• Barnett, T. P., , and Preisendorfer R. W. , 1978: Multifield analog prediction of short-term climate fluctuations using a climate state vector. J. Atmos. Sci., 35, 17711787, doi:10.1175/1520-0469(1978)035<1771:MAPOST>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., 1994: Linear statistical short-term climate predictive skill in the Northern Hemisphere. J. Climate, 7, 15131564, doi:10.1175/1520-0442(1994)007<1513:LSSTCP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., , and Livezey R. E. , 1989: An operational multifield analog/anti-analog prediction system for United States seasonal temperatures Part II: Spring, summer, fall, and intermediate 3-month period experiments. J. Climate, 2, 513541, doi:10.1175/1520-0442(1989)002<0513:AOMAAP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., , Glantz M. H. , , and He Y. , 1999: Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997–1998 El Niño episode and the 1998 La Niña onset. Bull. Amer. Meteor. Soc., 80, 217243, doi:10.1175/1520-0477(1999)080<0217:PSOSAD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bergen, R. E., , and Harnack R. P. , 1982: Long-range temperature prediction using a simple analog approach. Mon. Wea. Rev., 110, 10831099, doi:10.1175/1520-0493(1982)110<1083:LRTPUA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Casey, T. M., 1995: Optimal linear combination of seasonal forecasts. Aust. Meteor. Mag., 44, 219224.

  • Cavalcanti, I. F. A., and Coauthors, 2002: Global climatological features in a simulation using the CPTEC–COLA AGCM. J. Climate, 15, 29652988, doi:10.1175/1520-0442(2002)015<2965:GCFIAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ciancarelli, B., , Castro C. L. , , Woodhouse C. , , Dominguez F. , , Chang H.-I. , , Carrillo C. , , and Griffin D. , 2014: Dominant patterns of US warm season precipitation variability in a fine resolution observational record, with focus on the southwest. Int. J. Climatol., 34, 687707, doi:10.1002/joc.3716.

    • Search Google Scholar
    • Export Citation
  • Coelho, C. A. S., , Stephenson D. B. , , Balmaseda M. , , Doblas-Reyes F. J. , , and van Oldenborgh G. J. , 2006a: Toward an integrated seasonal forecasting system for South America. J. Climate, 19, 37043721, doi:10.1175/JCLI3801.1.

    • Search Google Scholar
    • Export Citation
  • Coelho, C. A. S., , Stephenson D. B. , , Doblas-Reyes F. J. , , Balmaseda M. , , Guetter A. , , and van Oldenborgh G. J. , 2006b: A Bayesian approach for multi-model downscaling: Seasonal forecasting of regional rainfall and river flows in South America. Meteor. Appl., 13, 7382, doi:10.1017/S1350482705002045.

    • Search Google Scholar
    • Export Citation
  • Compagnucci, R. H., , and Richman M. B. , 2008: Can principal component analysis provide atmospheric circulation or teleconnection patterns? Int. J. Climatol., 28, 703726, doi:10.1002/joc.1574.

    • Search Google Scholar
    • Export Citation
  • Compo, G. P., and Coauthors, 2011: The Twentieth Century Reanalysis Project. Quart. J. Roy. Meteor. Soc., 137, 128, doi:10.1002/qj.776.

    • Search Google Scholar
    • Export Citation
  • Diaz, A., , and Studzinski C. D. S. , 1994: Rainfall anomalies in the Uruguay-southern Brazil region related to SST in the Pacific and Atlantic Oceans using canonical correlation analysis. Proc. VIII Congresso Brasileiro de Meteorologia, Belo Horizonte, Brazil, Sociedade Brasileira de Meteorologia, 42–45.

  • Diaz, A., , Studzinski C. D. S. , , and Mechoso C. R. , 1998: Relationships between precipitation anomalies in Uruguay and southern Brazil and sea surface temperature in the Pacific and Atlantic Oceans. J. Climate, 11, 251271, doi:10.1175/1520-0442(1998)011<0251:RBPAIU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Douglas, A. V., , and Englehart P. J. , 1981: On a statistical relationship between autumn rainfall in the central equatorial Pacific and subsequent winter precipitation in Florida. Mon. Wea. Rev., 109, 23772382, doi:10.1175/1520-0493(1981)109<2377:OASRBA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gandin, L. S., , and Murphy A. H. , 1992: Equitable skill scores for categorical forecasts. Mon. Wea. Rev., 120, 361370, doi:10.1175/1520-0493(1992)120<0361:ESSFCF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gerrity, J. P., Jr., 1992: A note on Gandin and Murphy’s equitable skill score. Mon. Wea. Rev., 120, 27092712, doi:10.1175/1520-0493(1992)120<2709:ANOGAM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Grimm, A. M., , Barros V. R. , , and Doyle M. E. , 2000: Climate variability in southern South America associated with El Niño and La Niña events. J. Climate, 13, 3558, doi:10.1175/1520-0442(2000)013<0035:CVISSA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Grimm, A. M., , Pal J. S. , , and Giorgi F. , 2007: Connection between spring conditions and peak summer monsoon rainfall in South America: Role of soil moisture surface temperature and topography in eastern Brazil. J. Climate, 20, 59295945, doi:10.1175/2007JCLI1684.1.

    • Search Google Scholar
    • Export Citation
  • Hair, J., , Black W. , , Babin B. , , and Anderson R. , 2010: Multivariate Data Analysis. 7th ed. Pearson Prentice Hall, 785 pp.

  • Hall, A., , and Visbeck M. , 2002: Synchronous variability in the Southern Hemisphere atmosphere sea ice and ocean resulting from the annular mode. J. Climate, 15, 30433057, doi:10.1175/1520-0442(2002)015<3043:SVITSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Harnack, R., , Cammarata M. , , Dixon K. , , Lanzante J. , , and Harnack J. , 1985: Summary of US seasonal temperature forecast experiments. Preprints, Ninth Conf. on Probability and Statistics in the Atmospheric Sciences, Virginia Beach, VA, Amer. Meteor. Soc., 175–178.

  • Hastenrath, S., , and Greischar L. , 1993: Changing predictability of Indian monsoon rainfall anomalies. Proc. Ind. Acad. Sci., 102, 3547, doi:10.1007/BF02839181.

    • Search Google Scholar
    • Export Citation
  • Hastenrath, S., , Greischar L. , , and van Heerden J. , 1995: Prediction of the summer rainfall over South Africa. J. Climate, 8, 15111518, doi:10.1175/1520-0442(1995)008<1511:POTSRO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hastenrath, S., , Sun L. , , and Moura A. D. , 2009: Climate prediction for Brazil’s Nordeste by empirical and numerical modeling methods. Int. J. Climatol., 29, 921926, doi:10.1002/joc.1770.

    • Search Google Scholar
    • Export Citation
  • IRI, 2015: Seasonal climate verifications: Verification of IRI’s seasonal climate forecast. International Research Institute for Climate and Society. [Available online at http://iri.columbia.edu/our-expertise/climate/forecasts/verification/.]

  • Johansson, A., , Barnston A. G. , , Saha S. , , and Van den Dool H. M. , 1998: On the level of forecast skill in northern Europe. J. Atmos. Sci., 55, 103127, doi:10.1175/1520-0469(1998)055<0103:OTLAOO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Johnson, R. A., , and Wichern D. W. , 2007: Applied Multivariate Statistical Analysis. 6th ed. Prentice Hall, 800 pp.

  • Jolliffe, I. T., 2002: Principal Component Analysis. 2nd ed. Springer Verlag, 487 pp.

  • Kaplan, J., and Coauthors, 2015: Evaluating environmental impacts on tropical cyclone rapid intensification predictability utilizing statistical models. Wea. Forecasting, 30, 13741396, doi:10.1175/WAF-D-15-0032.1.

    • Search Google Scholar
    • Export Citation
  • Kayano, M. T., , and Sansigolo C. A. , 2012: Variações de precipitação e de temperaturas máxima e mínima no Rio Grande do Sul associadas à Oscilação Antártica. Proc. XVII Congresso Brasileiro de Meteorologia, Gramado, Brazil, Sociedade Brasileira de Meteorologia, 62QA. [Available online at http://www.sbmet.org.br/cbmet2012/pdfs/62QA.pdf.]

  • Keppenne, C. L., , and Ghil M. , 1992: Adaptive filtering and the Southern Oscillation index. J. Geophys. Res., 97, 20 44920 454, doi:10.1029/92JD02219.

    • Search Google Scholar
    • Export Citation
  • Knaff, J. A., , and Landsea C. W. , 1997: An El Niño–Southern Oscillation climatology and persistence (CLIPER) forecasting scheme. Wea. Forecasting, 12, 633652, doi:10.1175/1520-0434(1997)012<0633:AENOSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Livezey, R. E., , and Barnston A. G. , 1988: An operational multifield analog/antianalog system for United States seasonal temperatures: Part 1. System design and winter experiments. J. Geophys. Res., 93, 10 95310 974, doi:10.1029/JD093iD09p10953.

    • Search Google Scholar
    • Export Citation
  • Lúcio, P. S., and Coauthors, 2010: Um modelo estocástico combinado de previsão sazonal para a precipitação no Brasil. Rev. Bras. Meteor., 25, 7087, doi:10.1590/S0102-77862010000100007.

    • Search Google Scholar
    • Export Citation
  • Marengo, J. A., and Coauthors, 2003: Assessment of regional seasonal rainfall predictability using the CPTEC/COLA atmospheric GCM. Climate Dyn., 21, 459475, doi:10.1007/s00382-003-0346-0.

    • Search Google Scholar
    • Export Citation
  • Maroco, J., 2003: Análise Estatística com Utilização do SPSS. 2nd ed. Sílabo, 824 pp.

  • Mason, S. J., 1998: Seasonal forecasting of South African rainfall using a non-linear discriminant analysis model. Int. J. Climatol., 18, 147164, doi:10.1002/(SICI)1097-0088(199802)18:2<147::AID-JOC229>3.0.CO;2-6.

    • Search Google Scholar
    • Export Citation
  • Moura, A. D., , and Hastenrath S. , 2004: Climate prediction for Brazil’s Nordeste: Performance of empirical and numerical modeling methods. J. Climate, 17, 26672672, doi:10.1175/1520-0442(2004)017<2667:CPFBNP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mukhin, D., , Kondrashov D. , , Loskutov E. , , Gavrilov A. , , Feigin A. , , and Ghil M. , 2015: Predicting critical transitions in ENSO models. Part II: Spatially dependent models. J. Climate, 28, 19621976, doi:10.1175/JCLI-D-14-00240.1.

    • Search Google Scholar
    • Export Citation
  • Muza, M. N., , Carvalho L. M. V. , , Jones C. , , and Liebmann B. , 2009: Intraseasonal and interannual variability of extreme dry and wet events over southeastern South America and the subtropical Atlantic during austral summer. J. Climate, 22, 16821699, doi:10.1175/2008JCLI2257.1.

    • Search Google Scholar
    • Export Citation
  • Namias, J., 1989: Cold waters and hot summers. Nature, 338, 1516, doi:10.1038/338015a0.

  • Nobre, P., , and Shukla J. , 1996: Variations of sea surface temperature wind stress and rainfall over the tropical Atlantic and South America. J. Climate, 9, 24642479, doi:10.1175/1520-0442(1996)009<2464:VOSSTW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Polikar, R., 2006: Pattern recognition. Wiley Encyclopedia of Biomedical Engineering, M. Akay, Ed., J. Wiley and Sons, 122, doi:10.1002/9780471740360.ebs0904.

  • Potts, J. M., , Folland C. K. , , Jolliffe I. T. , , and Sexton D. , 1996: Revised “LEPS” scores for assessing climate model simulations and long range forecasts. J. Climate, 9, 3453, doi:10.1175/1520-0442(1996)009<0034:RSFACM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Radinovic, D., 1975: An analogue method for weather forecasting using the 500/1000 mb relative topography. Mon. Wea. Rev., 103, 639649, doi:10.1175/1520-0493(1975)103<0639:AAMFWF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rayner, N. A., , Parker D. E. , , Horton E. B. , , Folland C. K. , , Alexander L. V. , , Rowell D. P. , , Kent E. C. , , and Kaplan A. , 2003: Global analyses of sea surface temperature sea ice and night marine air temperature since the late nineteenth century. J. Geophys. Res., 108, 4407, doi:10.1029/2002JD002670.

    • Search Google Scholar
    • Export Citation
  • Richman, M. B., 1986: Rotation of principal components. J. Climatol., 6, 293335, doi:10.1002/joc.3370060305.

  • Sansigolo, C. A., 1991: Seasonal rainfall forecasting in the north-east region of Brazil. Grosswetter, 30, 3342.

  • Sansigolo, C. A., 1999: Verificação de um modelo discriminante de previsão das precipitações sazonais do Nordeste. Rev. Bras. Meteor., 14, 2935.

    • Search Google Scholar
    • Export Citation
  • Schneider, U., , Becker A. , , Meyer-Christoffer A. , , Ziese M. , , and Rudolf B. , 2011: Global precipitation analysis products of the GPCC. Global Precipitation Climatology Centre, DWD, 12 pp. [Available online at ftp://ftp-anon.dwd.de/pub/data/gpcc/PDF/GPCC_intro_products_2008.pdf.]

  • Shabbar, A., , and Barnston A. G. , 1996: Skill of seasonal climate forecasts in Canada using canonical correlation analysis. Mon. Wea. Rev., 124, 23702385, doi:10.1175/1520-0493(1996)124<2370:SOSCFI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Shahi, N. K., , Rai S. , , and Pandey D. K. , 2016: Prediction of daily modes of South Asian monsoon variability and its association with Indian and Pacific Ocean SST in the NCEP CFS V2. Meteor. Atmos. Phys., 128, 131142, doi:10.1007/s00703-015-0404-2.

    • Search Google Scholar
    • Export Citation
  • Shukla, J., 1998: Predictability in the midst of chaos: A scientific basis for climate forecasting. Science, 282, 728731, doi:10.1126/science.282.5389.728.

    • Search Google Scholar
    • Export Citation
  • Silvestri, G. E., , and Vera C. S. , 2003: Antarctic Oscillation signal on precipitation anomalies over southeastern South America. Geophys. Res. Lett., 30, 2115, doi:10.1029/2003GL018277.

    • Search Google Scholar
    • Export Citation
  • Sneyers, R., , and Goossens C. , 1988: The Principal Component Analysis Application to Climatology and to Meteorology. World Meteorological Organization, 55 pp.

  • Taschetto, A. S., , and Wainer I. , 2008: The impact of the subtropical South Atlantic SST on South American precipitation. Ann. Geophys., 26, 34573476, doi:10.5194/angeo-26-3457-2008.

    • Search Google Scholar
    • Export Citation
  • Timm, N. H., 2002: Applied Multivariate Analysis. Springer Verlag, 718 pp.

  • Tippett, M. K., , and DelSole T. , 2013: Constructed analogs and linear regression. Mon. Wea. Rev., 141, 25192525, doi:10.1175/MWR-D-12-00223.1.

    • Search Google Scholar
    • Export Citation
  • Van den Dool, H. M., 1994: Searching for analogues: How long must we wait? Tellus, 46A, 314324, doi:10.1034/j.1600-0870.1994.t01-2-00006.x.

    • Search Google Scholar
    • Export Citation
  • Van den Dool, H. M., 2007: Empirical Methods in Short-Term Climate Prediction. Oxford University Press, 215 pp.

  • Wang, L., , Yuan X. , , Ting M. , , and Li C. , 2016: Predicting summer Arctic sea ice concentration intraseasonal variability using a vector autoregressive model. J. Climate, 29, 15291543, doi:10.1175/JCLI-D-15-0313.1.

    • Search Google Scholar
    • Export Citation
  • Ward, M. N., , and Folland C. K. , 1991: Prediction of seasonal rainfall in the north Nordeste of Brazil using eigenvectors of sea-surface temperature. Int. J. Climatol., 11, 711743, doi:10.1002/joc.3370110703.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2006: Statistical Methods in the Atmospheric Sciences. 2nd ed. Elsevier, 627 pp.

  • View in gallery

    Location of the study area in South America with (bottom left) the topography highlighted and (right) the homogeneous rainfall regions defined through hierarchical cluster analysis of monthly GPCC-V6 rainfall anomalies.

  • View in gallery

    Predictor KRs selected via MDA used for monthly and seasonal rainfall categorical forecasting in southern Brazil HRs. Acronyms correspond to the month or season followed by the PC number: (a)–(l) Jan_HR1, Jan_HR2, Jan_HR3, Jan_HR4, Oct_HR1, Dec_HR2, Dec_HR3, Feb_HR4, DJF_HR1, DJF_HR2, DJF_HR3, and DJF_HR4. The gray shaded contours represent the correlation (>0.7) of principal component scores with spatial patterns (loadings).

  • View in gallery

    (a) Reliability diagram and (b) ROC curve for monthly and seasonal rainfall forecasting considering all periods and homogeneous regions. The bar graph in (a) represents the frequency histogram that indicates that each bin of probabilities is used an appropriate amount of times. Frequency histograms show the frequency of forecasts as a function of the probability bin. In (b), all monthly and seasonal forecasts were grouped according to probability categories in a single set of data to show the overall performance of the model.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 11 11 5
PDF Downloads 8 8 2

Monthly and Seasonal Rainfall Forecasting in Southern Brazil Using Multiple Discriminant Analysis

View More View Less
  • 1 Center for Weather Forecasting and Climate Studies, National Institute for Space Research, São José dos Campos, São Paulo, Brazil
© Get Permissions
Full access

Abstract

A multiple discriminant analysis was employed to forecast monthly and seasonal rainfall in southern Brazil. The methodology used includes six steps: data acquisition, preprocessing, feature extraction, feature selection, classification, and evaluation. The predictors (atmospheric, surface, and oceanic variables) and predictand (rainfall) were obtained from the Twentieth Century Reanalysis (version 2), as well as from the HadISST1 (Met Office Hadley Centre) and Global Precipitation Climatology Centre (GPCC) databases. The definition of key regions (feature extraction step) was performed using spatial principal component analysis. In the selection step, the rainfall time series were allocated into terciles, which were related to the predictors via multiple discriminating analyses. The results revealed that ⅓ of the predictors are associated with atmospheric pressure and also emphasized the role of atmospheric circulation over the Antarctic region and its surroundings. Surface variables (albedo and soil moisture) were also of great importance in the forecasting. The average skill score (gain over climatology) was 29%. It is concluded that the proposed model is a reliable alternative for use in forecasting monthly and seasonal rainfall over southern Brazil.

Corresponding author address: Denilson Ribeiro Viana, National Institute for Space Research, Center for Weather Forecasting and Climate Studies, Av. dos Astronautas 1758, São José dos Campos, São Paulo 12227-010, Brazil. E-mail: ribeiro.denilson@cptec.inpe.br, clovis.sansigolo@cptec.inpe.br

Abstract

A multiple discriminant analysis was employed to forecast monthly and seasonal rainfall in southern Brazil. The methodology used includes six steps: data acquisition, preprocessing, feature extraction, feature selection, classification, and evaluation. The predictors (atmospheric, surface, and oceanic variables) and predictand (rainfall) were obtained from the Twentieth Century Reanalysis (version 2), as well as from the HadISST1 (Met Office Hadley Centre) and Global Precipitation Climatology Centre (GPCC) databases. The definition of key regions (feature extraction step) was performed using spatial principal component analysis. In the selection step, the rainfall time series were allocated into terciles, which were related to the predictors via multiple discriminating analyses. The results revealed that ⅓ of the predictors are associated with atmospheric pressure and also emphasized the role of atmospheric circulation over the Antarctic region and its surroundings. Surface variables (albedo and soil moisture) were also of great importance in the forecasting. The average skill score (gain over climatology) was 29%. It is concluded that the proposed model is a reliable alternative for use in forecasting monthly and seasonal rainfall over southern Brazil.

Corresponding author address: Denilson Ribeiro Viana, National Institute for Space Research, Center for Weather Forecasting and Climate Studies, Av. dos Astronautas 1758, São José dos Campos, São Paulo 12227-010, Brazil. E-mail: ribeiro.denilson@cptec.inpe.br, clovis.sansigolo@cptec.inpe.br

1. Introduction

Climate forecasting is a topic of great scientific interest because it plays a decisive role in the organization of the various spheres of society. Forecasts can be obtained either through dynamic or empirical (statistical) models. Although seasonal climate predictions are currently performed using dynamic models, statistical methods can offer comparable, or even superior, predictive accuracy, at substantially lower cost (Barnston et al. 1999; Hastenrath et al. 2009; Moura and Hastenrath 2004; Van den Dool 2007). As a nonlinear dynamical system, the atmosphere is not perfectly predictable in a deterministic or dynamic sense, and consequently, statistical methods are useful, and indeed necessary, parts of the forecasting enterprise (Wilks 2006).

The most commonly used statistical methods for seasonal-to-interannual climate predictions are analogous and linear regression (Knaff and Landsea 1997; Tippett and DelSole 2013; Van den Dool 1994), singular spectrum analysis (Keppenne and Ghil 1992; Mukhin et al. 2015; Shahi et al. 2016), canonical correlation analysis (Barnston 1994; Ciancarelli et al. 2014; Johansson et al. 1998; Shabbar and Barnston 1996), discriminant analysis (Casey 1995; Hastenrath and Greischar 1993; Hastenrath et al. 1995; Kaplan et al. 2015; Mason 1998; Sansigolo 1991; Ward and Folland 1991), and autoregressive models (Lúcio et al. 2010; Wang et al. 2016).

Regarding predictor variables, Shukla (1998) discussed the scientific basis of climate prediction, noting that the circulation patterns in certain regions of the planet can be predicted on seasonal time scales because they are strongly determined by relatively stable fields, such as sea surface temperatures (SSTs). Atmospheric variables associated with geopotential height Z are also used to generate climate forecasts, and as one type of stable pattern, the Z patterns in hemispherical charts often reflect the general circulation characteristics of the atmosphere (Radinovic 1975).

Barnett and Preisendorfer (1978) and Bergen and Harnack (1982) used three fields—two atmospheric [700-mb height and thickness (1000–500 mb); where 1 mb = 1 hPa] and one oceanic (SST)—to predict seasonal temperature and rainfall in the United States. Additionally, based on the concepts of Barnett and Preisendorfer (1978) and Harnack et al. (1985), Livezey and Barnston (1988) and Barnston and Livezey (1989) used these same three variables to implement an operational system for seasonal climate forecasting in the United States. With regard to soil moisture, Namias (1989) emphasized the importance of its reduction in maintaining hot and dry conditions by reducing the evaporation rate.

In Brazil, the seasonal rainfall patterns in the North (Amazon basin), Northeast, and South regions are influenced by the equatorial Pacific SSTs, which, in turn, are associated with the El Niño–Southern Oscillation (ENSO). In general, only the equatorial Atlantic and Pacific SSTs are used as the predictor variables in statistical models (Coelho et al. 2006b; Lúcio et al. 2010). However, Taschetto and Wainer (2008) demonstrated that the South Atlantic SSTs are more important than the equatorial Pacific SSTs (ENSO region) in determining the position of the South Atlantic convergence zone (SACZ) over southeastern Brazil during summer, which accounts for most of the observed precipitation in this region during the warm period. Muza et al. (2009) also indicated that the South Atlantic SSTs appear to be related to interannual variations in extreme precipitation over southeastern Brazil. Diaz and Studzinski (1994) identified significant relationships between rainfall in southern Brazil and SST anomalies in the southwest Atlantic. In addition, fluctuations in sea ice concentrations in the Southern Hemisphere act as a forcing in the response of the Antarctic Oscillation index (Hall and Visbeck 2002), and they can be used to predict rainfall variability in southern Brazil (Kayano and Sansigolo 2012).

The purpose of this paper is to develop and evaluate an empirical method for monthly and seasonal rainfall forecasting in southern Brazil. The forecasts were in homogeneous regions of rainfall anomalies (predictand allocated in terciles), predefined by hierarchical clustering analysis. Atmospheric, oceanic, and surface variables (predictors) were submitted to dimensionality reduction through spatial principal component analysis. The predictor time series were correlated with rainfall anomalies terciles using multiple linear discriminant analysis to select the best ones, and the results were evaluated by a set of categorical and probabilistic scores.

2. Data, methodology, and evaluation

a. Data

The study area comprises the southern part of Brazil, an area south of 10°S that includes the South, Southeast, and Middle-West political–administrative regions of the country. This area was split into homogeneous regions (HRs) using hierarchical cluster analysis, based on monthly rainfall anomalies of reanalysis data from version 6 of the Global Precipitation Climatology Centre (GPCC-V6) dataset, with a spatial resolution of 0.5° × 0.5° (Schneider et al. 2011). The establishment of HRs, from the point of view of anomalies, is an objective forecast criterion because they account for the climatic characteristics and variability of a given area. It is assumed that these homogenous regions are driven by the same atmospheric, oceanic, and surface mechanisms. Figure 1 shows the location of the study area as well the HRs. Forecasts were made on monthly and seasonal time scales for each HR during the two wettest months and for the rainy season, as follows: HR1, January, October, and December–February (DJF); HR2, January, December, and DJF; HR3, January, December, and DJF; and HR4, January, February, and DJF.

Fig. 1.
Fig. 1.

Location of the study area in South America with (bottom left) the topography highlighted and (right) the homogeneous rainfall regions defined through hierarchical cluster analysis of monthly GPCC-V6 rainfall anomalies.

Citation: Weather and Forecasting 31, 6; 10.1175/WAF-D-15-0155.1

The predictor fields selected were the monthly and seasonal SSTs and sea ice concentrations (SICs) from the Met Office Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST1), with a spatial resolution of 1° × 1° (Rayner et al. 2003), as well as the monthly and seasonal averages of the geopotential height field Z at 850, 700, 500 and 250 mb; the sea level pressure (SLP); the air temperature at 850 mb (T850); the precipitable water content (PWC); the surface albedo (ALB); and the soil moisture content (SMC) from the Twentieth Century Reanalysis (version 2; R-2), with a spatial resolution of 2° × 2° (Compo et al. 2011). Both datasets cover the period 1951–2010, for a total of 60 yr of monthly observations (720 months). According to Table 1, the predictors were grouped into three categories: 1) oceanic (SSTs and SICs), 2) atmospheric (Z850, Z700, Z500 Z250, SLP, T850, and PWC), and 3) surface (ALB and SMC). The SSTs were divided between the Atlantic (SST_ATL) and Pacific (SST_PAC). The selection of predictor variables considered a lag of 1 month for the monthly forecast and 1 season for the seasonal forecast.

Table 1.

Predictors and predictand datasets.

Table 1.

b. Methodology

The methodology followed the steps proposed by Polikar (2006), which establish the guidelines for a statistical pattern recognition system. Regarding the predictand, monthly rainfall anomalies were computed for each grid point inside the study area, as shown in Fig. 1. The atmospheric predictors were initially defined for subsequent analysis between 30°N and 90°S and between 30° and 110°E. The SSTs, including the Atlantic and Pacific basins, were set between the limits of 70°N and 60°S and between 100° and 30°E. A single SIC anomaly time series was considered, and, finally, the surface fields (ALB and SMC) were regarded as the anomalies in the HRs.

In the feature extraction step, key regions (KRs) were defined using spatial principal component analysis (PCA). Varimax rotation was applied to better distribute the total variance among the patterns (Richman 1986; Sneyers and Goossens 1988; Wilks 2006). The concept of KRs was proposed by Barnett and Preisendorfer (1978) in order to characterize the variability of large-scale climatic features. The KRs are defined as regions of high covariability in a given climatic field, isolated through eigenvector analysis (PCA). Therefore, a regional average or index is then computed by averaging all data points within a given area (Douglas and Englehart 1981). In climatic applications, the Varimax rotation also allows the best physical interpretations of the statistical patterns (Compagnucci and Richman 2008). They also noted that PCA in spatial mode (S) is used when the goal is to identify spatial groups or teleconnections, precisely equivalent to the concept of KRs as defined Barnett and Preisendorfer (1978). The reason for applying PCA to atmospheric, oceanic, and surface data is to determine spatial patterns (loadings) and corresponding time series (scores) in order to reduce data dimensionality and to satisfy the multicolinearity assumption.

In the feature selection stage, the monthly and seasonal rainfall time series (dependent variable) were allocated into terciles (below, above, and near normal). The two rainiest months in each region was considered for monthly forecasting, and the wet season (summer) for seasonal ones. The series of atmospheric and oceanic predictor fields [principal component (PC) scores], ALB and SMC surface anomalies in each HR, and SIC anomalies (independent variable) were associated with rainfall categories via linear multiple discriminant analysis (MDA). Given a set of p variables and g groups, it is possible to establish m = g − 1 discriminant functions Z, which are linear combinations of the p variables:
e1
where a is the intercept and wi,1, wi,2, … , wi,p are weights, estimated in order to maximize the variability of the discriminant function scores among groups.

The number of independent variables in principal component analysis was defined considering a set of components accounting for ~70% of the total variance (Jolliffe 2002); this summed up 249 variables. Table 2 shows the predictor fields, highlighting the number of PC scores corresponding to ~70% of the cumulative variance for the atmospheric, oceanic, and surface variables. Regarding the number of predictor variables used in the analysis, Hair et al. (2010) indicates that MDA is very sensitive to the proportion between the sample size and the number of variables. The ideal size is about five cases by independent variable. Also, the smallest group in each category must be greater or equal to the number of dependent variables. As a practical guideline, each category must have at least 20 observations. As a result of the high number of independent variables (249), a preselection using the Pearson correlation was used to select the 20 independent variables best correlated with the rainfall.

Table 2.

Number of significant PC variables for each predictor field used to forecast monthly and seasonal rainfall anomalies in southern Brazil via MDA.

Table 2.

The significance of the discriminant functions was tested by the Wilks lambda statistics Λ for each Z function:
e2
where SSE is the sum of the square errors within groups and SST is the sum of the total squares. The distribution of Λ is not known and may be approximated by the F-Snedecor distribution with 2p and 2(Np − 2) degrees of freedom. The F-probability values correspond to the thresholds to the input and output variables, as a variable selection criterion within MDA. In the case of three groups, the F function is
e3
The normal distribution was accepted by the Kolmogorov–Smirnov test at 5% of significance for all-time series of independent preselected variables. The similarity of covariance matrices for the independent variables between groups was assessed by M-box tests (Johnson and Wichern 2007):
e4
where ni is the sample size of the ith group g and is the sample covariance matrix, given by
e5

The test can be approximated by Chi-square and F-Snedecor distributions, and cases with high significance values (α > 0.05) indicate that matrices are statistically different. Besides the procedures determined by Schneider et al. (2011), the presence of outliers was investigated by detrended normal QQ plots and appropriately treated. Because of the high number of independent variables (249), the plots are not shown. Finally, the multicolinearity was analyzed by cross correlations, after preselection and the correlated variables (α < 0.05) discarded.

The Mahalanobis distance was used as a measure of distance in the stepwise method to include/exclude variables. The Mahalanobis distance of an observation from a set observations with mean and covariance matrix is defined as
e6

When the Mahalanobis distance is used as a criterion for variables selection, it is calculated first, and the variable with the highest DM for the two closest groups will be selected for inclusion in the model. Values of F, at 10% and 20% significant levels, respectively, were used for input and output variables.

The classification step consisted of applying the discriminant functions to obtain the monthly and seasonal regional rainfall forecasts. Because of the relatively low number of cases (60 samples), the data were not split into two sets (training and classification). For division into two sets, Hair et al. (2010) recommended having at least 100 cases, which is not the case in the present study. The entire dataset (n months or seasons) was used for model development, and a (n − 1) dataset was created for a cross-validation evaluation procedure. The cross-validation method consists of the following steps: 1) a sample vector of observations is removed and (n1 + n2 − 1) remaining sample elements are used to construct the discrimination function; 2) the discrimination rule built in step 1 is used to classify the element that was separated from the discrimination rule, making sure that this rule hits its real origin; and 3) the sample element removed in step 1 is returned and a different one from the first element is withdrawn. Steps 1–3 must be repeated for all (n1 + n2) elements of the joint sample. These estimates are approximately unbiased and better than other methods for both normal and nonnormal populations (Timm 2002).

c. Postprocessing evaluation

The forecast postprocessing evaluations were performed using categorical skill scores in contingency tables. Among the categorical and probabilistic skill scores, the selected scores were the proportion correct score (PCS), which is the hit rate for the total number of predictions, and the Heidke skill score (HSS), which is a rescaled and calibrated version of the PCS. Given a set of pairs of predictions yi and observations oi, the HSS is given in terms of the joint distribution of forecasts and observations p(yi, oi), and the marginal prediction and observation distributions p(yi) and p(oi):
e7
Among the probabilistic scores, those that were selected were the equitable scores introduced by Gandin and Murphy (1992), which are sensitive to distance, thereby emphasizing correct predictions and penalizing incorrect predictions. In the calculation of these scores, an error in a far category receives a greater penalty. The result is a sum of the joint probability distributions p(yi, oj):
e8
where the si,j are a set of weights for three equiprobable classes (Gerrity 1992). Another score that was used was the categorical linear error in probability space (LEPS-CAT), which is calculated following the same methodology as that for GMSS but using a table with different weights, which emphasizes arrangements in extreme categories (Potts et al. 1996). In addition to these scores, the model was also evaluated using the Brier skill score (BSS), which is essentially the mean square error between pairs of observations and forecasts, where each observation is considered to be o1 = 1 if the event occurs and o2 = 0 if the event does not occur:
e9
where k is an index representing the n pairs of forecasts. The BSS is negatively oriented, and perfect estimates have BSS = 0.
A reliability diagram is a graphical device that shows the distribution of joint probability forecasts and observations of a binary predictand and is directly related to the BSS (Wilks 2006). Finally, a relative operating characteristic (ROC) diagram is another graphic method of forecast verification, based on plots of the normal probability rates Φ of hits H and false alarms F for a given forecast threshold. The area beneath the fitted curve is computed using
e10
The score associated with an ROC area Az can be calculated as follows, where ROCSS = 1 for perfect forecasts:
e11

3. Results and discussion

a. Climate forecast

The main evaluation parameters for the statistical models used to forecast monthly and seasonal rainfall via MDA are shown in Table 3. The model selection was performed considering the following conditions: (i) the significance of box M (α > 0.05), (ii) the number of model variables equal to or less than six (10% of the number of cases), (iii) a greater percentage of variance explained by the first PCA function (F1), (iv) a higher hit percentage of the original n classification, and (v) the (n − 1) cross classification, the last of the main evaluation criteria.

Table 3.

Model evaluation parameters for monthly and seasonal rainfall categorical forecasts in southern Brazil HRs.

Table 3.

The box-M significance is related to the multivariate normality assumption of predictor matrices. Hair et al. (2010) have noted that if data do not satisfy this assumption, this can lead to problems in estimating the discriminant functions. Table 3 shows that this statistic was acceptable in most cases (α > 0.05), except for HR1 and HR2 in DJF. However, Maroco (2003) notes that discriminant analysis is a technique that is robust to the violation of this assumption when the size of the smaller group is greater than the number of variables, a condition that was satisfied in the present case.

The independent variables (PC scores) to be included in the model were selected from the most significant ones, at a maximum of six, corresponding to 10% of cases (60 observations). Thus, the results in Table 3 show an average number of model variables of five, ranging between four and six. The average number of fields was slightly lower (four) and showed the highest variability (between two and six). It should be noted that the number of fields will always be less than or equal to the number of variables because a field can contain one or more variables. It is also worth noting the difference between a predictor and a predictor variable field, the latter of which is related to a single field that can be atmospheric, oceanic, or surface related (e.g., the SST or SLP). The predictor variables correspond to each of the PC scores of a given atmospheric or oceanic or surface field [e.g., 1st SLP PC (SLP_1) or 1st TSM_PAC PC (TSM_PAC_1)].

The percentage of forecast hits, which is equivalent to the PCS, ranged between 65% and 75% for the original n classification and between 58% and 68% for the (n − 1) cross-validation procedure; on average, the hit percentages summed up 69.2% and 61.8%, respectively (Table 3). These results are promising, especially for the Southeast and Middle-West regions of Brazil, where climate prediction has the lowest hit percentage and the impact of adverse weather conditions is great. Further details on the assessment of these results will be presented in the next section.

The variances of the first function (F1) and the Wilks lambda value Λ showed significance in all HRs and during all periods (α < 0.001). Both parameters correspond to the discriminatory power of the first function, and the average percentage of the F1 variance was 81.1% (Table 3). The second discriminant function (F2) was also significant (α < 0.05) in all cases (values not shown). Table 4 presents the variables included in the model and their respective coefficients for the first (F1) and second (F2) discriminant functions. The relative importance of the model variables will be discussed below, based on higher absolute values of the F1 coefficients. Figure 2 shows the spatial distributions of the selected variables, and the following discussions are similarly grouped according to HR.

Table 4.

Variables and coefficients for the first (F1) and second (F2) discriminant functions used for monthly and seasonal rainfall categorical forecasting in southern Brazil HRs.

Table 4.
Fig. 2.
Fig. 2.

Predictor KRs selected via MDA used for monthly and seasonal rainfall categorical forecasting in southern Brazil HRs. Acronyms correspond to the month or season followed by the PC number: (a)–(l) Jan_HR1, Jan_HR2, Jan_HR3, Jan_HR4, Oct_HR1, Dec_HR2, Dec_HR3, Feb_HR4, DJF_HR1, DJF_HR2, DJF_HR3, and DJF_HR4. The gray shaded contours represent the correlation (>0.7) of principal component scores with spatial patterns (loadings).

Citation: Weather and Forecasting 31, 6; 10.1175/WAF-D-15-0155.1

The greatest F1 coefficient in January was found for SST_PAC_3 in HR1, followed by SLP_19, both of which are located in the Pacific, surrounding the Australian continent. Located in the Atlantic, PWC_27 and SST_ATL_2 also exhibited relative importance, with coefficients > |0.5| (Table 4; Fig. 2a). In October, the main variable of the first function was found for Z250_1, representing the climatological position of the intertropical convergence zone at high levels throughout the year. In general, the KRs largely reflect the joint variability of the variable over time. The second relevant variable was SST_ATL_11, with a KR located in the Atlantic, to the southeast of HR1. Third, SST_PAC_3 also appeared to be significant, with coefficients near |0.5| (Table 4; Fig. 2e). In summer (DJF), the main predictor variable for HR1 was Z500_14, followed by SLP_16; both are located in the same area, in the southern region of the African continent. Ranking third and fourth were the variables Z250_3 and T850_30, located in the periphery of Antarctica and along the Brazilian coast, respectively (Table 4; Fig. 2i).

The albedo of the HR2 (ALB_HR2) was the main predictor variable in January. Notably, the same variable was also the most important for F2. Next, the other significant variables for the first function were T850_22, located in the Antarctic Ross Sea region, and SST_PAC_6, located along the western coast of the South American continent (Table 4; Fig. 2b). In December, the main predictor variable for HR2 was again a surface variable (SMC_HR3), followed by T850_37 and T850_22, both located along the periphery of Antarctica. It should be noted that the fourth most important variable for that month (Z850_1), although presenting a relatively low coefficient for the first function, was the most significant for F2; this variable is also located in Antarctica (Table 4; Fig. 2f). In the seasonal analysis of the DJF period for HR2, the two largest coefficients were found for PWC_25 and SLP_19, both in KRs situated on the African continent. The two next most important variables corresponded to the air temperature field at 850 mb: one located to the east of Australia (T850_32) and the other (T850_39) located in the interior of Africa (Table 4; Fig. 2j).

The forecast rainfall analysis for January in HR3 revealed that the main predictor was the soil moisture in the region (SMC_HR3), followed by PWC_43. With the exception of the first variable, all others (PWC_43, T850_32, Z500_11, SLP_18, and Z700_13) are located in the south-central sector of the Pacific Ocean, between 30° and 60°S (Table 4; Fig. 2c). The variable Z500_16, located to the southeast of HR3 in the Atlantic Ocean, was predominant in December, followed by four KRs of precipitable water content located in Antarctica (PWC_47) and in the eastern (PWC_16) and central Pacific (PWC_31 and PWC_59) (Table 4; Fig. 2g). The sea level pressure on the Antarctic continent (SLP_1) emerged as the main predictor variable for HR3 during summer (DJF), followed by two KRs of the geopotential height at 850 mb (Z850_10 and Z850_9). In addition, we observed strong contributions from the T850_25 and SLP_2 variables, located in the ENSO region and its surroundings, in the equatorial Pacific (Table 4; Fig. 2k).

Considering the HR4, the Pacific region near approximately 30°N was found to have a significant influence on rainfall over the region in January. Among the four most relevant variables, three are located in this area (PWC_63, T850_38, and SLP_20). In addition, the SST_PAC_19 and PWC_16 variables are also located in the Pacific, in the region surrounding the Australian continent, and also influence rainfall in the region (Table 4; Fig. 2d). In February, the Atlantic and Pacific SSTs in the Northern Hemisphere, at approximately 30°N, appeared to be the main predictor variables (SST_PAC_20 and SST_ATL_23), followed by SST ATL_3, which is located along the northeastern coast of Brazil. In addition, geopotential height variables (Z500_2 and Z850_6) located in Antarctica and its surroundings also exhibited relative importance as predictors of HR4 rainfall (Table 4; Fig. 2h). Finally, for the DJF period, the main predictor (Z850_7) is located over the Antarctic Peninsula; this predictor is followed in significance by SST_PAC_7, which is situated at approximately 30°S. Other relevant rainfall predictors for this region during summer were SST_PAC_17 and PWC_58, which are located relatively far from this homogeneous region (Table 4; Fig. 2l).

b. Teleconnection mechanisms associated with rainfall

Empirical analyses, such as that applied in this study, do not necessarily reflect the physical aspects of the relevant atmospheric processes. However, by observing the fields and variables that repeatedly emerge in different analyses and through comparisons with other studies, it is possible to infer several possible teleconnections between predictors and predictands. If properly understood, these teleconnections can contribute to improving empirical and dynamic climate forecasting models.

Regarding the contributions of the predictor fields, the geopotential heights at different levels (Z850, Z700, Z500, and Z250) constituted 23% of the predictor variables, whereas SLP variables constituted only 12%. Both fields are related to atmospheric pressure and together exceeded ⅓ of the predictor variables. In general, these variables were found to be preferentially in three regions: near the equator (Figs. 2e,k); at medium latitudes, near approximately 60°S (Figs. 2b,c,h,i,j); and over the Antarctic continent and its surroundings (Figs. 2f,h,i,k,l).

The PWC was found to be the more important field individually, contributing 25% of the selected variables in the discriminant analysis. These results indicate that this field is the second best predictor of rainfall. It is possible that several of the observed remote connections may represent merely statistical flukes; however, in some cases, the significant PWC variables appeared at locations near the considered region (Fig. 2j) or were associated with other variables in regions of the globe where a connection was suggested through wave trains (Fig. 2c).

The Atlantic and Pacific SSTs, which are the variables that are most commonly used in empirical climate prediction models (Nobre and Shukla 1996; Diaz et al. 1998; Coelho et al. 2006a), ranked third, accounting for 22% of the predictors. The number of Pacific variables corresponded to nearly double that of the Atlantic variables (nine versus five), and among the oceanic variables, SST_PAC_3 (Figs. 2a,e) and SST_PAC_6 (Figs. 2b,e) were significant for both HR1 and HR2.

Although no SIC variables were selected in the analysis, the atmospheric circulation over the Antarctic continent and its surroundings demonstrated considerable importance for the predictability of all HRs. Among the variables selected in the MDA, Z700_5 and Z850_7 on the Antarctic Peninsula (Figs. 2e,l), PWC_47 in the Weddell Sea (Figs. 2a,g), Z250_3 in the Amundsen Sea (Fig. 2i), and T850_22, T850_37, Z850_1, SLP_1, and Z250_2 over the Antarctic continent (Figs. 2b,f and 2h,k) are all related to the Antarctic region. Indeed, the influence of Antarctic climate variability on South America has previously been investigated by several authors, such as Silvestri and Vera (2003) and Kayano and Sansigolo (2012), who found significant correlations between the Antarctic Oscillation index and rainfall anomalies in southern Brazil.

Regarding the surface variables, although they accounted for only 5% of the predictors, they did play an important role in the cases in which they were selected. The regional albedo in HR2 (Fig. 2b) and the soil moisture in HR3 (Fig. 2f) were the most important predictors in January and December, respectively. For HR3, the regional SMC was also found to be the main predictor in January (Fig. 2c). This result reflects the role of soil cover and moisture as potential predictors of rainfall, as shown in studies by Namias (1989) and Grimm et al. (2007), with the latter highlighting the role of soil moisture specifically in the southeastern region of Brazil.

It should be emphasized that variables located over the ENSO occurrence area were observed to be significant in a single scenario (SLP_2), namely, the DJF seasonal forecast for HR3. This phenomenon is often claimed to be the primary source of interannual variability in rainfall over the region (Grimm et al. 2000); however, the cited authors did note that the impact of ENSO on rainfall in southern Brazil is stronger in spring, a period not represented in the present study. Grimm et al. (2000) also noted that in summer, the variability mode associated with ENSO impacts central-eastern Brazil (HR3), corroborating the results of this study (Fig. 2k).

c. Rainfall forecast evaluation

Table 5 shows the results of the categorical and probabilistic scores for monthly and seasonal rainfall forecasts in southern Brazil. The PCS ranged between 0.583 and 0.683, whereas the HSS was slightly lower, ranging between 0.375 and 0.525. The results for the PCS exhibit, on average, a 28.5% gain over climatology.

Table 5.

Categorical and probabilistic skill scores for monthly and seasonal rainfall forecasting in southern Brazil HRs.

Table 5.

With regard to the probability scores, the equitable scores were very similar, ranging between 0.338 and 0.6 (GMSS) and between 0.325 and 0.625 (LEPS-CAT) (Table 5). In almost all cases, LEPS-CAT was superior to GMSS, indicating better skill in extreme situations (above/below average), because the LEPS-CAT weights are greater compared to those of GMSS. As a comparison, Sansigolo (1999) found a LEPS-CAT value of 0.24 when evaluating a discriminant model for seasonal rainfall forecasting in northeastern Brazil using the PCA scores of the Pacific and Atlantic SSTs as predictors. The overall average value of the BSS was 0.175 (Table 5). However, it should be noted that the score is negatively oriented (a perfect forecast receives a score of 0), and consider the mean square errors between pairs of observations and forecasts, which were relatively small in the model.

The ROCSS was 0.533 on average and ranged from 0.466 to 0.632 (Table 5). Figure 3 illustrates the reliability diagram and the ROC curve for the model as a whole, considering all periods and HRs. The reliability diagram (Fig. 3a) indicates good model calibration with regard to the predicted and observed frequencies, as do the examples illustrated by Wilks (2006). The ROC curve (Fig. 3b) also exhibits a good fit, with an ROC area of 0.767. By comparison, although different criteria (period and study area) were used, the ROC area value of the CPTEC atmospheric general circulation model for South America in the summer period was found to be 0.57 (Cavalcanti et al. 2002; Marengo et al. 2003), whereas an evaluation of IRI’s climate models has revealed a pattern similar to that of the Centro de Previsão do Tempo e Estudos Climáticos (CPTEC) results, with overall ROC areas between 0.552 and 0.555 (IRI 2015).

Fig. 3.
Fig. 3.

(a) Reliability diagram and (b) ROC curve for monthly and seasonal rainfall forecasting considering all periods and homogeneous regions. The bar graph in (a) represents the frequency histogram that indicates that each bin of probabilities is used an appropriate amount of times. Frequency histograms show the frequency of forecasts as a function of the probability bin. In (b), all monthly and seasonal forecasts were grouped according to probability categories in a single set of data to show the overall performance of the model.

Citation: Weather and Forecasting 31, 6; 10.1175/WAF-D-15-0155.1

4. Conclusions

When a multiple linear discriminant model was used, monthly and seasonal rainfall forecasts in southern Brazil showed an average skill score, or gain over climatology, of 29%. The percentage of forecast hits, which is equivalent to PCS, ranged between 65% and 75% for the complete dataset n classification and between 58% and 68% for the (n − 1) cross-validation procedure. The variances of the first discriminant function F1 and the Wilks Lambda value Λ were significant (α < 0.001) in all HRs and during all periods, having an average variance of 81.1%.

The average number of variables in the model was five. Considering the contribution of the predictor fields, the geopotential heights at different levels (Z850, Z700, Z500, and Z250) constituted 23% of the variables, and SLPs only 12%. Both fields are related to atmospheric pressure and together exceeded half of the cases. The PWC was found to be the most important field individually, contributing to 25% of the selected variables in the discriminant analysis. The Atlantic and Pacific SSTs, the most commonly used in empirical climate prediction models, ranked third, accounting for 22% of predictors. Regarding the surface variables, although accounting for only 5% of the predictors, they played an important role in cases where selected. The regional albedo in HR2 and the soil moisture in HR3 were the most important predictors in January and December, respectively.

The forecast evaluations indicated that the best model performance was observed for the extreme cases (above/below average). The statistical pattern recognition approach was shown to be feasible from an operational point of view for rainfall climate forecasts in southern Brazil. It was observed that the use of a large number of predictors, and combinations of these, resulted in a significant improvement in the predictions. In summary, we conclude that for every three predictions, the model hits two, and the probability of success is higher for the extreme terciles (below/above normal). This feature becomes important since these categories are the most relevant and difficult to be predicted.

The set of atmospheric, oceanic, and surface patterns and teleconnection mechanisms associated was used jointly and objectively for seasonal rainfall climate forecasting. It is possible that teleconnections and the physical processes associated between the predictors key regions and the predictands (rainfall homogeneous regions) could be studied using dynamic modeling techniques as influence functions.

Acknowledgements

This paper is part of the DRV’s Ph.D. dissertation in meteorology at INPE in 2015. DRV acknowledges the CAPES and CNPq for the Ph.D. scholarship. We also thank the anonymous reviewers for their helpful comments and suggestions for improving the manuscript.

REFERENCES

  • Barnett, T. P., , and Preisendorfer R. W. , 1978: Multifield analog prediction of short-term climate fluctuations using a climate state vector. J. Atmos. Sci., 35, 17711787, doi:10.1175/1520-0469(1978)035<1771:MAPOST>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., 1994: Linear statistical short-term climate predictive skill in the Northern Hemisphere. J. Climate, 7, 15131564, doi:10.1175/1520-0442(1994)007<1513:LSSTCP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., , and Livezey R. E. , 1989: An operational multifield analog/anti-analog prediction system for United States seasonal temperatures Part II: Spring, summer, fall, and intermediate 3-month period experiments. J. Climate, 2, 513541, doi:10.1175/1520-0442(1989)002<0513:AOMAAP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Barnston, A. G., , Glantz M. H. , , and He Y. , 1999: Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997–1998 El Niño episode and the 1998 La Niña onset. Bull. Amer. Meteor. Soc., 80, 217243, doi:10.1175/1520-0477(1999)080<0217:PSOSAD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Bergen, R. E., , and Harnack R. P. , 1982: Long-range temperature prediction using a simple analog approach. Mon. Wea. Rev., 110, 10831099, doi:10.1175/1520-0493(1982)110<1083:LRTPUA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Casey, T. M., 1995: Optimal linear combination of seasonal forecasts. Aust. Meteor. Mag., 44, 219224.

  • Cavalcanti, I. F. A., and Coauthors, 2002: Global climatological features in a simulation using the CPTEC–COLA AGCM. J. Climate, 15, 29652988, doi:10.1175/1520-0442(2002)015<2965:GCFIAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ciancarelli, B., , Castro C. L. , , Woodhouse C. , , Dominguez F. , , Chang H.-I. , , Carrillo C. , , and Griffin D. , 2014: Dominant patterns of US warm season precipitation variability in a fine resolution observational record, with focus on the southwest. Int. J. Climatol., 34, 687707, doi:10.1002/joc.3716.

    • Search Google Scholar
    • Export Citation
  • Coelho, C. A. S., , Stephenson D. B. , , Balmaseda M. , , Doblas-Reyes F. J. , , and van Oldenborgh G. J. , 2006a: Toward an integrated seasonal forecasting system for South America. J. Climate, 19, 37043721, doi:10.1175/JCLI3801.1.

    • Search Google Scholar
    • Export Citation
  • Coelho, C. A. S., , Stephenson D. B. , , Doblas-Reyes F. J. , , Balmaseda M. , , Guetter A. , , and van Oldenborgh G. J. , 2006b: A Bayesian approach for multi-model downscaling: Seasonal forecasting of regional rainfall and river flows in South America. Meteor. Appl., 13, 7382, doi:10.1017/S1350482705002045.

    • Search Google Scholar
    • Export Citation
  • Compagnucci, R. H., , and Richman M. B. , 2008: Can principal component analysis provide atmospheric circulation or teleconnection patterns? Int. J. Climatol., 28, 703726, doi:10.1002/joc.1574.

    • Search Google Scholar
    • Export Citation
  • Compo, G. P., and Coauthors, 2011: The Twentieth Century Reanalysis Project. Quart. J. Roy. Meteor. Soc., 137, 128, doi:10.1002/qj.776.

    • Search Google Scholar
    • Export Citation
  • Diaz, A., , and Studzinski C. D. S. , 1994: Rainfall anomalies in the Uruguay-southern Brazil region related to SST in the Pacific and Atlantic Oceans using canonical correlation analysis. Proc. VIII Congresso Brasileiro de Meteorologia, Belo Horizonte, Brazil, Sociedade Brasileira de Meteorologia, 42–45.

  • Diaz, A., , Studzinski C. D. S. , , and Mechoso C. R. , 1998: Relationships between precipitation anomalies in Uruguay and southern Brazil and sea surface temperature in the Pacific and Atlantic Oceans. J. Climate, 11, 251271, doi:10.1175/1520-0442(1998)011<0251:RBPAIU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Douglas, A. V., , and Englehart P. J. , 1981: On a statistical relationship between autumn rainfall in the central equatorial Pacific and subsequent winter precipitation in Florida. Mon. Wea. Rev., 109, 23772382, doi:10.1175/1520-0493(1981)109<2377:OASRBA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gandin, L. S., , and Murphy A. H. , 1992: Equitable skill scores for categorical forecasts. Mon. Wea. Rev., 120, 361370, doi:10.1175/1520-0493(1992)120<0361:ESSFCF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gerrity, J. P., Jr., 1992: A note on Gandin and Murphy’s equitable skill score. Mon. Wea. Rev., 120, 27092712, doi:10.1175/1520-0493(1992)120<2709:ANOGAM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Grimm, A. M., , Barros V. R. , , and Doyle M. E. , 2000: Climate variability in southern South America associated with El Niño and La Niña events. J. Climate, 13, 3558, doi:10.1175/1520-0442(2000)013<0035:CVISSA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Grimm, A. M., , Pal J. S. , , and Giorgi F. , 2007: Connection between spring conditions and peak summer monsoon rainfall in South America: Role of soil moisture surface temperature and topography in eastern Brazil. J. Climate, 20, 59295945, doi:10.1175/2007JCLI1684.1.

    • Search Google Scholar
    • Export Citation
  • Hair, J., , Black W. , , Babin B. , , and Anderson R. , 2010: Multivariate Data Analysis. 7th ed. Pearson Prentice Hall, 785 pp.

  • Hall, A., , and Visbeck M. , 2002: Synchronous variability in the Southern Hemisphere atmosphere sea ice and ocean resulting from the annular mode. J. Climate, 15, 30433057, doi:10.1175/1520-0442(2002)015<3043:SVITSH>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Harnack, R., , Cammarata M. , , Dixon K. , , Lanzante J. , , and Harnack J. , 1985: Summary of US seasonal temperature forecast experiments. Preprints, Ninth Conf. on Probability and Statistics in the Atmospheric Sciences, Virginia Beach, VA, Amer. Meteor. Soc., 175–178.

  • Hastenrath, S., , and Greischar L. , 1993: Changing predictability of Indian monsoon rainfall anomalies. Proc. Ind. Acad. Sci., 102, 3547, doi:10.1007/BF02839181.

    • Search Google Scholar
    • Export Citation
  • Hastenrath, S., , Greischar L. , , and van Heerden J. , 1995: Prediction of the summer rainfall over South Africa. J. Climate, 8, 15111518, doi:10.1175/1520-0442(1995)008<1511:POTSRO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hastenrath, S., , Sun L. , , and Moura A. D. , 2009: Climate prediction for Brazil’s Nordeste by empirical and numerical modeling methods. Int. J. Climatol., 29, 921926, doi:10.1002/joc.1770.

    • Search Google Scholar
    • Export Citation
  • IRI, 2015: Seasonal climate verifications: Verification of IRI’s seasonal climate forecast. International Research Institute for Climate and Society. [Available online at http://iri.columbia.edu/our-expertise/climate/forecasts/verification/.]

  • Johansson, A., , Barnston A. G. , , Saha S. , , and Van den Dool H. M. , 1998: On the level of forecast skill in northern Europe. J. Atmos. Sci., 55, 103127, doi:10.1175/1520-0469(1998)055<0103:OTLAOO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Johnson, R. A., , and Wichern D. W. , 2007: Applied Multivariate Statistical Analysis. 6th ed. Prentice Hall, 800 pp.

  • Jolliffe, I. T., 2002: Principal Component Analysis. 2nd ed. Springer Verlag, 487 pp.

  • Kaplan, J., and Coauthors, 2015: Evaluating environmental impacts on tropical cyclone rapid intensification predictability utilizing statistical models. Wea. Forecasting, 30, 13741396, doi:10.1175/WAF-D-15-0032.1.

    • Search Google Scholar
    • Export Citation
  • Kayano, M. T., , and Sansigolo C. A. , 2012: Variações de precipitação e de temperaturas máxima e mínima no Rio Grande do Sul associadas à Oscilação Antártica. Proc. XVII Congresso Brasileiro de Meteorologia, Gramado, Brazil, Sociedade Brasileira de Meteorologia, 62QA. [Available online at http://www.sbmet.org.br/cbmet2012/pdfs/62QA.pdf.]

  • Keppenne, C. L., , and Ghil M. , 1992: Adaptive filtering and the Southern Oscillation index. J. Geophys. Res., 97, 20 44920 454, doi:10.1029/92JD02219.

    • Search Google Scholar
    • Export Citation
  • Knaff, J. A., , and Landsea C. W. , 1997: An El Niño–Southern Oscillation climatology and persistence (CLIPER) forecasting scheme. Wea. Forecasting, 12, 633652, doi:10.1175/1520-0434(1997)012<0633:AENOSO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Livezey, R. E., , and Barnston A. G. , 1988: An operational multifield analog/antianalog system for United States seasonal temperatures: Part 1. System design and winter experiments. J. Geophys. Res., 93, 10 95310 974, doi:10.1029/JD093iD09p10953.

    • Search Google Scholar
    • Export Citation
  • Lúcio, P. S., and Coauthors, 2010: Um modelo estocástico combinado de previsão sazonal para a precipitação no Brasil. Rev. Bras. Meteor., 25, 7087, doi:10.1590/S0102-77862010000100007.

    • Search Google Scholar
    • Export Citation
  • Marengo, J. A., and Coauthors, 2003: Assessment of regional seasonal rainfall predictability using the CPTEC/COLA atmospheric GCM. Climate Dyn., 21, 459475, doi:10.1007/s00382-003-0346-0.

    • Search Google Scholar
    • Export Citation
  • Maroco, J., 2003: Análise Estatística com Utilização do SPSS. 2nd ed. Sílabo, 824 pp.

  • Mason, S. J., 1998: Seasonal forecasting of South African rainfall using a non-linear discriminant analysis model. Int. J. Climatol., 18, 147164, doi:10.1002/(SICI)1097-0088(199802)18:2<147::AID-JOC229>3.0.CO;2-6.

    • Search Google Scholar
    • Export Citation
  • Moura, A. D., , and Hastenrath S. , 2004: Climate prediction for Brazil’s Nordeste: Performance of empirical and numerical modeling methods. J. Climate, 17, 26672672, doi:10.1175/1520-0442(2004)017<2667:CPFBNP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Mukhin, D., , Kondrashov D. , , Loskutov E. , , Gavrilov A. , , Feigin A. , , and Ghil M. , 2015: Predicting critical transitions in ENSO models. Part II: Spatially dependent models. J. Climate, 28, 19621976, doi:10.1175/JCLI-D-14-00240.1.

    • Search Google Scholar
    • Export Citation
  • Muza, M. N., , Carvalho L. M. V. , , Jones C. , , and Liebmann B. , 2009: Intraseasonal and interannual variability of extreme dry and wet events over southeastern South America and the subtropical Atlantic during austral summer. J. Climate, 22, 16821699, doi:10.1175/2008JCLI2257.1.

    • Search Google Scholar
    • Export Citation
  • Namias, J., 1989: Cold waters and hot summers. Nature, 338, 1516, doi:10.1038/338015a0.

  • Nobre, P., , and Shukla J. , 1996: Variations of sea surface temperature wind stress and rainfall over the tropical Atlantic and South America. J. Climate, 9, 24642479, doi:10.1175/1520-0442(1996)009<2464:VOSSTW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Polikar, R., 2006: Pattern recognition. Wiley Encyclopedia of Biomedical Engineering, M. Akay, Ed., J. Wiley and Sons, 122, doi:10.1002/9780471740360.ebs0904.

  • Potts, J. M., , Folland C. K. , , Jolliffe I. T. , , and Sexton D. , 1996: Revised “LEPS” scores for assessing climate model simulations and long range forecasts. J. Climate, 9, 3453, doi:10.1175/1520-0442(1996)009<0034:RSFACM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Radinovic, D., 1975: An analogue method for weather forecasting using the 500/1000 mb relative topography. Mon. Wea. Rev., 103, 639649, doi:10.1175/1520-0493(1975)103<0639:AAMFWF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rayner, N. A., , Parker D. E. , , Horton E. B. , , Folland C. K. , , Alexander L. V. , , Rowell D. P. , , Kent E. C. , , and Kaplan A. , 2003: Global analyses of sea surface temperature sea ice and night marine air temperature since the late nineteenth century. J. Geophys. Res., 108, 4407, doi:10.1029/2002JD002670.

    • Search Google Scholar
    • Export Citation
  • Richman, M. B., 1986: Rotation of principal components. J. Climatol., 6, 293335, doi:10.1002/joc.3370060305.

  • Sansigolo, C. A., 1991: Seasonal rainfall forecasting in the north-east region of Brazil. Grosswetter, 30, 3342.

  • Sansigolo, C. A., 1999: Verificação de um modelo discriminante de previsão das precipitações sazonais do Nordeste. Rev. Bras. Meteor., 14, 2935.

    • Search Google Scholar
    • Export Citation
  • Schneider, U., , Becker A. , , Meyer-Christoffer A. , , Ziese M. , , and Rudolf B. , 2011: Global precipitation analysis products of the GPCC. Global Precipitation Climatology Centre, DWD, 12 pp. [Available online at ftp://ftp-anon.dwd.de/pub/data/gpcc/PDF/GPCC_intro_products_2008.pdf.]

  • Shabbar, A., , and Barnston A. G. , 1996: Skill of seasonal climate forecasts in Canada using canonical correlation analysis. Mon. Wea. Rev., 124, 23702385, doi:10.1175/1520-0493(1996)124<2370:SOSCFI>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Shahi, N. K., , Rai S. , , and Pandey D. K. , 2016: Prediction of daily modes of South Asian monsoon variability and its association with Indian and Pacific Ocean SST in the NCEP CFS V2. Meteor. Atmos. Phys., 128, 131142, doi:10.1007/s00703-015-0404-2.

    • Search Google Scholar
    • Export Citation
  • Shukla, J., 1998: Predictability in the midst of chaos: A scientific basis for climate forecasting. Science, 282, 728731, doi:10.1126/science.282.5389.728.

    • Search Google Scholar
    • Export Citation
  • Silvestri, G. E., , and Vera C. S. , 2003: Antarctic Oscillation signal on precipitation anomalies over southeastern South America. Geophys. Res. Lett., 30, 2115, doi:10.1029/2003GL018277.

    • Search Google Scholar
    • Export Citation
  • Sneyers, R., , and Goossens C. , 1988: The Principal Component Analysis Application to Climatology and to Meteorology. World Meteorological Organization, 55 pp.

  • Taschetto, A. S., , and Wainer I. , 2008: The impact of the subtropical South Atlantic SST on South American precipitation. Ann. Geophys., 26, 34573476, doi:10.5194/angeo-26-3457-2008.

    • Search Google Scholar
    • Export Citation
  • Timm, N. H., 2002: Applied Multivariate Analysis. Springer Verlag, 718 pp.

  • Tippett, M. K., , and DelSole T. , 2013: Constructed analogs and linear regression. Mon. Wea. Rev., 141, 25192525, doi:10.1175/MWR-D-12-00223.1.

    • Search Google Scholar
    • Export Citation
  • Van den Dool, H. M., 1994: Searching for analogues: How long must we wait? Tellus, 46A, 314324, doi:10.1034/j.1600-0870.1994.t01-2-00006.x.

    • Search Google Scholar
    • Export Citation
  • Van den Dool, H. M., 2007: Empirical Methods in Short-Term Climate Prediction. Oxford University Press, 215 pp.

  • Wang, L., , Yuan X. , , Ting M. , , and Li C. , 2016: Predicting summer Arctic sea ice concentration intraseasonal variability using a vector autoregressive model. J. Climate, 29, 15291543, doi:10.1175/JCLI-D-15-0313.1.

    • Search Google Scholar
    • Export Citation
  • Ward, M. N., , and Folland C. K. , 1991: Prediction of seasonal rainfall in the north Nordeste of Brazil using eigenvectors of sea-surface temperature. Int. J. Climatol., 11, 711743, doi:10.1002/joc.3370110703.

    • Search Google Scholar
    • Export Citation
  • Wilks, D. S., 2006: Statistical Methods in the Atmospheric Sciences. 2nd ed. Elsevier, 627 pp.

Save