Extended Empirical Orthogonal Functions Research Articles

Sub-monthly evolution of the Caribbean Low-Level Jet and its relationship with regional precipitation and atmospheric circulation

The summer spatial structure and sub-monthly temporal evolution of one of the key dynamical features of Central American climate, the Caribbean Low-Level Jet (CLLJ), is investigated by means of extended empirical orthogonal functions (EEOFs). The Caribbean 925-hPa zonal wind from the CFSR reanalysis for the period 1979 – 2010 is used for the analysis. This approach reveals new insights into the dynamical processes and spatio-temporal evolution of the CLLJ summer intensification, and through lead and lag linear regressions, significant climate links in the broader Caribbean region are identified. The results show that the CLLJ generates significant precipitation and temperature responses with a distinct temporal evolution over the Caribbean-Atlantic domain to that over the tropical Pacific, which hints at different underlying controlling mechanisms over these two large-scale regions. These anomalies are linked with the mid and upper tropospheric circulation, where a vertical cell over the Caribbean (ascending at the jet exit and subsiding at its entrance) varies in phase with large-scale divergence over the Pacific Ocean. Extratropical hemispheric-wide waves and the weakening of a thermal low in northeast Mexico-central US are identified as potential triggering factors for the CLLJ summer intensification. Two leading modes of tropical variability, El Niño Southern Oscillation and the Madden-Julian Oscillation, are found to modulate the CLLJ by intensifying it and prolonging its life cycle. Details of the underlying mechanisms are provided. These results help to advance the understanding of the processes that modulate local climate variations, which is an important issue in view of the rapid climate change the region is undergoing.

Combining random forests and physics-based models to forecast the electricity generated by ocean waves: A case study of the Mutriku wave farm

This paper combines random forests with physics-based models to forecast the electricity output of the Mutriku wave farm on the Bay of Biscay. The period analysed was 2014–2016, and the forecast horizon was 24 h in 4-h steps. The Random Forest (RF) machine-learning technique was used, with three sets of inputs: i) the electricity generated at Mutriku, ii) the wave energy flux (WEF) prediction made by the ECMWF wave model at Mutriku's nearest gridpoint, and iii) ocean and atmospheric data for the Bay of Biscay. For this last input, extended empirical orthogonal functions (EOFs) were calculated to reduce the dimensionality of these data, while retaining most of the information. The forecasts are evaluated using the R-Squared, Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The model easily outperforms a persistence forecast at 8–10 h and beyond. The most accurate forecasts are achieved by using all three of these inputs. This approach may help to effectively integrate wave farms into the electricity market.

An Operational Tracking Method for the MJO Using Extended Empirical Orthogonal Functions

Several methods are available to track the intraseasonal oscillation, namely the Madden–Julian oscillation (MJO) and monsoon intraseasonal oscillation (MISO). However, no methods to track both the modes in a uniform framework for real-time application exist. A new method to track the smooth propagation of the MJO and MISO is proposed to use it for real-time monitoring. The new approach is based on extended empirical orthogonal function (EEOF) analysis of the combined field of meridionally averaged zonal wind at 850 hPa (U850), zonal wind at 200 hPa and the velocity potential at 200 hPa. The EEOF method does not merely capture the MJO but also smooths (i.e., filters out undesired modes) the temporal propagation in the phase space defined by first two leading principal components (PCs) of the EEOF. Using these leading PCs, we additionally introduce a seasonally varying regression coefficient to filter out the space time structure of the MJO in various fields (rainfall/outgoing long-wave radiation, etc.). These reconstructed fields are then used to link the bidirectional phase movement (i.e., northward propagating MISO and eastward propagating MJO) during boreal summer. The life cycle of the MJO and MISO could be captured with equal fidelity with this current method. MJO filtering could be carried out for any space–time data, not limited to the variables/fields used in EEOF analysis. Examples of the TOGA-COARE and DYNAMO period MJO as well as a few strong MISO events are discussed to check the robustness of the newly proposed method.

Correlated error reduction in GRACE data over Greenland using extended empirical orthogonal functions

AbstractSurface mass change estimates from Gravity Recovery and Climate Experiment (GRACE) spherical harmonic solutions are contaminated by north‐south stripe noise due largely to aliasing of high‐frequency variations into monthly samples. These meridional stripes are especially troubling for ice mass balance studies of the Greenland Ice Sheet (GrIS) where large ice mass variations are known to occur along north‐south trending coastlines. By assuming that mass variations and noise have different patterns in both space and time over Greenland, we use extended empirical orthogonal functions (EEOFs) to filter out this noise. The method is compared with a conventional approach, by examining both continent‐wide estimates and regional changes. GRACE results are compared with independent regional estimates derived from a climate model. The EEOF filter is effective at separating ice mass change signals from meridional stripe noise, with better rejection of high temporal frequency noise and less signal attenuation and spatial smoothing compared to a conventional method. We use EEOF‐filtered GRACE data to examine regional seasonal variations. Consistent with surface and other data, results show ice mass loss along the west, southwest, and east coasts during summer and gain in these regions during winter. In addition, there is summer ice mass gain in the central region of the GrIS.

Downscaling precipitation extremes

A new method for predicting the upper tail of the precipitation distribution, based on empirical–statistical downscaling, is explored. The proposed downscaling method involves a re-calibration of the results from an analog model to ensure that the results have a realistic statistical distribution. A comparison between new results and those from a traditional analog model suggests that the new method predicts higher probabilities for heavy precipitation events in the future, except for the most extreme percentiles for which sampling fluctuations give rise to high uncertainties. The proposed method is applied to the 24-h precipitation from Oslo, Norway, and validated through a comparison between modelled and observed percentiles. It is shown that the method yields a good approximate description of both the statistical distribution of the wet-day precipitation amount and the chronology of precipitation events. An additional analysis is carried out comparing the use of extended empirical orthogonal functions (EOFs) as input, instead of ordinary EOFs. The results were, in general, similar; however, extended EOFs give greater persistence for 1-day lags. Predictions of the probability distribution function for the Oslo precipitation indicate that future precipitation amounts associated with the upper percentiles increase faster than for the lower percentiles. Substantial random statistical fluctuations in the few observations that make up the extreme upper tail implies that modelling of these is extremely difficult, however. An extrapolation scheme is proposed for describing the trends associated with the most extreme percentiles, assuming an upper physical bound where the trend is defined as zero, a gradual variation in the trend magnitude and a function with a simple shape.

Current variability of the Kuroshio near the separation point from the western boundary

Direct current measurements were conducted from April 2003 to March 2004 to investigate the current variability of the Kuroshio near the separation point from the western boundary. During the study period, the main stream of the Kuroshio flowed northeastward in the upper layer slightly offshore from the array of four mooring systems, while a southwestward current was observed in the intermediate layer on the coastal side of the array. Analyses based on the velocity and temperature measurement of the mooring meter array revealed eddy‐to‐mean kinetic and mean‐to‐eddy potential energy conversion in both the upper and intermediate layers. Downstream‐propagating waves detected as significant extended empirical orthogonal functions (EEOFs) are predominant over velocity fluctuations of periods shorter than 50 days, explaining 67% of the total variance. The five apparent wave groups have periods of 7–18 days, wavelengths of 220–380 km, and phase velocities of 22–30 cm s−1, respectively, similar to the values reported in previous studies of upstream regions. Although the phase velocity at a given wavelength in the Kuroshio is lower than that in the Gulf Stream, the dispersion tendency (i.e., that phase velocity increases with decreasing period and wavelength) is the same for both currents. The relatively low phase velocity of the Kuroshio is considered to reflect its relatively low background velocity. Data regarding growth rate, vertical phase lags, and energetics suggest that kinetic energy in this region is transferred from small to large scales mainly via eddies resulting from baroclinic instability, which is possibly related to synoptic‐scale path variability and the penetration of areas of high kinetic energy into the Kuroshio Extension.

MJO‐related oceanic Kelvin waves and the ENSO cycle: A study with the NCEP Global Ocean Data Assimilation System

The surface wind anomalies associated with the Madden‐Julian oscillation (MJO) appear to play a critical role during the onset and termination phases of ENSO. The characteristics of the MJO‐related oceanic Kelvin waves have not been systematically studied due to a lack of ocean reanalysis that resolves intraseasonal variability. This study uses the operational ocean reanalysis for the period 1982–2003 produced by the state‐of‐art global ocean data assimilation system at NCEP to explore the relationship between SST anomalies of ENSO and MJO‐related oceanic Kelvin waves. The first four extended empirical orthogonal functions of the depth of 20°C isotherm are used to represent the dominant oceanic Kelvin waves. The wave activity is measured by seasonal variance of oceanic Kelvin waves (SVKW) at 130°W. SVKW peaks are associated with the onset stage of warm ENSO events since they occur during the transition period and tend to produce positive tendency in NINO3.4 and heat content, and lead mature phases by 5–11 months. MJO‐related oceanic Kelvin wave activity is also shown to impact the growth and termination of warm events. The consistent relationships do not occur in cold events. A real time monitoring tool using SVKW index is proposed to support the official ENSO forecast at NCEP.

Predictability of Indian Ocean sea surface temperature using canonical correlation analysis

There is strong evidence that Indian Ocean sea surface temperatures (SSTs) influence the climate variability of Southern Asia and Africa; hence, accurate prediction of these SSTs is a high priority. In this study, we use canonical correlation analysis (CCA) to design empirical models to assess the predictability of tropical Indian Ocean SST from sea level pressure (SLP) and SST themselves with lead-times up to one year. One model uses the first twelve empirical orthogonal functions (EOFs) of SLP over the Indian Ocean using different lead-times to predict SST. A CCA model with EOFs of SST as the predictor at the same lead-times is compared to SLP as a predictor and shows the auto-correlation of the system. A CCA using the first five extended empirical orthogonal functions (EEOFs) of sea level pressure over the Indian Ocean basin for an interval of two years combined with SST EOFs as predictors is found to produce the greatest correlation between forecast and observed SSTs. This model obtains higher skill by explicitly considering the development in time of SLP anomalies in the region. The skill of this model, assessed from retroactive forecasts of an 18 year period, shows improvement relative to other empirical forecasts particularly for the central and eastern Indian Ocean and boreal autumn months preceding the Southern Hemisphere summer rainfall season. This is likely due to the limited domain of this model identifying modes of variability that are more pronounced in these areas during this season. Finally, a nonlinear canonical correlation analysis (NLCCA) derived from a neural network is used to analyze the leading nonlinear modes. These nonlinear modes differ from the linear CCA modes with distinct cold and warm SST phases suggesting a nonlinear relationship between SST and SLP over the tropical Indian Ocean.

Improvement of Long-Range Forecasting by EEOF Extrapolation Using an AR-MEM Model

Abstract This paper presents an optimum combination of two robust statistical techniques that can be used to improve the skill of long-range weather forecasts. The first method uses decomposition and analysis based on extended empirical orthogonal functions (EEOFs), with a 3-month data window, for temperature and precipitation fields in Romania. Using rule N to select the significant components led to three modes for temperature and to nine modes for precipitation. An autoregressive (AR) model is used to produce forecasts of the time series of the EEOF components. The parameters of this model are determined by a method consistent with the maximum entropy method, which is why this model is named AR-MEM. In order to select model order, seven criteria are tested, some of which are efficient, while the others are consistent. The skill of these methods is tested using simulated time series. Model parameters are determined from observational data over the period 1950–90. The Heidke skill score is computed using...

Forecasting ENSO Events: A Neural Network–Extended EOF Approach

The authors constructed neural network models to forecast the sea surface temperature anomalies (SSTA) for three regions: Niño 4, Niño 3.5, and Niño 3, representing the western-central, the central, and the eastern-central parts of the equatorial Pacific Ocean, respectively. The inputs were the extended empirical orthogonal functions (EEOF) of the sea level pressure (SLP) field that covered the tropical Indian and Pacific Oceans and evolved for a duration of 1 yr. The EEOFs greatly reduced the size of the neural networks from those of the authors’ earlier papers using EOFs. The Niño 4 region appeared to be the best forecasted region, with useful skills up to a year lead time for the 1982–93 forecast period. By network pruning analysis and spectral analysis, four important inputs were identified: modes 1, 2, and 6 of the SLP EEOFs and the SSTA persistence. Mode 1 characterized the low-frequency oscillation (LFO, with 4–5-yr period), and was seen as the typical ENSO signal, while mode 2, with a period of 2–5 yr, characterized the quasi-biennial oscillation (QBO) plus the LFO. Mode 6 was dominated by decadal and interdecadal variations. Thus, forecasting ENSO required information from the QBO, and the decadal–interdecadal oscillations. The nonlinearity of the networks tended to increase with lead time and to become stronger for the eastern regions of the equatorial Pacific Ocean.

Distinguishing modulated oscillations from coloured noise in multivariate datasets

Extended empirical orthogonal functions (EEOFs), alternatively known as multi-channel singular systems (or singular spectrum) analysis (MSSA), provide a natural method of extracting oscillatory modes of variability from multivariate data. The eigenfunctions of some simple non-oscillatory noise processes are, however, also solutions to the wave equation, so the occurrence of stable, wave-like patterns in EEOF/MSSA is not sufficient grounds for concluding that data exhibits oscillations. We present a generalisation of the "Monte Carlo SSA" algorithm which allows an objective test for the presence of oscillations at low signal-to-noise ratios in multivariate data. The test is similar to those used in standard regression, examining directions in state-space to determine whether they contain more variance than would be expected if the noise null-hypothesis were valid. We demonstrate the application of the test to the analysis of interannual variability in tropical Pacific sea-surface temperatures.

Phase–Space Characteristics of the Tropical Stratospheric Quasi-Biennial Oscillation

Abstract Extended empirical orthogonal functions (EOFs) are used to define a phase space for the analysis of tropical stratospheric wind data, extending our previous study of the quasi-biennial oscillation (QBO) in several manners. First, the sensitivity of the analysis to the length of the window (w) is discussed in some detail. As w increases, the leading pair of EOFs become more concentrated on the period near 28 months; simultaneously, the signals contained in higher-order EOFs become more significant, with more clearly defined periodicities; however, for large w more EOFs are required to represent the same variance. There appear to be two stable regimes: when w is less than 20 months the first two EOFs describe a QBO with some irregularities in the onset of easterly wind regimes, whereas when w exceeds 30 months such irregularities are represented by the third and fourth EOFS. Second, the first pair of EOFs with w = 40 are regarded as representing a pure QBO signal, subject to variations in cycle len...

Variability of the summer monsoon rainfall over Thailand—comparison with features over India

AbstractIn this study, 20 years (1961–1980) of rainfall data for 34 stations over Thailand are used to investigate and understand the intraseasonal and interannual variability of the summer monsoon. Dominant structures of 5‐day and seasonal rainfall are determined through empirical orthogonal functions (EOFs). Monthly and seasonal spatial patterns and a map showing the coefficient of variation are also presented.On an intraseasonal time‐scale regions with high 30‐60‐day variances (Madden Julian oscillations—MJOs) and 10‐20‐day variances (Quasi‐biweekly oscillations—QBWOs) are identified using a band‐pass Butterworth filter for 5‐day rainfall. It is seen that the MJOs are dominant over the Indian region and the QBWOs are dominant over the Thailand region. Extended EOFs (EEOFs) have shown that the most important evolutionary feature over India is the northward propagation associated with the MJOs, whereas over the Thailand region it is westward, associated with the QBWOs. Northward propagation of rainfall anomalies is not observed over the Thailand region.On the interannual scale the area over north‐west Thailand is related well with rainfall variation over west‐central India. The Darwin pressure tendency (DPT) and the subtropical ridge over India shows significant relation with rainfall over northwest Thailand. However, the Northern Hemisphere surface temperature (NHST), Quasi‐biennial Oscillation (QBO), and West Pacific ridge (WPR) show no significant relation.

An investigation of the El Niño‐Southern Oscillation cycle With statistical models: 1. Predictor field characteristics

We have developed two sets of linear models for predicting equatorial Pacific sea surface temperatures (SSTs) from the Indo‐Pacific trade wind field and the near‐global sea level pressure (SLP) field. The models were constructed using a combination of extended empirical orthogonal functions (EEOFs) and canonical correlation analysis (CCA), a new approach in geophysical modeling. Our results are of interest both as they show the dominant modes of evolution in the SLP and wind fields through the El Niño‐Southern Oscillation cycle and with respect to the problem of predicting equatorial SSTs. This paper deals with the first issue above and describes some statistical composites that typify the development of features in the predictor fields over periods of years. The results of the EEOF analyses clearly show slowly propagating anomalies in both the near‐global SLP and trade wind fields. The CCA analysis, which highlights the co‐evolution of the two fields, suggests a strong coupling between the two and depicts the anomalous features as migrating centers of divergence and convergence that first appear over the eastern Indian Ocean. These features propagate slowly eastward, amplify as they expand into the western Pacific, decline as they cross the central ocean, then reamplify over the eastern Pacific. As reamplification takes place, new opposing anomalies appear in the Indo‐Pacific. Descriptions of the predictor data sets and details of the statistical techniques used may also be found in this paper. The SST data, model validation techniques, and forecast model results are presented in a companion paper (Graham et al., this issue).