Canonical Correlation Analysis Model Research Articles

A learning algorithm for adaptive canonical correlation analysis of several data sets

Canonical correlation analysis (CCA) is a classical tool in statistical analysis to find the projections that maximize the correlation between two data sets. In this work we propose a generalization of CCA to several data sets, which is shown to be equivalent to the classical maximum variance (MAXVAR) generalization proposed by Kettenring. The reformulation of this generalization as a set of coupled least squares regression problems is exploited to develop a neural structure for CCA. In particular, the proposed CCA model is a two layer feedforward neural network with lateral connections in the output layer to achieve the simultaneous extraction of all the CCA eigenvectors through deflation. The CCA neural model is trained using a recursive least squares (RLS) algorithm. Finally, the convergence of the proposed learning rule is proved by means of stochastic approximation techniques and their performance is analyzed through simulations.

Wavelet Analysis of Variability, Teleconnectivity, and Predictability of the September–November East African Rainfall

Abstract By applying wavelet analysis and wavelet principal component analysis (WPCA) to individual wavelet-scale power and scale-averaged wavelet power, homogeneous zones of rainfall variability and predictability were objectively identified for September–November (SON) rainfall in East Africa (EA). Teleconnections between the SON rainfall and the Indian Ocean and South Atlantic Ocean sea surface temperatures (SST) were also established for the period 1950–97. Excluding the Great Rift Valley, located along the western boundaries of Tanzania and Uganda, and Mount Kilimanjaro in northeastern Tanzania, EA was found to exhibit a single leading mode of spatial and temporal variability. WPCA revealed that EA suffered a consistent decrease in the SON rainfall from 1962 to 1997, resulting in 12 droughts between 1965 and 1997. Using SST predictors identified in the April–June season from the Indian and South Atlantic Oceans, the prediction skill achieved for the SON (one-season lead time) season by the nonlinear model known as artificial neural network calibrated by a genetic algorithm (ANN-GA) was high [Pearson correlation ρ ranged between 0.65 and 0.9, Hansen–Kuipers (HK) scores ranged between 0.2 and 0.8, and root-mean-square errors (rmse) ranged between 0.4 and 0.75 of the standardized precipitation], but that achieved by the linear canonical correlation analysis model was relatively modest (ρ between 0.25 and 0.55, HK score between −0.05 and 0.3, and rmse between 0.4 and 1.2 of the standardized precipitation).

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.

Downscaling of GCM scenarios to assess precipitation changes in the little rainy season (March-June) in Cameroon

CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 26:85-96 (2004) - doi:10.3354/cr026085 Downscaling of GCM scenarios to assess precipitation changes in the little rainy season (March-June) in Cameroon Edouard K. Penlap1,2,*, Christoph Matulla1,3, Hans von Storch1, F. Mkankam Kamga2 1Institute for Coastal Research, GKSS Research Centre, Max-Planck-Straße, 21502 Geesthacht, Germany 2Atmospheric Sciences Lab, Dept of Physics, Faculty of Sciences, University of Yaoundé I, PO Box 812, Yaoundé, Cameroon 3Institute of Meteorology, University of Natural Resources and Applied Life Sciences, 1180 Vienna, Austria *Email: epenlap@uycdc.uninet.cm ABSTRACT: Large-scale climate forcings on local precipitation in Cameroon are analysed during the little rainy season (March-June). Variables found to have strong influence are used to downscale GCM projected rainfall for 2010-2049. In particular, 2 IPCC IS92a scenarios, simulated by the ECHAM4/OPYC3 climate model, are investigated. First, monthly precipitation data from 1951-1990 at 33 meteorological stations are grouped into homogeneous rainfall regions using self-organising feature maps (SOFMs). SOFMs identified 3 groups of stations with related time-series variability. Then, an empirical orthogonal function procedure, followed by canonical correlation analysis (CCA), is used to derive statistical relationships between the homogeneous regions and large-scale variables from the NCEP/NCAR Reanalysis Project. A CCA model is established for every region. Numerous fields at different pressure levels are used as macro-scale predictors. All possible combinations of 2 predictors are systematically tested in 3 validation experiments. Those combinations that perform well in the experiments are used to derive local-scale precipitation scenarios from the general circulation model (GCM) climate projection experiments. Different combinations of large-scale variables enter the model depending on region. A composite analysis suggests that precipitation is related to an advective (convective) phenomenon in the northern (southern) part of the study domain. Moreover, precipitation changes based on 2 IS92a emission scenarios as simulated by ECHAM4/OPYC3 are calculated. The trace-gas-only and the trace-gas-plus-sulphate integrations induce changes ranging locally from +44 to -10% and from +36 to -9% respectively, relative to the 1951-1990 control period. KEY WORDS: Cameroon · Precipitation · Regionalisation · Downscaling · Climate change Full article in pdf format NextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 26, No. 2. Online publication date: May 25, 2004 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2004 Inter-Research.

Recalibration of general circulation model output to austral summer rainfall over southern Africa

AbstractEmpirical techniques are developed to adjust dynamic model forecasts on the seasonal time scale for southern African summer rainfall. The techniques, perfect prognosis and model output statistics (MOS), are utilized to ‘recalibrate’ the CSIRO 9 general circulation model (GCM) large‐scale fields statistically to three equi‐probable rainfall categories for December to February. The recalibration is applied to a GCM experiment where simultaneously observed sea‐surface temperature fields serve as the lower boundary forcing. An optimal canonical correlation analysis model is designed for MOS and perfect prognosis and the 700 hPa geopotential height field is selected as the single predictor field in the two sets of statistical equations that are subsequently used to produce recalibrated rainfall simulations over a 10 year independent test period. MOS produced the higher forecast skill for southern Africa over the independent test period. Copyright © 2003 Royal Meteorological Society

Exploring two methods for statistical downscaling of Central European phenological time series.

In this study we set out to investigate the possibility of linking phenological phases throughout the vegetation cycle, as a local-scale biological phenomenon, directly with large-scale atmospheric variables via two different empirical downscaling techniques. In recent years a number of methods have been developed to transfer atmospheric information at coarse General Circulation Model's grid resolutions to local scales and individual points. Here multiple linear regression (MLR) and canonical correlation analysis (CCA) have been selected as downscaling methods. Different validation experiments (e.g. temporal cross-validation, split-sample tests) are used to test the performance of both approaches and compare them for time series of 17 phenological phases and air temperatures from Central Europe as microscale variables. A number of atmospheric variables over the North Atlantic and Europe are utilized as macroscale predictors. The period considered is 1951-1998. Temporal cross-validation reveals that the CCA model generally performs better than MLR, which explains 20%-50% of the phenological variances, whereas the CCA model shows a range from 40% to over 60% throughout most of the vegetation cycle. To show the validity of employing phenological observations for downscaling purposes both methods (MLR and CCA) are also applied to gridded local air temperature time series over Central Europe. In this case there is no obvious superiority of the CCA model over the MLR model. Both models show explained variances from 40% to over 70% in the temporal cross-validation experiment. The results of this study indicate that time series of phenological occurrence dates are very compatible with the needs of empirical downscaling originally developed of local-scale atmospheric variables.

Using Mean Flow Change as a Proxy to Infer Interdecadal Storm Track Variability

Abstract Several recent studies, based mainly on analyses of reanalysis data, have suggested that the Northern Hemisphere storm tracks have intensified during the second half of the twentieth century. However, comparisons with rawinsonde observations over land areas suggest that eddy variance/covariance statistics may contain spurious jumps that had led to an exaggeration of the storm track secular trend. In this study, storm track variations are inferred from mean flow anomalies using canonical correlation analysis (CCA). A CCA model relating storm track anomalies to mean flow anomalies is derived using recent, more reliable data. The model is then applied to infer storm track anamalies using mean flow anomalies for earlier periods, when storm track analyses are deemed more suspect (or even nonexistent). Results of the CCA analyses suggest that the strong secular trend observed over the Atlantic basin and Europe is consistent with mean flow anomalies, while CCA predictions based on mean flow changes suggest only a much weaker trend in the Pacific storm track activity than that present in the reanalysis data. Over the regions where comparisons with rawinsonde data can be made, the interdecadal trends inferred by the CCA model are quite consistent with rawinsonde data over the Pacific storm track entrance and exit regions, as well as the Atlantic storm track exit regions, but are inconsistent with rawinsonde observations and reanalysis data over northeastern North America, where CCA predictions are generally poor. A CCA hindcast based on Trenberth and Paolino mean sea level pressure data as a predictor shows no indication that the secular increase in storm track intensity extends further back prior to 1960, suggesting that during the entire twentieth century, storm track activity was weakest during the 1960s.

Association between winter temperature in China and upper air circulation over East Asia revealed by canonical correlation analysis

Canonical correlation analysis (CCA) was used to study the relationship between the winter temperature in China and the circulation at 500 hPa over East Asia. CCA identifies a number of paired patterns that depend on Principle Component (PC) truncation of the two fields. Retaining more PCs usually gives more physically meaningful CCA patterns, but the leading paired pattern has often less explained variance. When fewer PCs are adopted, the leading pattern possesses larger variance. However, it is often distorted in comparison with PC or rotated PC patterns. Various combinations with different PC and CCA patterns remained were tried, which shows that retaining as many PCs as possible and using the first several CCAs instead of only the first give most reasonable connection mechanisms. A statistical downscaling model based on CCA modes linking temperature with circulation was established to quantify the extent to which temperature variation can be explained by circulation. The model was optimised by varying numbers of the PCs and the CCA modes retained. With 13th PC truncation in the circulation and 8th PC truncation in the temperature as well as five CCA modes retained, the optimal CCA model is achieved based on cross-validation. The optimal downscaling model accounts for 47.5% temperature variance on average. However, there is a remarkable regional difference, which ranges from 10% to 70% in brier-based score (BBS). It is concluded that 500-hPa circulation is strongly linked to surface temperature in parts of the country, but it alone is not sufficient to achieve a successful statistical downscaling of the temperature for whole China.

Conditional stochastic model for generating daily precipitation time series

The purpose of this paper is the construction of a conditional stochastic model to gener- ate daily precipitation time series. The model is a mixture of a 2-state first-order Markov chain and a statistical downscaling model based on canonical correlation analysis (CCA). The CCA model links the large-scale circulation, represented by the European sea-level pressure (SLP) field, with 4 pre- cipitation distribution parameters: i.e. 2 transition probabilities and 2 gamma distribution parameters. This model is tested for the Bucharest station, for which long observed daily time series were avail- able (1901-1999). The comparison of the capabilities of the conditional stochastic model and an unconditional stochastic model (based only on a Markov chain) is presented using ensembles of 1000 runs of the 2 models. The performance of the conditional stochastic model is analyzed in 2 steps. First, the ability of the CCA model for estimating the 4 precipitation distribution parameters is assessed. Second, the performance of both stochastic models in reproducing the statistical features of the observed precipitation time series is analyzed. The CCA model is most accurate for winter and autumn (transition probabilities), less accurate for the mean precipitation amount on wet days and inaccurate for the shape parameter. There are no significant dissimilarities between the conditional and unconditional models regarding their performance except for the linear trend and interannual variability, which are better captured by the conditional model. Some statistical features are well reproduced by both stochastic models for all seasons, such as mean and expected maximum duration of wet/dry intervals, daily mean of precipitation for wet days. Other statistical features are only par- tially reproduced by both models or are better reproduced by one of the models, such as mean dura- tion of dry interval, standard deviation of daily precipitation amount, seasonal mean of rainy days and expected maximum daily precipitation. For all seasons, generally, the frequency of shorter dry inter- vals is underestimated and that of longer dry intervals (greater than 9 d) is overestimated. In conclu- sion, the conditional stochastic model presented in this paper can be used to generate daily precipi- tation time series for winter and autumn. For the other seasons, the unconditional model can be used to reproduce some statistical features.

Statistical downscaling of monthly forecasts

Canonical correlation analysis (CCA) is used to downscale large-scale circulation forecasts by the Centre for Ocean–Land–Atmosphere studies (COLA) T30 general circulation model (GCM) statistically to regional rainfall in South Africa. Monthly GCM ensemble forecasts available from 1979 to 1995 have been generated using NCEP reanalysis data as initial input and globally observed sea-surface temperature (SST) data at the lower boundary. Altogether, 51 30-day cases of GCM simulations, spanning 17 years, within the target season of December–February (DJF), are produced. This period is very important for agriculture and maize, in particular. A model output statistics (MOS) procedure is used to downscale GCM forecast sea-level pressure and 500 hPa height fields to regional rainfall for 30-day periods over South Africa. The CCA model is trained on the first 31 cases (up to February 1989) and forecasts are subsequently made for the remaining 20 cases. These retro-active real-time forecasts have a high potential (correlations >0.5) over most of the interior of South Africa and, furthermore, the prediction of extreme events seems feasible. CCA diagnostics of the GCM-output against rainfall reveal that favourable rainfall over most of the interior is associated with low pressure systems at the surface over the west coast, with an associated ridging high. This is supported by other observational studies. Copyright © 2000 Royal Meteorological Society

Monthly mean pressure reconstruction for the Late Maunder Minimum Period (AD 1675-1715)

The Late Maunder Minimum (LMM; 1675–1715) delineates a period with marked climate variability within the Little Ice Age in Europe. Gridded monthly mean surface pressure fields were reconstructed for this period for the eastern North Atlantic–European region (25°W–30°E and 35–70°N). These were based on continuous information drawn from proxy and instrumental data taken from several European data sites. The data include indexed temperature and rainfall values, sea ice conditions from northern Iceland and the Western Baltic. In addition, limited instrumental data, such as air temperature from central England (CET) and Paris, reduced mean sea level pressure (SLP) at Paris, and monthly mean wind direction in the Øresund (Denmark) are used. The reconstructions are based on a canonical correlation analysis (CCA), with the standardized station data as predictors and the SLP pressure fields as predictand. The CCA-based model was performed using data from the twentieth century. The period 1901–1960 was used to calibrate the statistical model, and the remaining 30 years (1961–1990) for the validation of the reconstructed monthly pressure fields. Assuming stationarity of the statistical relationships, the calibrated CCA model was then used to predict the monthly LMM SLP fields. The verification results illustrated that the regression equations developed for the majority of grid points contain good predictive skill. Nevertheless, there are seasonal and geographical limitations for which valid spatial SLP patterns can be reconstructed. Backward elimination techniques indicated that Paris station air pressure and temperature, CET, and the wind direction in the Øresund are the most important predictors, together sharing more than 65% of the total variance. The reconstructions are compared with additional data and subjectively reconstructed monthly pressure charts for the years 1675–1704. It is shown that there are differences between the two approaches. However, for extreme years the reconstructions are in good agreement. Copyright © 2000 Royal Meteorological Society

Canonical correlation analysis (CAA) model for long-range forecasts of sub-divisional monsoon rainfall over India

Using the canonical correlation analysis (CCA) approach, a forecast model for long range forecasts of monsoon (June-September) rainfall of 27 meteorological sub-divisions over India was developed, A set of 12 parameters, which have significant correlation with Indian monsoon rainfall, was used as predictors, The model was developed with the data of the period 1958-1994 and by retaining three significant canonical modes, The model showed useful predictive skill in of respect of meteorological sub-divisions over central parts of India and NW India with low errors and high skill scores for categorical forecasts, The model showed no predictive skill in respect of meteorological sub-division over south peninsula, Orissa, West Bengal and Bihar. The CCA model has been also found to perform better than another statistical model developed using the 12 same predictors, The CCA model also showed moderate skill in forecasting excess and deficient rainfall categories of sub-divisional monsoon rainfall during the extreme years.

Short‐term climate prediction of Mei‐Yu rainfall for Taiwan using canonical correlation analysis

Canonical correlation analysis (CCA) is used for predicting Mei‒Yu (May–June) rainfall for eight major stations in Taiwan based on the antecedent November–December sea‒surface temperatures (SSTs) over the Pacific Ocean (50°N–40°S, 120°E–90°W). To reduce the large dimensionality of the SST data set, an empirical orthogonal function analysis is first performed and the leading nine eigenmodes of SST are retained as predictors. The root‒mean‒square error and the Pearson product‒moment correlation coefficient are used to serve as a yardstick in overall forecast evaluation. Forecasts are made for the period 1986–1995, which is independent from the developmental data sets. A moderate skill is achieved for most stations. In particular, Mei‒Yu rainfall is more predicable for the last 3 years (1993–1995), when the island experienced a long spell of deficient rainfall. A cross‒validation technique is used to estimate the overall hindcast skill of the CCA model for the period of 1956–1995 and results suggest that certain stations have more skill than others. Likewise, a CCA ‘climatological prediction’ is conducted in a cross‒validated mode. © 1998 Royal Meteorological Society.

Short-term climate prediction of Mei-Yu rainfall for Taiwan using canonical correlation analysis

Canonical correlation analysis (CCA) is used for predicting Mei‒Yu (May–June) rainfall for eight major stations in Taiwan based on the antecedent November–December sea‒surface temperatures (SSTs) over the Pacific Ocean (50°N–40°S, 120°E–90°W). To reduce the large dimensionality of the SST data set, an empirical orthogonal function analysis is first performed and the leading nine eigenmodes of SST are retained as predictors. The root‒mean‒square error and the Pearson product‒moment correlation coefficient are used to serve as a yardstick in overall forecast evaluation. Forecasts are made for the period 1986–1995, which is independent from the developmental data sets. A moderate skill is achieved for most stations. In particular, Mei‒Yu rainfall is more predicable for the last 3 years (1993–1995), when the island experienced a long spell of deficient rainfall. A cross‒validation technique is used to estimate the overall hindcast skill of the CCA model for the period of 1956–1995 and results suggest that certain stations have more skill than others. Likewise, a CCA ‘climatological prediction’ is conducted in a cross‒validated mode. © 1998 Royal Meteorological Society.

Prediction of ENSO Episodes Using Canonical Correlation Analysis

Abstract Canonical correlation analysis (CCA) is explored as a multivariate linear statistical methodology with which to forecast fluctuations of the El Nino/Southern Oscillation (ENSO) in real time. CCA is capable of identifying critical sequence of predictor patterns that tend to evolve into subsequent patterns that can be used to form a forecast. The CCA model is used to forecast the 3-month mean sea surface temperature (SST) in several regions of the tropical Pacific and Indian oceans for projection times of 0 to 4 seasons beyond the immediately forthcoming season. The predictor variables, representing the climate situation in the four consecutive 3-month periods ending at the time of the forecast, are 1) quasi-global seasonal mean sea level pressure (SLP) and 2) SST in the predictand regions themselves. Forecast skill is estimated using cross-validation, and persistence is used as the primary skill control measure. Results indicate that a large region in the eastern equatorial Pacific (120°−170°W lon...