Stiftung Alfred-Wegener-Institut f ¨ur Polar- und Meeresforschung
Budgets of heat, salt, biological, and geochemical tracers in an eddy in the
Southern Ocean Polar Frontal Zone estimated from a regional high resolution data set and an inverse coupled general circulation ecosystem model
Martin Losch, Volker Strass, and Boris Cisewski
Alfred-Wegener-Institut f ¨ur Polar- und Meeresforschung, Bremerhaven, Germany, email: mlosch@awi-bremerhaven.de
1 Overview
Combining models and data with data as- similation or state estimation techniques is promising when both data and mod- els separately exhibit some skill. How- ever, in oceanography more often than not, data and in particular sub-surface data are sparse and the prediction skill of ocean models tends to be poor on long time scales. We present a state estimation ex- periment, in which we exploit the avail- ability of a high-resolution regional data set: Hydrographic, tracer and velocity data from the European Iron Fertilization EX- periment (EIFEX) are used to constrain a high-resolution coupled ecosystem-ocean circulation model of the experimental site in Atlantic sector of the Antarctic Polar Frontal Zone.
2 EIFEX: European Iron Fertilization EXperi- ment
EIFEX was aimed at testing the hypothe- sis that iron limits phytoplankton blooms in the Southern Ocean. For the open ocean experiment, a patch with a diame- ter of 16 km inside of a cyclonic, mesoscale eddy in the polar frontal zone was fertilized on February 12–13 and February 26–27, 2004 with dissolved iron. Subsequently the oceanic response was monitored. The eddy was identified with the help of in-situ mea- surements (CTD sensor and ship mounted ADCP) and satellite altimetry. It extended over 60 km by 100 km. with the center near 49◦24’S 02◦15’E in the South Atlantic
During the course of the experiment both hydrographic and dynamic parameters and bio-geochemical quantities were measured at CTD stations inside and outside the fertilized patch and along the ship track.
Many measurements covered the water col- umn down to 500 m depth.
3 MITgcm and state estimation
The M.I.T. general circulation model (MITgcm Marshall et al., 1997) has been adapted for use with the Tangent linear and Adjoint Model Compiler (TAMC), and its successor TAF (Transformation of Algorithms in Fortran, Giering and Kaminski, 1998). Efficient (w.r.t. CPU/memory), exact (w.r.t. the model’s transient state) derivative code can be generated for up-to-date versions of the MITgcm and its newly developed packages in a wide range of configurations (Heimbach et al., 2002, 2004). Here, the MITgcm is configured to cover the ex- perimental region of the EIFEX cruise of appoximately 150 km by 194 km with a mean horizontal grid spacing of approximately 3.6 km; vertical grid spacing increases from 10 m near the surface to 25 m at 500 m depth. The integration time spans the length of the experiment (39 days).
0 20 40 60 80 100 120 140 160
10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 100
iteration
total T/S−data U/V−data
T/S initial conditions buoyancy flux wind stress τ open boundaries
Figure 1: Evolution of different contribu- tions to the objective function J with iteration number of the BFGS-descend algorithm. Hy- drographic data from CTD-stations and ship- mounted ADCP-current measurements are used to assimilate the model using the variational data assimilation technique (state estimation, “4D- VAR”). During the minimization of the objec- tive function J that describes the quadratic de- viation of the model from data and also penal- izes deviations from the first guess, initial con- ditions for temperature and salinity, open bound- ary conditions for temperature, salinity, and ve- locity, and surface fluxes of heat, fresh water, and momentum are adjusted to give the best fit to observations.
data
40’
2oE 20’ 40’
3oE 20’
20’
50oS
40’
20’
49oS
first guess solution
40’
2oE 20’ 40’
3oE 20’
20’
50oS
40’
20’
49oS
salinity
33.75 33.8 33.85 33.9 33.95
optimized solution
40’
2oE 20’ 40’
3oE 20’
20’
50oS
40’
20’
49oS
Figure 2: Comparison with in-situ data shows that data assimilation improves the position of the eddy by adjusting open boundary conditions, initial hydrography, and (to a lesser extend) surface flux boundary conditions. Left:
surface salinity from hydrographic measurements, average over first 10 days of the experiment. Center: surface salinity of modeled eddy on day 5 without data assimilation; initial conditions and boundary conditions for this first guess are obtained by interpolating and extrapolating all available data; the amount of data is not sufficient to allow for time dependent boundary conditions, which appears to be the major problem for this solution. Right: surface salinity of modeled eddy on day 5 after full time-dependent state estimation; the eddy has moved southward and away from the boundary and its position is now in much better agreement with observations (Left).
Hind-Cast Mesoscale Altimetry - Mar 20, 2004
1˚E 1˚E
2˚E 2˚E
3˚E 3˚E
4˚E 4˚E
51˚S 51˚S
50˚S 50˚S
49˚S 49˚S
48˚S 48˚S
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 Sea Surface Height Anomaly (cm)
Sea Surface Height [cm]
−30−25−20−15−10 −5 0 5 10 15 20 25 30 first guess SSH
1oE 2oE 3oE 4oE 51oS
50oS 49oS 48oS
Sea Surface Height [cm]
−30−25−20−15−10 −5 0 5 10 15 20 25 30 optimized SSH
1oE 2oE 3oE 4oE 51oS
50oS 49oS 48oS
Figure 3: Left: sea surface height (SSH) anomaly from satellite altimetry on day 37 of the experiment (not used in the assimila- tion; source: http://www-ccar.colorado.edu/˜realtime/gsfc_
global-real-time_ssh). Center: SSH of modeled eddy on day 37 with- out data assimilation. Right: SSH of modeled eddy on day 37 after full time- dependent state estimation; the eddy extends further south than before, but the comparison of absolute SSH with height anomalies is ambiguous.
measurements
5 10 15 20 25 30 35 40
−150
−100
−50 0
optimized solution
5 10 15 20 25 30 35 40
−150
−100
−50 0
temperature [degC]
3.8 4 4.2 4.4
temperature trend (warming) in the mixed layer
first guess solution
day of experiment
5 10 15 20 25 30 35 40
−150
−100
−50 0
measurements
z [m]
5 10 15 20 25 30 35 40
−150
−100
−50 0
salinity
33.87 33.875 33.88 33.885 33.89 33.895 33.9
first guess solution
z [m]
day of experiment
5 10 15 20 25 30 35 40
−150
−100
−50 0
salinity trend (freshening) in the mixed layer
optimized solution
z [m]
5 10 15 20 25 30 35 40
−150
−100
−50 0
Figure 4: Horizontally averaged temperature (left) and salinity (right) in the fertilized patch; data (top panels), optimized model (middle panels), first guess model (bottom panels). The optimization improves the description of the mixed layer depth dramatically, so that the optimized solution describes the warming and freshening of the mixed layer more accurately than the first guess solution.
4 Ecosystem Model REcoM and SIR
In a one-dimensional configuration, a mixed layer model (KPP, Large et al., 1994) is driven by meterological parameters (POL- DAT, G. K¨onig-Langlo) that were collected during the EIFEX cruise to obtain vertical mixing coefficients. The mixed-layer dynamics drives a regulated ecosystem model (REcoM, M. Schartau and M. Losch, personal communications) that includes phytoplankton, heterotrophic zooplankton and detritus, dissolved inorganic matter and extra cellular organic matter for three nu- trient groups (nitrate, carbon, and silicium) and the limiting effect of iron. With the physical parameters held fixed, REcoM is assimilated to chlorophyll bottle data collected during the EIFEX cruise (C. Klaas, personal communications) in order to obtain an optimal parameter set for the time of the cruise. Ecosystem model dynamics are notoriously nonlinear. Therefore we use a Sequential Importance Resampling (SIR) filter for the assimilation.
0.4 0.2 0.6
10 20 30 0
0.1
α
relative frequency 24
8 6
10 20 30 0
0.2
pcm
0.005 0.015 0.01
0.02
10 20 30 0
0.1
degCHL
0.2 0.1 0.3
10 20 30 0
0.1
lossN
0.2 0.1 0.3
10 20 30 0
0.1
lossC
relative frequency 0.050.1
0.2 0.15
10 20 30 0
0.1
reminN 0.2
0.6 0.4
10 20 30 0
0.1
reminC 0.01
0.03 0.02 0.04
10 20 30 0
0.1
reminSi
0.4 0.2 0.6
10 20 30 0
0.1
rhoN
relative frequency 0.5
1.5 1 2
10 20 30 0
0.1
rhoC1 0.1 0.05
0.2 0.15
10 20 30 0
0.2
rhoC2 0.3 0.2 0.1
0.5 0.4
10 20 30 0
0.1
grazmax
1 0.5 2 1.5
10 20 30 0
0.1
ε
relative frequency 0.20.4
0.8 0.6 1
10 20 30 0
0.2
aggPD 0.06 0.04 0.02
0.1 0.08
10 20 30 0
0.1
aggPP 1 0.5
2 1.5
10 20 30 0
0.2
vPhy
100 50 200 150
10 20 30 0
0.1
vDet
relative frequency 24
8 6
10 20 30 0
0.1
kSi 0.3 0.2 0.1
0.5 0.4
10 20 30 0
0.1
filter step kFe
Figure 5: Evolution of 19 adjusted model parameters with filter step in the one-dimensional experiment. After 30 in- tegrations (filter steps) of 500 Ensemble members, some pa- rameters emerge with clear optimal values, for example, the maximum of the C-specific rate of photosynthesis Pcm and the sinking velocities vDet and vP hy; other parameters have a bimodal PDF, for example, the Chl-specific initial slope of the P-I curve α and the degradations constations of extracellular organic carbon ρC1. The grey bars represent the first guess values, the red bars represent the maximum of the PDF.
0.5 1 1.5 2 2.5 3 3.5
z [m]
first guess
5 10 15 20 25 30 35
−150
−100
−50 0
0.5 1 1.5 2 2.5 3 3.5
CHL a [mg/m3]
days
z [m]
optimized solution
5 10 15 20 25 30 35
−150
−100
−50 0
Figure 6: Temporal evolution of cholorphyll a (Chl a) without data assimilation (top) and with data assimilation (bottom) in the one-dimensional experiment. Filled circles represent data values used in assimilation. The assimilated model captures the beginning and the end of the phytoplankton bloom where the unassimilated model fails. Mixed layer physics is not ad- justed not affected by data assimilation, therefore the mixed layer is too shallow in both models; consequently they fail to explain high chlorophyll values at the bottom of the observed mixed layer which extends below 100 m depth.
5 Coupling of Optimized Ecosytem Model to the Optimized Circu- lation Model
z [m]
longitude [degE]
1.5 2 2.5 3
−300
−250
−200
−150
−100
−50 0 day 37
40’ 2oE 20’ 40’ 3oE 20’
20’
50oS
40’
20’
49oS
Chl a [mg/l]
0.5 1 1.5 2 2.5 3
Figure 7: 24 h-mean of mod- eled chlorophyll concentration on day 37 of the experiment with the optimized coupled ecosystem circulation model;
left: top view; right: sec- tion through the fertilized patch along black line of top-view graph. Dashed black lines are contours of potential den- sity that show the stratification.
Mixed layer depth is indicated by the thick white line.
−6 −4 −2 0 2 4 6
−500
−450
−400
−350
−300
−250
−200
−150
−100
−50 0
inside fertilized patch
10−5 mmol C m−2 s−1
−6 −4 −2 0 2 4 6−500
−450
−400
−350
−300
−250
−200
−150
−100
−50 0 outside fertilized patch
10−5 mmol C m−2 s−1
z [m]
first guess
optimized physics
optimized physics and biology
Figure 8: Vertical flux of particulate organic carbon (POC, in mmol C m−2 s−1) averaged over the fertilized patch and the entire experiment period for three different experiments: (1) first guess physics and ecosystem pa- rameters (blue), (2) assimilated physical trajectory and first guess ecosystem parameters (green), (3) assimilated physical trajectory and optimized ecosystem parameters (red). Clearly, improving the physical trajectory has a larger impact than optimizing the ecosystem model’s pa- rameters. Outside the fertilized patch the effects of im- proved physics and biology are small.
References
Giering, R. and Kaminski, T. (1998). Recipes for adjoint code construction. ACM Transactions
on Mathematical Software, 24:437–474.
Heimbach, P., Hill, C., and Giering, R. (2002).
Automatic generation of efficient adjoint code for a parallel Navier-Stokes solver. In J.J.
Dongarra, P.M.A. Sloot and C.J.K. Tan, edi- tor, Computational Science – ICCS 2002, vol- ume 2331, part 3 of Lecture Notes in Computer Science, pages 1019–1028. Springer-Verlag, Berlin (Germany).
Heimbach, P., Hill, C., and Giering, R. (2004). An efficient exact adjoint of the parallel MIT gen- eral circulation model, generated via automatic differentiation. Future Generation Computer Systems, in press.
Large, W. G., McWilliams, J. C., and Doney, S. C.
(1994). Oceanic vertical mixing: A review and a model with a nonlocal boundary layer param- eterization. Rev. Geophys., 32(4):363–404.
Marshall, J., Hill, C., Perelman, L., and Adcroft, A. (1997). Hydrostatic, quasi-hydrostatic and nonhydrostatic ocean modeling. J. Geo- phys. Res., 102, C3:5,733–5,752.
