Preliminary Test of Glider Data Assimilation Along the Labrador Sea Shelf Break

Transcription

1 Preliminary Test of Glider Data Assimilation Along the Labrador Sea Shelf Break Third Annual VITALS Science Meeting October 19, 2015 Changheng Chen, K. Andrea Scott Department of Systems Design Engineering University of Waterloo 1 / 13

2 Objectives of assimilating glider data Objectives : The paths of two gliders from July to August 2014 overlaid on bathymetry (data credit : Palter, deyoung et. al, 2014). To improve model predictions of the thermohaline structure, lateral fluxes, and mixed layer depth ; To provide an initial state for the model to produce better forecasts. 2 / 13

3 Oceanographic data assimilation Main sources of errors in numerical modeling of the ocean state : Numerical schemes and parameterizations ; Inaccurate initial conditions, forcing, and boundary conditions (Kalnay et al., 1996). Oceanographic data assimilation is to seek the best estimate of the oceanic flow by statistically combining observations and model simulations. Analysis (upd Observation Data Assimil Data Assimilation System Backgrou und (forecasted Analysisocean (updated Observat ocean state) tion Numerical Model Background (forecasted Analysis ocean (updstate) dated ocean state) 3 / 13

4 Optimal interpolation method The analysis equations : x a = x b + W(y o Hx b ) Analysis Background Optimal weight (Innovation) Typically, x =[T S u v w p] T. W = BH T (R + HBH T ) 1 B : background error covariance matrix ; H : interpolation matrix R : observation error covariance matrix ; y o : observation Essentially, the analysis step tries to balance the uncertainty in the observation and in the background. 4 / 13

5 Ensemble optimal interpolation (EnOI) The most important element in optimal interpolation method is the background error covariance, B. EnOI method uses a stationary ensemble of model anomalies to estimate the background error (Evensen, 2003 ; Oke et al., 2005). Disadvantage : The ensemble is fixed, and thus the background error does not evolve with the ocean state. Advantage : It is computationally efficient for the situations, where a large ensemble is expensive. 5 / 13

6 Test of EnOI with a quasi-geostrophic model The QG model Time-mean gyre flow Experiment Setup True Ocean Assimilated Ocean Unassimilated Ocean gives a "true" evolution an independent evolution an independent evolution of the ocean state of the ocean state of the ocean state provides "observational streamfunction no data assimilated data" (x= ) assimilated 6 / 13

7 Evolution of the mid-latitude jet is reconstructed with the observational data. Truth Ocean Assimilated Ocean Unassimilated Ocean. Day 1. Day / 13

8 Conclusions : key factors in implementing EnOI The ensemble anomalies should be representative of B, and the number of the ensemble should be large enough and yet computationally efficient (Evensen, 2003, Oke et al., 2007). Localization is required to limit spurious long-distance correlations (Oke et al., 2007). Some studies assumed that R has constant values (e.g., Sakov and Sandery, 2015) ; while others calculate R as a function of depth (e.g., Mignac et al., 2015). 8 / 13

9 Introduction EnOI Method Data Assimilation with a QG Model Assimilation of Glider Data into NEMO Preliminary results : Spatial correlations Introduction Introduction EnOIScheme Scheme EnOI DataAssimilation Assimilation Introduction witha aqg QGModel Model EnOI EnOI Scheme Assimilat Assimil Data Introduction with Scheme Preliminary results results :: Spatial Spatialcorrelations correlations Preliminary (B)results results: :Spatia Spat Preliminary Preliminary (B) The The the background correlations error for The spatial spatial correlations correlationsfor forttand andssbased basedon on The thespatial spatial background correlations errorcovaria covari fortta (L (L (L B) B) :: TT SS (L B) B): :TTSS The spatial correlations for T and S based on the background error covariance matrix, B. The spatial correlation structure is anisotropic and elongated along the path of the Labrador Current ; Thus, the thermohaline information can be transferred upstream and downstream by the nonlinear advection of the Labrador Current. 9 / 13

10 Preliminary results : Innovation (y o Hx b ) Temperature and salinity from glider, x =[T of the North Atlantic Ocean. S] T will be assimilated into NEMO model. There is a 20-year cycle of warming/salting and cooling/freshening cycle of the Labrador Sea (Yashayaev and Clarke, 2006). The 2014 vertical profiles of T and S are close to the 2002 ocean state from NEMO simulations. The main discrepancies are around the thermocline layer. Assimilation of the glider data may be able to improve the thermohaline structure. 10 / 13

11 Future work Construct and evaluate an ensemble of the model state from the 2014 ocean state from NEMO simulation ; Test and determine the key factors (choice of ensemble members, localization scale, observation error variance) for the EnOI method ; Assimilate the glider data and compare the assimilated ocean state with independent datasets (withheld glider data, Argo float data, mooring data) ; Evaluate the impact of the glider date in constraining the model predictions. 11 / 13

12 References Evensen, G., 2003 : The ensemble Kalman filter : theoretical formulation and practical implementation, Ocean Dyn., 53, Kalnay, E, : Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, Cambridge, UK, New York, USA, 341 pp. Mignac, D., Tanajura, C. A. S., Santana, A. N., Lima, L. N., and Xie, J., 2015 : Argo data assimilation into HYCOM with an EnOI method in the Atlantic Ocean, Ocean Sci., 11, Oke, P. R. and Schiller, A., 2007 : Impact of Argo, SST, and altimeter data on an eddy-resolving ocean reanalysis, Geophys. Res. Lett., 34, L Sakov, P., Sandery, P.A., 2015 : Comparison of EnOI and EnKF regional ocean reanalysis systems. Ocean Model., 89, Yashayaev, I. and Clarke, A : Recent warming of the Labrador Sea. AZMP Bulletin PMZA 5 : / 13

13 Appendix : EnOI method x a = x b + W(y o + x b ) W =(L B) H T h R + H(L B)H T i 1 B = N 1 A0 A 0T x a : analysis x b : background y o : observation W : gain matrix B : background error covariance L : localization matrix H : interpolation matrix R : observation error covariance : a scaling factor (0,1] N : the number of ensemble members ; A 0 =[A 1 0, A 1 0,...,A N 0 ] : the matrix of background ensemble anomalies ; A 0 is anomalies of temperature, salinity, velocity, etc, depending on the data being assimilated. 13 / 13