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SUPPLEMENTARY INFORMATION TO
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“Reliability of the steric and mass components of Mediterranean sea level as estimated
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from hydrographic gridded products”, by G. Jordà and D. Gomis
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Formulation of the steric and mass components of sea level variability
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Let us consider a water column of small horizontal section δA, located over a depth H
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and with a free surface height η(t), being H and η(t) referred to some kind of vertical
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reference at which we set z=0. The mass of the water column δm(t) is then given by:
mt   A
z  ( t )
  ( z, t )dz
(1)
z  H
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where ρ(z,t) is the density distribution along the water column. Taking the time
derivative of (1) results in:
z  ( t )
 (m)

 


 A  ( z   , t )
 
dz 
t
t z  H t 


(2)
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where ρ(z=η,t) is the surface density, hereafter referred to as ρs(t). Changes in the height
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of the water column can then be obtained as:

1

t
s
z  ( t )

z  H

1  m
dz 
t
 s t   A 
STERIC COMPONENT
(3)
MASS COMPONENT
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The first term on the right hand side is the steric component of sea level change, while
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the second term is the mass component. It is important to emphasize from (3) that the
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steric component does not account for volume variations, but for density variations, that
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is to say for changes in the volume per mass unit. Changes in the temperature of the
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water column are not associated with mass changes and therefore they translate into
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actual volume (and therefore sea level) variations. Conversely, salinity changes can be
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associated with mass changes, either because of a decrease/increase in the amount of
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freshwater (e.g. due to evaporation/precipitation) or because of changes in the salt
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content (e.g. derived from the advection of higher/lower salinity water). When salinity
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advection takes place keeping the geostrophic balance, the bottom pressure (and hence
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the mass content) of the water column remains constant and the halosteric term will also
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reflect actual sea level changes; this is often the case in the open ocean. When dealing
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with mean sea level in semi-enclosed basins such as the Mediterranean Sea, however, a
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geostrophic balance between the basin and the open ocean can hardly be established due
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to topographic constraints; in that case, changes in the mean salinity of the basin will
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imply changes in the mass content of the basin.
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Therefore, in order to obtain actual sea level changes, the mass component must
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be added to the steric component and it must account for both, changes in the amount of
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salt (msalt) and in the amount of freshwater (mfreshwater):

1

t
s
z  ( t )

z  H

1    msalt
dz 
t
s t   A
 1    m freshwater 



A 
  s t 
(4)
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If we have estimates of total sea level changes (e.g. from a sea level reconstruction or
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altimetry), of the steric component and of the salt content (e.g. from hydrographic
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datasets) then we can in principle infer the changes in the amount of freshwater.
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Spatial structure of trends
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Complementary information to the results shown in the paper can be obtained
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looking at the spatial structure of the trends (Fig. S1). EN3, ISHIIUPD and
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MEDATLAS2 show similar spatial patterns for the steric component, with the largest
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negative values in the Eastern basin and smaller negative values in the Central
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Mediterranean and the Adriatic Sea. In the Western Mediterranean the three products
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show larger differences, especially in the Alboran Sea and the Algerian basin. Also, the
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ISHIIUPD values are in general smaller than the other two products. The ISHII product
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shows a rather different pattern, with marked positive values in the Central
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Mediterranean and the Adriatic Sea, small negative values in the Eastern basin and
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markedly negative values in the Western basin.
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The thermosteric component shows a similar pattern for the EN3, ISHII and
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MEDATLAS2, with positive values in the Western basin and negative values in the
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Eastern basin. The ISHIIUPD product differs in that it does not show negative values in
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the Eastern basin. However, the magnitude of the trends is rather different at sub-basin
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scale: in the Western basin EN3 shows the largest values (~0.5 mm/yr) and
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MEDATLAS2 the lowest values (~0.1 mm/yr); in the Eastern basin MEDATLAS2 is
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the one showing the larger negative values (~ -0.8 mm/yr) while EN3 and ISHII are
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similar (~ -0.2 mm/yr) and ISHIIUPD shows small positive values (~0.1 mm/yr). The
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halosteric component presents larger discrepancies in the spatial patterns: while EN3
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and ISHIIUPD show large negative values everywhere, ISHII shows negative values in
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the Western basin and positive in the Eastern basin and MEDATLAS2 shows small
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negative values everywhere except in the central part of the basin, where it shows small
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positive values.
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Fig SI-1- Spatial distribution of steric, thermosteric and halosteric trends (in mm/yr)
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computed for the period 1960-2000 and referenced to 700 m using data from EN3 (first
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row), ISHII (second row), ISHIIUPD (third row) and MEDATLAS2 (bottom row). The
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black line indicates the 0 value.
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