AOSN-II in Monterey Bay:

Data Assimilation, Adaptive Sampling and Dynamics

Allan R. RobinsonPierre 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: http://www.deas.harvard.edu/~leslie/AOSNII/index.html 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 AugGreen – 13 Aug

Solid – ForecastDash – Persistence

T Difference for 13 August

Persistence – Data Forecast – Data

Bias EstimateHorizontally-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 AnalysisMS-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 DecompositionLeft – Total TemperatureCenter – 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 450 2-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: dPe/dt = A Pe + Pe AT + Q – Ke R KeT

Dynamics-misfits covariance: dPd/dt = D Pd + Pd DT – Kd R Kd

T

Coverage-misfits covariance: dPc/dt = C Pc + Pc CT – Kc R KcT

where: all K’s = K(H,R), with Ke= Pe H R-1

Metric or Cost function: e.g.

Find Hi and Ri

Dynamics: dx/dt =Ax + ~ (0, Q)Measurement: y = H x + ~ (0, R)

Definition of metric for adaptive sampling:Illustration for linear systems

dtt

ttPtrMinortPtrMin

f

RiHif

RiHi 0

,,))(())((

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(Pe +Pd + Pc)

• 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 tf (trace of ``information matrix’’ at final time) or over [t0 , tf ]

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 model1. 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.) KT = ||uT||2 and K=max(KS, KT)

ii. Modification of bottom stress =CD ||uS+ uT || uS

iii. Horiz. momentum tidal Reyn. stresses (Reyn. stresses averaged over own T)

iv. Horiz. tidal advection of tracers ½ free surface

v. Forcing for free-surface HOPS full free surface

T section across Monterey-BayTemp. 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 fields Balanced 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