Complexity and predictability of the monthly Western Mediterranean Oscillation index

Abstract

19The complexity, predictability and predictive instability of the Western Mediterranean 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 The contents of the paper include a description of the WeMOi, its cumulative distribution 72 (Section 2), monofractal properties (Section 3) and multifractal characteristics derived from 73 the multifractal detrended fluctuaction analysis, MF-DFA, which is also succinctly described 74 (Section 4). A comparison of the mono-and multifractal properties for the WeMO, NAO and 75 AMO indices, and the validity of fGn series to simulate the WeMOi are presented in Section 5. 76Section 6 introduces results derived from the ARIMA process and the Conclusions Section 77 outlines the main WeMOi fractal features and reviews the autoregressive prediction results. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 P e e r R e v i e w O n l y The monthly Western Mediterranean Oscillation index, WeMOi 82The WeMOi was proposed by Martín-Vide and López-Bustins (2006) to detect atmospheric 83 circulation patterns related to rainfall shortage or excess affecting the eastern Iberian 84Peninsula López-Bustins et al., 2008; Gonzalez-Hidalgo et al., 2009), 85 being also used in other regional climatic applications (Azorín-Molina and Lopez-Bustins, 2008; 86 Sánchez-Lorenzo et al., 2009;Vicente-Serrano et al., 2009;Ouachani et al., 2013; El Kenawy et 87 al., 2013;Beranová and Kyselý, 2015;Ríos-Cornejo et al., 2015). (Figure 1b), strongly suggests that this decreasing tendency could be mainly 107 linked to the behaviour of WeMOi at spring and summer seasons. The cumulative distribution 108 of WeMOi (Figure 2) is Gaussian, the observations being kept within the 95% confidence bands 109 derived from the Kolmogorov-Smirnov test (Benjamin and Cornell, 1970;Press et al., 1992). 110 Figure 3 represents WeMOi for several return periods, given in months, compared with 111 theoretic return values for a Gaussian distribution. Empiric values are also quite well described 112 by a logarithmic law, by taking as argument the return period (months). Taking into account 113 the symmetry of the Gaussian distribution, similar results would be obtained for negative 114 WeMOi. 115 116On the other hand, it is well known that the Mediterranean climate is submitted to the NAO 117 (Trigo et al., 2002;Lionello et al., 2006; López-Moreno et al., 2011) region, NAO plays a significant role on decadal variance in precipitation, especially...

Monthly rain amounts at Fabra Observatory (Barcelona, NE Spain): fractal structure, autoregressive processes and correlation with monthly Western Mediterranean Oscillation index

“…In agreement with results obtained from the reconstruction theorem and parameters of the multifractal spectrum, it has to be accepted the prediction of MRA as complex, similar to the WeMOi (Lana et al , ). By comparing the obtained values of MAD and the standard deviation of MRA, fGn are just simulation series reproducing mean, standard deviation, Hurst and Hausdorff exponents and the β exponent of the power law related to the power spectrum.…”

“…Another property to be considered for comparison between both signals is their statistical distribution. While MRA are gamma distributed, with discrepancies between empiric and theoretical model within the Kolmogorov–Smirnov 95% confidence bands all along the MRA range (Lana and Burgueño, , ), the WeMOi are Gaussian distributed (Lana et al ., ). Only minor discrepancies on the MRA fit to the gamma model, without exceeding the confidence bands, are observed for MRA ≤ 10 mm month −1 .…”

“…In agreement with the spectral contents depicted in Figure (b), two clear periodicities are detected: 1 year and half a year, the rest of periods remaining with low spectral amplitude. When comparing WeMOi periodicities (Lana et al , ) with those detected for MRA, only the 1‐year periodicity is coincident. Half a year periodicity does not appear in WeMOi, and conversely, 19.1 years periodicity for WeMOi is not found for MRA.…”

“…One of the main objectives of the present analysis is the fractal characteristics of MRA and comparison of their mono-and specially multifractal results with those obtained for the WeMOi (Lana et al, 2015), taking advantage of the known correlation between MRA and WeMOi (Martín-Vide and López-Bustins, 2006). In particular, the multifractal detrended fluctuation analysis (MF-DFA) allows a reliable characterization of multifractal non-stationary and stationary time series (Kantelhardt et al, 2002).…”

Topographic Spatial Variation Analysis of Loess Shoulder Lines in the Loess Plateau of China Based on MF-DFA

“…MF-DFA has successfully been applied to fields as diverse as finance and stock markets [43][44][45], seismicity [46][47][48], mineral grade detection [49], climate change [50][51][52][53][54], traffic flow [55,56], speech signal characteristics [57], plant species identification [58], air pollution [59,60], and heart rate dynamics [61]. It is very valuable to introduce this method into the analysis of shoulder-lines.…”