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@InProceedings{MaiaMein:2006:DiCoLi, author = "Maia, Aline de Holanda Nunes and Meinke, Holger", affiliation = "Embrapa Meio Ambiente, PO Box 69, Jaguari{\'u}na, SP, Brazil (Maia) and Department of Primary Industries and Fisheries, PO Box 102, Toowoomba, Qld 4350, Australia (Meinke) and {}", title = "Assessing uncertainty of seasonal probabilistic forecasts: distribution-free confidence limits", booktitle = "Proceedings...", year = "2006", editor = "Vera, Carolina and Nobre, Carlos", pages = "569--573", organization = "International Conference on Southern Hemisphere Meteorology and Oceanography, 8. (ICSHMO).", publisher = "American Meteorological Society (AMS)", address = "45 Beacon Hill Road, Boston, MA, USA", keywords = "probabilistic forecasts, uncertainty, confidence intervals.", abstract = "Probabilistic climate forecasts often rely on information coming from historical climate series of prognostic variables, represented by cumulative distribution probabilities functions (CDFs) or their complement, probability of exceeding functions (POEs). They are a simple and convenient way to represent probabilistic information arising from a time series that exhibit no or only weak auto-correlation patterns. However, if the time series shows moderate to strong auto-correlation patterns, a CDF/POE summary will result in some loss of information. Yearly sequences of rainfall data from a specific month or period generally exhibit only weak auto-correlation, thus allowing the CDF/POE representation to convey seasonal climate forecast information. Useful information required by decision makers is then derived from such distribution and expressed as the probability of exceeding a certain threshold (e.g. probability of exceeding historical median value of rainfall or any other derived quantity such as agricultural yield or income). Such estimates are frequently reported without any measure of uncertainty. The degree of uncertainty depends on the length of the time series and its internal variability. Lack of uncertainty assessments can lead to misguided beliefs about the true performance of the forecast systems (e.g. due to the possible existence of artificial skill, especially if forecasts are based on short time series) possibly resulting in inappropriate actions by the decision maker. Parametric methods to assess uncertainty of percentiles and probability of exceeding estimates are frequently based on normality assumptions. However, distributions of some important climate variables, such as rainfall, are notoriously skewed, particularly in areas with strong seasonality that can result in high frequencies of zero rainfall amounts. For such cases there are often no mathematical transformations available that would overcome this lack of normality. As an alternative for Normal-based procedures, we propose the use of distribution free methods for constructing percentile and POE confidence limits. Those distribution-free tools are particularly useful for spatial uncertainty assessments that would require a tedious, location-by-location checking of assumptions regarding underlying probability distributions. Normal-based and distribution-free methods are both available in The Capability Procedure of the Statistical Analysis System (SAS, version 7 and latter releases). In this work, we discuss the rationale, advantages and limitations of both, parametric and non-parametric approaches. We illustrate these methods by assessing the uncertainty of percentiles and POEs estimates for 3-monthly rainfall series from locations in Australia and South America. The SAS codes for computing the uncertainty measures will also be presented.", conference-location = "Foz do Igua{\c{c}}u", conference-year = "24-28 Apr. 2006", language = "en", organisation = "American Meteorological Society (AMS)", ibi = "cptec.inpe.br/adm_conf/2005/10.31.10.20", url = "http://urlib.net/rep/cptec.inpe.br/adm_conf/2005/10.31.10.20", targetfile = "569-573.pdf", type = "Climate predictions", urlaccessdate = "25 jan. 2021" }

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