Abstract
In the present study, an ANOVA-like inference technique is used aiming at to assess if Alentejo, southern Portugal, could be considered a homogeneous region for drought management purposes. First, Alentejo was divided into four sub-regions according to latitude (north and south), and longitude (west and east). Inside each sub-region, 10 weather stations were considered. The time series of the Standardized Precipitation Index (SPI) were obtained for these stations using precipitation data for the period 1932–1999 (67 years). Contingency tables for the transitions between SPI drought classes were obtained for these time series. Loglinear models were fitted to these contingency tables to estimate the probabilities for drought class transitions. An ANOVA-like inference was applied considering the four sub-regions like treatments of a two way layout with two factors, latitude and longitude, each one with two levels, north and south, and west and east respectively. The weather stations of each sub-region were treated as replicates. Significant differences between west and east were found, that allowed to consider that Alentejo could be composed by two sub-regions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agresti A (1990) Categorical data analysis. Wiley, New York
Bonaccorso B, Bordi I, Cancelliere A, Rossi G, Sutera A (2003) Spatial variability of drought: an analysis of the SPI in Sicily. Water Resour Manag 17:273–296
Bordi I, Fraedrich K, Jiang J-M, Sutera A (2004) Spatio-temporal variability of dry and wet periods in eastern China. Theor Appl Climatol 79:81–91
Bordi I, Fraedrich K, Sutera A (2009) Observed drought and wetness trends in Europe: an update. Hydrol Earth Syst Sci. 13:1519–1530
Cebrian AC, Abaurrea J (2011) Risk measures for events with a stochastic duration: an application to drought analysis. Stoch Environ Res Risk Assess. doi:10.1007/s00477-011-0521-5
Dubreuil P (1974) Initiation à l’Analyse Hydrologique. Masson & Cie, Editeurs, Paris
Helsel DR, Hirsch RM (1992) Statistical methods in water resources. Elsevier, Amsterdam
Hocking R (2003) Methods and applications of linear models. Wiley, New York
Ito K (1980) Robusteness of ANOVA and MANOVA test procedures, In: Krishnaiah PR (ed) Handbook of statistics, vol. 1. North-Holland Publishing Company, Amsterdam, pp 199–236
Matias PG (1998) Análise de Frequência de Séries Hidrológicas Anuais. DER/ISA, Lisbon
McKee TB, Doesken NJ, Kleist J (1993) The relationship of drought frequency and duration to time scales. In: 8th conference on applied climatology. American Meteorology Society, Boston, pp 179–184
McKee TB, Doesken NJ, Kleist J (1995) Drought monitoring with multiple time scales. In: 9th conference on applied climatology. American Meteorology Society, Boston, pp 233–236
Militino AF, Ugarte MD, Ibáñez B (2008) Longitudinal analysis of spatially correlated data. Stoch Environ Res Risk Assess 22(Suppl 1):S49–S57
Montgomery DC (1997) Design and analysis of experiments—5th edition. Wiley, New York
Moreira EE, Paulo AA, Pereira LS, Mexia JT (2006) Analysis of SPI drought class transitions using loglinear models. J Hydrol 331:349–359
Moreira EE, Coelho CA, Paulo AA, Pereira LS, Mexia JT (2008) SPI-based drought category prediction using loglinear models. J Hydrol 354:116–130
Moreira E, Mexia J, Zmyslony R, Fonseca M (2009) L models and multiple regression designs. Stat Pap 50:869–885
Moustakas A, Silvert W (2011) Spatial and temporal effects on the efficacy of marine protected areas: implications from an individual based model. Stoch Environ Res Risk Assess 25:403–413
Nelder JA (1974) Loglinear models for contingency tables: a generalization of classical least squares. Appl Stat 23:23–329
NSSTC (2003) NASA working to take the guesswork out of long-term drought prediction (http://www.msfc.nasa.gov/news/NSSTC/news/releases/2003/N03-008.html)
OMM (1970) Guide des Pratiques Hydrométéorologiques (2eme édition), OMM/WMO Nr. 168 TP 82, Geneve
Paulo AA, Pereira LS, Matias PG (2003) Analysis of local and regional droughts in southern Portugal using the theory of runs and the Standardized Precipitation Index. In: Rossi G, Cancelliere A, Pereira LS, Oweis T, Shatanawi M, Zairi A (eds.) Tools for drought mitigation in Mediterranean regions. Kluwer, Dordrecht, pp 55–78
Paulo AA, Ferreira E, Coelho C, Pereira LS (2005) Drought class transition analysis through Markov and Loglinear models, an approach to early warning. Agric Water Manag 77:59–81
Paulo AA, Pereira LS (2006) Drought concepts and characterization: comparing drought indices applied at local and regional scales. Water Int 31(1):37–49
Paulo AA, Pereira LS (2007) Prediction of SPI drought class transitions using Markov chains. Water Resour Manag 21:1813–1827
Paulo AA, Pereira LS (2008) Stochastic prediction of drought class transitions. Water Resour Manag 22(9):1277–1296
Rao R, Srinivas V (2006) Regionalization of watersheds by hybrid-cluster analysis. J Hydrol 318:37–56
Rao R, Srinivas V (2006) Regionalization of watersheds by fuzzy cluster analysis. J Hydrol 318:57–79
Raziei T, Bordi I, Pereira L (2008) A precipitation-based regionalization for Western Iran and regional drought variability. Hydrol Earth Syst Sci 12:1309–1321
Raziei T, Bahram S, Paulo A, Pereira L, Bordi I (2009) Spatial patterns and temporal variability of drought in Western Iran. Water Resour Manag 23(3):439–455
Rosa R D, Paulo A, Matias P, Espirito Santo M and Pires (2010) Tratamento da qualidade das séries de dados climáticos quanto a homogeneidade, aleatoriedade e tendência e completagem de séries de dados. In: Pereira LS, Mexia JT, Pires CAL (eds), Gestão do Risco em Secas. Métodos, Tecnologias e Desafios, Edições Colibri, CEER, pp 119–139.
Santos MA (1983) Regional droughts: a stochastic characterization. J Hydrol 66:183–211
Santos JF, Pulido-Calvo I, Portela M (2010) Spatial and temporal variability of droughts in Portugal. Water Resour Res 46:W03503, pp 13
Scheffé H (1959) The analysis of variance. Wiley, New York
She D, Xia J (2012) The spatial and temporal analysis of dry spells in the Yellow River basin, China. Stoch Environ Res Risk Assess. doi:10.1007/s00477-011-0553-x
Suhailaa J, Jemainb AA, Hamdana MF, Zinb ZW (2011) Comparing rainfall patterns between regions in Peninsular Malaysia via a functional data analysis technique. J Hydrology. doi:10.1016/j.jhydrol.2011.09.043
Taskinen A, Sirvio H, Bruen M (2008) Modelling effects of spatial variability of saturated hydraulic conductivity on autocorrelated overland flow data: linear mixed model approach. Stoch Environ Res Risk Assess 22:67–82
Vicente-Serrano SM (2006) Differences in spatial patterns of drought on different time scales: an analysis of the Iberian Peninsula. Water Resour Manag 20:37–60
Vogel RM, Stedinger JR (1985) Minimum variance streamflow record augmentation procedures. Water Resour Res 21(5):715–723
Wilhite DA, Hayes MJ, Knutson C, Smith KH (2000) Planning for drought: moving from crisis to risk management. J Am Water Resour Assoc 36:697–710
Wijngaard JB, Klein Tank AMG, Können GP (2003) Homogeneity of 20th century European daily temperature and precipitation series. Int J Climatol 23:679–692
Acknowledgements
This work was partially supported by the research project PTDC/AGR-AAM/71649/2006-Droughts Risk Management: Identification, Monitoring, Characterization, Prediction and Mitigation as well as by CMA/FCT/UNL under the project PEst-OE/MAT/UI0297/2011.
Author information
Authors and Affiliations
Corresponding author
Appendix: Estimators of the parameters of the loglinear models
Appendix: Estimators of the parameters of the loglinear models
See Table 6.
Rights and permissions
About this article
Cite this article
Moreira, E.E., Mexia, J.T. & Pereira, L.S. Assessing homogeneous regions relative to drought class transitions using an ANOVA-like inference. Application to Alentejo, Portugal. Stoch Environ Res Risk Assess 27, 183–193 (2013). https://doi.org/10.1007/s00477-012-0575-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-012-0575-z