Ocean Data Assimilation and Analysis

Ocean Data Assimilation and analysis

DA training course 2020

Hao Zuo With inputs from M Balmaseda, K Mogensen, M Chrust, P Browne, E de Boisseson, R Buizza and many others [email protected]

• Ocean system and ocean observations • NEMOVAR ocean data assimilation system • Bias correction in ODA • Assimilation of sea-level data • Assimilation of SST data • Assimilation of sea-ice data • Ocean (re)analysis system and its applications

EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS 2 Why do we do Ocean DA?

• Forecasting: initialization of coupled models • NWP, monthly, seasonal, decadal • Seasonal forecasts need calibration

• Towards coupled DA system (weakly -> quasi-strong -> strong …) • See Phil’s presentation

• Climate application: reconstruct & monitor the ocean (re-analysis)

• Verification/evaluation of Global Ocean observing network (OSE/OSSE)

• Other applications • Commercial applications (oil rigs, ship route …), safety and rescue, environmental (algii blooms, spills) Ocean versus Atmosphere

Spatial/time scales The radius of deformation in the ocean is small (~30km) compared to the atmosphere (~3000km). Time scales varies from hours (mixing) to decades (overturning).

Ocean is a data sparse system, in-situ observation is limited and mostly covers upper ocean only, satellite observation only covers ocean surface.

The ocean is forced at the surface and land boundary, by the wind/waves, heating/cooling and fresh-water fluxes Uncertainty in forcing fluxes contributes to uncertainty in model results.

The ocean is strongly stratified in the vertical, although deep convection also occurs Density is determined by Temperature and Salinity

The ocean has continental boundaries; dealing with them is not trivial in data assimilation Ocean time scales: from hours to centuries

Wind Driven: Gyres, Western Boundary Currents, Upwelling regions (coastal, equatorial), Ekman pumping and subduction

Density Driven: Thermohaline Circulation

Ocean is a system with much longer memory but slow response compared to the Atmosphere 2 - Ocean Weather Ocean spatial scales

Satellite image of SST in the North Atlantic Ocean (from NOAA) 1/50 degree Ocean surface relative vorticity (CHASSIGNET and Xu, 2017)

mesoscale and submesoscale eddies Ocean variables with various spatial scales: from hundred meters to hundreds of km Ocean is forced by external forcings

Impact of Atmospheric forcing Impact of land freshwater input

SST spread due to atmospheric forcing perturbation SSS spread due to land freshwater input perturbation

de Boisséson et al., 2020 Zuo et al., 2020 Ocean is a data sparse system

Obs used (M) Obs received (M) Ocean observation is about Ocean 1/1000 to 1/10000 smaller than Atmosphere Atmospheric observation 0 150 300 450 600

Daily obs

8 Ocean in-situ observations

New observations types are emerging: gliders, Deep Argo, BioArgo, drifter, saildrone …

October 29, 2014 The Global Ocean Observing System (GOOS)

Ocean in-situ observations used in OCEAN5 (5-days in Feb 2019)

October 29, 2014 Impact on ocean data assimilation system

Maps of normalized RMSD of Temperature (upper 700m) in OSEs

Moored buoys Ship-based (CTD/XBT/MBT)

Argo Floats All in-situ

Zuo et al., 2019 Satellite ocean surface observations SST (IR, PMW) Sea-ice concentration

Ocean model Sea-Level Anomaly (Altimeter) Sea-ice thickness

October 29, 2014 Observations impact on the ocean state estimation

Temperature RMSE: 0-1000m Observations are essential for improving Model free run initialization

ORAS5 MRB: moored buoy OSD: CTD sonde With DA XBT: Expendable bathythermograph PFL: Argo float

Assimilation of ocean in-situ observations helps to constrain the 3D ocean, therefore providing better estimation of the ocean initial condition for the coupled forecasting system Impact of Ocean DA in Seasonal Forecast

A proper initialisation played a key role in seasonal forecasts ENSO forecast

SEAS5 +1m SEAS5-NoOObs +1.5m ---Persistence

SEAS5 is the new ECMWF seasonal forecasting systems (Johnson et al 2018, GMD) SEAS5 initialized by Ocean Reanalyses ORAS5 (Zuo et al, 2018)

SEAS5-NoOObs is initialized by an “Ocean Simulation” where Ocean observations have are not assimilated (Only winds and SST) October 29, 2014 • Ocean system and ocean observations • NEMOVAR Ocean data assimilation system • Bias correction in ODA • Assimilation of sea-level data • Assimilation of SST data • Assimilation of sea-ice data • Ocean (re)analysis system and its applications

EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS 15 Ocean DA at ECMWF: NEMOVAR

• The “NEMOVAR” assimilation system used in ECMWF.

• Variational DA system as a collaborative project among CERFACS, ECMWF, INRIA and the Met Office for assimilation into the NEMO ocean model. • Solves a linearized version of the full non-linear cost function. • Incremental 3D-Var FGAT running operational, 4D-Var in research model • Background correlation model based diffusion operators • Background errors are correlated between different variables through balance operator

• To avoid initialization shock increments are typically applied via Incremental Analysis Update (IAU) which applies the increments as a forcing term over a period of time. NEMOVAR: 3D-Var FGAT

Daget et al 2009 NEMOVAR: Linearized Cost function Weaver et al 2003,2005 Daget et al 2009 Mogensen et al 2012 Balmaseda et al 2013

4D observation array Balance operator w is the control vector Departure vector linearly independent

Solution: • Balance operator: convert to w space, B becomes block diagonal, representing the spatial covariance model. • Diffusion operator: The spatial covariances is specified by diffusion operator (Weaver and Courtier IAU,Bloom et al 1996 2001) NEMOVAR: Linearized Balance Operator

Define the balance operator symbolically by the sequence of equations

Temperature

Salinity

SSH Treated as u-velocity approximately mutually v-velocity independent without cross correlations

Density

Pressure

Weaver et al., 2005, QJRMS NEMOVAR: balance operator

Salinity balance k k −1 S z k SB =  ( ) ( ) T (approx. T-S conservation) z S =S k−1 T T =T k−1 0 0 k k SSH balance (  H) = −   ( (z) /  )dzSdz (baroclinic) B   0 z=−H z=z Tanal 1 W W 1   1 ~p k u-velocity balance u k = −  f +   (geostrophy with B   f  Sanala   a  β-plane approx. near eq.) 0   Tmodel ~k k 1 W f 1 p v-velocity vB = Smodel (geostrophy, zero at eq.) A) Lifting of 0 f acos  the profile Density k k −1 k k −1 B)k Applyingk (linearized eq. of state)  = 0 (− T +  (salinitySB +  IncrementsSU )) 0 Pressure ~k k k k p (z) =  (z) g dz + 0 g(BRicci+ et Ual.) 2005 (hydrostatic approx.)T/S/SSH balance: vertical displacement of the profile. z=z NEMOVAR: BGE covariance parameters

General B formulation in NEMOVAR

푩풎 is covariance model for each variable, 푪풎 is correlation matrix (including diffusion operator), and 푫풎 is a diagonal matrix of variance (block-diagonal).

Horizontal correlation length-scales used in ORAP5

Representation of diffusion operator that requires de-correlation length-scales Zuo et al., 2015 NEMOVAR: BGE covariance parameters

ORAS5 background error (BGE) standard Mogensen et al., 2012 deviations for unbalanced variables at 100m Cooper and Haines, 1996

Temperature

b T

Unbalanced Salinity 퐷푇푆 is the depth where max ds/dt happens

Zuo et al., 2019 NEMOVAR: Horizontal cross-correlation of T at 100m

T S

U V

SSH

• From single observation of temperature experiment. • The specific background determines the shape due to the balance relations. • S, U, V, SSH increments are from balance with T only. On-going development in ocean DA

• Flow-dependent B (푩풎 + BGE std dev for unbalanced variables

푩풆 , hybrid …) parametrized with analytical function ensemble estimation from ORAS5

• Multi-grid capability

• Multiple spatial scales Temperature • Enhanced perturbation scheme (SPP, SPPT SKEB)

• 4DVar (tangent linear and adjoint model) Salinity • Ocean system and ocean observations • NEMOVAR ocean data assimilation system • Bias correction in ODA • Assimilation of sea-level data • Assimilation of SST data • Assimilation of sea-ice data • Ocean (re)analysis system and its applications

EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS 25 Why do we need bias correction in ODA

• To correct systematic errors in models/forcing and bias introduced by DA • To mitigate changes in the observing system GOOS

1980

Salt content (0-700m) in the Southern Ocean

No bias correction

No obs + obs

2009 with bias correction ഥ Bias Correction scheme A prior bias (풃풌) estimation (ORAS5)

Bias term include two parts, (a) a prior bias for systematic errors, and (b) a temporal variable bias for slow evolving signals (Balmaseda et al, 2007)

ff bbbkkk=+

Seasonal term, Slow varying term, estimated offline estimated online from from rich-data assimilation increments (Argo) Period dk

'' bk=+ b k−1 A()y d k

A(y): Partition of bias into T/S and pressure gradient.

(Zuo et al 2018) Temporal variable bias term

The latitude dependent partition coefficients determine the proportion of online bias corrections applied directly on T/S, and on pressure term. These values ensure that at low latitude the dominant bias term is pressure correction.

Pressure correction 1 % increment T/S correction

0.1 % increment A: Partition matrix, The coefficients in A is latitude Zuo et al., 2015 dependent in NEMOVAR Effect of bias correction on ocean reanalysis Temperature RMSE: 0-1000m

ORAS5 Mean: 2005-2014 No bias correction

T RMS S RMS Estimation of a reduction reduction prior bias ORAS5 In-situ 65% 90% Bias-corr. 14% 10%

Bias correction in ODA is essential, and in particular important for mitigating spurious signals introduced due to changes in the observing system • Ocean system and ocean observations • NEMOVAR Ocean data assimilation system • Bias correction in ODA • Assimilation of sea-level data • Assimilation of SST data • Assimilation of sea-ice data • Ocean (re)analysis system and its applications

EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS 30 Assimilation of Sea Surface Height (SSH)

Altimeter measures SSH (respect reference Alternative: Assimilate Sea Level Anomalies (SLA) respect ellipsoide) a time mean Model represents η (ssh referred to the Obs: SSH anomalies = SSH-MSSH = Obs SLA Geoid) Mod: η anomalies = η – MDT = Mod SLA

SSH-Geoid= η Where: MSSH= Temporal Mean SSH ; MDT = Temporal Mean of model SL Mean Geoid was poorly known (until recent years) Dynamic Topography and changes in time MSSH – Geoid = MDT Assimilation of SSH: MDT

• 푀퐷푇푚 : model MDT as mean(푆푆퐻푚 ), mean model biases not corrected (Balmaseda et al., 2013)

• 푀퐷푇표 : observation MDT as mean(푆푆퐻표 ), observation bias not corrected (Waters et al., 2015 and Lellouche et al., 2018)

• 푏푖푎푠 푐표푟푟. 푀퐷푇표 : observation biases corrected (Lea et al., 2008)

푴푫푻풎 − 푴푫푻풐 풊풏 풎 T ∆RMSE (O-B): 풃풊풂풔 풄풐풓풓. 푴푫푻풐 − 푴푫푻풎 Assimilation of SSH: pre-process obs

• The SLA along track data has very high spatial (9-14km) resolution for the operational ocean assimilation systems. • Features in the data which the model can not represent • “Overfitting” to SLA obs • This can be dealt with in different ways: • Inflate the observation error • Construction of “superobs” or thinning Thinning of SLA obs Inflate OBE std dev of SSH Assimilation of SSH: impact on ocean states

Assimilation of SSH improves simulated ocean states

CryoSat2 Jason-3 Jason-3 Sentinel-3A Jason-2 AltiKa 25 June 24 Dec S3A/S3B 2016 2016 Daily NRT SLA along-track

T ∆RMSE (O-B): Temporal correlation (monthly) to AVISO data assim. SSH – not assim. SSH ORAS5-NoAlti Zuo et al., 2018 ORAS5 • Ocean system and ocean observations • NEMOVAR Ocean data assimilation system • Bias correction in ODA • Assimilation of sea-level data • Assimilation of SST data • Assimilation of sea-ice data • Ocean (re)analysis system and its applications

EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS 35 Assimilation of SST: nudging

A simple nudging scheme to L4 objective analysis data (e.g. OSTIA)

Haney 1917

non-solar total heat flux Fixed negative feedback coefficient

ESA CCI2 SST data (Jan 2016)

SST(model)=T_layer(x)

SST(target) = SSTfnd Impact of SST nudging Global mean SST • Overall very effective except for some OSTIA areas with weak vertical stratification With SST nudging • Not accounting complicated error characteristics in the L4 SST analysis

• Not accounting vertical correlation when No SST nudging apply SST constrain in the surface

SST bias: free run - OSTIA SST bias: ORAS5 - OSTIA Flow-dependent SST nudging

푑푄 A flow-dependent relaxation coefficient can be obtained by 푄푠푠푡 = (푆푆푇 − 푆푆푇 ) 푠푠푡 푛푠 푑푇 푚표푑푒푙 푡푎푟푔푒푡 filtering of 푄푛푠 in order to avoid introducing spurious convection in regions where surface stratification is very relaxation coefficient weak. departure computation Anomaly correlation map of T2M, verified against ERA-int 풔풔풕 Feb 푸풏풔

W/m2 Johnson et al., 2019

38 Assimilation of L2P SST with 3DVAR

Temperature increments

Daily L2P SST obs (24 Nov 2010) SST Nudging

SST relaxation – MLD param ~1e6 /day

SST assimilation

• In general 3DVar DA does a better job than SST nudging • Pre-processing including bias correction to SST observation is critical

• Flow-dependent vertical correlation length-scale is vital in SST assim – MLD param determining vertical propagation of the T increment • Ocean system and ocean observations • NEMOVAR Ocean data assimilation system • Bias correction in ODA • Assimilation of sea-level data • Assimilation of SST data • Assimilation of sea-ice data • Ocean (re)analysis system and its applications

EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS 40 Assimilation of SIC: L4 gridded data Sea-Ice Concentration data from L4 analysis is assimilated through Regular thinning 3DVar scheme • Treated as univariate • Pre-thinned via regular or stratified random sampling • Assimilated through outer-loop coupling in NEMO-LIM2

random thinning

Zuo et al., 2017 Assimilation of SIC: L4 Without SIC DA With SIC DA gridded data

SIC bias (1980-2016) Ref data: OSI-SAF 430

Positive impact on both SIC In percent and SIT state

SIT bias (2011-2016) Ref data: CS2SMOS merged data

In m Assimilation of SIC: L3 data

Daily SIC on 20130118 L4 SIC analysis L3 SIC data

L4 analysis: with filtering, masking, infilling with 10km resolution there is ~1 milion obs to produce a gap-free product per day from L3 OSI-SAF, with no infilling created observation Assimilation of sea-ice thickness (SIT): nudging scheme

Difference in forecast Integrated Ice Edge Error (2011-2016, verified against OSI-401b) with SIT nudging – No SIT nudging where 푆퐼푇푛 is the nudged thickness, 푆퐼푇푚 is the modelled thickness, 푆퐼푇표 is the observed thickness, tau is the nudging coefficient

Sea-ice forecasts

Jan SIT bias

Balan Sarojini, et al. 2019 No SIT nudging with SIT nudging • Ocean system and ocean observations • NEMOVAR Ocean data assimilation system • Bias correction in ODA • Assimilation of sea-level data • Assimilation of SST data • Assimilation of sea-ice data • Ocean (re)analysis system and its applications

EUROPEAN CENTRE FOR MEDIUM-RANGE WEATHER FORECASTS 45 ECMWF Ocean Reanalysis-analysis system

OCEAN5 is the 5th generation of ECMWF ocean and sea-ice ensemble reanalysis-analysis system (Zuo et al., 2018, 2019).

• Ocean: NEMOv3.4 • Sea-ice: LIM2 • Resolution: ¼ degree with 75 levels • Assimilation: 3DVAR-FGAT • 5 ensemble member Zuo et al., 2019 • Forcing: ERA-int Overview of the OCEAN5 setup Application of Ocean analysis: coupled forecasts

Forecast lead month for correlation above 0.9 in NINO3.4 SST anomalies OCEAN5 provides ocean and sea-ice initial conditions for all ECMWF coupled forecasting system: (ENS, HRES, 4.54.5 Seasonal). OCEAN5 also provides SST 3.5 3.83.8 3.5 3.2 and SIC conditions for the ECMWF 2.8 3 3 atmospheric analysis system (Browne et 2.8

al., 2018) Lead Time (months) Time Lead S1 S2 S3 S4 S5 S5-NoOobs S1 S2 S3 S4 S5 1997 2002 2006 2011 2017

• Gain about 2 months in ENSO prediction • Without Ocean observation and DA, we would lose about 15 years of progress. Application of Ocean reanalysis: calibration and reforecasts

• Correcting model error • Extreme Events • Tailored products (health, energy, agriculture) Ocean/Atmosphere Real time Probabilistic reanalyses Coupled Forecast time

Hindcasts, needed to estimate climatological PDF, require a Consistency between historical ocean and historical and real-time atmospheric reanalyses initial conditions is required. Application of Ocean ReAnalysis: climate monitoring

ORAS4 suggests that there is more heat absorbed by the deeper ocean after 2004.

ocean heat content changes

Sea-ice extent anomalies

2016 September

Zuo & Lien, 2018 Balmaseda et al., 2013 Application of ocean analysis: RT monitoring

Real-Time monitoring of ENSO state Ref: 1981-2010

-ORAS5 -ORAS4

Contribution to the ORIP-RT project • Update on the 1st day each month • Compare the latest mean ocean state with 8 other RT Ocean analysis products

October 29, 2014 50 Summary

• Data assimilation in the ocean serves a variety of purposes, from climate monitoring to initialization of coupled model forecasts and ocean mesoscale prediction. • This lecture dealt mainly with ocean DA for initialization of coupled forecasts and reanalyses, with a global ocean model in climate resolution and use NEMOVAR as an example. • ECMWF NEMOVAR uses a incremental 3DVar-FGAT configuration and linearized cost function. The BGE covariance is modelled use balance operator and diffusion operator.

• Compared to the atmosphere, ocean observations are sparse. The main source of information are temperature and salinity profiles, sea level from altimeter, SST/SIC/SIT from satellite and in- situ.

• Assimilation of ocean observations reduces the large uncertainty due to both model and forcing errors. It improves the initialization of coupled forecasts in NWP, and provides calibration and initialization for reforecast for seasonal forecasts and decadal forecasts.

• Data assimilation changes the ocean mean state. consistent ocean reanalysis requires an explicit treatment of the bias. Further Readings Ocean Data assimilation

• Balmaseda, M. A., Dee, D., Vidard, A., & Anderson, D. L. T. (2007). A multivariate treatment of bias for sequential data assimilation: Application to the tropical oceans. Quarterly Journal of the Royal Meteorological Society, 133(622), 167–179. • Mogensen, K., Alonso Balmaseda, M., & Weaver, A. (2012). The NEMOVAR ocean data assimilation system as implemented in the ECMWF ocean analysis for System 4. Technical Memorandum (Vol. 668). • Weaver, A. T., Deltel, C., Machu, É., Ricci, S., & Daget, N. (2005). A multivariate balance operator for variational ocean data assimilation. Quarterly Journal of the Royal Meteorological Society, 131(613), 3605–3625. • Zuo, H., Balmaseda, M. A., Boisseson, E. De, Hirahara, S., Chrust, M., & Rosnay, P. De. (2017). A generic ensemble generation scheme for data assimilation and ocean analysis. ECMWF Tech Memo, 795. Ocean DA and Reanalysis

• Balmaseda, M. A., Mogensen, K., & Weaver, A. T. (2013). Evaluation of the ECMWF ocean reanalysis system ORAS4. Quarterly Journal of the Royal Meteorological Society, 139(674), 1132–1161. • Zuo, H., Balmaseda, M. A., & Mogensen, K. (2015). The new eddy-permitting ORAP5 ocean reanalysis: description, evaluation and uncertainties in climate signals. Climate Dynamics. • Zuo, H., Balmaseda, M. A., Tietsche, S., Mogensen, K., & Mayer, M. (2019). The ECMWF operational ensemble reanalysis-analysis system for ocean and sea-ice : a description of the system and assessment. Ocean Science, (January), 1–44.