Identification of Inhomogeneities in Precipitation Time Series Using Stochastic Simulation

Transcription

1 Identification of Inhomogeneities in Precipitation Time Series Using Stochastic Simulation A. C. M. Costa, J. Negreiros and A. Soares Abstract Accurate quantification of observed precipitation variability is required for a number of purposes. However, high quality data seldom exist because in reality many types of non-climatic factors can cause time series discontinuities which may hide the true climatic signal and patterns, and thus potentially bias the conclusions of climate and hydrological studies. We propose the direct sequential simulation (DSS) approach for inhomogeneities detection in precipitation time series. Local probability density functions, calculated at known monitoring stations locations, by using spatial and temporal neighbourhood observations, are used for detection and classification of inhomogeneities. This stochastic approach was applied to four precipitation series using data from 62 surrounding stations located in the southern region of Portugal ( ). Among other tests, three well established statistical tests were also applied: the Standard normal homogeneity test (SNHT) for a single break, the Buishand range test and the Pettit test. The inhomogeneities detection methodology is detailed, and the results from the testing procedures are compared and discussed. Introduction Precipitation is one of the most important climate variables. Accurate quantification of its observed variability is required for a number of purposes. Long series of reliable precipitation records are essential for climate changes monitoring, general circulation models and regional climate models, modelling of erosion, runoff and pollutant transport, among other applications for ecosystem and hydrological impact modelling. However, high quality data seldom exist because in reality many types of non-climatic factors (e.g. monitoring stations relocations, changes of the surroundings, different observational and calculation procedures, etc.) can cause time series discontinuities which may hide the true climatic signal and patterns, and thus potentially bias the conclusions of climate and hydrological studies. Therefore, A. C. M. Costa ISEGI, Universidade Nova de Lisboa, Campus de Campolide, Lisbon, Portugal ccosta@isegi.unl.pt A. Soares et al. (eds.), geoenv VI Geostatistics for Environmental Applications, C Springer Science+Business Media B.V

2 276 A. C. M. Costa et al. it is recommended that, besides routine quality control, the homogeneity testing of data to be evaluated before performing those studies (Aguilar et al. 2003). Several techniques have been developed for detecting inhomogeneities in time series of weather elements. The approaches underlying the homogenization techniques are quite different and typically depend on the type of element (temperature, precipitation, pressure, evaporation, etc.), the temporal resolution of the observations (annual, seasonal, monthly or sub-monthly), the availability of metadata (station history information) and the monitoring stations network density (spatial resolution). A review of different statistical methods is presented in (Peterson et al. 1998) and guidelines on homogenization from the World Meteorological Organization are provided by (Aguilar et al. 2003). We propose the direct sequential simulation (DSS) approach, introduced by (Soares 2001), for inhomogeneities detection in precipitation time series. Unlike most of the traditional testing procedures described in the literature (e.g. Peterson et al. 1998, Aguilar et al. 2003), the proposed technique accounts for the joint spatial and temporal dependence between observations, and enhances the pre-eminence of the closer stations, both in spatial and correlation terms. The inhomogeneities detection procedures applied in this study used an annual resolution testing variable derived from the daily precipitation data, namely the wet day count with 1mm as threshold, which is expected to be representative of important characteristics of variation at the daily scale (Wijngaard et al. 2003). The stochastic simulation approach was applied to the testing variable data from four ( candidate ) stations using data from 62 surrounding stations ( reference stations, presumed homogeneous) located in the southern region of Portugal ( ). As with other relative homogeneity testing approaches, reference stations data are used to account for regional climate changes and to isolate the effects of station irregularities (Peterson et al. 1998). Amongothertests, threewell established statistical tests were also applied to the candidate stations time series: the Standard normal homogeneity test (SNHT) for a single break (Alexandersson 1986), the Buishand range test (Buishand 1982) and the Pettit test (Pettit 1979). The inhomogeneities detection methodology is detailed, the results from the testing procedures are compared and discussed, and finally some conclusions of this study are drawn. Precipitation Data and Previous Homogeneity Testing The daily precipitation series used in this study were compiled from the European Climate Assessment (ECA) dataset and the National System of Water Resources Information (SNIRH Sistema Nacional de Informação de Recursos Hídricos, managed by the Portuguese Institute for Water) database, and are available through free downloads from the ECA website ( and the SNIRH website ( respectively. The analysed precipitation series, from monitoring stations located in the southern region of Portugal with records within the period

3 Identification of Inhomogeneities in Precipitation Time Series , were downloaded during the first semester of All stations with at least 30 years with less than 5% of observations missing were selected. In order to select a larger set of reference series, shorter series with at least 10 years lacking a maximum of 5% of data were also chosen, and hence the series with too many gaps were discarded. Using those criterions, long-term series of daily precipitation from 42 weather stations were selected, and 54 shorter series were accepted as eligible reference series. Before being compiled for this study, the daily series of the ECA dataset had already been subject to four statistical homogeneity tests which were applied to each station data separately (absolute tests were applied rather than relative tests because of the sparse density of the ECA station network). For precipitation, the testing variable used was the annual wet day count using 1 mm as threshold. The precipitation series compiled from the ECA dataset for this study were all marked as useful, as the four homogeneity tests did not reject the homogeneity hypothesis, at the 1% significance level. For further details see (Wijngaard 2003, Wijngaard et al. 2003), and the ECA project website ( Regarding the series from the SNIRH database, some homogeneity testing of the annual precipitation amounts has already been carried out by (Nicolau 1999), for the period 1959/ /91. This author used three absolute homogeneity tests and one subjective relative test and found no inhomogeneities in the annual precipitation series of the stations considered here. As recommended by (Auer et al. 2005), we assumed that the 96 daily precipitation series could contain potential breaks, and thus several homogenization procedures were applied to all of them in order to select a subset of series with quality data. The homogeneity testing followed the hybrid approach proposed by (Wijngaard et al. 2003) for the ECA dataset, and used the same annual resolution testing variable. The absolute approach used comprises the application of six statistical tests to the testing variable at all locations and using the full length of the series: the Mann-Kendall test (Mann 1945, Kendall 1975), the Wald-Wolfowitz runs test (Wald and Wolfowitz 1943), the Von Neumann ratio test (Von Neumann 1941), the Standard normal homogeneity test (SNHT) for a single break, the Pettit test, and the Buishand range test. Series for which two or more absolute tests rejected the homogeneity hypothesis, at a 5% significance level, were excluded from this study. Consequently, a set of 66 series (Fig. 1) was selected to be used in the stochastic simulation approach: 14 long-term and 42 short-term series were considered as homogeneous by all tests, and for 10 long-term series only one of the six tests rejected the homogeneity hypothesis. To illustrate the proposed methodology, four candidate stations were chosen: Beja (ECA 666), Aljezur (SNIRH 30E.01), Alferce (SNIRH 30G.01), and Santiago do Escoural (SNIRH 22H.02). Note that if an absolute test detects a break in a station s time series it may indicate an inhomogeneity or it may simply indicate an abrupt change in the regional climate. Historic metadata support is then essential for evaluating the breaks detected through absolute testing. Therefore, relative approaches are usually preferred, as they intend to isolate the non-climatic influences (Peterson et al. 1998).

4 278 A. C. M. Costa et al. Fig. 1 Locations of the 66 monitoring stations. Candidate stations are marked with pentagons Methodological Framework For the detection of inhomogeneities, we propose the DSS algorithm (Soares 2001) to calculate the local probability density functions (pdfs) at candidate stations locations, by using spatial and temporal observations from nearby reference stations and without taking into account the candidate data. The local pdfs from each year can then be used to verify the existence of irregularities: a break year is identified whenever the interval of a specified probability p (e.g. 0.95) centred in the local pdf does not contain the observed (real) value of the candidate station. In practice, the local pdfs are provided by the histograms of simulated maps, thus this rule implies that if the observed (real) value lies below or above the predefined percentiles of the histogram of a given year then it is not considered as homogeneous. The inhomogeneities detection procedures used in this study followed the hybrid approach proposed by (Wijngaard et al. 2003) for the ECA dataset, and used as testing variable the annual wet day count with 1 mm as threshold. For illustration purposes, the stochastic simulation approach was applied to the testing variable data from four candidate stations. Techniques that use series from surrounding stations, some times run the test once, relying the reference to be homogeneous, or engage in an iterative procedure in which all the stations in the data set are seen consecutively as candidates and references (Aguilar et al. 2003). Following this methodology, the local pdfs of each year of the candidate series, derived from 50 simulated maps, were computed using data not only from the 62 references but also from the other 3 candidate stations. The analysed period was

5 Identification of Inhomogeneities in Precipitation Time Series 279 Fig. 2 Spatial and temporal experimental semivariograms of the testing variable data with the model fitted: (a) spatial isotropic semivariogram, (b) temporal semivariogram The stochastic simulations used a spherical semivariogram model fitted to the testing variable data from the complete set of 66 monitoring stations (Fig. 2): the spatial dimension was modelled using an isotropic semivariogram with a range of 72 km, and the temporal one with the range equal to 1.8 years. The results from the proposed technique are compared with the results from three well established homogeneity tests that used two reference series for each candidate and the full length of the series. The SNHT, Pettit and Buishand range tests were applied to composite (ratio) reference series (Alexandersson and Moberg 1997), which were derived from the testing variable. Further methodological details and additional results from this approach are described by (Costa and Soares 2006). Results and Discussion The proposed approach allowed us to identify several inhomogeneities by comparing the observed (real) values of the candidate series, for each year, with the 2.5% and the 97.5% percentiles of the corresponding histograms of 50 simulated maps. This methodology identified not only the same break years (or within oneyear range) as the other three testing procedures, but also revealed inhomogeneities

6 280 A. C. M. Costa et al. Fig. 3 One simulated realization of the annual wet day count in 1991, computed without data from Beja, at the nodes of a 1 km 1kmgrid in other years that were not detected by any of the three statistical tests, at a 5% significance level. For station Aljezur, the four approaches considered the series as homogeneous. The series from Beja was considered as homogeneous by the three statistical tests, whereas the stochastic approach identified a break in 1991 (Fig. 3 and Fig. 4). For station Alferce, the SNHT concluded the series as homogeneous, the Buishand and Pettit tests detected a break in 1984, and the stochastic approach identified a break in The candidate series from Santiago do Escoural was considered as inhomogeneous by all techniques: the SNHT detected a break in 1989, the Buishand and Pettit tests identified a breakpoint in 1988, and the proposed procedure detected breaks in 1987, 1988 and Fig. 4 Histogram of the 50 simulated realizations, computed without data from Beja, of the annual wet day count in 1991 at Beja location (the real value at Beja is 60 days)

7 Identification of Inhomogeneities in Precipitation Time Series 281 Final Remarks The promising results from this case study indicate the stochastic approach as a valuable tool for inhomogeneities detection in climate time series. All break years identified by the three well established statistical tests considered were also detected by the proposed technique. Moreover, the stochastic simulations approach allowed for the identification of breaks near the end of the series that were not detected by the other methods. In fact, this is one of the advantages of the proposed methodology relatively to other testing procedures commonly used which have less power in detecting breakpoints near the start and end of a series (Aguilar et al. 2003). The evidences provided by the case study results indicate that the potential advantages of the proposed methodology are that it allows to: account for the detection of multiple breaks simultaneously identify breakpoints near the start and end of a series use different sets of neighbouring stations at different years, including shorter and non-complete records enhance the pre-eminence of the closer stations, both in spatial and correlation terms account for the joint spatial and temporal dependence between observations The main disadvantage of the proposed approach is that it is computationally intensive, even though simple to apply. Nevertheless, as it allows accounting for the detection of multiple breaks simultaneously, it might be less time consuming than other testing techniques that are used iteratively by systematically dividing the tested series into smaller segments when a break is detected, and then perform the test on those segments. We would like to suggest for future research the application of direct sequential cosimulation (Soares 2001) so that the inhomogeneities detection procedure incorporates covariates, such as altitude and distance from the coastline, which are known to influence the precipitation distribution. List of Abbreviations DSS - direct sequential simulation ECA - European Climate Assessment pdf - probability density function pdf - probability density functions SNHT - Standard normal homogeneity test SNIRH - National System of Water Resources Information (Sistema Nacional de Informação de Recursos Hídricos)

8 282 A. C. M. Costa et al. References Aguilar E, Auer I, Brunet M, Peterson TC, Wieringa J (2003) Guidelines on climate metadata and homogenization. WMO-TD No 1186, WCDMP No 53, World Meteorological Organization, Geneva Alexandersson H (1986) A homogeneity test applied to precipitation data. J Climatol 6: Alexandersson H, Moberg A (1997) Homogenization of Swedish temperature data, Part I: Homogeneity test for linear trends. Int J Climatol 17:25 34 Auer I, Böhm R, Jurkovic A, Orlik A, Potzmann R, Schöner W, Ungersböck M, Brunetti M, Nanni T, Maugeri M, Briffa K, Jones P, Efthymiadis D, Mestre O, Moisselin J-M, Begert M, Brazdil R, Bochnicek O, Cegnar T, Gajic-Capka M, Zaninovic K, Majstorovic Z, Szalai S, Szentimrey T, Mercalli L (2005) A new instrumental precipitation dataset for the greater alpine region for the period Int J Climatol 25: Buishand TA (1982) Some methods for testing the homogeneity of rainfall records. J Hydrol 58:11 27 Costa AC, Soares A (2006) Identification of inhomogeneities in precipitation time series using SUR models and the Ellipse test. In: Caetano M, Painho M (eds.) Proceedings of Accuracy th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences. Instituto Geográfico Português, pp Kendall MG (1975) Rank correlation methods. Charles Griffin, London Mann HB (1945) Mann HB (1945) Non-parametric test against trend. Econometrika 13: Peterson TC, Easterling DR, Karl TR, Groisman P, Nicholls N, Plummer N, Torok S, Auer I, Boehm R, Gullett D, Vincent L, Heino R, Tuomenvirta H, Mestre O, Szentimrey T, Salinger J, Forland EJ, Hanssen-Bauer I, Alexandersson H, Jones P, Parker D (1998) Homogeneity adjustments of in situ atmospheric climate data: A review. Int J Climatol 18: Pettit AN (1979) A non-parametric approach to the change-point detection. Appl Stat 28: Soares A (2001) Direct Sequential Simulation and Cosimulation. Math Geol 33: Von Neumann J (1941) Distribution of the ratio of the mean square successive difference to the variance. Ann Math Stat 13: Wald A, Wolfowitz J (1943) An exact test for randomness in the non-parametric case based on serial correlation. Ann Math Stat 14: Wijngaard JB (2003) Homogeneity of daily European Climate Assessment and Dataset series. In: World Meteorological Organization (ed) Proceedings of the Second Seminar for Homogenization of Surface Climatological Data. WMO-TD No 962, WCDMP No 41, WMO, Geneva, pp Wijngaard JB, Klein Tank AMG, Können GP (2003) Homogeneity of 20th century European daily temperature and precipitation series. Int J Climatol 23: