TREND EXTRACTION FROM PRECIPITATION DATA BY USING SINGULAR SPECTRUM ANALYSIS
Kasım KOÇAK, Evren ÖZGÜR and Burcu SALDAMLI Istanbul Technical University, Department of Meteorology
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Abstract: One of the most important problems encountered by the megacities is water scarcity. As a megacity, Istanbul experiences serious water problem from time to time. Thus, it is important to study both spatial and temporal characteristics of precipitation in Istanbul city. Eight observation stations separated through Istanbul city are considered in this study. Both individual station data and areal average of these stations are examined with regard to trend extraction via singular spectrum analysis (SSA). The result of this trend analysis revealed that precipitation of Istanbul shows a cyclic trend component which enables us to predict the next drought event. Keywords: Trend extraction, Singular spectrum analysis, Istanbul, Precipitation
Introduction In recent years, climate change has become an important research area. On the other hand, some adverse effects of climate change on environment were started to observe. The most disastrous effect of climate change is expected on the water resources. Both observations and many climate models dictate that the global warming will amplify water shortages. On the other hand , there is a great risk on the big population of megacities like Istanbul. Thus, prediction of drought events is of crucial importance in the management of water resources. In literature there are various methods to investigate the trend in a given time series. One of them is the Mann-Kendall trend analysis (Mann, 1945; Kendall, 1975). In recent years, the SSA has began become an important tool to investigate some hidden properties of a time series (Broomhead and King, 1986; Vautard et al, 1992; Unal and Ghil, 1995; Ghil et al., 2002). By using SSA, it is possible to obtain oscillatory, trend and noise components of a time series. In this study, a novel method developed by Alexandrov (2009) has been utilized in order to extract the tren d component of the precipitation data measured in Istanbul city. The trend extraction method mentioned above applied to eight observation stations located in Istanbul. These stations are Bahçeköy, Florya, Göztepe, Kandilli, Kartal, Kireçburnu, Kumköy and Şile. Half of these stations are in Anatolia, the other half are in European Part of Turkey.
Methods An approach developed by Alexandrov in 2009 was used in this study. In the way of SSA, the trend is defined as a smooth component containing information about time series global change. A simple approach to trend extraction in SSA is to reconstruct a trend from several first SVD components (by visual examination of singular values and vectors)(Taibi et al., 2013). However, this approach fails when the values of a trend are small enough as compared with other components such as oscillations and noise, or when a trend has a complicated structure and is characterized by many SVD components (Alexandrov et al., 2008).
Let us consider the periodogram IX (ω) of a vector Y RM, Y=(y0, y1, ….., yM-1) T: (1) which can be interpreted as the contribution of the frequency k/M. The cumulative contribution is evaluated as: (2) For ω0 (0, 0.5), the contribution of low frequencies to Y RM is defined as: (3) Let us consider eigenvectors Uj. Then, given ω0(0, 0.5) and C 0[0,1], SVD components were selected with eigenvectors satisfying C(Uj,ω0) C 0. One may interpret this method as a selection of SVD components characterized mostly by low-frequency fluctuations. The low-frequency boundary ω 0 defines the scale of the extracted trend; the lower ω 0 is, the slower the trend varies. The parameter C0 regulates an acceptable share of higher frequencies in the extracted component. In brief, it is important to choose reasonable ω 0 and C 0 to success of trend analysis (Taibi et al., 2013). The used approach for trend extraction has carried out with AutoSSA program developed by Alexandrov in 2005. AutoSSA is not only used to investigate trend, but also used to present periodic components and predict signal (Alexandrov and Golyandina, 2005).
Application to precipitation data Figure 1 shows the last 65-year areal average precipitation time series of Istanbul city. This time series was obtained from 8 observation stations located at different places of Istanbul. These stations are Bahçeköy, Florya, Göztepe, Kandilli, Kartal, Kireçburnu, Kumköy and Şile. From these stations Bahçeköy and Göztepe were closed to meteorological observations since 2007 and 2009, respectively. Missing observations of these two stations were filled by using multiple regression analysis. As shown from Figure 1, the lowest value of the areal average precipitation of the last 65 years has been observed in the year 2013 with only 530 mm. In other words, the most severe meteorological drought of the last 65 years was realized in this year. This value is under the areal average precipitation of Istanbul, which is 800 mm, and even under the Turkey’s areal average precipitation, which is 650 mm. The other most severe droughts of the last 65 years were experienced in the year 1989 with 531 mm and in the year 2007 with 553 mm. Figure 1 reveals another important aspect of the areal average precipitation. If examined carefully, it will be seen easily that there are two different time periods regarding variability of the precipitation. These time periods are those lasting up to 1970 and following it. In the first period, areal average precipitation fluctuates around 800 mm which is the Istanbul average with a low variability. Contrary to the first period, average precipitation fluctuates with a high variability in the second period. On the other hand, there is a significant change in the frequency of the number of serious drought events. From the same figure it is observed that there are 10 considerable precipitation shortages compared to Turkey’s overall average during the last 65 years. 4 out of 10 events occurred before the year 1970 whereas 6 out of 10 events occurred after this year which means 60% of these events took place in the last years. Besides this, not only low precipitation events but also very high precipitation events have been increased in the last years. To sum up, both variability and frequency of the extreme events have been changed dramatically as stressed in the report of IPCC (2001).
Figure 1. Areal average precipitation time series of İstanbul for the last 65 years. These considerations have caused this study to be fulfilled. Because Istanbul is an important megacity with the population of 14 million. More importantly, Istanbul has not got enough water resources. Thus a severe drought can cause serious social disorder in the city. This necessitates the detailed study of meteorological droughts in Istanbul. In this study, trend analysis of yearly precipitation of eight observation stations and yearly areal average precipitation of whole city were realized by using SSA. Figure 2 and 3 show the oscillatory and linear trend components in the areal average precipitation series.
Figure 2. Oscillatory trend component in the Istanbul areal average precipitation.
Figure 3. Liner trend component in the Istanbul areal average precipitation.
Conclusion and recommendations
In this study, SSA trend analysis of yearly average precipitation of eight observation stations and yearly areal average precipitation of the whole city were realized. Two kinds of trend components are examined; these are oscillatory and linear trend components. Especially oscillatory trend component of areal precipitation reveals very important information about cyclic behavior of drought in Istanbul. This information enables us to predict the future behavior of drought phenomenon. The results of this study can be given as follows: a. Yearly areal average precipitation series shows periodicity with 18-year time period. b. Precipitation series of four observation stations (Göztepe, Florya, Kandilli and Şile) have also 18-year time period. c. The two stations, namely Bahçeköy and Kumköy, have longer periodicity than the first four stations. d. The remaining two stations, namely Kireçburnu and Kartal, have no periodic trend component. e. Yearly areal average precipitation series has increasing linear trend. f. Four stations, namely Bahçeköy, Florya, Göztepe, and Kandilli, show no linear trend in time, g. The three stations, namely Kireçburnu, Kumköy and Şile, have increasing trend, h. Only one station, namely Kartal, has decreasing trend. i. If carefully examined, Figure 2 and 3 indicate edge effect. If we do not consider the edge effect, then it can be claimed that the next possible serious meteorological drought will be expected in the year 2025. j. If this cyclic behavior of areal average precipitation holds, then the next wet year will be in the year 2017.
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