MAIA, A. de H. N.

MEINKE, H.

RCAAP - Repositório Científico de Acesso Aberto de Portugal

Quantifying uncertanties associated with climate variability and climate change studies: the Cox'S semiparametric approach.

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, The prevailing climate on our country is due to its location in dry and semi-<lry district, as a result, droughtis the commonest phenomenon in this country. One of the drought and climatologic drought's definitions is as follow. If the precipitalion is less than average during long-term períod, it is called drought. The drQught of northwestem of lran which is due to the shortage of precipitation has caused starvation and poverty.First, the research framework, theoretical principie, and study of precipitalion fluctuations, trend, temperature, humidity, wind, évapotranspiration of stations are under study. Then lhe precipitation correlation between stationsand"precipitatibn andtemPerature correlation with respect to altitudes have been studied. In order to determine lhe reasons of drought in the region which is under study, primaríly, lhe fluctuations of time,.frequency and degree of drought as per Z score have been examined whieh prove in statistical and synopticnetwork that due to simultaneous drought in regionin terms of severity, ~kness frequency, time,location at different stations are different. And later on study of reasons of drought with regard to lhe paltem movement of general circulation of Climate with Tel connection which results in changing in paltem pressure in regian and movement of circumpolar westem line and blocking systems by benefiting from normal distribution probability the retum period 2,5,20,100,1000 were determiried and the 'occurrence of probability in distribution 0/020 & 80%was calculated and retum period with ~year'dróUghtrange and 5-year humid period range. Quantifying Uncertanties Assoeiatf!d With Climate Variaihlity and Climate Change Studies: the C-QX'S Semiparametric Approac"" Aline de Holanda Nun!'S Maia e-mail:ahmaia@cnpma.embrapa.br Elnbrapa Meio Ambiente Holger Meinke e-mail:holger.meinke@wur.nl Wageningen University, Department ofPlant Sciences A wide range of probabilistic approaches havé been used for assessing climatic risks and aSSociated iJncertainties:, multiple linear' regression (Martis et ai, 2002), logistic regression (Nichols, 1984; Lo et ai, 2007), nonparametric approaches based on empirical cumulative ,distribution functions (Maia & Meinke, 1998; Maia et ai, 2004), among others. In this paper, we quantify risks by using probability of exeedance curves (PECs) and propose the useof the proportional hazards, model (also referred to as Cox model - Cox, 1972; . CPH model)to·investiglilte the influence of continuous (e.g. oceaniclatmospheríc indexes) or categorical pradiCtors (e.g. classes deríved from EINiflolSouthern Oscillation) on these risks. CPH model is widely used in medicai analyses of survivaf data that examine the effect of explanatory varii!lbles on survival times. This allows the ranking af risk fi!lctors and quantitative assessments of lheir impacts. These methods are well established in medicai research and " used routinely'for- risk assessment,in medicai studies (e.g. Finkelstein et ai, 1993; De Lorgeril, .. 132 \ ,. 1999; Smith et ai, 2001; Gibbons, 2002) where data are rarely normally distributed and often incomplete. To our knowledge, this study is the fjrst using lhe CPH framework to analyse the linkage amQllg oceaniélatmospheric indexes and climate. risks. This constitutes a major step towards better quantification of climate related uncertainties in climate variability and climate change studies. ,Some of the advantages of using the CI?H model include: a) lhe method was developed to accommodate censored data (incomplete information) without lhe need to balance the data set thereby discarding potentially valuable information;b) in contrast to ordinary least squares mU,ltiple linear regression or logistic regression, CPH model does not require assumptions regarding lhe type of unl:lerlying probability distributions; proportionality af hazards' is the only assumption necessary for CPH model, and even thls can be relaxed via an appropriate generalization;c) it overcomes lhe problemof having to estimate probabilities of' exceedance for each Ihreshold in order to compose a PEC, a limilation of lhe logistic regression approach as used in Lo et ai (2007);d) when compared wilh . lhe nonparametric approach used by Maiaet ai (2007), CPH frameworkis superior because it allOW$inllestigating simultaneously inflúences o'many predictorson'risks;:the contribution of each 'candidate' can objectlvely be 'evaluated vi.a likelihood tests;e) methods for assessing uncer!aintiesof PEC (and Iher:efore uncertail)ties of risk estimates) are readily available. níese methods have well established theoretical basis. (Kalbfleisch and Pr'entice, 1(80); . , We demonstratelhe adequacy and usefulness of lhe proposedapproach by analysing the .. influence of.two oceaniélaunospheric indexes on the onset of rnonsoonal wet season at Darwin, 'Ausfralia, as suggested by Lo elal (2007): the Southem Oscillation Index (mean of lhe Julyand AUgust monthly SOllialues) and lhe first rotated principal component (SST1) of large scaleSea SuÍface Temperatures anomalies (DrosdowSky and Chambers, 2001). When applied U;grided data,. the CPH approach allows objective spatial assessment of é.itherindividual or joiÍlt influences of such predictors onrisks. Mapping the coefficients of the . Cox mede! (which expreSs the màgnitude of lhe predictor's influence) and p-values resulting trom lil<elihood tests prOvldes a cempletedescriptive and inferential assessment of predictor influence on the riSks. under investigation. Once the stronges! predictors are selected at a IoC!ltion, Pro.babilities of eX<:éÊ!din\l any particular Ihreshold (preferabLy within the range of óbserved datá) tan be 'estimated for any combination of predictor values. The resulting risk estimates and their. respective uncertainties provide valuàble InfOrmation for decision making in climatesensitive industries. References Drosdowsky,.W. and L E. Chambers, 2001: Nearijlobal sea surface temperature anomalies .aspredictorsof Australian seasonal rainfáll; Joumal of Climate, 14, 1677-1687 .. Cox, D.R, 1972: "RegressionModels and Life-Tables (with Discussion)," Joumal of lhe RoyalStatistical Society, Series B, 34, 187-220. , . De Lorgaril M.;Salen P.; Martin J-L.; MonjalJd I.; Delaye J.; N. Mamelle, 1999: Mediterranean diet, traditional risl( fáctors, and the rale of cardiovascular complications after myocardial infárction. Final report of the Lyon Diet Heart Study. Circulation, 99, 779-85. 133 Finkelstein, D. M.; MOI?re, D. F.; D. A. Schoenfeld, .1993: A Proportional Hazards Model for Truncated AIDS Data. Biometrics, 49 (3), 731-740. Gibbons, L.E.; TeriL.; Logsdon R; McCurry S.M,; Kukull W.2; Bowen J.; McCormick w.; E. Larson, 2002: Anxiely Symptoms as Predictors of Nursing Home Placement in Patients with Alzheimer's Diseáse. Joumal of Clinicai Geropsychology, 8 (4), 335-342. Kalbfleisch, J.D. and PrE!ntice,RL.,1980:The Statistical Analysis of Failure Time Data, New York: John Wiley & Sons, Inc. " Lo F:, M. Wheeler, H. Meinke and A. Donald,2oo7: Probabilistic forecasts of tI1e onset of the north Australian wet season. Monlhly Weather Review (in press). Maia, A. de H.N. and H. Meinke, 1999: Non-paràmetrical survival analysis as a statistical tool in agricultural ,decision making. Intemational Symposium, Modeling Cropping Systems, f'roceedings European Soe. For Agronomy, Div. Agroclimatology and Agronomic Modeling, Lleida,Spain, 21-23 June 1999, 103:-104. ,'Maia, A H: N.; Meinke, H.; S. Lerinox, 2004: Assessmentof probabilistic forecast 'skill'using p-values, Proc, 4th IntelTléltional Crop Science Congress, Brisbane, Australia, available aI: Ilttp:/IINww:cropscience.org.au/icsc2004lpoSterl2l6/1360 maiaa.htm. Maia, A. H. N.; H. Meinke, S. Lennox; R C. Stone, 2007: Inferential, non-parametric statistics , tO'a,ssess quality of probabilistic forecast systems. Monthly Weather RéView, 135(2),351-362. MartiS, A; G. J. van Oldenborgh; G. Burgers, 2002: Predicting rainfall in the Dutch Caribbean -móre Ihan EINillo? In!. J. Climatology, 22, 1219-1234. ' Nicholls, N., 1984: A systern for predicting the onset of the north Australian wet-season, JÓlJmal of Clirnatology, 4, 4~.5435. • Nicholls~ N.; McBride. J. L.; R/Ormerod, 1982: On predicting lhe onset of the Australian \vet~~l!on at Darwin, MonthlyWeather Review; 110, 14-17. Smith. G. E.; O'Brien, P. C.; Ivnik, R J.; Kokmen, E. 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Quantifying uncertanties associated with climate variability and climate change studies: the Cox'S semiparametric approach.

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RCAAP - Repositório Científico de Acesso Aberto de Portugal

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