On the Persistence and Predictability Properties of North Atlantic Climate Variability

Transcription

1 466 J O U R N A L O F C L I M A T E VOLUME 24 On the Persistence an Preictability Properties of North Atlantic Climate Variability CHRISTIAN FRANZKE British Antarctic Survey, Cambrige, Unite Kingom TIM WOOLLINGS Department of Meteorology, University of Reaing, Reaing, Unite Kingom (Manuscript receive 22 March 2010, in final form 8 September 2010) ABSTRACT The persistence an climate noise properties of North Atlantic climate variability are of importance for tren ientification an assessing preictability on all time scales from several ays to many ecaes. Here, the authors analyze these properties by applying empirical moe ecomposition to a time series of the latitue of the North Atlantic ey-riven jet stream. In previous stuies, it has been argue that a slow ecay of the autocorrelation function at large lags suggests potential extene-range preictability uring the winter season. The authors show that the increase autocorrelation time scale oes not necessarily lea to enhance intraseasonal preictive skill. They estimate the fraction of interannual variability that likely arises ue to climate noise as 43% 48% in winter an 70% 71% in summer. The analysis also inentifies a significant polewar tren of the jet stream that cannot be explaine as arising from climate noise. These finings have important implications for the preictability of North Atlantic climate variability. 1. Introuction The climate of the North Atlantic sector has a strong impact on European weather an climate, particularly through north south shifts of the atmospheric eyriven jet stream. The jet stream steers weather systems across the North Atlantic, etermining the storm climate an influencing precipitation an temperature across large areas of Europe. In this stuy, we use a measure of the latitue of the jet stream as a proxy of North Atlantic climate variability to examine its climate noise, extenerange preictability, an tren characteristics. Previous work in this area has focuse on one aspect of jet stream variability, the North Atlantic Oscillation (NAO), an on whether its recent variations are significantly ifferent from the characteristics of simple stochastic processes. For example, Wunsch (1999) showe that the winter NAO can be well represente as a first-orer Markov process, although Stephenson et al. (2000) showe that a process with long-range epenence provies a better fit. Corresponing author aress: Dr. C. Franzke, British Antarctic Survey, High Cross, Maingley Roa, Cambrige CB3 0ET, Unite Kingom. chan1@bas.ac.uk One simple measure of persistence an preictability is the autocorrelation function. In recent stuies, it has been pointe out that the NAO exhibits unusual persistence, as evience by a shouler of slow ecay in the autocorrelation function between 10 an 30 ays (e.g., Ambaum an Hoskins 2002; Rennert an Wallace 2009). However, Keeley et al. (2009) showe that this shouler feature is sensitive to the presence of interannual variability, an as such it may not reflect enhance preictability on intraseasonal time scales. The interannual variability itself is a combination of externally force variations an variations arising from climate noise: that is, from sampling variability associate with the averaging of shorter time-scale intraannual fluctuations (Felstein 2000, 2002; Franzke 2009; Keeley et al. 2009). The fraction of interannual variability, which is externally force an hence potentially preictable, is of obvious interest for seasonal an longer-range forecasting. Here, we investigate these issues by applying an empirical moe ecomposition (EMD) to an inex of the jet stream latitue to separate variability on ifferent time scales an examine their impact on extene-range preictability. The relatively fast ecorrelation of the NAO time series within the first 10 ays has, along with the climate noise estimates, motivate a focus on synoptic time DOI: /2010JCLI Ó 2011 American Meteorological Society

2 15 JANUARY 2011 F R A N Z K E A N D W O O L L I N G S 467 FIG. 1. Autocorrelation functions of aily JLI for (a) winter an (b) summer seasons. Black soli line: unfiltere JLI; green soli line: etrene (EMD tren) JLI; re soli line: intraseasonal (IMF 1 6) JLI; blue soli line: intraseasonal an interseasonal JLI (IMF 1 8); an cyan soli line: JLI with iniviual winter means subtracte. Autocorrelation values outsie the shae area are statistically significant at the 5% level. scales in the stuy of the NAO (e.g., Beneict et al. 2004). However, this synoptic focus was challenge by Rennert an Wallace (2009), who suggeste that the fast ecorrelation results from the contamination of the aily NAO inex by intermeiate (6 30 ay) frequency variability ominate by linear Rossby waves. This contamination was envisage to arise from the partial projection of the wave patterns onto the spatial pattern of the NAO. The approach taken here of iagnosing the jet latitue may be less sensitive to the presence of wavelike variability than methos base on the projection of spatial patterns. 2. North Atlantic climate variability inex The jet latitue inex (JLI) is a measure of the variability in the position of the ey-riven jet stream over the North Atlantic region (Woollings et al. 2010). The JLI covers the perio 1 December 1957 through 28 February 2002 using ata from the 40-yr European Centre for Meium-Range Weather Forecasts (ECMWF) Re- Analysis (ERA-40; Uppala et al. 2005). The JLI is erive in the following way: 1) a mass-weighte average of the aily mean zonal win is taken over the vertical levels 925, 850, 775, an 700 hpa an over the Atlantic sector W. 2) Wins polewar of 758N an equatorwar of 158N are neglecte. 3) The resulting win fiel is low-pass filtere, only retaining perios greater than 10 ays. 4) The JLI is efine as the latitue at which the maximum win spee is foun. 5) A smooth annual cycle is subtracte from the resulting time series. See Woollings et al. (2010) for more etails, where it is also shown that this inex escribes jet stream variations that are associate with both the NAO an the east Atlantic (EA) teleconnection pattern an therefore represents a goo general proxy of North Atlantic climate variability. In aition to its generality, the JLI has an avantage over patternbase inices such as the NAO in that it can be trivially calculate over all seasons with no complications arising from the changing of patterns uring the annual cycle. 3. Time scale an climate noise The autocorrelation function of the JLI is isplaye as a black line in Figs. 1a,b for the winter an summer seasons, respectively. The autocorrelation function ecays rather quickly in the first few ays in both seasons. Although in summer the autocorrelation function ecays to zero after about 10 ays, in winter it stays at significantly nonzero values for up to lag 30 ays. The plateau between lag 10 an lag 30 ays of the relate NAO autocorrelation function is usually referre to as the shouler feature, an it was attribute to interannual variability by Keeley et al. (2009). Here, we examine the contributions of ifferent time scales to this autocorrelation function plateau an assess if it potentially enhances preictability. For this purpose, we utilize avance timeseries methos. The EMD is a recently evelope algorithm (Huang et al. 1998; Huang an Wu 2008; Franzke 2009, 2010) to ecompose a univariate time series into a finite number of components calle intrinsic moe functions (IMFs), M x(t) 5å c j (t) 1 R(t), (1) j51 where the jth IMF c j can be written in polar coorinates c j (t) 5 r j (t) sin[u j (t)] where r j is the jth amplitue, u j is

3 468 J O U R N A L O F C L I M A T E VOLUME 24 the jth instantaneous frequency, an R the instantaneous mean. Both the amplitue an frequency are time epenent an thus ifferent from Fourier moes where both r j an u j are time inepenent. An IMF is efine by the following two properties (Huang et al. 1998): 1) each IMF c j has exactly one zero crossing between two consecutive local extrema an 2) the mean of each IMF c j is zero. A etaile escription of the algorithm is given by Huang et al. (1998) an Franzke (2009). Here, we use the same setup as in Franzke (2009, 2010). The major avantage of EMD over stanar wavelet an Fourier analyses is that it is a ata aaptive methoology, whereas wavelet an Fourier analyses use a priori efine basis functions. See Huang et al. (1998) for an extensive iscussion of the avantages of EMD over wavelet an Fourier analysis. The ability an robustness of EMD to extract nonlinear trens from noisy time series has been emonstrate by Franzke (2010), though it shoul be remembere that any efinition of a tren epens on the metho use to ientify it. The JLI has been ecompose into IMFs an an instantaneous mean, which we will interpret as a tren in this stuy an will be calle the EMD tren. Each IMF moe has a mean perio that is efine here as the average time between two local maxima. This analysis reveals that IMF moes 1 6 correspon to intraseasonal variability an IMFs 9 12 correspon to interannual variability (Fig. 2 an Table 1). This allows us to use EMD as a nonlinear filter an utilize the IMFs to efine the following frequency bans: intraseasonal with mean perios less than 90 ays (sum of IMFs 1 6), interseasonal with mean perios between 90 an 365 ays (IMFs 7 8), an interannual with mean perios larger than 365 ays (IMFs 9 12). The ifferent filtere time series are uncorrelate an thus orthogonal. The intraseasonal, interseasonal, an interannual bans explain 89.5%, 7.7%, an 2.8% of the total variability, respectively. The EMD analysis also reveals a statistically significant tren that is ifferent from a linear least squares fit (Fig. 2n). The EMD tren is steeper than the linear least squares tren in the perio an then levels off after this. The tren is associate with a polewar shift of the jet stream, which is consistent in sign with the projecte jet stream changes in Intergovernmental Panel on Climate Change (IPCC) scenario climate moel projections (Yin 2005; Lorenz an DeWeaver 2007). Most stuies assume that climate variability can be reasonably well represente by a first-orer Markov process in the form of a simple autoregressive process of first-orer [AR(1)] (e.g., Wilks 1995; Wunsch 1999; Felstein 2000; Masato et al. 2009). This process has a memory epth of 1; that is, to preict the next value one only nees to know the current value, an thus knowlege of past values will not increase the preictive skill. However, this can be a problematic choice, as recently shown by Keeley et al. (2009), because it can overestimate the autocorrelation time scale. A more flexible approach is to use an autoregressive moving average (ARMA) moel (Jones 1980; Wilks 1995), which is given by p 1 å f i L i Ax t 5@ 1 1 å u i L i Az t, (2) i51 where x t inicates the state variable at time t; L enotes the lag operator L k x t 5 x t2k ; an p an q are the orers of the autoregressive an moving average parts, respectively. Here, z t is stanar Gaussian istribute white noise an f an u are the autoregressive an moving average coefficients. By setting p 5 1anq 5 0, the ARMA(p, q) moel simplifies to the stanar AR(1) moel. We utilize the ARMA process to get a rough estimate of the memory epth of the JLI. We enote as memory epth the orer of the ARMA(p, q) moel; that is, the larger of p an q enotes the memory epth. The optimal moel orer is estimate using the algorithm of Broersen (2000). The unfiltere time series has p 5 3anq 5 2forthewinter[December February (DJF)], spring [March May (MAM)] an summer [June August (JJA)] seasons an p 5 2anq 5 1for autumn [September November (SON)]; thus, the memory epth is 3 for both the winter an summer seasons. The orers reuce to p 5 2anq 5 1 for the intraannual filtere time series so that the memory epth is 2. This suggests that aily climate inices are not necessarily firstorer Markov processes. We now test the statistical significance of the iniviual IMF moes by using the seasonally varying ARMA moel to moel the intraseasonal JLI variability (Franzke 2009). Here, we assume the null hypothesis that all IMFs are inistinguishable from the seasonal ARMA moel. The coefficients of the ARMA moel have been erive from the intraseasonally filtere ata because the aim is to etermine whether the variations on interannual time scales are istinct from sampling variability of the intraannual variations: that is, istinct from climate noise (Franzke 2009). Because the fraction of variance ue to climate noise is unknown, we performe two ifferent sets of ARMA simulations. The first set (ARMA1) has the same variance as the sum of the IMF moes of the JLI with intraseasonal perios (IMFs 1 6), whereas in the secon set, enote as ARMA2, the variance of ARMA1 has been rescale to fit the variance of the JLI. In ARMA2, we assume that all JLI variability is cause i51

4 15 JANUARY 2011 F R A N Z K E A N D W O O L L I N G S 469 FIG. 2. IMFs of EMD for the aily JLI. (n) The ashe line is the linear least squares fit of the JLI. The numbers in parentheses are the explaine variance an the mean perio of the IMFs, respectively. by short-term (intraseasonal) fluctuations. This test uses a Mahalanobis metric (Mahalanobis 1936), which takes into account both the mean perio an the variance of the respective IMFs. The results are isplaye in Table 1 an reveal that IMF moes 1 3, 5 7, an 9 10 an the instantaneous mean are significantly ifferent from the best-fit seasonally varying ARMA process at the 2.5% level for ARMA1, whereas for ARMA2 only the first three IMFs an the instantaneous mean are significantly ifferent at the 2.5% level. Although the intraseasonal IMFs explain almost 90% of the JLI variance, rescaling the ARMA1 moel to have the JLI variance (ARMA2) negates the statistical significance of the interannual IMFs. This suggests that climate noise is potentially able to explain most of the interannual variability. Furthermore, the IMF moes that are significant against both

5 470 J O U R N A L O F C L I M A T E VOLUME 24 TABLE 1. Mean perios of JLI an corresponing seasonal ARMA(p, q) process in ays. The mean perio is efine as the mean istance between two consecutive maxima. IMF moes significant at the 2.5% level are highlighte by an X in rows 3 an 4. For rows 3 an 4, ARMA processes with variance equal to the corresponing intraseasonal (for ARMA1) an total (for ARMA2) variance have been use. IMF Resiual Mean perio JLI Mean perio ARMA Significant ARMA1 X X X X X X X X X Significant ARMA2 X X X X ARMA moels can be consiere to be robust. The fact that the EMD tren is statistically significant when teste against both ARMA1 an ARMA2 suggests that the EMD tren is very robust an cannot be explaine as arising from climate noise. Thus, the EMD tren is likely to have arisen because of external forcing, such as oceanic forcing, cryospheric forcing, or anthropogenic warming. The existence of a statistically significant tren raises the question of whether the shouler feature in the autocorrelation function coul be ue to the tren. However, the autocorrelation function of the etrene JLI (Fig. 1a, green line) shows a very similar behavior to the autocorrelation function of the raw JLI; therefore, the shouler feature is not an artefact of the tren. Now we assess whether certain frequency bans are responsible for the shouler feature. The autocorrelation function of the sum of IMF 1 6 (intraseasonal moes) shows a rapi ecay to insignificant values at about lag 7 ays (Fig. 1a, re line). The autocorrelation function of the sum of IMF 1 8 (intraannual moes; Fig. 1a, blue line) also has a weaker shouler than the unfiltere JLI, showing that all three frequency ban contributions are neee to explain the slow ecay of the unfiltere JLI. This suggests that although the interseasonal an interannual variability only explain about 10% of the total variance, they have a large impact on the ecay of the autocorrelation function at long lags. This is in goo agreement with the results of Keeley et al. (2009), who subtracte iniviual seasonal means from the ata before calculating the autocorrelation function. For reference, we applie the same proceure, an the result (Figs. 1a,b; cyan line) is very close to the intraseasonal autocorrelation function for both summer an winter an is even closer to the combination of intraseasonal an interannual autocorrelation function for the winter season (not shown). The results are very similar for the summer season, with the exception that the interannual frequency ban makes very little contribution to the autocorrelation function of the unfiltere JLI. Next we utilize seasonal ARMA moels fitte to the JLI (IMF 1 12; ARMA3) an to IMF 1 8 (intraannual moes; ARMA4) to generate surrogate time series an calculate autocorrelation functions to compare their ecay with the JLI. Figures 3a,b show that these ARMA moels provie an excellent fit to the autocorrelation functions apart from for the unfiltere case in winter at long lags. In this case, both ARMA moels capture the initial ecay of the respective inices well until lag 9 ays but not afterwar. We calculate significance levels for the autocorrelation functions by using ensembles of ARMA realizations with 1000 members for each of the 44 seasons. This allows us to empirically estimate the 2.5 an 97.5 percentiles from the ensemble. The ARMA moels can prouce significant autocorrelation values up to lag 20 ays, which is less than the observe unfiltere JLI but also much longer than the mean autocorrelation function of the ARMA ensembles, which is compute as the average over all autocorrelation functions of the ensemble. This sampling uncertainty therefore suggests that part of the shouler feature coul in fact stem from intraseasonal fluctuations. We also calculate rough estimates for the fraction of interannual variability, which likely arises because of climate noise. The climate noise fraction is estimate from an ensemble of 1000 members of the seasonal ARMA1 an ARMA2 moels as the ratio between the respective ARMA interannual variability, which is calculate from seasonal averages of the aily surrogate ata, an the variance of seasonal means of the JLI. By oing so, we estimate that uring winter about 43% 48% an uring summer about 70% 71% of interannual variability is ue to climate noise. In both seasons the lower value correspons to the ARMA1 an the higher value to the ARMA2 estimate. 4. Preictability The slow ecay of the autocorrelation function of the unfiltere JLI suggests enhance extene-range preictability. Here, we test whether this is inee the case. For this purpose, we perform preictability experiments by utilizing the ARMA1 moel. We carry out leave-oneout hincast experiments; that is, for preicting the winter of 2000 we use all winter seasons but 2000 to fit the ARMA1 parameters an then perform preictability

6 15 JANUARY 2011 F R A N Z K E A N D W O O L L I N G S 471 FIG. 3. Autocorrelation functions for (a) winter an (b) summer season. Black soli line: unfiltere JLI; re soli line: ensemble-mean ARMA3 of unfiltere JLI; black ashe line: intraannual JLI; an re ashe line: ensemble mean ARMA4 of intraannual JLI. The thin blue lines inicate the 2.5% an 97.5% percentiles of ensembles of 1000 ARMA3 simulations fitte to the JLI (the percentiles for the ARMA4 ensembles are very similar). Autocorrelation values outsie the shae area are statistically significant at the 5% level. experiments for the winter of We now perform two sets of hincast experiments: 1) where we hincast the intraannual JLI using the ARMA1 moel an 2) where we assume perfect preictability of the interannual variability (e.g., IMF 9 12) but use the same ARMA1 moel as for set 1. To compare both sets of hincast experiments we use the skill score SS (MSE 1 /MSE 2 ) (Wilks 1995), where MSE i enotes the mean square error between hincast experiment i an the unfiltere JLI average over all winter seasons an all starting ays of the hincasts. The skill score is calculate for preictions of particular ays but also for 10-ay averages out to a lea time of 30 ays. We o ensemble hincasts with the ARMA moel with 100 ensemble members with ifferent noise realizations an then use the ensemble mean for the hincast skill. Both sets of hincast experiments have about the same mean square error; thus, the skill score is close to zero (not shown). Using both interseasonal an intraannual IMFs (IMF 7 12) for set 2 of the hincast experiments gives very similar results. This suggests that the shouler feature of the autocorrelation function oes not imply enhance preictability on intraseasonal time scales when the unerlying process generating the intraseasonal variability is represente by an ARMA moel. Using the ARMA4 moel gives qualitatively very similar results. 5. Concluing iscussion Our main results are as follows: The shouler feature in the autocorrelation function oes not lea to enhance intraseasonal preictability in hincast experiments with a seasonal ARMA moel, even if the time scales that lea to the shouler are assume to be perfectly preictable. The JLI exhibits a significant polewar tren over the ERA-40 perio that oes not arise from climate noise. About 97% of JLI variability is in the intraannual range. In winter an summer, 43% 48% an 70% 71% of JLI interannual variability, respectively, is likely ue to climate noise. These results have important implications for the preictability of North Atlantic weather an climate on several time scales. With respect to preiction on seasonal an longer time scales, we estimate that the potentially preictable, externally force variability comprises about 52% 57% of the total interannual variance in winter an 29% 30% in summer. In winter, this estimate is slightly lower than that of about 70% suggeste by Keeley et al. (2009). In summer, however, our estimate is higher, which may reflect the influence of the Atlantic multiecaal oscillation on the summer NAO on interecaal time scales (Follan et al. 2009). Although a large fraction of interannual variability is potentially preictable, its effective preictability appears to be low because much of the jet stream variability occurs on intraannual time scales. With respect to extene-range weather forecasting, the jet stream location is not preictable on horizons longer than a week. Note, however, that the autocorrelation function provies an average measure of preictability, which may be higher at some times (e.g., uring blocking; Masato et al. 2009) an of course lower at other times.

7 472 J O U R N A L O F C L I M A T E VOLUME 24 Acknowlegments. This stuy is part of the British Antarctic Survey Polar Science for Planet Earth Programme. It was fune by The Natural Environment Research Council. We thank the European Centre for Meium-Range Weather Forecasts for proviing the ERA-40 an the anonymous reviewers for their constructive comments, which helpe to improve the manuscript. REFERENCES Ambaum, M. H. P., an B. J. Hoskins, 2002: The NAO troposphere stratosphere connection. J. Climate, 15, Beneict, J. J., S. Lee, an S. B. Felstein, 2004: Synoptic view of the North Atlantic Oscillation. J. Atmos. Sci., 61, Broersen, P. M. T., 2000: Autoregressive moel orers for Durbin s MA an ARMA estimators. IEEE Trans. Acoust., Speech, Signal Process., 48, Felstein, S. B., 2000: The timescale, power spectra, an climate noise properties of teleconnection patterns. J. Climate, 13, , 2002: The recent tren an variance increase of the annular moe. J. Climate, 15, Follan, C. K., J. Knight, H. W. Linerholm, D. Fereay, S. Ineson, an J. W. Hurrell, 2009: The summer North Atlantic Oscillation: Past, present, an future. J. Climate, 22, Franzke, C., 2009: Multi-scale analysis of teleconnection inices: Climate noise an nonlinear trens. Nonlinear Processes Geophys., 16, , 2010: Long-range epenence an climate noise characteristics of Antarctic temperature ata. J. Climate, 23, Huang, N. E., an Z. Wu, 2008: A review on Hilbert-Huang transform: Metho an its applications to geophysical stuies. Rev. Geophys., 46, RG2006, oi: /2007rg , an Coauthors, 1998: The empirical moe ecomposition an the Hilbert spectrum for nonlinear an non-stationary time series analysis. Proc. Roy. Soc. Lonon, 454A, Jones, R. H., 1980: Maximum likelihoo fitting of ARMA moels of time series with missing observations. Technometrics, 22, Keeley, S. P. E., R. T. Sutton, an L. C. Shaffrey, 2009: Does the North Atlantic Oscillation show unusual persistence on intraseasonal timescales? Geophys. Res. Lett., 36, L22706, oi: /2009gl Lorenz, D. J., an E. T. DeWeaver, 2007: Tropopause height an zonal win response to global warming in the IPCC scenario integrations. J. Geophys. Res., 112, D10119, oi: / 2006JD Mahalanobis, P. C., 1936: On the generalise istance in statistics. Proc. Natl. Inst. Sci. Inia, 2, Masato, G., B. Hoskins, an T. Woollings, 2009: Can the frequency of blocking be escribe by a re noise process? J. Atmos. Sci., 66, Rennert, K. J., an J. M. Wallace, 2009: Cross-frequency coupling, skewness, an blocking in the Northern Hemisphere winter circulation. J. Climate, 22, Stephenson, D. B., V. Pavan, an R. Bojariu, 2000: Is the North Atlantic Oscillation a ranom walk? Int. J. Climatol., 20, Uppala, S. M., an Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, Wilks, D. S., 1995: Statistical Methos in the Atmospheric Sciences. Acaemic Press, 464 pp. Woollings, T., A. Hannachi, an B. Hoskins, 2010: Variability of the North Atlantic ey-riven jet stream. Quart. J. Roy. Meteor. Soc., 136, Wunsch, C., 1999: The interpretation of short climate recors, with comments on the North Atlantic an Southern Oscillations. Bull. Amer. Meteor. Soc., 80, Yin, J. H., 2005: A consistent polewar shift of the storm tracks in simulations of 21st century climate. Geophys. Res. Lett., 32, L18701, oi: /2005gl