AOSN-II in Monterey Bay: Data Assimilation, Adaptive Sampling and Dynamics Allan R. Robinson Pierre F.J. Lermusiaux Harvard University Harvard Contributors: Patrick J. Haley, Jr., Wayne G. Leslie, X. San Liang, Oleg Logoutov, Patricia Moreno, Gianpiero Cossarini (Trieste)

HOPS – AOSN-II Accomplishments 23 sets of real-time nowcasts and forecasts of temperature, salinity and velocity released from 4 August to 3 September -Assimilated ship (Pt. Sur, Martin, Pt. Lobos), glider (WHOI and Scripps) and aircraft SST data, within 24 hours of appearance on data server (after quality control) -Forecasts forced by 3km and hourly COAMPS flux predictions Data analyzed and quality controlled daily for real-time forecasts Web: for daily distribution of field and error forecasts, scientific analyses, data analyses, special products and control-room presentations Features analyzed and described daily. Formed basis for adaptive sampling recommendations Boundary conditions and model parameters for atmospheric forcing calibrated and modified in real-time to adapt to evolving conditions

HOPS – AOSN-II Accomplishments (cont.) 10 sets of real-time ESSE forecasts issued from 4 Aug. to 3 Sep. – total of 4323 ensemble members (stochastic model, BCs and forcings), 270 – 500 members per day -ESSE fields included: central forecasts, ensemble means, forecast errors, a priori and a posteriori error estimates, dominant singular vectors and covariance fields ESSE text products included: descriptions of uncertainty initialization and forecast procedures, analyses of ESSE prediction results (uncertainties and dynamics) and adaptive sampling recommendations Real-time research work on: multi-scale energy and vorticity analysis, coupled physics-biology, tides, free-surface PE model

This sequence of snapshots spans the time period 6 August to 6 September. The frames are at one-day intervals. The three columns represent total velocity (left), regional-scale (center) and meso-scale (right) velocity. This animation is a sequence of concatenated snapshots from the real-time simulations. As such there are jumps in the field evolution due to the sequence of forecast restarts. However, it is possible to follow, especially in the meso-scale velocity plots, the movement of features over the passage of time. A smooth animation is being constructed.

Oceanic responses and atmospheric forcings during August 2003 Upwelling Relaxation

Oceanic responses and atmospheric forcings during August 2003 Aug 10: Upwelling Aug 16: Upwelled Aug 20: Relaxation Aug 23: Relaxed

Forecast RMS Error Estimate– Temperature (left), Salinity (right) Blue – 12 Aug Green – 13 Aug Solid – Forecast Dash – Persistence T Difference for 13 August Persistence – Data Forecast – Data

Bias Estimate Horizontally-averaged data-model differences Verification data time: Aug 13 Nowcast (Persistence forecast): Aug 11 1-day/2-day forecasts: Aug 12/Aug 13

Real-time predictions of forecast errors with a significant number of ensemble members and ESSE assimilation is possible Novel group of experimentalists, modelers and managers provided an unprecedented picture of a variety of Monterey Bay processes and phenomena Effective communication among and integration of assets requires a cooperative effort greater than AOSN-II but can only be accomplished with real-time practice Need for a priori and ongoing regular inter-calibration between assets Initialization survey needed to be completed prior to start of real-time forecasting period Maintenance of background circulation with adequate coverage critical Anomalous conditions in 2003 proved challenging for HOPS set-up methodology Model details (e.g. BC, response to forcing) must be anticipated to be adapted in real-time. Resources for such adaptation must be included in logistics. High temporal resolution forcing lends greater importance to diurnal cycle – impacts data assimilation protocol HOPS – AOSN-II Lessons Learned

Generate consistent 4-D simulations of the physical (and coupled physical- biological fields) for August 2003 (re-analysis fields) o Improve the forecast protocol for hindcasting – data compatibility, assimilation methodology and domains to be re-evaluated o Hindcast additions – T/S feature model, tides Summarize kinematic and dynamical findings of Monterey Bay, as well as California Current System interactions and fluxes (balance of terms, etc) Multi-Scale Energy and Vorticity Analysis of the dynamical evolution Complete forecast skill evaluation of fields/errors with classic and new generic/specific metrics. Issues include: definition of “persistence”, accounting for phase error, etc. Predictability studies, ensemble properties (mean, mpf, std, sv, etc), energetics, improve stochastic forcings (data/model errors) Develop and carry out interdisciplinary adaptive sampling OSSEs on multiple scales HOPS – AOSN-II Research Tasks

Multi-Scale Energy and Vorticity Analysis MS-EVA is a new methodology utilizing multiple scale window decomposition in space and time for the investigation of processes which are: multi-scale interactive nonlinear intermittent in space episodic in time Through exploring: pattern generation and energy and enstrophy transfers, transports, and conversions, MS-EVA helps unravel the intricate relationships between events on different scales and locations in phase and physical spaces.

Multi-Scale Energy and Vorticity Analysis (Cont.) Temperature Decomposition Left – Total Temperature Center – Regional Scale (> 75km) Right – Mesoscale (8-75km)

(a)Rate of potential energy transfer from large-scale window to meso-scale window (b)Rate of kinetic energy transfer from large-scale window to meso-scale window (c)Meso-scale buoyancy conversion rate (d)Vertical pressure working rate on the meso-scale window These plots are for 30m on 17 August.

Interdisciplinary Adaptive Sampling Use forecasts and their uncertainties to alter the observational system in space (locations/paths) and time (frequencies) for physics, biology and acoustics. Predict most useful regions/variables to sample, based on: Uncertainty predictions (error variance, higher moments, pdf’s) Interesting physical/biological/acoustical phenomena predictions (feature extraction, Multi-Scale Energy and Vorticity analysis) Synoptic accuracy/coverage predictions Plan observations under operational, time and cost constraints to maximize information content (e.g. minimize uncertainty at final time or over the observation period).

Real-time Adaptive Sampling – Pt. Lobos Large uncertainty forecast on 26 Aug. related to predicted meander of the coastal current which advected warm and fresh waters towards Monterey Bay Peninsula. Position and strength of meander were very uncertain (e.g. T and S error St. Dev., based on day fcsts). Different ensemble members showed that the meander could be very weak (almost not present) or further north than in the central forecast Sampling plan designed to investigate position and strength of meander and region of high forecast uncertainty. Temperature Error Fcst.Salinity Error Fcst. Surf. Temperature Fcst.

 Real-time 3-day forecast of cross- sections along 1 ship-track (all the way back to Moss Landing)  Such sections were provided to R/V Pt Lobos, in advance of its survey

 Real-time 3-day forecast of the expected errors in cross-sections along 1 ship- track (all the way back to Moss Landing)  Such error sections were provided to R/V Pt Lobos, in advance of its survey

Error Covariance:dP e /dt = A P e + P e A T + Q – K e R K e T Dynamics-misfits covariance:dP d /dt = D P d + P d D T – K d R K d T Coverage-misfits covariance:dP c /dt = C P c + P c C T – K c R K c T where: all K’s = K(H,R), with K e = P e H R -1 Metric or Cost function: e.g. Find H i and R i Dynamics: dx/dt =Ax +  ~ (0, Q) Measurement:y = H x +  ~ (0, R) Definition of metric for adaptive sampling: Illustration for linear systems

Current Quantitative Adaptive Sampling Developments In realistic cases, need to account for: -Nonlinear systems and large covariances => ESSE -Operational constraints -Multiple objectives and integration, e.g. Min tr(P e +  P d +  P c ) With nonlinear systems, posterior pdf (and error covariances) are a function of data values and pdfs Quantitative adaptive sampling via ESSE (Mark 1 software written) -Select sets of candidate sampling regions and variables that satisfy operational constraints -Forecast reduction of errors for each set based on a tree structure of ensembles and data assimilation -Sampling path optimization: select sequence of sub-regions/variables which maximize the nonlinear error reduction at t f (trace of ``information matrix’’ at final time) or over [t 0, t f ]

ESSE DA properties: Error covariance function predicted for 28 August

ESSE T error-Sv ESSE Field and Error Modes Forecast for August 28 (all at 10m) ESSE S error-Sv T S

Observed Tidal Effects Temperature at M1 CODAR Velocity Tidal-series least-square fit to data: For T at 300m, 10-30% total amp. For U,V at 0m, 20-40% total amp.

Modeling of tidal effects in HOPS Obtain first estimate of principal tidal constituents via a shallow water model 1.Global TPXO5 fields (Egbert, Bennett et al.) 2.Nested regional OTIS inversion using tidal-gauges and TPX05 at open-boundary Used to estimate hierarchy of tidal parametrizations : i.Vertical tidal Reynolds stresses (diff., visc.)K T =  ||u T || 2 and K=max(K S, K T ) ii.Modification of bottom stress  =C D ||u S+ u T || u S iii.Horiz. momentum tidal Reyn. stresses   (Reyn. stresses averaged over own T  ) iv.Horiz. tidal advection of tracers½ free surface v.Forcing for free-surface HOPSfull free surface

T section across Monterey-Bay Temp. at 10 m No-tides Two 6-day runs Tidal effects Vert. Rey. Str. Horiz. Momen. Str.

Dominant dynamical balances for initial biogeochemical fields/parameters Balance subject to observed variables and parameters constraints

Dominant dynamical balances for initial biogeochemical fields/parameters (Cont.) Observed fieldsBalanced fields

Monterey Bay-CCS in August 2003: Daily real-time predictions of field and errors, DA, adaptive sampling and dynamical analyses Preliminary kinematic and dynamical processes : –Two successions of upwelling and relaxed states: Pt AN << Pt Sur, but in phase –Local upwellings at Pts. AN/Sur join, along-shelf upwelling, warm croissant along Monterey Bay coastline: this favors a cyclonic circulation in the Bay (occurs without tides, hence tidal effects likely not a cause) –Relaxation process very interesting: Release of KE, possible increase of APE due to N(z) profile variation Since KE/APE ~ (R/L) 2 : more geostrophic turbulence, baroclinic instability potential, more internal jets, squirts, filaments, eddies –Daily cycles matter: e.g. modulate downwelling-driven northward coastal jets –Observed bifurcation (separatrix /LCS front) at Monterey Bay Peninsula –Some tidal effects matter: regional-scale offshore, (sub)-mesoscale in the Bay CONCLUSIONS