SOSE and related

activities

Matt Mazloff ! (SIO-UCSD)!

FOCUS

•  To make everyone familiar with the Southern

Ocean State Estimate (SOSE) resource

•  Give SOSE status

•  Describe SOSE related activities with a focus on

– Science

– State estimation machinery development

– Future work

Ocean State Estimation method:

4dvar: weighted least squares optimization

Find forward model state, L (u,v,w,t,s,p)

Model inputs are control parameters, u

(e.g. param. coef., ini. cond., atm. state)

Define cost function: here a weighted model-observation misfit

J (u) = Σ{Li - obsi}2 σi -2 + Σ{uj - datai}2 σj

-2

Model state, and thus cost, is a function of controls: L(u)

Optimization problem: adjust controls to minimize the cost

Adjoint model gives the gradient of J wrt u: ∇uJ(u)

Use this information to infer update, ∆u, of controls:

un+1 = un + ∆u and iteratively minimize cost

method:

SOSE is a science resource, not short-term prediction

•  Sequential methods optimize over short periods (24 hours to 24 days) and then patch solutions together

•  Our assimilation window is multi-year, so there are no unphysical jumps in the governing dynamics. There are no terms nudging towards observations either. SOSE obeys model dynamics and thermodynamics first (hard-constraint).

Southern Ocean State Estimate Configuration

§  780 South to 24.70 South §  1/60 Horizontal resolution (eddy permitting) §  42 depth levels (partial cells) §  ICs and open northern BCs derived from and constrained to G. Forget!s (2010) 1o

resolution global state estimate (OCCA) §  Atmospheric boundary layer scheme §  Constrained to NCEP re-analysis atmospheric state §  KPP §  Full sea-ice model §  Adjoint generated via AD tool TAF §  Currently optimizing years 2008-09 §  Resources provided by TACC and NCAR

method:

maximize benefit of SO observations

•  Temporal relevance: –  The 2005 to 2007 solution is available on the server –  The goal is now to attain a 2008 to "present# solution (relevance to

cDrake and DIMES). Now optimizing 2008 and 2009. Will extend to 2010 as soon as feasible.

•  Relevance to atmospheric and biogeochemistry community: –  Add in DIC package (Dutkiewicz) cycling DIC, Alk, PO4, DOP, O2, and

Fe and constrain to observed concentrations –  Constrain to atmospheric observations, providing feedback to

atmospheric community.

•  Relevance to observational community –  Working to minimize model representation error, account for error

covariances, and improve control vector (i.e. get most out of obs.). –  Development goal is to advance state estimation to a level where it is

worthy of being made part of an observational plan (as oppose to being part of a modeling or analysis plan) making it relevant to everyone

goal:

http://sose.ucsd.edu/DATA/ access:

"please let us know if you require diagnostics not presently hosted on this site.#

Journal of Climate 2011

•  Ocean state estimation corrected many of the known biases in NCEP atmospheric flux

•  Ocean is an integrator of air-sea fluxes. Atmospheric reanalysis can be improved using ocean observations.

•  SOSE derived atmospheric surface state is not worse than reanalysis and comes with consistent full ocean state – making it a desirable product for studies of water mass formation, eddy heat flux, etc.

•  Future work: better constrain to atmospheric state – assimilate atmospheric observations.

•  Providing correlation length-scales to atmospheric constraints using method of Weaver and Courtier 2001. Future work is to better determine what these length scales should be.

Drake Passage transport

GRL 2009 GRL 2009

As part of cDrake Chereskin et al. (GRL 2009) find significant currents

50 meters off the bottom

4.5 years of velocity observations to 1000m from SADCP

Mean obs. transport of ACC in top 1000m is 95 ± 2 Sv. (71% of canonical 134 Sv)

Firing et al. JGR 2011

At 1000m mean speeds are still strong 10-20cm/s.

Mean observed Mean SOSE

Firing et al. JGR 2011

SADCP, LADCP, and SOSE are used to explore vertical structure functions.

A number of functions give good fits explaining > 75% of variance, but no one function works everywhere.

Using exponential fits to extrapolate to full depth yields an estimated ACC transport of 154 ± 38 Sv.

SOSE 2005-2006 vertically integrated transport La

titud

e Tr

ansp

ort [

Sv]

- 40 Sv

240

Days since 1 Jan. 2005

Zonal transport time series

SR1 avg=153 Sv SR3 avg=164 Sv SR2 avg=154 Sv

Vertically integrated transport streamfunction [Sv]

ACC transport well correlated at each longitude

•  Development: now constraining to cDrake inverted echo sounders, meaning heat content is now well constrained at Drake Passage.

•  Future work: examine heat content and heat divergence along ACC and heat divergence along ACC

Mean dynamic ocean topography (MDT) is very uncertain in SO due to lack of geoid observations

Griesel, Gille, Mazloff. To be published in JGR

Differences between popular MDT products > 20 cm

Differences shown also

due to temporal discrepencies, not just geoid issues…

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For MDT products issues with temporal and spatial scales.

Performance of products in SOSE optimization suggests adding drifters not helping

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Using hydrography and thermal wind, and using MDT products as reference velocity,

we could not conserve ocean volume

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Devel and fut. work: properly constrain to altimetry and geoid while estimating error structure

As σg >> σa must constrain to mean and anomaly separately , Is large spatial correlation in σm, so can account for with and can study these optimization determined functions wrt

different gridded geoid products to learn about error structure

•  Sea-ice adjoint is now available thanks to I. Fenty, P. Heimbach, D. Menemenlis, M. Losch, JM. Campin, C. Hill, and others.

•  Allows direct assimilation to sea-ice concentration (or thickness, etc.)

•  Allows sensitivity experiments, e.g., What sets the summer sea-ice volume in the Ross sea?

Heimbach et al. 2010 Ocean Modelling

Development: Controlling open boundary conditions using modal decomposition. (w/ N. Martinez & B. Cornuelle) For a well posed optimization must separate sensitivity to barotropic and baroclinic boundary condition � OM) GAA� � OM) GAA� CA�

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Fig. 1 Fig. 2

Development: Looking at sensitivity (and perhaps controlling) vertical mixing, kz

MODEL SENSITIVITY CALCULATIONS IN FORWARD & REVERSE

Forward finite difference approach

• Take a Green!s function perturbation (e.g., zonal wind stress, δ ) and determine its impact on model output (e.g., Drake Passage transport, TrDP)

• Subtraction from an unperturbed run determines:

• Requires many perturbations, ,

to determine impact on output

Reverse/adjoint approach • Calculate full time-varying sensitivity field: Let , and the adjoint runs back in time to yield:

J = TrDP u = τ(x, y, t)

δτ(x, y, t)�δTrDP

∇uJ (u) = ∂TrDP

�∂τ(x, y, t)

δτ(x, y, t)

Slide adapted from P. Heimbach (MIT)

Forward perturbation on zonal wind speed: Gaussian perturbation (standard deviation = 1o) at 181oE, 56oS,

Latit

ude

2-Jan-2005 4-Jan-2005 6-Jan-2005

Linearly perturb zonal wind over 4 days with amplitude 5m/s

Response to perturbation

Verically integrated transport in DP

Convolution of adjoint sensitivity with perturbation gives hindcast of response of Drake Passage transport. Success of adjoint hindcast means model response was approximately linear.

Response function of DP Transport to zonal (left) and meridional (right) windstress after 1 day (snapshot)

Response function of DP Transport to zonal (left) and meridional (right) windstress after 13 day

Sensitivity of the mean Drake Passage transport to wind stress. Zonal on left and

meridional on right

Sensitivity of the mean Drake Passage transport to wind stress. Zonal on left and

meridional on right

Summary

The adjoint model highlights locations where the ocean is especially responsive to the atmospheric state

Response to a wind stress perturbation: •  Barotropic waves significantly increase Drake Passage

transport over first day or two and then decays over the period of about 10 days. Sensitivity magnitudes show topographic influence.

•  Sensitivity after 10 days shows mesoscale structure that is especially enhanced where the ACC interacts with topography. The structure is indicative of a sensitivity to wind-stress curl.

•  Sensitivity to wind-stress near continents: increase ACC transport by raising sea surface height on coasts north of the ACC, and decreasing it around Antarctica

Implications

•  Magnitude of ocean response to a wind perturbation

has mesoscale structure, thus the ocean response to a changing wind forcing (climate) depends on magnitude and specific structure of change.

•  All atmospheric observations (constraints) are not equal in the information provided to ocean research. In general, the ocean circulation is more responsive to atmosperic momentum flux in regions of complex topography.

Development

•  CASE: an eddy resolving state estimate of the California Current System. –  A quiet and well observed region to develop the method

Verdy, A., B.D. Cornuelle, S.Y. Kim, M.R. Mazloff (in prep). Wind-driven sea surface height variability on the California coast.

Todd, R.E., D.L. Rudnick, M.R. Mazloff, R.E. Davis, B.D. Cornuelle (2011). Poleward flows in the southern California Current System: Glider observations and numerical simulation. J. Geophys. Res., 116

CASE results

Todd, R.E., D.L. Rudnick, M.R. Mazloff, B.D. Cornuelle, R.E. Davis (submitted).

Upper ocean thermohaline structure in the California Current System.

Todd, R.E., D.L. Rudnick, M.R. Mazloff, B.D. Cornuelle, R.E. Davis (submitted) Upper ocean thermohaline structure in the California Current System.

Todd, R.E., D.L. Rudnick, M.R. Mazloff, B.D. Cornuelle, R.E. Davis (submitted) Upper ocean thermohaline structure in the California Current System.

Summary of development wrt constraints

•  Status quo –  In situ T and S –  SST from radiometers

•  Working to improve uncertainty estimate –  Altimeters and geodetic satellites

•  Recently added –  Sea-ice concentration (as a direct constraint) –  Inverted echo sounders

•  To add –  Atmospheric measurements, Bottom pressure ,Velocity –  What else is available?: chemistry, ice thickness,

tomography, tracer release (Ledwell), float trajectories