Alfred Wegener Institute for Polar and Marine Research
Verification of an ocean general circulation model with time varying GRACE geoid data
M.Wenzel 1 , F.Flechtner 2 , R.Schmidt 2 , Ch.Reigber 2 , V.Seufer 2 , B.Fritzsch 1 , J.Schr¨oter 1
1
Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany
2
Geoforschungszentrum Potsdam, Potsdam, Germany
Introduction
A global data assimilation experiment was performed with the goal of a better understanding of sea level rise. For this satellite altime- try referenced to the GRACE geoid is assimilated together with a set of oceanographic data into an ocean general circulation model (OG- CM).
The OGCM that is used for this study is based on the Hamburg Large Scale Geostrophic model LSG. The main improvement of the model is the ability to estimate the single contributions to sea level change, the steric (thermosteric, halosteric) and the non-steric effects (local freshwater balance, mass redistribution) seperately.
The model has a 2o × 2o horizontal resolution, 23 vertical layers and a ten day timestep. Nine years (1993-2001) of respective TO- PEX/Poseidon (T/P) sea surface height anomalies are assimilated in- to the model. In addition the SHOM98.2 mean sea surface relative to the GRACE geoid (GfZ) as well as sea surface temperatures and ice cover information from Reynolds (2002) are assimilated into the mo- del. Furthermore background information from the Levitus WOA98 is used.
To adjust the model to the data the adjoint method is employed. The control parameters of this optimization are the models initial tem- perature and salinity state as well as the forcing fields (windstress, air temperature and surface freshwater flux). For verification the mo- dels bottom pressure anomalies are compared to the geoid variations derived from the GRACE mission.
Sea Level Evolution
∂
∂ t ζ =
P – E freshwater flux
+ ∇ · Z
ζ−H
~ v dz divergence + Z
ζ−H
1 α
∂α
∂ T
S,p
∂
∂ t T dz thermosteric effect + Z
ζ−H
1 α
∂α
∂ S
T,p
∂
∂ t S dz halosteric effect
+ A
h∆ ζ subgrid processes
ζ : sea level ; H : depth ; P : precipitation ; E : evaporation
T : temperature ; S : salinity ; p : pressure ; α = 1/ρ : specific volume
~v : horizontal velocity ; Ah : diffusion coefficient
Global Mean Sea Level
1993 1994 1995 1996 1997 1998 1999 2000 2001
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
cm
T/P model steric eustatic
B2ntp Global Ocean
1993 1994 1995 1996 1997 1998 1999 2000 2001
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
cm
thermosteric
1993 1994 1995 1996 1997 1998 1999 2000 2001
-0.04 -0.02 0.00 0.02 0.04 0.06
cm
[2250m-bottom] [512-2250m] [ -512m] [ -bottom]
halosteric
Global mean sea level anomalies: The top graph shows the compa- rison of the OGCM with the T/P data as well as the models steric and non-steric contributions. The steric components are further de- composed in the graphs below.
Area Mean Comparison
2002 2003 2004
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
cm
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
mbar
GRACE (data) GRACE (fitted sin) model (mean cycle)
global ocean
2002 2003 2004
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
cm
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
mbar
GRACE (data) GRACE (fitted sin) model (mean cycle)
North Pacific
2002 2003 2004
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
cm
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
mbar
GRACE (data) GRACE (fitted sin) model (mean cycle)
tropical Pacific
2002 2003 2004
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
cm
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
mbar
GRACE (data) GRACE (fitted sin) model (mean cycle)
South Pacific
Area mean bottom pressure anomalies (mean annual cycle) as com- pared to the GRACE geoid variations. Areas shown are (top to bot- tom): global ocean, North Pacific (20N-60N), tropical Pacific (20S- 20N) and South Pacific (58S-20S)
Local Annual Cycle
1.0 1.8
0.2 1.0
0.2
1.0
0.2
1.0 1.0
1.0
0.2 0.8 1.0
0.8
0.6 0.8
0.6
0.8
0.6 1.4
0.6 0.6
0.8
0.6 0.8
0.6 0.8 0.6
0.8
0.6 0.8
0.4 0.4
0.4
0.4
0.4
0.4 0.4
0.4
0.4
0.4 1.2
30 60 90 120 150 180 210 240 270 300 330 360 -90
-60 -30 0 30 60 90
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
0.60
area RMS: c.i. 0.2 mbar
bottom pressure anomaly
0.54
annual cycle: amplitude B2ntp
270 240
240
240
240
240 240 150
150
30
150 30
150
150
150
150
150
150
210
210
90
90
120
210
210
210 120
210 180
180
180
180 180 180
180
180 180
30 60 90 120 150 180 210 240 270 300 330 360 -90
-60 -30 0 30 60 90
30 60 90 120 150 180 210 240 270 300 330 360
185.41
area RMS: day of the year
bottom pressure anomaly
178.30
annual cycle: phase B2ntp
8 4
4 6
4
4
4 4
4
4
4 4
4 4
4 4
4
4
4
4
4
4
6
4
4 6
4
4
6
4 4
4
4 4
4
4 2 4
2 2
2
2
2 2
2
2
2
2 2
2
2 2
2
2 2
2
2
2 2
2 2
2 2
2 2
2 2
2
2
30 60 90 120 150 180 210 240 270 300 330 360 -90
-60 -30 0 30 60 90
0 2 4 6 8 10 12 14 16
3.11
area RMS: c.i. 2 cm
geoid variations
2.68
annual cycle: amplitude
smoothed with 3000km radius
GfZ
270 270
270 270
270
270
270 270
270 270
270
270
270
270
270 240
240
240
240
240
240
240
240
240 240
240
240
240
240
240 240
240 240
240 30
150 150
150
150
150 150
30
30
30 30
150
150
150 150
150 150 150
210
210
300
90 90 120
120
90 210
210 300
90 90
90 60
60 60
180 330
330
30 60 90 120 150 180 210 240 270 300 330 360 -90
-60 -30 0 30 60 90
30 60 90 120 150 180 210 240 270 300 330 360
202.57
area RMS: day of the year
geoid variations
178.61
annual cycle: phase
smoothed with 3000km radius
GfZ
Global distribution of the amplitude and phase of the mean annual cycle for the models bottom pressure anomalies (top row) as compared to the corresponding estimates for the geoid variations (bottom row, in cm water analog). The annual cycle is estimated locally by fitting a sin-curve to the data. For the model a trend elimination was applied prior to fitting the sin to the nine year timeseries.
