2.2 STATISTICAL ANALYSIS OF SEA SURFACE TEMPERATURE IN THE NORTH ATLANTIC OCEAN. Constantin Andronache* Boston College, Chestnut Hill, Massachusetts

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1 . STATISTICAL ANALYSIS OF SEA SURFACE TEMPERATURE IN THE NORTH ATLANTIC OCEAN Constantin Andronache* Boston College, Chestnut Hill, Massachusetts. INTRODUCTION The importance of sea surface temperature anomalies (SSTA) for the climate of the North Atlantic region has been documented in previous studies (for instance, see Marshall et al., ; Sutton and Hodson,, ; Desser et al., ). Over ocean regions, there is significant covariance between SSTA and the anomalies of air temperature at surface, in monthl, seasonal and annual average values. Such covariance is due to exchange of heat and momentum between the upper ocean laer and the air near surface (Desser et al., ). Oceans have significant thermal inertia and provide slow variations of the lower boundar of the atmosphere (Saravanan, ). This feature is useful in studies of climate predictabilit at time scales from season to decade. SSTA variations have been linked to climate variations in North America and Europe. Such studies are supported b statistical analsis of observations as well as b recent modeling studies (Marshall et al., ). A notable phenomenon for the long term SST behavior in North Atlantic in the Atlantic Multidecadal Oscillation (AMO) which provides support for climate predictions at decadal time scale (Knight et al., ; ). It has been reported that some climate predictabilit might be possible at various scales, as long as strong SST signals or oscillations are identified (such as ENSO, events, for example) (Keller, ; Marshall et al., ; Andronache and Phillips, ). Research is underwa to address the climate prediction at seasonal scale and develop practical applications, where such forecasts can have significant impact (Palmer, ; Timofeeva, ; Tugrul Yilmaz, ). In the context of the climate predictabilit, we address the problem of SSTA persistence at seasonal scale in North Atlantic ocean. The data and methodolog are presented in the next section.. SST DATA There are complete global monthl SST analses, used extensivel in climate studies (Renolds and Smith, ; Kaplan et al., ). Such data sets are constrained b qualit, quantit and distribution of the original measurements (Hurrell and Trenberth, ). *Corresponding author address: Constantin Andronache, Boston College, Chestnut Hill, MA, andronac@bc.edu. Before the satellite era, observations did not cover the whole ocean, and various techniques have been emploed to produce global data sets. Since the s satellites have been increasingl utilized to measure SST and have provided an enormous rise in the abilit to view the spatial and temporal variation in SST. Such advances in observations contribute to improvement of model initial and boundar conditions specification, as well as in statistical analses of climate variations (Marshall et al., ). In this stud we use the NOAA SST monthl time series ( ), and the NCEP/NCAR SST data sets ( ) for the North Atlantic ocean.. METHOD Three methods are used to obtain the monthl SST residuals of importance for seasonal climate variations at the time scale of interest. These methods aim to obtain approximatel stationar earl time series of the monthl SSTA. We are particularl interested in the correlation between SSTA between various months, in the stationar time series (Wilkis, ; von Storck and Zwiers, ). The presence of the long term trend and AMO tpe variations in the original SSTA time series tends to produce high correlations. We attempt to describe the SSTA correlations at short time scales (such as season), which might become more evident after achieving stationar conditions. These three methods are briefl described here. ) For each month, from the earl time series: a) remove the linear trend; b) remove the AMO tpe of oscillation (Andronache, ). The long term trend is largel attributed to increase of global temperature over the last centur (Andronache and Phillips, ). The AMO phenomenon is an internal oscillation of the ocean circulation, driven b a natural mode of variabilit in the thermohaline circulation in the North Atlantic, with possible alterations due to climate change (Delworth and Mann ; Knight et al., ). ) Remove the linear trend between breakpoints (BP) in the time series. This method does not make an assumptions about long term trend over the whole time interval, and does not consider explicitl an low-frequenc oscillation. Instead, it finds the local min and max SST values over few decades, and does a linear regression between two such consecutive local extreme values. Thus, it removes

2 the linear trend established between such BP, as will be illustrated in Figure. ) Remove a polnomial fit of the SST time series (Andronache et al., ). This method does a least squares (LS) fit with low order polnomials, as an approximation of the data over the whole observation period. The method works well for short time series, and for low order polnomials. High order polnomials tend to present too much detail of the original time series, and have large errors at the end of the time interval. Notations used in this stud: the earl time series of the monthl average SST for a given month; LT the linear trend of ; AMO the sine LS fit of the (- LT ); r = - LT AMO the SST residual of after removal of linear trend and AMO approximation. For method, the residual r is defined as r =- BP (the difference between and the LS linear fit between breaking points of ). For method, the residual r is r =- P (the difference between and the polnomial fit of, where the order of the polnomial used in this stud is n = ). The three methods provide similar results, and the were used to check the robustness of the first one which is illustrated here in detail. The time series of the SST residuals obtained b the above methods are stationar in weak sense (the mean and the variance are constant in time). We illustrate how SST residuals are obtained b removing the linear trend and the AMO tpe oscillation.. RESULTS AND DISCUSSION Figure shows the SST time series for each month. Due to the annual ccle, there are pairs of months with ver similar variations. For instance, at the bottom of the plot, Februar and March SST have ver similar behavior, and the seem highl correlated. These months correspond to the lowest SST values during the cold season in North Atlantic region. At the top of the plot, August and September SST have similar variations, corresponding to the highest values in the warm season. Few characteristics are evident: a) the long term positive trend; b) the multidecadal oscillation. We are interested to find out a statistical relationship between SST in various months, and we have to produce SST time series that are stationar. These conditions are illustrated in Figures and for the month of Januar. Figure shows: the time series of monthl SST for Januar, versus time in ears. The LS linear trend is shown; the monthl SST residual for Januar, which is the difference ( LT ), versus time, in ears. This residual SST has no trend but exhibits a multidecadal oscillator component. Figure shows: The Januar monthl SST residual ( LT ) and the least square of a sine function, versus time, in ears; The Januar monthl SST residual r, versus time, in ears. This residual time series is approximatel stationar. Jan Feb Mar Apr Ma Jun Jul Aug Sep Oct Nov Dec Fig.. Time series of the monthl SST versus time, in ears. ) (C). LT. Fig.. Time series of monthl SST for Januar, versus time in ears. The linear trend in least square sense is shown; The monthl SST residual for Januar, ( LT ), versus time, in ears. This procedure in applied for all months. We note that AMO, approximated b a sine function with three parameters (amplitude, period, and phase) is the first Fourier component of the time series, which correspond to a well defined phsical phenomenon (AMO). B taking more Fourier series terms, we can obtain a better approximation of the ( LT ) data, at shorter time scales, but our purpose here is to remove onl the dominant multidecadal oscillator features (such as AMO). The application of this method for all twelve months produced some variabilit in the fitting parameters (amplitude, period, and phase), consistent with previous results.

3 . Correlation of SST residuals ) (C) Residual r (C) ) AMO.. Fig. The Januar monthl SST residual ( LT ) and the least squares of a sine function, versus time, in ears; The Januar monthl SST residual r, versus time, in ears. Next subsection provides a brief account of AMO as a phsical low-frequenc oscillation in the North Atlantic ocean.. AMO SST in North Atlantic show variations with a period of ears, a phenomenon called Atlantic Multidecadal Oscillation (Schlesinger and Ramankutt ; Delworth and Mann ). There is extensive literature on AMO and its effects on climate, and there is potential predictabilit at decadal time scales in the North Atlantic region based on this phenomenon. AMO is associated with large scale precipitation changes in Sahel, US, and Brazil (Knight et al.,, ). It is also associated with the variations in the frequenc of severe Atlantic hurricanes (Goldenberg et al., ). AMO is correlated with Arctic temperature changes (Chlek et al., ). Based on results from model simulations, AMO is considered a natural mode of oscillation of the Atlantic Ocean thermohaline circulation (Delworth and Mann ) and this conjecture is supported b available observations. Some caveats need to be noted concerning the present state of AMO understanding. The observational SST time series are too short to infer oscillations with a quasi-period of ears with high degree of reliabilit. Longer time series, extending in the past, using prox data, would be beneficial to investigate AMO in the North Atlantic region. The coupled ocean-atmosphere models need to reproduce the thermohaline circulation and its characteristics. For such aim, long term records of deep ocean data becomes paramount. We note first that the residuals obtained b the three methods are similar. Figure a shows the SST and the linear regression between BP in the time series. Figure b shows the polnomial fit (order = ) of the same data. Figure c compares the three residuals obtain using these methods. More detailed tests (not shown) were performed to determine an significant variations between these methodologies, and we found that the produce similar stationar time series of the SST residuals. residual (C).... Figure. Residuals obtained b the three methods: a) BP; b) polnomial fit; c) comparison of residuals from the three methods. Figure shows the contour plot of the SST residual obtained above. For an given month, there are significant variations at time scales of several ears, likel linked to ENSO events and teleconnections between Atlantic Ocean and other regions (Penland and Matrosova, ; Marshall et al., ; Andronache and Phillips, ). For an given ear, we note some persistence of the SST anomal. This is more visible if we take a smaller time interval such as that shown in Figure for the period -. It is apparent that SSTA persistence at few months is common, while does not seem to be a simple rule. (c) BP P r r r Fig. Contour plot of SST residual, r for the time interval -.

4 ..... matrix is valuable in studies of climate predictabilit at regional scale and will be explored in more details to account for the role of the spatial distribution of the SSTA. Preliminar results show that the spatial distribution of SSTA provides a detailed structure of interactions between ocean and atmospheric circulation. Further work will address the connection between North Atlantic SSTA and tropical storms, the role of SST in Arctic climate variations, and the role of ENSO in North Atlantic region climate.. ACKNOWLEDGMENTS Fig.. Contour plot of the SST residual r for the time interval. The author thanks Vaughan Phillips and Charles Seman for helpful discussions, and acknowledges the use of SST data from NOAA... REFERENCES... Fig. Contour plot of the correlation coefficient for the matrix r of the SST residuals. We estimate the correlation coefficients between r in various months. Figure shows the contour plot of the correlation coefficients of the matrix r of SST residuals. It illustrates that significant correlation exist between consecutive months. Thus, for example, Februar, March, and April correlate well with Januar. Generall, in most cases, each month correlates well with previous three to five months. This result confirms that in the monthl SSTA anomalies (after removal of decadal trend and oscillations), there is significant persistence at season time scale (few months up to about six months or so). While this result is applicable for the average SSTA for the whole North Atlantic, preliminar studies show the importance of spatial distribution, well illustrated and documented b previous studies (Penland C, and L. Matrosova, ; Marshall et al., ).. CONCLUSIONS For the North Atlantic region, the monthl SST residuals obtained after removal of long term trend and AMO tpe oscillation, show significant persistence at seasonal time scale and beond. The significant covariance in the SST residual.. Andronache C.,, Principal component analsis of sea surface temperature in the North Atlantic ocean, International Journal of Modern Phsics C, Vol., No.,. Andronache C., N. Suciu and C. Vamos,, Revue D'Analse Numerique et de Theorie de L'Approximation, -. Andronache C., and V. Phillips,, Eos Trans. AGU ; Jt. Assem. Suppl., Abstract AB. Chlek, Petr, Chris K. Folland, Glen Lesins, Manvendra K. Dube, and Muin Wang,, Arctic air temperature change amplification and the Atlantic Multidecadal Oscillation, Geophs. Res. Lett., L, doi:./gl. Delworth T. L. and M. E. Mann,, Observerd and simulated multidecadal variabilit in the Northern Hemisphere, Clim. Dn., -. Deser et al.,, Understanding the Persistence of Sea Surface Temperature Anomalies in Midlatitudes, J. Climate,. Enfield D. B., A. M. Mestas-Nunez and P. J. Trimble,, The Atlantic Multidecadal Oscillation and its relation to rainfall and river flows in the continental U.S., Geophs. Res. Lett.,. Goldenberg S. B. et al.,, The Recent Increase in Atlantic Hurricane Activit: Causes and Implications, Science, -. Hurrell W. James, and Kevin E. Trenberth,, Global Sea Surface Temperature Analses:

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