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Temporal variability of the Baltic Sea level based on satellite observations
Accepted Manuscript Temporal variability of the Baltic Sea level based on satellite observations Malgorzata Stramska PII:
S0272-7714(13)00401-0
DOI:
10.1016/j.ecss.2013.09.002
Reference:
YECSS 4254
To appear in:
Estuarine, Coastal and Shelf Science
Received Date: 4 April 2013 Revised Date:
30 August 2013
Accepted Date: 2 September 2013
Please cite this article as: Stramska, M., Temporal variability of the Baltic Sea level based on satellite observations, Estuarine, Coastal and Shelf Science (2013), doi: 10.1016/j.ecss.2013.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Temporal variability of the Baltic Sea level based on satellite observations
2 Malgorzata Stramska*1,
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4 Institute of Oceanology of the Polish Academy of Sciences ul. Powstańców Warszawy 55, 81-712 Sopot, Poland
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* corresponding author
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Phone: (+48 58) 73 11 600
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Fax: (+48 58) 55 12 130
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Email: [email protected], [email protected]
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Index terms: Satellite Sensing, Satellite Altimetry, Baltic Sea, Sea Level
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Abstract
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The main objective of this paper is to determine what are the most important time scales
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of variability of the sea level in the open Baltic Sea. The study is based on the 7-day
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resolution multimission global gridded sea level anomalies (SLA) for years 1992-2012
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distributed by AVISO. For comparison satellite-derived SLA from the North Sea and
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North Atlantic, coastal data from the Stockholm tide gauge, the NCEP meteorological
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data, and river runoff data from the Balt-HYPE model have been also analyzed. We have
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applied time series analysis algorithms (Bendat and Piersol, 2011). Supporting earlier
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research, our results show that the variability of the sea level in the open Baltic Sea is
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highly coherent with the sea level in the North Sea. We have found out that the annual
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peak is not well pronounced in the open Baltic Sea SLA spectrum, but the semiannual
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peak is the most prevailing. In contrast, the annual peak is significant in the North Sea
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SLA power spectrum. The coherence between the open Baltic Sea and the Stockholm
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SLA is high and the SLA variability in these two locations is in phase. The results of the
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cross-spectral analysis between the SLA in the Baltic Sea and meteorological parameters
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(wind stress magnitude, zonal and meridional wind stress components, and barometric
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pressure at sea level) show that coherence is highest with the zonal wind stress
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component. Coherence between the river runoff and the SLA in Stockholm is not
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significant.
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1. Introduction One of the most direct pieces of evidence of climate change is the observed rise of
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globally averaged sea level (IPCC, 2007; Church et al., 2010; Meehl et al., 2007;
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Rahmstorf 2007; Horton et al., 2008). Because of possible negative consequences for
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safety and regional economy, the impacts of sea level rise are of particular concern in
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coastal regions. These regional trends can differ significantly from global trends. One
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region where sea level has been closely monitored for many years is the landlocked, non-
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tidal Baltic Sea, located in densely populated northern Europe. Understanding sea level
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trends and variations in this region is crucial, because of their impacts on coastal
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infrastructure, and also because of their links with the mechanisms of exchange of water
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between the Baltic and the North Seas (Samuelsson and Stigebrandt, 1996; Gustafsson
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and Andersson, 2001; Ekman, 2009). This exchange has a key influence on water
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balance, deep-water renewal rates, and other oceanographic processes in the Baltic Sea.
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In particular, the major events of oceanic water inflow affect the eutrophication status of
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the Baltic Sea (e.g., Omsted et al., 2004; HELCOM, 2009; Leppäranta and Myrberg,
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2009).
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Previous research on Baltic Sea levels has been mostly based on coastal tide
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gauge time series data (e.g. Ekman and Makinen, 1996; Hünicke and Zorita, 2006; 2008,
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Hünicke et al., 2008; Ekman, 2009; Donner et al., 2012). This research has greatly
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increased our understanding of the spatial and temporal variability of the Baltic Sea
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levels. For example, it has been shown that trends in local sea levels recorded by coastal
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stations vary with the geographic positions of these stations (e.g., Ekman, 2009). It has
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been also documented that the variability of the Baltic Sea level is significantly correlated
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with large-scale wind and air pressure fields, which are strongly influenced by the North
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Atlantic Oscillation (NAO) index (e.g., Andersson, 2002; Jevrejeva et al., 2005; Ekman,
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2009; Stramska and Chudziak, 2013). Other meteorological quantities such as air
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temperature and precipitation also considerably influence the level of the Baltic Sea
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(Hünicke and Zorita, 2006).
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Interpretation of the tide gauge data in terms of the basin scale trends and patterns
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of variability of the Baltic Sea level can be difficult. Nonuniform spatial distribution of
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tide gauges, tectonic land uplift and regional postglacial rebound rates, as well as
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topographic effects can have substantial impacts on the interpretation of data recorded by
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coastal stations (e.g., Peltier 1998; 2004; Soudarin et al., 1999; Tamisiea et al., 2010). In
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contrast, these issues should not confound analysis of the open sea levels obtained from
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satellite altimetry. In the last 20 years satellite altimetry methods (TOPEX/Poseidon,
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ERS-1 and -2, GFO, Envisat, Jason-1 and 2) for routine monitoring of sea levels have
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been increasingly popular and are now used as a standard of reference (e.g., Cotton et al.,
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2004; Bouffard et al., 2008; 2011; Vignudelli et al., 2011). Satellite measurements of sea
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levels allow us to take a unique look at sea levels globally and regionally (e.g., Leuliette
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et al., 2004; Church and White 2006; Nerem et al., 2010; Vignudelli et al., 2011).
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The main objective of this paper is to determine what are the most important time
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scales of variability in the Baltic Sea level observed from satellites. Previous studies
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investigating the Baltic Sea level variability were mostly based on long-term (50 years
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and more) monthly coastal data records (e.g., Plag and Tsimplis, 1999; Ekman and
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Stigebrandt, 1990; Ekman, 1998; 2009; Hünicke and Zorita, 2008). In comparison to
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these previous studies, our analysis is based on open sea satellite-derived data that are not
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affected by coasts and have better temporal resolution (weekly data), though time series
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data available for our analysis are considerably shorter (about 20 years). Therefore our
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research is focused on the most recent variability of Baltic Sea level. Our research should
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be of interest to regional physical oceanographers and to modelers who are interested in
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using altimetry data for improving their models. A target audience includes also
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researchers and coastal managers interested in better understanding conditions favoring
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the occurrence of storm surges and coastal erosion.
2. Data Sets and Methods
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This study is based on Sea Level Anomalies (SLA) extracted from the delayed time
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global
gridded
data
product
available
at
AVISO
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(www.aviso.oceanobs.com). The SLA data are continuously updated by AVISO and
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referenced to the 7-year (1993 - 1999) mean sea surface height. For this study we have
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used all the available DT SLA data, covering the time period from October 4, 1992 to
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July 18, 2012 (almost 20 years). The SLA data have been interpolated by AVISO on 1/3°
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spatial resolution Mercator grid with 7-day temporal resolution, using computing
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methods based on objective analysis. The error in the SLA data estimated by AVISO is
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about 1-2 cm. Thus, these research quality data allow monitoring of ocean sea level
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variability due to seasonal and climatic variations. Detailed information about standard
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data processing methods can be found at www.aviso.oceanobs.com. For our study we
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have extracted data for the open Baltic Sea, in a region that is not likely to be affected by
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sea ice (55.44 oN, 18.33 oE). For comparison we have also used satellite altimetry data
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from the North Sea (56.93 oN 5.0 oE) and the North Atlantic (55.06 oN, 20.0 oW) (see
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Figure 1). Another data set used in our study includes the coastal tide gauge records from
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Stockholm. Research quality daily data of relative sea levels recorded at this station have
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been provided by the University of Hawaii (Sea Level Center, uhslc.soest.hawaii.edu).
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Note that the local tide gauges measure sea level relative to the local land surface, this is
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why the measurement is referred to as the "relative sea level" (RSL). Land surfaces are
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dynamic, and in particular the glacial isostatic adjustment (GIA, see Peltier, 1998; 2004)
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is known to affect the relative sea level recorded in Stockholm. However these vertical
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movements of land should not significantly affect the periodic variability of the SLA on
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scales as short as ~ 2 years and less, which are considered in this paper. For our analysis,
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we have converted tide gauge data to sea level anomalies by subtracting the 7-year mean
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(1993 - 1999) from the original time series.
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To evaluate the role of atmospheric forcing we have used the meteorological data
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from the NOAA-CIRES Climate Diagnostic Center NCEP/NCAR (National Centers for
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Environmental Prediction and National Center for Atmospheric Research) Reanalysis 2.
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The Reanalysis Project employs a state-of-the-art analysis/forecast system to assimilate
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global meteorological data from various available sources from 1948 to the present. In
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particular we have used the daily zonal and meridional wind stress components and
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barometric pressure at sea level. The NCEP data from 1992-2012 were extracted for
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locations in the open Baltic Sea (56.19 oN, 20.63 oE) and in the North Sea (56.19 oN, 5.63
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o
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basin. These data were taken from the HYPE model for years 1988 to 2008 (model Balt-
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HYPE, data at balt-hypeweb.smhi.se, Donnelly et al., 2011). The hydrological Balt-
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E). In addition, in our analysis we have also used river runoff data for the Baltic Sea
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HYPE model has been driven by data from the NCEP reanalysis and verified with in situ
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data (Donnelly et al., 2011). After 2008 HYPE model data were not available. To define the most important temporal scales of variability of the SLA, we
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performed a time series analysis using algorithms described by Bendat and Piersol
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(2011). First, we subtracted off a linear trend, which was fitted to each time series record
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by a least-square method. A series transformed this way had a mean value of virtually
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zero. Next, the power spectra of the data series were obtained using a Fourier transform
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of the autocovariance function. To describe joint properties of the time series considered,
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we applied a Fourier transform to the crosscovariance functions and estimated squared
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coherence and phase functions. The Parzen weighting function was applied to the
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covariance functions. According to the Nyquist theorem our analysis is limited to periods
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longer than 14 days, or more conservatively longer than 28 days (Bloomfield, 2000).
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Thus, the relatively rapid variations of sea level in response to wind events on time scale
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of few days are not included in our analysis. Despite of these limitations our analysis
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covers a range of scales that are of interest in the Baltic Sea.
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In all cases considered here, each time series record consists of a total number of
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N = 1024 data points. The auto- and crosscovariance functions were calculated with the
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maximum time lag M = 150. This corresponds to the frequency resolution bandwidth of
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0.00095 cycle/day. The M value of 150 is a little beyond the value usually recommended
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(M = 0.1N), but this higher value of M increased the spectral resolution. Tests with
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gradually increasing the time lag from 100 to 150 indicated that the calculated spectra
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changed smoothly, and there were no spurious effects. Therefore all Figures included in
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the Results section are based on calculations with M = 150. The standard error is ~34%
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of the power spectral estimates. The coherence above 0.283 is statistically significant at
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95% confidence level (Bloomfield, 2000).
154 3. Results and discussion
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In Figure 2 we have plotted full (~20-years long) time series of the 7-day
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resolution sea level anomalies (SLA) used in this study. Time series shown in Figure 2
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include the SLA in the North Atlantic, North Sea, and open Baltic Sea (Baltic Proper). In
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addition sea level anomalies based on Stockholm observations are plotted in Figure 2. It
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is clear that there are many scales of variability present in the data. Visual inspection of
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the time series leads to the conclusion that many patterns of variability are similar in the
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Baltic and North Seas SLA time series. It is also obvious that the time series from the
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coastal station in Stockholm are characterized by the greatest amplitude of variability
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(standard deviation = 18.8 cm), while the data from the North Atlantic have the smallest
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amplitude (standard deviation = 6.5 cm). The standard deviations for the SLA time series
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in the open Baltic Sea and North Sea are 14.2 and 9.3 cm, respectively. These standard
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deviations were estimated after removing a small multiyear trend (for example 0.33
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cm/year in the open Baltic Sea, Stramska and Chudziak, 2013).
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The power spectra estimated for the SLA in the open North Sea and North
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Atlantic are displayed in Figure 3a. Figure 3b compares the power spectra obtained for
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the SLA time series in the open Baltic Sea and at the coastal station in Stockholm. The
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spectra are plotted as a function of frequency, but for convenience we have marked on the
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bottom axis (black dots) the periods of 2 years, 1 year, 6 month, and 3 month. The most
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dominant peak in the SLA power spectra in the North Atlantic and North Sea is the
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annual peak. In contrast the annual peak is not well pronounced in the open Baltic Sea
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and Stockholm power spectra. This can be also noticed in Figure 4, where we compared
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the normalized power spectral density for the SLA in the open Baltic Sea and Stockholm
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with the normalized power spectral density of the wind stress magnitude in the Baltic
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Sea. The power spectra displayed in Figure 4 are normalized to the total variance of each
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data set, respectively. The power spectrum of wind stress magnitude exhibits a striking
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annual maximum. The power spectra of the SLA in the open Baltic and Stockholm have
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statistically significant peaks (95% level) for the time periods of ~2 years, 6 months and 3
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months. The annual peak is not significant. The 6-month peak is also present in the North
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Sea data, but not in the North Atlantic data (Figure 3). The fact that the annual peak is not
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well pronounced in the Baltic Sea time series (coastal and open sea data) might seem
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somewhat surprising. This peak has been described before in the literature (see Hünicke
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and Zorita, 2008; Ekman, 2009; and the references therein). Note however, that these
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previous results were based on monthly data and long data records (50 years and more).
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Longer data records might be more efficient in separating the annual cycle, in particular
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if this cycle is well defined and strong in some years.
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Importantly, as has been noted by Ekman (2009), the annual cycle in the Baltic
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Sea level is somewhat asymmetrical and can be decomposed by the spectral analysis into
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two or more harmonics. This asymmetry of the annual sea level cycle in the Baltic Sea is
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also seen in our data sets (Figure 5). The 19-year averaged SLA shown in Figure 5
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displays a regular (symmetric) annual cycle in the North Atlantic, but when we look at
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the Baltic Sea SLA data, we note that the annual cycle is quite asymmetric. The time
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period when the SLA series in the open Baltic Sea are below annual mean value is shorter
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than the time period when the average SLA series are above the annual mean value. In
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addition, the annual amplitude in the averaged SLA time series seems to be much more
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pronounced in the Baltic Sea data than in the North Atlantic data. We suggest that the
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monthly averaged Baltic Sea level data might lead to some deformation of the temporal
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progression of the annual cycle, making it seem to be more symmetrical than it really is.
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The 7-day data can likely better resolve the time evolution of this cycle than the monthly
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data. In this case, the 7-day time series data (better resolving the asymmetry of the annual
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cycle) can lead to a more pronounced semiannual peak in a power spectrum in
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comparison to the power spectrum based on monthly data. Therefore, the annual peak in
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the power spectrum based on the 7-day data would be weaker than in the power spectrum
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based on the monthly data.
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Figures 6 - 8 summarize the results of the cross-spectral analysis between selected
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pairs of the SLA time series. In these figures solid and dashed lines indicate the squared
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coherence and phase functions, respectively. The coherence above 0.283 is statistically
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significant at 95% level (Bloomfield, 2000; Bendat and Piersol, 2011). Note that for an
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ideal linear system the coherence would be one. Our data sets are generally characterized
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by coherence less than one. This can result from not quite a linear response of the system.
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In addition a coherence less than unity can be due to the fact that other inputs (not
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included in the analysis) contribute to the observed output (SLA variability).
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Nevertheless, the coherence values displayed in Figures 6 - 8 indicate that the data series
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are significantly correlated with each other in some frequencies. In particular, in Figure 6
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we can see that the coherence between SLA in the North and Baltic Seas is above 0.3 for
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frequencies lower than 0.007 and higher than 0.022 cycle/day (periods longer than about
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140 days and shorter than about 45 days). A similar pattern is observed in Figure 7 for the
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coherence spectrum between the SLA in the North Sea and in Stockholm, but the
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coherence values are lower. The highest coherence among the SLA data sets considered
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is, as one would expect, between the SLA in the open Baltic Sea and in Stockholm
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(Figure 8). In this case the coherence is around 0.7 for frequency lower than 0.007
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cycle/day (periods >140 days) and varies between 0.5 and 0.8 for periods between 50 -
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150 days. We have also estimated the coherence between the SLA in the open Baltic Sea
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and in the North Atlantic, but these SLA time series are not significantly correlated
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(results not shown).
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The dashed lines in Figures 6 - 8 indicate the phase shift between various time
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series. The SLA in the open Baltic Sea and in Stockholm are in phase with the SLA in the
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North Sea at lower frequencies. At higher frequencies the Baltic Sea SLA are delayed in
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comparison to the SLA in the North Sea (Figures 6 and 7). The observed oscillations of
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phase are meaningless when there is not significant coherence between the data series.
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The SLA in the open Baltic Sea and in Stockholm (Figure 8) are in phase and the phase
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spectra vary smoothly, which is indicative of a good correlation. The small slope in the
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phase spectrum can indicate that there is a time delay of few days between the data series.
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This time delay is consistent with the observations that SLA variability on the time scales
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considered is mainly caused by persistent winds redistributing water between the Atlantic
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Ocean (the North Sea) and the Baltic Sea (e.g., Ekman, 2009). If we assume the current
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speed of ~ 1 m/s we can estimate that it will take about 3.5 days to transport the water
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mass over a distance of 300 km. Thus the time delay of few days is not unrealistic when
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considering a relationship between SSH in distant locations of the Baltic Sea. Because
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our system is not quite linear, the estimated phase function is not exactly a simple straight
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line. Summarizing these results, it is evident from our analysis that the SLA variability
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in the Baltic Sea is coherent with the SLA variability in the North Sea. This observation
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is in agreement with previous analyses of the Baltic Sea level data (e.g. Ekman, 2009).
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Note that prior publications stressed that annual patterns in the Baltic Sea level variability
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recorded by the tide gauges depend on the geographical location of the tide gauge (e.g.,
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Hünicke and Zorita, 2008). One of the reasons for this is that sea level variability
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observed at a coastal station is significantly influenced by the geometry of the coast and
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the direction of the wind. This is also most likely the reason why the coherence between
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the SLA in the open Baltic Sea and in Stockholm is significantly less than one, while the
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coherence between the satellite-derived SLA in different parts of the Baltic Proper
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(results not shown) is approximately equal one in the frequency range discussed here.
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We have attempted to check what are the links between atmospheric forcing and
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the SLA in the Baltic Sea. The results of the cross-spectral analysis between the
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meteorological parameters (wind stress magnitude, zonal and meridional wind stress
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components, and barometric pressure at sea level) and the SLA in the open Baltic Sea can
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be summarized as follows. Among the meteorological quantities considered, the
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coherence is highest between the zonal wind stress component and the SLA. The results
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are shown in Figure 9. (We obtained similar results if the zonal wind stress component
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from the North Sea instead from the Baltic Sea was used in this analysis). The coherence
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between the wind stress magnitude and the SLA as well as the coherence between the
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meridional wind stress component and the SLA (not shown) is generally lower than the
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coherence shown in Figure 8, and significantly different from zero only for frequencies
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between 0.0033 - 0.0048 cycle/day (periods 210-350 days). The coherence between
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barometric pressure and the SLA (not shown) is not significant at lower frequencies, but
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increases at higher frequencies, exceeding a value of 0.4 at frequency 0.023 cycle/day
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(period of ~ 45 days). This is in agreement with the conclusion reached before by Ekman
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(2009) that the response of the Baltic Sea level to barometric pressure is more evident at
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shorter times scales.
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Finally, we have considered the influence of the water runoff on the SLA. Water
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runoff into the Baltic Sea was approximated by a total discharge from the 75 largest
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rivers in the region, and estimated by the Balt-Hype model (Donnelly et al., 2011). River
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data were not available after 2008. Therefore, our analysis is based on the 20-years time
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series starting in 1988, and is limited to river discharge and the SLA in Stockholm. (The
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time period when both the river runoff data and the satellite-derived SLA were available
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was too short for this analysis, since the satellite data were available from October 1992).
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The coherence between river discharge and Stockholm SLA is not significant; it is above
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the 0.283 value only for periods of about 210-260 days (results not shown).
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The interpretation of our results is generally in agreement with Ekman (2009).
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Ekman distinguished the two most important time scales in the variability of the Baltic
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Sea level. These are: 1) short-term variations (time scale of days) in response to
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barometric pressure and short-term wind events; this variability affects more the sea level
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near the coasts than at the open sea and is significantly influenced by the geometry of the
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coastline and wind direction; and 2) long-term variability (time scale of months) in
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response to persistent winds redistributing water in the North Atlantic, North Sea, and
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Baltic Sea; this variability affects the level of the entire Baltic Sea. Our analysis was
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mostly limited to long-term variability. The time scale on the order of days cannot be
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resolved by our 7-day resolution time series data. We plan to extend this analysis to
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shorter time scales after we reprocess the satellite altimetry data in the Baltic Sea using
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the novel methods of coastal altimetry (Bouffard et al., 2008; 2011; Vignudelli et al.,
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2011). This reprocessing will also allow for a better spatial resolution and will allow us to
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quantify the geographical/regional differences in the SLA variability. Such data will also
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allow us to make a better interpretation of the coastal effects through more rigorous
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comparisons of the satellite-derived altimetry data with coastal stations. Finally, in the
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nearest future, we plan to complete comparisons of satellite-derived SLA with our
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numerical model of the Baltic Sea.
301 4. Summary
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There have been only few attempts to use satellite altimetry data in the Baltic Sea
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in the past. These include analyses of sea level data (e.g., Poutanem and Stipa, 2001;
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Madsen et al., 2007) and validation of the operational wave models (Solvsteen and
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Hansen, 2006). Our results based on time series analysis of almost 20-years of data of
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satellite altimetry in the open Baltic Sea support some of the earlier findings based on
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coastal data (e.g., Ekman, 2009). We have confirmed that the variability of the sea level
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in the Baltic Sea is coherent with the sea level in the North Sea. However, we found that,
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unlike in the North Sea, the annual peak is not well pronounced in the open Baltic Sea
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SLA spectrum. The semiannual peak is the most prevailing in the open Baltic Sea SLA
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spectrum. This is in contrast to earlier publications, which reported that the annual peak
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in the Baltic Sea level variability as highly significant. We suggest that one of the reasons
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for this discrepancy is that we have used data series with a higher temporal resolution (7
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days in comparison to monthly data used in previous research). The annual cycle of the
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open Baltic Sea level is asymmetrical, as suggested by Ekman (2009). This asymmetrical
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cycle is probably decomposed by the spectral analysis into 2 or more components of
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variability in our 7-day resolution SLA time series. We have documented that the SLA
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variability is in phase in the open Baltic Sea site considered and at the coastal station in
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Stockholm. The coherence between the SLA in these two locations is high, but
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significantly less than unity. One of the most likely reasons for this is the fact that the sea
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level in Stockholm is influenced by the coastal topography, while the open sea data are
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not. The results of the cross-spectral analysis between meteorological parameters (wind
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stress magnitude, zonal and meridional wind stress components, and barometric pressure
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at sea level) and the SLA in the open Baltic Sea show that the coherence is highest
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between the zonal wind stress component and the SLA. In addition our results indicate
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that the coherence between the river runoff and the SLA in Stockholm is not significant.
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Our analysis is limited to variability on a long-term scale (> month), because the time
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scale on the order of days cannot be resolved by our 7-day resolution time series data. In
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the near future, we plan to extend the results presented in this paper to shorter time scales
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after the satellite altimetry data in the Baltic Sea are reprocessed using the novel methods
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of coastal altimetry (Bouffard et al., 2008; 2011; Vignudelli et al., 2011).
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Acknowledgments: This work was supported through the SatBaltic project funded by the
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European Union through the European Regional Development Fund, (contract No.
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POIG.01.01.02-22-011/09 entitled ‘The Satellite Monitoring of the Baltic Sea
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Environment’). The altimeter data were processed by Ssalto/Duacs and distributed by
338
AVISO, with support from Cnes (http://www.aviso.oceanobs.com/duacs/). The
339
meteorological data were obtained from the National Centers for Environmental
340
Prediction and National Center for Atmospheric Research (NCEP/NCAR) Reanalysis
341
Project
342
(http://www.esrl.noaa.gov/psd/). The river runoff data were made available by the
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Swedish Meteorological and Hydrological Institute (balt-hypeweb.smhi.se/).
the
NOAA/OAR/ESRL
PSD,
Boulder,
Colorado,
USA
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Sciences, 32,111-149. Poutanen, M., Stipa T., 2001. Temporal and spatial variation of the sea surface
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Figure captions Figure 1. Map showing the geographical positions corresponding to the data series used in this paper: 1 – North Atlantic, 2 - North Sea, 3 – open Baltic Sea, 4 - Stockholm.
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Figure 2. Time series of sea level anomalies (SLA) used in this study. See Figure 1 for the geographical position corresponding to each of the time series.
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Figure 3. Power spectral density of SLA calculated from time series shown in Figure 2. a) North Atlantic and North Sea b) open Baltic Sea and Stockholm. Vertical bars indicate standard errors of the most significant peaks. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 4. Comparison of the normalized power spectral density for SLA in the open Baltic Sea and at coastal station in Stockholm with the normalized power spectral density of wind stress magnitude. Power spectra are normalized to the total variance. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis. Figure 5. Annual cycle in the 19-year averaged SLA in the North Atlantic (NA), North Sea (NS), open Baltic Sea (BS) and Stockholm (S).
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Figure 6. Squared coherence (solid dark line) and phase functions (dashed line) between the SLA in the North Sea and in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 7. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the North Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis. Figure 8. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the open Baltic Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 9. Squared coherence (solid line) and phase functions (dashed line) between zonal component of wind stress and SLA in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 2. Time series of sea level anomalies (SLA) used in this study. See Figure 1 for the geographical position corresponding to each of the time series.
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Figure 3. Power spectral density of SLA calculated from time series shown in Figure 2. a) North Atlantic and North Sea b) open Baltic Sea and Stockholm. Vertical bars indicate standard errors of the most significant peaks. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 4. Comparison of the normalized power spectral density for SLA in the open Baltic Sea and at coastal station in Stockholm with the normalized power spectral density of wind stress magnitude. Power spectra are normalized to the total variance. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 5. Annual cycle in the 19-year averaged SLA in the North Atlantic (NA), North Sea (NS), open Baltic Sea (BS) and Stockholm (S).
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Figure 6. Squared coherence (solid dark line) and phase functions (dashed line) between the SLA in the North Sea and in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 7. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the North Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 8. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the open Baltic Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 9. Squared coherence (solid line) and phase functions (dashed line) between zonal component of wind stress and SLA in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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S0272-7714(13)00401-0
DOI:
10.1016/j.ecss.2013.09.002
Reference:
YECSS 4254
To appear in:
Estuarine, Coastal and Shelf Science
Received Date: 4 April 2013 Revised Date:
30 August 2013
Accepted Date: 2 September 2013
Please cite this article as: Stramska, M., Temporal variability of the Baltic Sea level based on satellite observations, Estuarine, Coastal and Shelf Science (2013), doi: 10.1016/j.ecss.2013.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Temporal variability of the Baltic Sea level based on satellite observations
2 Malgorzata Stramska*1,
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4 Institute of Oceanology of the Polish Academy of Sciences ul. Powstańców Warszawy 55, 81-712 Sopot, Poland
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* corresponding author
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Phone: (+48 58) 73 11 600
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Fax: (+48 58) 55 12 130
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Email: [email protected], [email protected]
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Index terms: Satellite Sensing, Satellite Altimetry, Baltic Sea, Sea Level
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Abstract
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The main objective of this paper is to determine what are the most important time scales
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of variability of the sea level in the open Baltic Sea. The study is based on the 7-day
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resolution multimission global gridded sea level anomalies (SLA) for years 1992-2012
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distributed by AVISO. For comparison satellite-derived SLA from the North Sea and
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North Atlantic, coastal data from the Stockholm tide gauge, the NCEP meteorological
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data, and river runoff data from the Balt-HYPE model have been also analyzed. We have
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applied time series analysis algorithms (Bendat and Piersol, 2011). Supporting earlier
27
research, our results show that the variability of the sea level in the open Baltic Sea is
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highly coherent with the sea level in the North Sea. We have found out that the annual
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peak is not well pronounced in the open Baltic Sea SLA spectrum, but the semiannual
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peak is the most prevailing. In contrast, the annual peak is significant in the North Sea
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SLA power spectrum. The coherence between the open Baltic Sea and the Stockholm
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SLA is high and the SLA variability in these two locations is in phase. The results of the
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cross-spectral analysis between the SLA in the Baltic Sea and meteorological parameters
34
(wind stress magnitude, zonal and meridional wind stress components, and barometric
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pressure at sea level) show that coherence is highest with the zonal wind stress
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component. Coherence between the river runoff and the SLA in Stockholm is not
37
significant.
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1. Introduction One of the most direct pieces of evidence of climate change is the observed rise of
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globally averaged sea level (IPCC, 2007; Church et al., 2010; Meehl et al., 2007;
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Rahmstorf 2007; Horton et al., 2008). Because of possible negative consequences for
42
safety and regional economy, the impacts of sea level rise are of particular concern in
43
coastal regions. These regional trends can differ significantly from global trends. One
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region where sea level has been closely monitored for many years is the landlocked, non-
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tidal Baltic Sea, located in densely populated northern Europe. Understanding sea level
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trends and variations in this region is crucial, because of their impacts on coastal
47
infrastructure, and also because of their links with the mechanisms of exchange of water
48
between the Baltic and the North Seas (Samuelsson and Stigebrandt, 1996; Gustafsson
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and Andersson, 2001; Ekman, 2009). This exchange has a key influence on water
50
balance, deep-water renewal rates, and other oceanographic processes in the Baltic Sea.
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In particular, the major events of oceanic water inflow affect the eutrophication status of
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the Baltic Sea (e.g., Omsted et al., 2004; HELCOM, 2009; Leppäranta and Myrberg,
53
2009).
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Previous research on Baltic Sea levels has been mostly based on coastal tide
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gauge time series data (e.g. Ekman and Makinen, 1996; Hünicke and Zorita, 2006; 2008,
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Hünicke et al., 2008; Ekman, 2009; Donner et al., 2012). This research has greatly
57
increased our understanding of the spatial and temporal variability of the Baltic Sea
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levels. For example, it has been shown that trends in local sea levels recorded by coastal
59
stations vary with the geographic positions of these stations (e.g., Ekman, 2009). It has
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been also documented that the variability of the Baltic Sea level is significantly correlated
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with large-scale wind and air pressure fields, which are strongly influenced by the North
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Atlantic Oscillation (NAO) index (e.g., Andersson, 2002; Jevrejeva et al., 2005; Ekman,
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2009; Stramska and Chudziak, 2013). Other meteorological quantities such as air
64
temperature and precipitation also considerably influence the level of the Baltic Sea
65
(Hünicke and Zorita, 2006).
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Interpretation of the tide gauge data in terms of the basin scale trends and patterns
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of variability of the Baltic Sea level can be difficult. Nonuniform spatial distribution of
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tide gauges, tectonic land uplift and regional postglacial rebound rates, as well as
69
topographic effects can have substantial impacts on the interpretation of data recorded by
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coastal stations (e.g., Peltier 1998; 2004; Soudarin et al., 1999; Tamisiea et al., 2010). In
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contrast, these issues should not confound analysis of the open sea levels obtained from
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satellite altimetry. In the last 20 years satellite altimetry methods (TOPEX/Poseidon,
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ERS-1 and -2, GFO, Envisat, Jason-1 and 2) for routine monitoring of sea levels have
74
been increasingly popular and are now used as a standard of reference (e.g., Cotton et al.,
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2004; Bouffard et al., 2008; 2011; Vignudelli et al., 2011). Satellite measurements of sea
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levels allow us to take a unique look at sea levels globally and regionally (e.g., Leuliette
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et al., 2004; Church and White 2006; Nerem et al., 2010; Vignudelli et al., 2011).
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The main objective of this paper is to determine what are the most important time
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scales of variability in the Baltic Sea level observed from satellites. Previous studies
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investigating the Baltic Sea level variability were mostly based on long-term (50 years
81
and more) monthly coastal data records (e.g., Plag and Tsimplis, 1999; Ekman and
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Stigebrandt, 1990; Ekman, 1998; 2009; Hünicke and Zorita, 2008). In comparison to
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these previous studies, our analysis is based on open sea satellite-derived data that are not
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affected by coasts and have better temporal resolution (weekly data), though time series
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data available for our analysis are considerably shorter (about 20 years). Therefore our
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research is focused on the most recent variability of Baltic Sea level. Our research should
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be of interest to regional physical oceanographers and to modelers who are interested in
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using altimetry data for improving their models. A target audience includes also
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researchers and coastal managers interested in better understanding conditions favoring
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the occurrence of storm surges and coastal erosion.
2. Data Sets and Methods
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This study is based on Sea Level Anomalies (SLA) extracted from the delayed time
(DT)
multimission
global
gridded
data
product
available
at
AVISO
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(www.aviso.oceanobs.com). The SLA data are continuously updated by AVISO and
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referenced to the 7-year (1993 - 1999) mean sea surface height. For this study we have
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used all the available DT SLA data, covering the time period from October 4, 1992 to
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July 18, 2012 (almost 20 years). The SLA data have been interpolated by AVISO on 1/3°
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spatial resolution Mercator grid with 7-day temporal resolution, using computing
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methods based on objective analysis. The error in the SLA data estimated by AVISO is
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about 1-2 cm. Thus, these research quality data allow monitoring of ocean sea level
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variability due to seasonal and climatic variations. Detailed information about standard
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data processing methods can be found at www.aviso.oceanobs.com. For our study we
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have extracted data for the open Baltic Sea, in a region that is not likely to be affected by
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sea ice (55.44 oN, 18.33 oE). For comparison we have also used satellite altimetry data
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from the North Sea (56.93 oN 5.0 oE) and the North Atlantic (55.06 oN, 20.0 oW) (see
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Figure 1). Another data set used in our study includes the coastal tide gauge records from
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Stockholm. Research quality daily data of relative sea levels recorded at this station have
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been provided by the University of Hawaii (Sea Level Center, uhslc.soest.hawaii.edu).
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Note that the local tide gauges measure sea level relative to the local land surface, this is
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why the measurement is referred to as the "relative sea level" (RSL). Land surfaces are
112
dynamic, and in particular the glacial isostatic adjustment (GIA, see Peltier, 1998; 2004)
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is known to affect the relative sea level recorded in Stockholm. However these vertical
114
movements of land should not significantly affect the periodic variability of the SLA on
115
scales as short as ~ 2 years and less, which are considered in this paper. For our analysis,
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we have converted tide gauge data to sea level anomalies by subtracting the 7-year mean
117
(1993 - 1999) from the original time series.
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To evaluate the role of atmospheric forcing we have used the meteorological data
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from the NOAA-CIRES Climate Diagnostic Center NCEP/NCAR (National Centers for
120
Environmental Prediction and National Center for Atmospheric Research) Reanalysis 2.
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The Reanalysis Project employs a state-of-the-art analysis/forecast system to assimilate
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global meteorological data from various available sources from 1948 to the present. In
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particular we have used the daily zonal and meridional wind stress components and
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barometric pressure at sea level. The NCEP data from 1992-2012 were extracted for
125
locations in the open Baltic Sea (56.19 oN, 20.63 oE) and in the North Sea (56.19 oN, 5.63
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o
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basin. These data were taken from the HYPE model for years 1988 to 2008 (model Balt-
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HYPE, data at balt-hypeweb.smhi.se, Donnelly et al., 2011). The hydrological Balt-
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E). In addition, in our analysis we have also used river runoff data for the Baltic Sea
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HYPE model has been driven by data from the NCEP reanalysis and verified with in situ
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data (Donnelly et al., 2011). After 2008 HYPE model data were not available. To define the most important temporal scales of variability of the SLA, we
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performed a time series analysis using algorithms described by Bendat and Piersol
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(2011). First, we subtracted off a linear trend, which was fitted to each time series record
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by a least-square method. A series transformed this way had a mean value of virtually
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zero. Next, the power spectra of the data series were obtained using a Fourier transform
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of the autocovariance function. To describe joint properties of the time series considered,
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we applied a Fourier transform to the crosscovariance functions and estimated squared
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coherence and phase functions. The Parzen weighting function was applied to the
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covariance functions. According to the Nyquist theorem our analysis is limited to periods
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longer than 14 days, or more conservatively longer than 28 days (Bloomfield, 2000).
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Thus, the relatively rapid variations of sea level in response to wind events on time scale
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of few days are not included in our analysis. Despite of these limitations our analysis
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covers a range of scales that are of interest in the Baltic Sea.
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In all cases considered here, each time series record consists of a total number of
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N = 1024 data points. The auto- and crosscovariance functions were calculated with the
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maximum time lag M = 150. This corresponds to the frequency resolution bandwidth of
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0.00095 cycle/day. The M value of 150 is a little beyond the value usually recommended
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(M = 0.1N), but this higher value of M increased the spectral resolution. Tests with
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gradually increasing the time lag from 100 to 150 indicated that the calculated spectra
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changed smoothly, and there were no spurious effects. Therefore all Figures included in
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the Results section are based on calculations with M = 150. The standard error is ~34%
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of the power spectral estimates. The coherence above 0.283 is statistically significant at
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95% confidence level (Bloomfield, 2000).
154 3. Results and discussion
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In Figure 2 we have plotted full (~20-years long) time series of the 7-day
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resolution sea level anomalies (SLA) used in this study. Time series shown in Figure 2
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include the SLA in the North Atlantic, North Sea, and open Baltic Sea (Baltic Proper). In
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addition sea level anomalies based on Stockholm observations are plotted in Figure 2. It
160
is clear that there are many scales of variability present in the data. Visual inspection of
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the time series leads to the conclusion that many patterns of variability are similar in the
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Baltic and North Seas SLA time series. It is also obvious that the time series from the
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coastal station in Stockholm are characterized by the greatest amplitude of variability
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(standard deviation = 18.8 cm), while the data from the North Atlantic have the smallest
165
amplitude (standard deviation = 6.5 cm). The standard deviations for the SLA time series
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in the open Baltic Sea and North Sea are 14.2 and 9.3 cm, respectively. These standard
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deviations were estimated after removing a small multiyear trend (for example 0.33
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cm/year in the open Baltic Sea, Stramska and Chudziak, 2013).
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The power spectra estimated for the SLA in the open North Sea and North
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Atlantic are displayed in Figure 3a. Figure 3b compares the power spectra obtained for
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the SLA time series in the open Baltic Sea and at the coastal station in Stockholm. The
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spectra are plotted as a function of frequency, but for convenience we have marked on the
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bottom axis (black dots) the periods of 2 years, 1 year, 6 month, and 3 month. The most
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dominant peak in the SLA power spectra in the North Atlantic and North Sea is the
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annual peak. In contrast the annual peak is not well pronounced in the open Baltic Sea
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and Stockholm power spectra. This can be also noticed in Figure 4, where we compared
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the normalized power spectral density for the SLA in the open Baltic Sea and Stockholm
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with the normalized power spectral density of the wind stress magnitude in the Baltic
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Sea. The power spectra displayed in Figure 4 are normalized to the total variance of each
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data set, respectively. The power spectrum of wind stress magnitude exhibits a striking
181
annual maximum. The power spectra of the SLA in the open Baltic and Stockholm have
182
statistically significant peaks (95% level) for the time periods of ~2 years, 6 months and 3
183
months. The annual peak is not significant. The 6-month peak is also present in the North
184
Sea data, but not in the North Atlantic data (Figure 3). The fact that the annual peak is not
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well pronounced in the Baltic Sea time series (coastal and open sea data) might seem
186
somewhat surprising. This peak has been described before in the literature (see Hünicke
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and Zorita, 2008; Ekman, 2009; and the references therein). Note however, that these
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previous results were based on monthly data and long data records (50 years and more).
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Longer data records might be more efficient in separating the annual cycle, in particular
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if this cycle is well defined and strong in some years.
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Importantly, as has been noted by Ekman (2009), the annual cycle in the Baltic
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Sea level is somewhat asymmetrical and can be decomposed by the spectral analysis into
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two or more harmonics. This asymmetry of the annual sea level cycle in the Baltic Sea is
194
also seen in our data sets (Figure 5). The 19-year averaged SLA shown in Figure 5
195
displays a regular (symmetric) annual cycle in the North Atlantic, but when we look at
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the Baltic Sea SLA data, we note that the annual cycle is quite asymmetric. The time
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period when the SLA series in the open Baltic Sea are below annual mean value is shorter
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than the time period when the average SLA series are above the annual mean value. In
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addition, the annual amplitude in the averaged SLA time series seems to be much more
200
pronounced in the Baltic Sea data than in the North Atlantic data. We suggest that the
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monthly averaged Baltic Sea level data might lead to some deformation of the temporal
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progression of the annual cycle, making it seem to be more symmetrical than it really is.
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The 7-day data can likely better resolve the time evolution of this cycle than the monthly
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data. In this case, the 7-day time series data (better resolving the asymmetry of the annual
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cycle) can lead to a more pronounced semiannual peak in a power spectrum in
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comparison to the power spectrum based on monthly data. Therefore, the annual peak in
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the power spectrum based on the 7-day data would be weaker than in the power spectrum
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based on the monthly data.
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Figures 6 - 8 summarize the results of the cross-spectral analysis between selected
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pairs of the SLA time series. In these figures solid and dashed lines indicate the squared
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coherence and phase functions, respectively. The coherence above 0.283 is statistically
212
significant at 95% level (Bloomfield, 2000; Bendat and Piersol, 2011). Note that for an
213
ideal linear system the coherence would be one. Our data sets are generally characterized
214
by coherence less than one. This can result from not quite a linear response of the system.
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In addition a coherence less than unity can be due to the fact that other inputs (not
216
included in the analysis) contribute to the observed output (SLA variability).
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Nevertheless, the coherence values displayed in Figures 6 - 8 indicate that the data series
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are significantly correlated with each other in some frequencies. In particular, in Figure 6
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we can see that the coherence between SLA in the North and Baltic Seas is above 0.3 for
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frequencies lower than 0.007 and higher than 0.022 cycle/day (periods longer than about
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140 days and shorter than about 45 days). A similar pattern is observed in Figure 7 for the
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coherence spectrum between the SLA in the North Sea and in Stockholm, but the
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coherence values are lower. The highest coherence among the SLA data sets considered
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is, as one would expect, between the SLA in the open Baltic Sea and in Stockholm
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(Figure 8). In this case the coherence is around 0.7 for frequency lower than 0.007
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cycle/day (periods >140 days) and varies between 0.5 and 0.8 for periods between 50 -
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150 days. We have also estimated the coherence between the SLA in the open Baltic Sea
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and in the North Atlantic, but these SLA time series are not significantly correlated
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(results not shown).
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The dashed lines in Figures 6 - 8 indicate the phase shift between various time
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series. The SLA in the open Baltic Sea and in Stockholm are in phase with the SLA in the
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North Sea at lower frequencies. At higher frequencies the Baltic Sea SLA are delayed in
233
comparison to the SLA in the North Sea (Figures 6 and 7). The observed oscillations of
234
phase are meaningless when there is not significant coherence between the data series.
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The SLA in the open Baltic Sea and in Stockholm (Figure 8) are in phase and the phase
236
spectra vary smoothly, which is indicative of a good correlation. The small slope in the
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phase spectrum can indicate that there is a time delay of few days between the data series.
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This time delay is consistent with the observations that SLA variability on the time scales
239
considered is mainly caused by persistent winds redistributing water between the Atlantic
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Ocean (the North Sea) and the Baltic Sea (e.g., Ekman, 2009). If we assume the current
241
speed of ~ 1 m/s we can estimate that it will take about 3.5 days to transport the water
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mass over a distance of 300 km. Thus the time delay of few days is not unrealistic when
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considering a relationship between SSH in distant locations of the Baltic Sea. Because
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our system is not quite linear, the estimated phase function is not exactly a simple straight
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line. Summarizing these results, it is evident from our analysis that the SLA variability
247
in the Baltic Sea is coherent with the SLA variability in the North Sea. This observation
248
is in agreement with previous analyses of the Baltic Sea level data (e.g. Ekman, 2009).
249
Note that prior publications stressed that annual patterns in the Baltic Sea level variability
250
recorded by the tide gauges depend on the geographical location of the tide gauge (e.g.,
251
Hünicke and Zorita, 2008). One of the reasons for this is that sea level variability
252
observed at a coastal station is significantly influenced by the geometry of the coast and
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the direction of the wind. This is also most likely the reason why the coherence between
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the SLA in the open Baltic Sea and in Stockholm is significantly less than one, while the
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coherence between the satellite-derived SLA in different parts of the Baltic Proper
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(results not shown) is approximately equal one in the frequency range discussed here.
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We have attempted to check what are the links between atmospheric forcing and
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the SLA in the Baltic Sea. The results of the cross-spectral analysis between the
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meteorological parameters (wind stress magnitude, zonal and meridional wind stress
260
components, and barometric pressure at sea level) and the SLA in the open Baltic Sea can
261
be summarized as follows. Among the meteorological quantities considered, the
262
coherence is highest between the zonal wind stress component and the SLA. The results
263
are shown in Figure 9. (We obtained similar results if the zonal wind stress component
264
from the North Sea instead from the Baltic Sea was used in this analysis). The coherence
265
between the wind stress magnitude and the SLA as well as the coherence between the
266
meridional wind stress component and the SLA (not shown) is generally lower than the
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coherence shown in Figure 8, and significantly different from zero only for frequencies
268
between 0.0033 - 0.0048 cycle/day (periods 210-350 days). The coherence between
269
barometric pressure and the SLA (not shown) is not significant at lower frequencies, but
270
increases at higher frequencies, exceeding a value of 0.4 at frequency 0.023 cycle/day
271
(period of ~ 45 days). This is in agreement with the conclusion reached before by Ekman
272
(2009) that the response of the Baltic Sea level to barometric pressure is more evident at
273
shorter times scales.
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Finally, we have considered the influence of the water runoff on the SLA. Water
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runoff into the Baltic Sea was approximated by a total discharge from the 75 largest
276
rivers in the region, and estimated by the Balt-Hype model (Donnelly et al., 2011). River
277
data were not available after 2008. Therefore, our analysis is based on the 20-years time
278
series starting in 1988, and is limited to river discharge and the SLA in Stockholm. (The
279
time period when both the river runoff data and the satellite-derived SLA were available
280
was too short for this analysis, since the satellite data were available from October 1992).
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The coherence between river discharge and Stockholm SLA is not significant; it is above
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the 0.283 value only for periods of about 210-260 days (results not shown).
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The interpretation of our results is generally in agreement with Ekman (2009).
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Ekman distinguished the two most important time scales in the variability of the Baltic
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Sea level. These are: 1) short-term variations (time scale of days) in response to
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barometric pressure and short-term wind events; this variability affects more the sea level
287
near the coasts than at the open sea and is significantly influenced by the geometry of the
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coastline and wind direction; and 2) long-term variability (time scale of months) in
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response to persistent winds redistributing water in the North Atlantic, North Sea, and
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Baltic Sea; this variability affects the level of the entire Baltic Sea. Our analysis was
291
mostly limited to long-term variability. The time scale on the order of days cannot be
292
resolved by our 7-day resolution time series data. We plan to extend this analysis to
293
shorter time scales after we reprocess the satellite altimetry data in the Baltic Sea using
294
the novel methods of coastal altimetry (Bouffard et al., 2008; 2011; Vignudelli et al.,
295
2011). This reprocessing will also allow for a better spatial resolution and will allow us to
296
quantify the geographical/regional differences in the SLA variability. Such data will also
297
allow us to make a better interpretation of the coastal effects through more rigorous
298
comparisons of the satellite-derived altimetry data with coastal stations. Finally, in the
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nearest future, we plan to complete comparisons of satellite-derived SLA with our
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numerical model of the Baltic Sea.
301 4. Summary
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There have been only few attempts to use satellite altimetry data in the Baltic Sea
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in the past. These include analyses of sea level data (e.g., Poutanem and Stipa, 2001;
305
Madsen et al., 2007) and validation of the operational wave models (Solvsteen and
306
Hansen, 2006). Our results based on time series analysis of almost 20-years of data of
307
satellite altimetry in the open Baltic Sea support some of the earlier findings based on
308
coastal data (e.g., Ekman, 2009). We have confirmed that the variability of the sea level
309
in the Baltic Sea is coherent with the sea level in the North Sea. However, we found that,
310
unlike in the North Sea, the annual peak is not well pronounced in the open Baltic Sea
311
SLA spectrum. The semiannual peak is the most prevailing in the open Baltic Sea SLA
312
spectrum. This is in contrast to earlier publications, which reported that the annual peak
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in the Baltic Sea level variability as highly significant. We suggest that one of the reasons
314
for this discrepancy is that we have used data series with a higher temporal resolution (7
315
days in comparison to monthly data used in previous research). The annual cycle of the
316
open Baltic Sea level is asymmetrical, as suggested by Ekman (2009). This asymmetrical
317
cycle is probably decomposed by the spectral analysis into 2 or more components of
318
variability in our 7-day resolution SLA time series. We have documented that the SLA
319
variability is in phase in the open Baltic Sea site considered and at the coastal station in
320
Stockholm. The coherence between the SLA in these two locations is high, but
321
significantly less than unity. One of the most likely reasons for this is the fact that the sea
322
level in Stockholm is influenced by the coastal topography, while the open sea data are
323
not. The results of the cross-spectral analysis between meteorological parameters (wind
324
stress magnitude, zonal and meridional wind stress components, and barometric pressure
325
at sea level) and the SLA in the open Baltic Sea show that the coherence is highest
326
between the zonal wind stress component and the SLA. In addition our results indicate
327
that the coherence between the river runoff and the SLA in Stockholm is not significant.
328
Our analysis is limited to variability on a long-term scale (> month), because the time
329
scale on the order of days cannot be resolved by our 7-day resolution time series data. In
330
the near future, we plan to extend the results presented in this paper to shorter time scales
331
after the satellite altimetry data in the Baltic Sea are reprocessed using the novel methods
332
of coastal altimetry (Bouffard et al., 2008; 2011; Vignudelli et al., 2011).
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Acknowledgments: This work was supported through the SatBaltic project funded by the
335
European Union through the European Regional Development Fund, (contract No.
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POIG.01.01.02-22-011/09 entitled ‘The Satellite Monitoring of the Baltic Sea
337
Environment’). The altimeter data were processed by Ssalto/Duacs and distributed by
338
AVISO, with support from Cnes (http://www.aviso.oceanobs.com/duacs/). The
339
meteorological data were obtained from the National Centers for Environmental
340
Prediction and National Center for Atmospheric Research (NCEP/NCAR) Reanalysis
341
Project
342
(http://www.esrl.noaa.gov/psd/). The river runoff data were made available by the
343
Swedish Meteorological and Hydrological Institute (balt-hypeweb.smhi.se/).
the
NOAA/OAR/ESRL
PSD,
Boulder,
Colorado,
USA
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Stramska M., Chudziak N., 2013. Multiyear trends in the Baltic Sea level, Oceanologia, in press.
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T., 2010. Impact of self-attraction and loading on the annual cycle in sea level.
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Figure captions Figure 1. Map showing the geographical positions corresponding to the data series used in this paper: 1 – North Atlantic, 2 - North Sea, 3 – open Baltic Sea, 4 - Stockholm.
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Figure 2. Time series of sea level anomalies (SLA) used in this study. See Figure 1 for the geographical position corresponding to each of the time series.
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Figure 3. Power spectral density of SLA calculated from time series shown in Figure 2. a) North Atlantic and North Sea b) open Baltic Sea and Stockholm. Vertical bars indicate standard errors of the most significant peaks. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 4. Comparison of the normalized power spectral density for SLA in the open Baltic Sea and at coastal station in Stockholm with the normalized power spectral density of wind stress magnitude. Power spectra are normalized to the total variance. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis. Figure 5. Annual cycle in the 19-year averaged SLA in the North Atlantic (NA), North Sea (NS), open Baltic Sea (BS) and Stockholm (S).
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Figure 6. Squared coherence (solid dark line) and phase functions (dashed line) between the SLA in the North Sea and in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 7. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the North Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis. Figure 8. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the open Baltic Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 9. Squared coherence (solid line) and phase functions (dashed line) between zonal component of wind stress and SLA in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 1. Map showing the geographical positions corresponding to the data series used in this paper: 1 – North Atlantic, 2 - North Sea, 3 – open Baltic Sea, 4 - Stockholm.
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Figure 2. Time series of sea level anomalies (SLA) used in this study. See Figure 1 for the geographical position corresponding to each of the time series.
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Figure 3. Power spectral density of SLA calculated from time series shown in Figure 2. a) North Atlantic and North Sea b) open Baltic Sea and Stockholm. Vertical bars indicate standard errors of the most significant peaks. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 4. Comparison of the normalized power spectral density for SLA in the open Baltic Sea and at coastal station in Stockholm with the normalized power spectral density of wind stress magnitude. Power spectra are normalized to the total variance. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 5. Annual cycle in the 19-year averaged SLA in the North Atlantic (NA), North Sea (NS), open Baltic Sea (BS) and Stockholm (S).
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Figure 6. Squared coherence (solid dark line) and phase functions (dashed line) between the SLA in the North Sea and in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 7. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the North Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 8. Squared coherence (solid line) and phase functions (dashed line) between the SLA in the open Baltic Sea and at the coastal station in Stockholm. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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Figure 9. Squared coherence (solid line) and phase functions (dashed line) between zonal component of wind stress and SLA in the open Baltic Sea. Horizontal line indicates that the coherence > 0.283 is significant at 95% confidence level. The frequencies corresponding to periods of 2 years, 1 year, 6 month, and 3 month are marked by black dots on the X axis.
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