LINKING INFORMATION FROM SSS TO OCEANIC FRESHWATER FLUXES USING NEAR-SURFACE SALINITY BUDGETS

NADYA T. VINOGRADOVA1 RUI M. PONTE1

MARTHA W. BUCKLEY2

1 Atmospheric and Environmental Research (AER), USA 2 George Mason University (GMU), USA

Aquarius/SAC-D Science Team Meeting, Seattle, WA November 2014

CHANGES IN SSS AS INDICATOR OF E-P?

STD E-P (NCEP) STD SSS-TENDENCY (AQUARIUS, v3.0)

m/mo psu/mo

Linking surface salinity to freshwater flux is an important subject (e.g., Durack et al. 2012; Pierce et al., 2012; Terray et al., 2011; Bingham et al., 2011; Yu 2011), but is difficult in practice (Vinogradova and Ponte 2013)

EXAMPLE

¨  Can net freshwater flux be inferred from globally-averaged SSS from an ocean estimate?

¨  Salinity-derived freshwater flux = α� S’ ¨  Non-linear relationship confirms the importance of

ocean fluxes in regulating global-mean changes in SSS.

1992 1994 1996 1998 2000 2002 2004−0.03

−0.025

−0.02

−0.015

−0.01

−0.005

0

_ = 0.68; r = 0.66; a = 44%; Fs F

2 4 6 8 10 12−0.01

−0.005

0

0.005

0.01

Fs F

Net freshwater flux: SSS-derived (black) vs Observed (red) Annual cycle

Vinogradova and Ponte, JGR 2013

SALINITY BUDGET FRAMEWORK

¨  Salinity budget : S’ = F + O ¨  Differences between S’ and F related to O affect

regression (Vinogradova and Ponte 2013). ¨  Inclusion of information about O from data can

improve estimates of F. ¨  Objectives:

¤ Where, when can F be inferred from partial knowledge of the budget terms?

¤  Develop practical methodologies on how to use Aquarius measurements to infer meaningful values of F

BASIC APPROACH

¨  Explore salinity budgets within the constrained estimation of the oceanic state: ¤ Guaranteed budget closure ¤ Solutions are close to observations (including salinity) ¤ Dynamical consistency with all the forcing fields

ECCO SOLUTION

¨  Ocean state estimate is obtained from model/data synthesis produced by the ECCO consortium [1], [2]

¨  ECCO solution is close to observations within prescribed data errors

¨  Future ECCO solutions will include Aquarius/SMOS SSS constraints (Vinogradova et al., 2014)

Estimating the Circulation and Climate of the Ocean (ECCO) [1] Wunsch et al., 2009; [2] Speer and Forget 2013

ECCO IN SITU AQUARIUS

ECCO SOLUTION

¨  It is important to accurately represent the effects of freshwater fluxes ¤ “Virtual” salt flux (previous versions) ¤ Real freshwater flux (current analysis)

¨  Freshwater flux modifies tracer concentration and ocean volume:

SALINITY BUDGET IN MITGCM V4

The salinity conservation equation is:

(1)⇥(hS)

⇥t= �⇥ · (hSu)�⇥ ·K + Sflux

where S is salinity, h = H + � is the height of the water column, H is the ocean depth, �is sea surface height, u is velocity, ⇥ ·K is the di�usive flux of salinity, and Sflux is theair-sea flux of salt. Use the quotient rule to split the left hand side term into

(2)⇥(Sh)

⇥t= h

⇥S

⇥t+ S

⇥h

⇥t

where the first term is variations in salinity, the second is variations in mass. Use thecontinuity equation to relate �h

�t to E � P �R and ocean convergence of mass:

(3)⇥h

⇥t= �(E � P �R)�⇥ · (hu)

Substitute (3) into (1) and divide by h:

(4)⇥S

⇥t=

Sflux

h+

(E � P �R)

h+ S

⇥ · (hu)h

� ⇥ · (uS)h

� ⇥ ·Kh

where the terms on the right hand side are: (1) air-sea salt flux (e.g., a brine rejection termor any other way that precipitation/runo� has salt), (2) dilution term due to atmosphericfreshwater fluxes, (3) ocean convergence of freshwater, (4) advective fluxes of salinity, (5)di�usive fluxes of salinity.

Figure 1 shows the standard deviation of each term based on the model’s top layersolution. The major di�erence from our previous results that were based on v.2 mixed-layer averages is a non-zero surface convergence term (3), which disappears below thesurface in r coordinates (when all free surface variations are in the top layer). Here thesurface convergence term (3) is non-zero1. Not only term (3) is large, it is highly anti-correlated with the atmospheric freshwater flux, term (2). I suppose it is not surprisingand follows from equation (3) that requires that the atmospheric and oceanic freshwaterfluxes nearly cancel each other so that variations in the free surface height are small. Inthe mean, we expect all atmospheric freshwater flux P + R � E to be balanced by theocean transport of freshwater to conserve mass. What is puzzling for me now is whether itis possible to apply the ocean rain gauge concept in such formulation. If we use equation

1It will also unlikely disappear when we average over the mixed layer, because in r⇤ coordinates used in

v.4 the free surface variations are distributed within all layers proportional to their thickness

1

SALINITY BUDGET IN MITGCM V4

The salinity conservation equation is:

(1)⇥(hS)

⇥t= �⇥ · (hSu)�⇥ ·K + Sflux

where S is salinity, h = H + � is the height of the water column, H is the ocean depth, �is sea surface height, u is velocity, ⇥ ·K is the di�usive flux of salinity, and Sflux is theair-sea flux of salt. Use the quotient rule to split the left hand side term into

(2)⇥(Sh)

⇥t= h

⇥S

⇥t+ S

⇥h

⇥t

where the first term is variations in salinity, the second is variations in mass. Use thecontinuity equation to relate �h

�t to E � P �R and ocean convergence of mass:

(3)⇥h

⇥t= �(E � P �R)�⇥ · (hu)

Substitute (3) into (1) and divide by h:

(4)⇥S

⇥t=

Sflux

h+

(E � P �R)

h+ S

⇥ · (hu)h

� ⇥ · (uS)h

� ⇥ ·Kh

where the terms on the right hand side are: (1) air-sea salt flux (e.g., a brine rejection termor any other way that precipitation/runo� has salt), (2) dilution term due to atmosphericfreshwater fluxes, (3) ocean convergence of freshwater, (4) advective fluxes of salinity, (5)di�usive fluxes of salinity.

Figure 1 shows the standard deviation of each term based on the model’s top layersolution. The major di�erence from our previous results that were based on v.2 mixed-layer averages is a non-zero surface convergence term (3), which disappears below thesurface in r coordinates (when all free surface variations are in the top layer). Here thesurface convergence term (3) is non-zero1. Not only term (3) is large, it is highly anti-correlated with the atmospheric freshwater flux, term (2). I suppose it is not surprisingand follows from equation (3) that requires that the atmospheric and oceanic freshwaterfluxes nearly cancel each other so that variations in the free surface height are small. Inthe mean, we expect all atmospheric freshwater flux P + R � E to be balanced by theocean transport of freshwater to conserve mass. What is puzzling for me now is whether itis possible to apply the ocean rain gauge concept in such formulation. If we use equation

1It will also unlikely disappear when we average over the mixed layer, because in r⇤ coordinates used in

v.4 the free surface variations are distributed within all layers proportional to their thickness

1

SALINITY BUDGET IN MITGCM V4

The salinity conservation equation is:

(1)⇥(hS)

⇥t= �⇥ · (hSu) +⇥ · (K⇥S) + Sflux

where S is salinity, h = H + � is the height of the water column, H is the ocean depth, �is sea surface height, u is velocity, ⇥ ·K is the di�usive flux of salinity, and Sflux is theair-sea flux of salt. Use the quotient rule to split the left hand side term into

(2)⇥(Sh)

⇥t= h

⇥S

⇥t+ S

⇥h

⇥twhere the first term is variations in salinity, the second is variations in mass. Use thecontinuity equation to relate �h

�t to E � P �R and ocean convergence of mass:

(3)⇥h

⇥t= �(E � P �R)�⇥ · (hu)

(4)⇥S

⇥t=

S(E � P �R)

h� ⇥ · (uS)

h+

⇥ · (K⇥S)

h

(5) h⇥S

⇥t= S(E � P �R)�⇥ · (uS) +⇥ · (K⇥S)

Substitute (3) into (1) and divide by h:

(6)⇥S

⇥t=

Sflux

h+

(E � P �R)

h+ S

⇥ · (hu)h

� ⇥ · (uS)h

� ⇥ ·Kh

where the terms on the right hand side are: (1) air-sea salt flux (e.g., a brine rejection termor any other way that precipitation/runo� has salt), (2) dilution term due to atmosphericfreshwater fluxes, (3) ocean convergence of freshwater, (4) advective fluxes of salinity, (5)di�usive fluxes of salinity.

Figure 1 shows the standard deviation of each term based on the model’s top layersolution. The major di�erence from our previous results that were based on v.2 mixed-layer averages is a non-zero surface convergence term (3), which disappears below thesurface in r coordinates (when all free surface variations are in the top layer). Here thesurface convergence term (3) is non-zero1. Not only term (3) is large, it is highly anti-correlated with the atmospheric freshwater flux, term (2). I suppose it is not surprising

1It will also unlikely disappear when we average over the mixed layer, because in r⇤ coordinates used in

v.4 the free surface variations are distributed within all layers proportional to their thickness

1

SALINITY BUDGET IN MITGCM V4

The salinity conservation equation is:

(1)⇥(hS)

⇥t= �⇥ · (hSu) +⇥ · (K⇥S) + Sflux

where S is salinity, h = H + � is the height of the water column, H is the ocean depth, �is sea surface height, u is velocity, ⇥ ·K is the di�usive flux of salinity, and Sflux is theair-sea flux of salt. Use the quotient rule to split the left hand side term into

(2)⇥(Sh)

⇥t= h

⇥S

⇥t+ S

⇥h

⇥twhere the first term is variations in salinity, the second is variations in mass. Use thecontinuity equation to relate �h

�t to E � P �R and ocean convergence of mass:

(3)⇥h

⇥t= �(E � P �R)�⇥ · (hu)

(4)⇥S

⇥t=

S(E � P �R)

h� ⇥ · (uS)

h+

⇥ · (K⇥S)

h

(5) h⇥S

⇥t= S(E � P �R)�⇥ · (uS) +⇥ · (K⇥S)

Substitute (3) into (1) and divide by h:

(6)⇥S

⇥t=

Sflux

h+

(E � P �R)

h+ S

⇥ · (hu)h

� ⇥ · (uS)h

� ⇥ ·Kh

where the terms on the right hand side are: (1) air-sea salt flux (e.g., a brine rejection termor any other way that precipitation/runo� has salt), (2) dilution term due to atmosphericfreshwater fluxes, (3) ocean convergence of freshwater, (4) advective fluxes of salinity, (5)di�usive fluxes of salinity.

Figure 1 shows the standard deviation of each term based on the model’s top layersolution. The major di�erence from our previous results that were based on v.2 mixed-layer averages is a non-zero surface convergence term (3), which disappears below thesurface in r coordinates (when all free surface variations are in the top layer). Here thesurface convergence term (3) is non-zero1. Not only term (3) is large, it is highly anti-correlated with the atmospheric freshwater flux, term (2). I suppose it is not surprising

1It will also unlikely disappear when we average over the mixed layer, because in r⇤ coordinates used in

v.4 the free surface variations are distributed within all layers proportional to their thickness

1

ECCO SALINITY BUDGET: STD

SALINITY TENDENCY DILUTION DUE TO FRESHWATER FLUXES

ADVECTIVE SALINITY FLUX DIFFUSIVE SALINITY FLUX

psu/mo psu/mo

psu/mo psu/mo

ECCO SALINITY BUDGET: TIME MEAN

SALINITY TENDENCY DILUTION DUE TO FRESHWATER FLUXES

ADVECTIVE SALINITY FLUX DIFFUSIVE SALINITY FLUX

psu/mo psu/mo

psu/mo psu/mo

FUTURE PLANS

¨  Preliminary results show that ocean contribution to salinity variations

is particular important in the tropics and many coastal regions, which may complicate the use of salinity observations as a direct proxy of freshwater flux, at least on timescales from months to years

¨  Future analysis of the mixed-layer salinity budget and decomposition of oceanic fluxes will be used to explore how freshwater fluxes can be expressed as a combination of ocean variables, including SSS:

n  E.g., do Ekman advection and surface fluxes dominate in any region or time scale?

n  What is the impact of Aquarius data constraints on the upper ocean salinity and surface freshwater fluxes?