component in the second half of the Scenario A experiment. The projections onto EOFs 1 and 2 of the control run indicate that Scenario D has a large common variability and/or drift component with the control run. This common component is also apparent between years 30 and 50 of the Scenario A experiment, but is small in the 2 × CO2 integration. The trajectories of the dominant Scenario A and control run modes evolve differently, regardless of the basis vectors chosen for projection, thus making it feasible to separate signal and noise within the first two decades of the experiments. For Scenario D it may not be possible to discriminate between the dominant signal and noise modes until the final 2–3 decades of the 100-year integration.

Analytic results are obtained for the mean and covariance structure of an idealized zonal jet that fluctuates in strength, position, and width. Through a systematic perturbation analysis, the leading empirical orthogonal functions (EOFs) and principal component (PC) time series are obtained. These EOFs are built of linear combinations of basic patterns corresponding to monopole, dipole, and tripole structures. The analytic results demonstrate that in general the individual EOF modes cannot be interpreted in terms of individual physical processes. In particular, while the dipole EOF (similar to the leading EOF of the midlatitude zonal mean zonal wind) describes fluctuations in jet position to leading order, its time series also contains contributions from fluctuations in strength and width. No simple interpretations of the other EOFs in terms of strength, position, or width fluctuations are possible. Implications of these results for the use of EOF analysis to diagnose physical processes of variability are discussed.

<p>Analogies between similar past forecasts, measurements, or analyses are a potentially useful tool when the training dataset is long enough, thus enabling an adequate identification of true analogs. Reducing the number of degrees of freedom in the matching procedure makes the analog-based method an excellent candidate for point-based post-processing. However, accurate forecasts at remote locations are used to drive many user-specific applications (e.g., road temperature forecasts along an entire roadway or wind speed for windfarms). For that reason, besides the point-based post-processing for the measuring sites, there is also an increasing demand for gridded (2D) products. The latter is a direct motivation for the adaptation of analog-based method to produce gridded output based on an analysis.</p><p>In this work, the control member of the ECMWF ensemble forecast is used as a raw forecast as input to the analog method, whereas the gridded INCA analysis fields are used similar to the observations in the point-based analog approach. All experiments use wind speed and direction variables as predictors, normalized by standard deviation. The domain is defined by ECMWF resolution and INCA domain size, covering Austria. The first experiment (EX1) is based on the simplest transfer from point-based to gridded products: treating every grid point as an independent location. Alternatively, an average error on the entire field is used to choose the most similar historical field (EX2). The latter generates comparable results to the EX1 when using training datasets of the same length. In addition to these experiments, a simplification of the procedure for choosing the best analogs using empirical orthogonal functions (EOF) is also tested (EX3). The training data is used to calculate EOFs for EX3, and training is thus saved as EOFs and corresponding principal components (PCs) time series. Results show that using only a few EOFs might capture the majority of the variance in the training. The best match to the current raw forecast is determined using PCs. Even though EX3 is not as skillful as EX1 and EX2, the approach using EOFs is notably more computationally efficient. For that reason, it is possible to include longer training than for EX1 and EX2. Moreover, the setup can be further optimized to improve results (e.g., increasing the number of predictors or implementing a predictor-weighting strategy), which is a natural next step in future work.</p>

The role of El Nino/Southern Oscillation (ENSO) and the mechanism through which ENSO influences the precipitation variability over northwest India and the adjoining (NWIA) region is well documented. In this study, the relative role of North Atlantic Oscillation (NAO)/Arctic Oscillation (AO) and ENSO in modulating the Asian jet stream in the Northern Hemisphere winter and their relative impact on the precipitation variability over the region have been estimated through analysis of observed data. It is seen that interannual variations of NWIA precipitation are largely influenced by ENSO. An empirical orthogonal function (EOF) analysis has been carried out to understand dominant modes of interannual variability of zonal wind at 200 hPa of the Northern Hemisphere. The EOF-1 pattern in the tropical region is similar to that of an ENSO pattern, and the principal component (PC) time series corresponds to the ENSO time series. The EOF-2 spatial pattern resembles that of NAO/AO with correlation of PC time series with AO and NAO being 0.74 and 0.62, respectively. The precipitation anomaly time series over the region of interest has marginally higher correlation with the PC-2 time series as compared to that of PC-1. Regression analysis of precipitation and circulation parameters indicates a larger contribution of the second mode to variability of winds and precipitation over the NWIA. Moisture transport from the Arabian Sea during the active phase of NAO/AO and the presence of a cyclonic anomaly lead to higher precipitation over the NWIA region.

This study investigates the variability and predictability of snow depth anomalies over the Eurasian continent at the end of winter, as represented in 12 ensembles of General Circulation Model simulations performed at the European Centre for Medium‐Range Weather Forecasts. Each ensemble includes nine integrations performed with the same prescribed sea surface temperature, but started from time‐lagged initial conditions. An empirical orthogonal function (EOF) analysis shows that the leading EOF of Eurasian snow depth in March has a zonally‐oriented dipole structure, with a band of positive anomalies covering northern Europe and Siberia, and negative anomalies over central Europe, the Himalayas and north China. A significant relationship is found between the positive/negative phase of this snow‐depth anomaly and warm/cold El Niño Southern Oscillation events. The positive phase of the snow‐depth EOF1 is associated with a wintertime circulation characterized by a strengthening of the westerly winds over Europe and Siberia; in the upper troposphere, this westerly anomaly is accompanied by negative zonal wind anomalies over Eurasia around 30‐40°N and positive zonal wind anomalies between the equator and 25°N over Africa and south‐east Asia. A good degree of predictability is found in the snow‐related circulation anomalies; considering 500‐hPa height, 850‐hPa zonal wind and 200‐hPa zonal wind, the interannual variations of the ensemble‐mean fields show a correlation of 48%, 56% and 65% (respectively) with the corresponding observed anomalies over the eastern half (0° to 180° E) of the northern hemisphere. The tropical component of the zonal wind anomaly associated with snow‐depth EOF1 is strongly predictable; it shows a marked persistence from winter to the early summer, and affects the large‐scale circulation over south Asia in the early and central periods of the monsoon season.

An efficient data processing approach for frequency modulated thermal wave imaging for inspection of steel material

We study the two primary modes of variability associated with the East Asian summer monsoon, as identified using a multivariate Empirical Orthogonal Function (EOF) analysis. The second mode is shown to be related to changes in intensity of the South Asian High at 100 hPa while, consistent with previous work, the first mode is associated with an index for the shear vorticity of the 850 hPa zonal wind over the monsoon region. We show that a linear, dry dynamical model, when driven by the diabatic heating anomalies associated with each mode, can reproduce many of the anomalous circulation features, especially for the first EOF and in the lower troposphere. The model results indicate the importance of diabatic heating anomalies over the tropical Indian Ocean in the dynamics of both modes, especially EOF-1, and illustrate the role of local diabatic feedback for intensifying the circulation anomalies; in particular, the subtropical anticyclonic anomalies that are found in the positive phase of both modes, and the circulation anomaly associated with the Meiyu/Changma/Baiu rain band. A running cross-correlation analysis shows that the second EOF is consistently linked to both the decaying and the onset phase of El Nino/Southern Oscillation (ENSO) events throughout the study period (1958-2001). We attribute the connection in the onset phase to zonal wind anomalies along the Equator in the west Pacific associated with this mode. On the other hand, a link between the first EOF and ENSO is found only in the post-1979 period. We note also the role of sea-surface temperature anomalies in the tropical Indian Ocean in the dynamics of EOF-1, and a link to the variability of the Indian summer monsoon in the case of EOF-2. Copyright © 2010 Royal Meteorological Society

Stratosphere–troposphere interactions are conventionally characterized using the first empirical orthogonal function (EOF) of fields such as zonal-mean zonal wind. Perpetual-winter integrations of an idealized model are used to contrast the vertical structures of EOFs with those of principal oscillation patterns (POPs; the modes of a linearized system governing the evolution of zonal flow anomalies). POP structures are shown to be insensitive to pressure weighting of the time series of interest, a factor that is particularly important for a deep system such as the stratosphere and troposphere. In contrast, EOFs change from being dominated by tropospheric variability with pressure weighting to being dominated by stratospheric variability without it. The analysis reveals separate tropospheric and stratospheric modes in model integrations that are set up to resemble midwinter variability of the troposphere and stratosphere in both hemispheres. Movies illustrating the time evolution of POP structures show the existence of a fast, propagating tropospheric mode in both integrations, and a pulsing stratospheric mode with a tropospheric extension in the Northern Hemisphere–like integration.

Freshwater delivery is an important factor determining estuarine character and health and may be influenced by large-scale climate oscillations. Variability in freshwater delivery (precipitation and discharge) to the Altamaha River estuary (GA, USA) was examined in relation to indices for several climate signals: the Bermuda High Index (BHI), the Southern Oscillation Index (SOI), the Improved El Nino Modoki Index (IEMI), the North Atlantic Oscillation (NAO), the Atlantic Multidecadal Oscillation (AMO), the Pacific Decadal Oscillation (PDO), and the Pacific/North American Pattern (PNA). Discharge to this estuary has been linked to key ecosystem properties (e.g., salinity regime, water residence time, nutrient inputs, and marsh processes), so understanding how climate patterns affect precipitation and river discharge will help elucidate how the estuarine ecosystem may respond to climate changes. Precipitation patterns in the Altamaha River watershed were described using empirical orthogonal functions (EOFs) of the combined multidecadal time series of precipitation at 14 stations. The first EOF (67 % of the variance) was spatially uniform, the second EOF (11 %) showed a spatial gradient along the long axis of the watershed (NW–SE), and the third EOF (6 %) showed a NE–SW pattern. We compared the principal components (PCs) associated with these EOFs, monthly standardized anomalies of Altamaha River discharge at the gauge closest to the estuary, and the climate indices. Complex, seasonally alternating patterns emerged. The BHI was correlated with June–January discharge and precipitation PC 1. The SOI was correlated with January–April discharge and precipitation PC 2, and also weakly correlated with PC 1 in November–December. The AMO was correlated with river discharge and precipitation PC 3 mainly in December–February and June. The correlation patterns of precipitation PCs with PDO and PNA were similar to those with SOI, but weaker. There were no consistent relationships with two NAO indices or IEMI. Connections between climate signals and estimates of nutrient loading were consistent with the connections to discharge. The occurrence of tropical storms in the region was strongly related to the BHI but not to the other climate indices, possibly representing the influence of storm tracking more than the rate of storm formation. Comparison with the literature suggests that the patterns found may be typical of southeastern USA estuaries but are likely to be different from those outside the region.

The spatial structure and temporal characteristics of prominent anomalies occurring in a 15-year simulation with a GFDL spectral general circulation model are examined using empirical orthogonal functions, teleconnection patterns, composite charts, lagged correlation functions and frequency spectra. Despite the absence of any nonseasonal perturbation in the prescribed forcing such as sea surface temperature, insolation and cloud cover, the simulated circulation exhibits an appreciable degree of temporal variability on monthly time scales. The standing oscillation in the Northern Hemisphere winter which accounts for the largest fraction of this variance has a coherent three-dimensional structure. In the middle and upper troposphere, this preferred mode of oscillation is characterized by a wavelike pattern with multiple centers of action. The corresponding anomaly pattern at the sea level is dominated by north–south pressure seesaws over the North Atlantic and North Pacific. The flow patterns associated with these pressure anomalies are consistent with the principal temperature anomaly pattern in the lower troposphere. The large-scale features of the above anomaly patterns are similar to those associated with the most prevalent standing oscillation observed in the atmosphere. The synoptic behavior and hydrological processes in the model atmosphere during the outstanding anomalous episodes are internally consistent. The spatial structure of the principal mode in the simulation is rather insensitive to the averaging period of the model data. The autocorrelation function and frequency spectrum of the first principal component, as determined from daily data, are characteristic of persistent phenomena with no preferred periodicity. The autocorrelation time scale associated with this anomaly pattern is estimated to be ∼ 15 days. The principal anomaly pattern in the Northern Hemisphere summer is relatively less organized, while those for the Southern Hemisphere and the tropics are noted for their zonal symmetry. The east–west sea level pressure seesaw associated with the observed Southern Oscillation over the Pacific is not simulated by the model, thus suggesting the potential role of nonseasonal forcing mechanisms (such as sea surface temperature anomalies) in that phenomenon.

EOF analysis of a time series with application to tsunami detection

The authors suggest an approach to analyze the effects of small-scale afforestation on the surrounding climate of a large heterogenic area. While simple statistics have difficulty identifying the effect, here a well-known eigenvector technique is used to overcome several specific challenges that result from a limited research region, complex topography, and multiple atmospheric circulation patterns. This approach is applied to investigate the influence of the isolated Yatir forest, at the north edge of Israel’s Negev Desert. It was found that this forest does influence the daily climate, primarily seen in the main pattern of the empirical orthogonal function (EOF) of temperature and humidity. The EOF explains 93% and 80%, respectively, of the total variance in the data. Although the Yatir forest is small, it is significant in regulating the climate in the nearby surroundings, as it is located in a sharp transition area toward an arid climate. The results are presented as maps of correlation and regression between the normalized principal component time series of each pattern as well as other time series of the raw data and spatially interpolated data stations. Analysis of short-term campaign measurements around the Yatir forest supports the EOF results, and shows the forest’s influence to the south, mainly during nighttime when the forest becomes cooler than its surroundings. Overall, results suggest that in areas of transition to semiarid climates, forests regulate the surrounding surface air temperature and humidity fields. Wind analysis based on a complex EOF technique reveals the pattern of the daily cycle of surface wind over the region.

This study discusses the representation of the intraseasonal oscillation (ISO) in three simulations with the ECHAM4 atmosphere general circulation model (GCM). First, the model is forced by AMIP sea surface temperatures (SST), then coupled to the OPYC3 global ocean GCM and third forced by OPYC3 SSTs to clarify possible air-sea interactions and connections of the ISO and the ENSO cycle. The simulations are compared to ECMWF reanalysis data and NOAA outgoing longwave radiation (OLR) observations. Although previous studies have shown that the ECHAM4 GCM simulates an ISO-like oscillation, the main deficits are an overly fast eastward propagation and an eastward displacement of the main ISO activity, which is shown with a composite analysis of daily data between 1984 to 1988 for the reanalysis and the AMIP simulation, 25 years of the coupled integration, and a five year subset of the coupled SST output used for the OPYC3 forced atmosphere GCM experiment. These deficits are common to many atmospheric GCMs. The composites are obtained by principal oscillation pattern (POP). The POPs are also used to investigate the propagation speed and the interannual variability of the main ISO activity. The present coupled model version reveals no clear improvements in the ISO simulation compared to the uncoupled version forced with OPYC3 SSTs, although it is shown that the modeled ISO influences the simulated high-frequency SST variability in the coupled GCM. Within the current analysis, ECHAM4 forced by AMIP SSTs provides the most reasonable ISO simulation. However, it is shown that the maximum amplitudes of the annual cycle of the ISO variability in all analyzed model versions are reached too late in the year (spring and summer) compared to the observations (winter and spring). Additionally, the ENSO cycle influences the interannual variability of the ISO, which is revealed by 20 years of daily reanalysis data and 100 years of the coupled integration. The ENSO cycle is simulated by the coupled model, although there is a roughly 1 K cold bias in the East Pacific in the coupled model. This leads to a diminished influence of the ENSO cycle on the spatial variability of the modeled ISO activity compared to observations. This points out the strong sensitivity of the SST on the ISO activity. Small biases in the SST appear to cause large deterioration in the modeled ISO.

Long‐term variability in the hydrologic cycle is poorly simulated by current generation global climate models (GCMs), partly due to known climatological biases at shorter timescales. We demonstrate that a prototype Multi‐scale Modeling Framework (MMF) provides a superior representation of the spatial and temporal structure of precipitation at diurnal timescales than a GCM. Results from empirical orthogonal function (EOF) decomposition of the boreal summer climatological composite diurnal cycle of precipitation in an MMF are compared to a GCM and satellite data from the Tropical Rainfall Measuring Mission. The eigenspectrum, principal component time series, and the spatial structure of leading EOFs in an eigenmode decomposition of the MMF composite day are a much better match to observations than the GCM. Regional deficiencies in the MMF diurnal cycle are manifest as localized anomalies in the spatial structures of the first two leading EOFs.

The “Principal Oscillation Pattern” technique is used to derive an index of the 30- to 60-day oscillation in the tropical troposphere. In the 200-mb equatorial velocity potential field, one dominant pair of POPS is found. Its properties compare very well with the properties of the oscillation identified in previous studies. In particular, a good correlation between the time evolution of the POP coefficients and area-averaged outgoing long-wave radiation (ORL) is found. The POPS are derived from a 2-year subinterval of the whole 5-year data set. This leaves independent data for subsequent verification. The patterns and their characteristic numbers are almost unchanged if the whole data set is analysed. Also, the analysis is insensitive to changes of the analysis area: if the analysis is limited to 90°-longitude equatorial sectors, the signal is also identified and its patterns are consistent with the patterns derived from the full data set. Interestingly, the signal is best defined in the eastern hemisphere. The POPS may be used to derive “associated correlation patterns” of other quantities in winter and summer separately. The path of the oscillation has a marked annual cycle: in northern winter it migrates from the Indian Ocean across northern Australia into the region of the South Pacific Convergence Zone (SPCZ) and in northern summer it moves from the Indian Ocean across South Asia along the intertropical Convergence Zone (ITCZ) to South America. The POP coefficient may be seen as a bivariate index of the state (phase and strength) of the 30- to 60-day oscillation. Since the POP technique incorporates a prediction equation for the phase of the POP coefficients, the POP model allows for the prediction of the complex amplitude of the oscillation. In a sequence of forecast experiments, of which about two-thirds used independent data, the POP forecasts were found to be useful in about half of all cases for lead times of several days. The correlation and RMS skills were calculated for the POP forecast and for persistence. The POP forecast appears to be considerably better with respect to both measures. The correlation skill scores 60% after 7 days. The POP forecast is most skillful in northern winter and if strong signals are present with minima of velocity potential in the eastern hemisphere.