advantages of data assimilation in coastal ocean circulation models: oregon perspective
Post on 15-Jan-2016
40 Views
Preview:
DESCRIPTION
TRANSCRIPT
1
Advantages of data assimilation in coastal ocean circulation models:
Oregon perspective
Alexander L. Kurapov, J. S. Allen, G. D. Egbert, R. N. MillerAlexander L. Kurapov, J. S. Allen, G. D. Egbert, R. N. Miller COAS/Oregon State University
In cooperation with P. M. Kosro, M. D. Levine, T. Boyd, J. A. Barth, J. N. Moum, P. T. Strub, S. Erofeeva
29 January 2004, AGU/Ocean Sciences
http://www.coas.oregonstate.edu/po/research/kurapov/main.html
2
wind stress (upwelling favorable) is dominant forcing
strong effects of flow-topography interactions
energetic internal tide
Summer circulation on the Oregon shelf:
HF radarsHF radarsMoorings Moorings
(ADP, T, S)(ADP, T, S)
currents: 3D+time density:
3D+time
Summer 2001: DA system is implemented with data from COAST observational program
Data assimilation:
improves prediction of the ocean state,
provides solution error estimates,
is used as a tool for data synthesis,
helps to design an observational system (e.g., suggests optimal observational locations)
3
Dual approach:
Variational
(generalized inverse)
DA method Simpler, sequential
(optimal interpolation)
Linearized Dynamics Fully non-linear
Internal tides Application Wind-driven circulation
Objectives:
• to develop practical, but still nearly optimal methods for the assimilation of data into coastal circulation models
• to apply these methods to measurements from the Oregon shelf
• to utilize DA to increase scientific understanding of shelf circulation
4
Model of of M2 internal tide [Kurapov et al., JPO 33, 2003]
- linearized, primitive eqns, 3D, periodic in time [~exp(it)]
- terrain following coordinates
20
oMgH H K
i g dH H
u
u f u
e.g., momentum equations:
HF
(P. M. Kosro)
HF
ADPADP
Model domain: 40 60 km, x=1 km, 21 -layers
- Zone of coverage of 2 HF radars (May-July 1998)
- Efficient model solver (direct factorization of the model operator)
- Address open boundary issues
Most internal tide comes from outside the computational domain
DA: corrects open boundary baroclinic flux
5
Generalized Inverse Method (GIM):
Solution minimizes a cost function:
Cost Function = || Model error ||2 + || BCond error ||2 + || Obs error ||2 min
- Explicit statistical assumptions about errors in the inputsExplicit statistical assumptions about errors in the inputs
- Statistics in the output (prior model and inverse solutions) are computed Statistics in the output (prior model and inverse solutions) are computed [[Bennett, 1992, 2002]]
State vector: v = {velocity, sea surface elevation, density}
Model+BCond: S v = f + em
Data: L v = d + ederrors in model forcing and data
( ) ( ) ( ) ( )CF 1 1m dSv f C Sv f Lv d C Sv d
Cov( , ) Cov( , ) m m d dm dC e e C e e
specified prior to assimilation
6
Use of Representers:
1
1
Inverse solution = Prior Solution +
Representer: , where is the row of the data functional
K
k kk
k k k
b
1m
r
r S C S l l L
Model+BCond: S v = f + em
Data: L v = d + ed
Adjoint solverFwd solver
1 1( ) ( )o
1m db LS C S L C d Lv
Reduce burden of representer computation with:
- reduced basis representer approach
- indirect representer approach [Egbert et al., JGR, 1994]
HF radars: K=900 locations where radial velocity components are available
Standard feature in Inverse Ocean Modeling system [IOM, Chua and Bennett, Ocean Modeling, 2001]
vo
Strongly constrained dynamics:
0 0
0
INTERIORm
OB
CC
C
7
Solution sensitivity to the choice of model error covariance COB (in an experiment with synthetic data)
-”true” solution: forced at open boundary (OB) with a significantly baroclinic flux
-synthetic data (velocity harmonic constants) are sampled from true solution
-prior model: forced with depth-averaged OB current
-DA: corrects OB baroclinic fluxes
Depth-ave RMS error with respect to true solution
Prior DA, COB (Type I) DA, COB (Type II)
these two solutions allow for OB b/clinic correction of the same magnitude (but
different correlation structure)
8
DA COB (Type I) is obtained by nesting approach:
In a large domain, compute representers for small domain boundary data
then sample these representers along the OB of small domain
COB (covariance for the errors on the OB of the small domain, with a dynamically consistent spatial structure)
COB controls radiation at an open boundary
representer column of prior solution error covariance matrix
COB (Type II): our best guess w/out nesting
9
A series of M2 tidal solutions, May-July 1998
Internal tide intermittence: analysis in 2-week overlapping time windowsDA: in each time window
Validation ADP
DA solution
No DA
deviations from depth-ave. (CW)
depth-ave (rotating CCW)
Assimilation of HF surface currents improves prediction at depth
Tidal ellipses of horizontal currents at ADP location, vs depth: (a) observed, (b) prior model, (c) DA.
ADPADP
10
M2 tidal ellipses on the surface: internal tide velocities can be twice as large as barotropic tidal velocities
CCW rotation
CW rotation
Depth-aveDeviations from depth-ave (time window centered on day 139)
11
Energy balance is closed : Data assimilation corrects only boundary inputs
40 W m-1
Most baroclinic signal comes into the computational domain from outside
Some persistent features are found: e.g., baroclinic phase and energy propagation is from NW.
Terms in the baroclinic energy equation (time and space averaged)
Baroclinic energy flux (depth-integrated and time-ave.)
day, 1998
12
Baroclinic KE
averaged over a series of days 139-167: a) surface, b) bottom, c) cross-section north of Stonewall Bank, d) cross-section through Stonewall Bank.
Zones of higher KE variability are aligned along the coast, consistent with energetic of a internal Poincare wave
interaction with bathymetry
Dominance of 1st baroclinic mode
beams over Stonewall B
A series of tidal solutions (constrained by HF radar data) provides a uniquely detailed description of spatial and temporal variability of M2 internal tide
13
Model of wind-driven circulation:
AV
HR
R S
ST
, o C[c
ou
rte
sy P
.T.
Str
ub
]
-Princeton Ocean Model: 220350 km, periodic OB conditions (south-north), x~2 km, 31 -layers
-Forcing: alongshore wind stress, heat flux
-Data assimilation: Optimal Interpolation
-Initial implementation (summer 1998): assimilation of HF radar data improves modeled circulation at depth [Oke et al., JGR-Oceans, 2002]
-Data from COAST program (summer 2001): assimilate moored ADP currents
14
Optimal Interpolation (3DVAR):
,a ft t t POMν ν
( )a f ft t t t ν ν G obs Hν
1Gain matr x: i
f f
dG P H HP H C
matrix matching observations to state vector
||Error||
Time
model w/out DA
DAforecast
analysis
Forecast error covariance (stationary in OI): Pf = Pm F (lagged Pm, Cd) where Pm is the covariance of errors in the model solution not constrained by the data (in contrast, Pf is conditioned upon previously assimilated data) [Kurapov et al., Mon. Wea Rev., 2002]
Pf has a shorter horizontal scale in the alongshore direction than Pm (effect of propagation)
Pm: could be obtained as representer calculation, if an adjoint model were available
Presently, Pm is computed from an ensemble of model solutions
Incremental approach: correction is applied gradually over the analysis time window (1/4 of inertial period)
15
Spatial structure of Pf:
NMS,
12m
SSB,
16m
[cm2 s-2]
16
Time- and depth-ave terms in the momentum eqn. (along-jet direction)
no DA
DA (ADPs in south)
Dominant dynamical balance is preserved
Smooth, large scale correction (in this case, DA tends to reduce upwelling intensity)
17
Assimilation of moored ADP velocities (May-Aug 2001):
90 k
m
Central part of model domain with mooring locations, Bathymetry each 100 m (black) and 10 m (half-tone, from 0 to 200 m)
Moorings: Lines N and S – COAST (Kosro, Levine, Boyd), NH10 – GLOBEC (Kosro)
Study is focused on:
- Distant effect of data assimilation- Multivariate capabilities (effect on SSH, isopycnals, temperature, salinity transport, turbulent dissipation rate
18
Case 1: assimilate currents at Northern Line improve currents at NH10, SSB
Correction can be advected by a predominantly southward current
90 k
m
ADP sites, May-Aug 2001Assimilated ADP sitesSites where DA is better than model only solution (smaller model-data rms error, larger correlation)
NH10
SSB
rmse: 7.8 5.8 cm s1, corr: 0.18 0.71
rmse: 9.6 7.1 cm s1, corr: 0.36 0.70
Alongshore depth-ave current: obs, no DA, DA
19
Case 2: assimilate ADP currents at Southern Line improve currents up North
Correction can be propagated northward with coastal trapped waves
NMS
NH10
rmse: 11.3 7.9 cm s1, corr: 0.46 0.79
rmse: 7.8 6.9 cm s1, corr: 0.18 0.63
Alongshore depth-ave current: obs, no DA, DA
ADP sites, May-Aug 2001Assimilated ADP sitesSites where DA is better than model only solution (smaller model-data rms error, larger correlation)
20
Posterior error statistics analysisE.g., compare expected and actual analysis rms error as a consistency test for Pf
Expected performance
diag (Pm) and (Pa) are compared, where Pa = Pf – G H Pf is the analysis error covariance
Actual performance
Assimilated siteDA is better than model only solutionDA is worse than model only solution
Discrepancy between expected and actual outcome when assimilating inner-shelf data :
artificially large decorrelation scale in Pf
inclusion of a more realistic spatially varying wind stress is a necessity
21
Multivariate capabilities
no DA DA (South)SeaSoar measurements (Barth et al.)
e.g., effect on SSH (validation - tide gauge data):
effect on isopycnal slope:Model-data Corr.: 0.51 0.78, rmse: 5.4 3.8 cm
SSH: obs, model only, DA (Lines N+S)
(white contours are measured 24, 25, and 26 kg m-3)
+ improvement in temperature correlations, surface salinity transport
22
Turbulent Dissipation rate ()
Microstructure data [J. Moum, A. Perlin] No DA DA (North)
12 transects on Line N
32 3
2
POM:
(m s ),16.6
where is TKE 2
is turb. length scale
q
L
q
L
yearday, 2001
Time series of averaged near bottom (in box area)
DA correction in near-bottom velocity field yields improvement in
Analysis of BBL dynamics is extended for the whole study period – presentation OS52I-08
23http://www.coas.oregonstate.edu/po/research/kurapov/main.html
SUMMARY:
Progress has been made on both aspects of the dual approach to coastal ocean DA
Linearized dynamics, variational DA (internal tides)
-has provided unique information on spatial and temporal variability of internal tide from HF radar measurements of surface currents
-has given us experience in open boundary DA
Nonlinear dynamics, sequential OI DA (wind-driven circulation)
- has shown the value of assimilation of currents from HF radar and from moored ADPs (distant effect, multivariate capabilities, BBL analysis)
-has provided information on optimal ADP mooring locations and on effective alongshore scales of ADP current measurements
In both cases, formulation of error hypotheses is the science and art of DA
DA is utilized to increase scientific understanding of shelf circulation
24
PLANNED RESEARCH:
Merger of approaches: use tangent linear and adjoint codes for a fully non-linear ocean circulation model (ROMS)
Use data assimilation to help provide open boundary conditions for high-resolution limited-area coastal models
Tidal research: study effect of wind-forced subinertial flows on internal tide propagation
Study of wind-forced upwelling circulation: analyze cross-shelf transport, bottom boundary layer processes, dynamical balances
top related