Harvard - MURI
Allan R. Robinson, Pierre F.J. Lermusiaux,
Patrick J. Haley and Wayne G. Leslie
Division of Engineering and
Applied Sciences
Department of Earth and
Planetary Sciences
http://www.deas.harvard.edu/~robinson
http://www.deas.harvard.edu/~pierrel
Table of Contents
1.
2.
3.
Top three tasks to carry out/problems to address
What we need most?
Recent results relevant to MURI effort
• Quantitative Autonomous Adaptive Sampling
• Multi-Scale Energy and Vorticity Analysis
• Multi-Model Adaptive Combination
Top Three Tasks to Carry Out/Problems to Address
1. Determine details of three metrics for adaptive sampling
(coverage, dynamics, uncertainties) and develop
schemes and exercise software for their integrated use
2. Carry out cooperative real-time data-driven predictions
with adaptive sampling
3. Advance scientific understanding of 3D
upwelling/relaxation dynamics and carry out budget
analyses as possible
What Do We Need Most?
• Effective collaboration
• Integrated software
• Good quality data with error estimates
Determine details of three metrics for adaptive sampling and
develop schemes and exercise software for their integrated use
1. The three metrics:
i. Coverage (maintain synoptic accuracy)
ii. Dynamics (maximize sampling of predicted dynamical events)
iii. Uncertainty (minimize predicted uncertainties)
2. Integrate these adaptive sampling metrics and schemes with
platform control and LCS metrics and schemes
• Multiple platforms of different types used together in overall conceptual
framework
3. Adaptive sampling schemes and software in pre-exercise simulations
• Continue development of ESSE and MsEVA nonlinear adaptive sampling
• Implement simple glider/AUV models within HOPS for i) measurement
model and ii) data predictions
• Continue development error models for HOPS and for
glider/AUV/ship/aircraft data (with experimentalists)
Carry-out real-time data-driven predictions with adaptive sampling
1. Work in real-time with a committed general team of
experimentalists and carry out adaptive sampling
•
Link and/or integrate HOPS with control theory and LCS software
2. Carry out real-time HOPS/ESSE (sub)-mesoscale field and
uncertainty predictions with integrated 3-metrics adaptive sampling
•
1-way and/or 2-way nested HOPS simulations (333m into 1km into 3km)
•
Sub-mesoscale effects including tidal effects
3. Efficient measures and assessment of predictive skill
•
Real-time forecast skill and hindcast skill of fields and uncertainties
•
Theory and software to measure skill of upwelling center/plume estimate:
e.g. shape/size of plume, scales of jet and eddies at plume edges, thickness
of boundary layers, surface/bottom fluxes
4. Real-time physical-acoustical DA with MIT and real-time biologicalphysical DA as possible with collaborators
Advance scientific understanding of 3D upwelling/relaxation dynamics
and carry-out budget analyses on several scales
1. Develop and implement software for momentum, heat and mass budgets
• On several scales and term-balances: e.g. point-by-point, time-dependent
plume-averaged, Ms-EVA, etc.
• Compare data-based budgets to data-model-based budgets
2. Science-focused studies of sensitivity of upwelling/relaxation processes
• e.g. effects of atmospheric conditions and resolution, idealized geometries,
tides/internal tides or boundary layer formulations on plume formation and
relaxation
3. Improve model parameterizations based on model-data misfits (local
and budgets)
4. Estimate predictability limits for upwelling/relaxation processes
What Do We Need Most?
• Effective collaboration, rapid and efficient communication and real
integrated system and system software
• Effective integration of software
– LCS with HOPS
– Glider/AUV models with HOPS
• Good forcing functions and good initial conditions
• Real-time inter-calibration data stations to avoid false circulation features
• Occasional and simultaneous sampling by pairs of platforms, efficiently
scheduled by real-time control groups
• Documented feedback from experimentalists
• Both in real-time and after experiment
Quantitative Adaptive Sampling via ESSE
1. Select sets of candidate sampling paths/regions and variables that satisfy
operational constraints
2. Forecast reduction of errors for each set based on a tree structure of small
ensembles and data assimilation
3. Optimization of sampling plan: select sequence of paths/regions and
sensor variables which maximize the predicted nonlinear error reduction
in the spatial domain of interest, either at tf (trace of ``information
matrix’’ at final time) or over [t0 , tf ]
- Outputs:
- Maps of predicted error reduction for each sampling paths/regions
- Information (summary) maps: assigns to the location of each sampling
region/path the average error reduction over domain of interest
- Ideal sequence of paths/regions and variables to sample
Which sampling on Aug 26 optimally reduces uncertainties on Aug 27?
4 candidate tracks, overlaid on surface T fct for Aug 26
IC(nowcast)
Forecast DA
Aug 24
Aug 26
ESSE fcts after
DA of each track
Aug 27
DA 1
ESSE for Track 1
DA 2
ESSE for Track 2
DA 3
ESSE for Track 3
DA 4
ESSE for Track 4
2-day ESSE fct
Which sampling on Aug 26 optimally reduces uncertainties on Aug 27?
track i
(27 - 27 ) / 27…..for 27 > noise
0………………for 27  noise
2. Create relative error reduction maps for each sampling tracks, e.g.:
1. Define relative error reduction as:
3. Compute average over domain of interest for each variable, e.g. for full domain:
Best to worst error reduction: Track 1 (18%), Pt Lobos (17%), …., Track 3 (6%)
4. Create “Aug 26 information map”: indicates where to sample on Aug 26 for optimal
error reduction on Aug 27
Multi-Scale Energy and Vorticity Analysis
• Multiscale window decomposition in space and time (wavelet-based) of energy/vorticity eqns.
• For example, consider Energetics During Relaxation Period:
Large-scale Available Potential Energy (APE)
Large-scale Kinetic Energy (KE)
August 18
August 19
August 20
August 18
August 19
August 20
August 21
August 22
August 23
August 21
August 22
August 23
• Both APE and KE decrease during the relaxation period
• Transfer from large-scale window to mesoscale window occurs to account for
decrease in large-scale energies (as confirmed by transfer and mesoscale terms)
Windows: Large-scale (>= 8days; > 30km), mesoscale (0.5-8 days), and sub-mesoscale (< 0.5 days)
Dr. X. San Liang
Approaches to Multi-Model Adaptive Forecasting
Combine ROMS/HOPS re-analysis temperatures
to fit the M2-buoy temperature at 10 m
By combining the models x1 and x2 we attempt to:
1. eliminate and learn systematic errors
2. reduce random errors
Sigmoidal Transfer Function
• Approach utilized here: neural networks
• A neural network is a non-linear operator which can be
adapted (trained) to approximate a target arbitrary nonlinear function measuring model-data misfits:
d
Two fits tested
i) Linear least-squares:
ii) Single Sigmoidal layer:
Oleg Logoutov
• Observed (black) temp at the M2mooring
• Modeled temp at the M2mooring:
ROMS re-analysis, HOPS re-analysis
Top: Green – HOPS/ROMS reanalysis
combined via neural network trained on the
first subset of data (before Aug 17).
Bottom: Green – HOPS/ROMS reanalysis
combined via adaptive neural network also
trained on the first subset of data (before Aug
17), but over moving-window of 3 days
decorrelation
Neural Network Least Squares Fit
Linear Least Squares Fit
Equal Weights
Individual
Models
Extra Vugrafs
ESSE Surface Temperature Error Standard Deviation Forecasts
Aug 12
Aug 13
Start of Upwelling
Aug 24
End of Relaxation
Aug 14
First Upwelling period
Aug 27
Aug 28
Second Upwelling period
ESSE: Uncertainty Predictions and Data Assimilation
1. Dynamics:
2. Measurement:
dx =M(x)dt+ d
y = H(x) + 
3. Non-lin. Err. Cov. evolution:
 ~ N(0, Q)
 ~ N(0, R)
P(0)=P0
dP / dt  ( x  xˆ )( M ( x)  M ( xˆ ))T    ( M ( x)  M ( xˆ )( x  xˆ )T  Q
4. Error reduction by DA:
P( )  ( I  KH ) P( )
where K is the reduced Kalman Gain
• ESSE retains and nonlinearly evolves uncertainties that matter, combining,
i.
Proper Orthogonal Decompositions (PODs) or Karhunen-Loeve (KL) expansions
ii.
Time-varying basis functions, and,
iii. Multi-scale initialisation and Stochastic ensemble predictions
to obtain a dynamic low-dimensional representation of the error space.
• Linked to Polynomial chaos, but
with time-varying error KL basis:
Adaptive sampling schemes via ESSE
Adaptive Sampling: Use forecasts and their uncertainties to predict the most useful
observation system in space (locations/paths) and time (frequencies)
Dynamics:
Measurement:
 ~ N(0, Q)
 ~ N(0, R)
dx =M(x)dt+ d
y = H(x) + 
Non-lin. Err. Cov.:
dP / dt  ( x  xˆ )( M ( x)  M ( xˆ ))T    ( M ( x)  M ( xˆ )( x  xˆ )T  Q
Adaptive Sampling Metric or Cost function:
e.g. Find Hi and Ri such that
tf
Min tr ( P(tf ))
Hi , Ri
or
Min
Hi , Ri
t tr( P(t ))
0
dt
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 parameterizations :
i. Vertical tidal Reynolds stresses (diff., visc.)
ii. Modification of bottom stress
iii. Horiz. momentum tidal Reyn. stresses
iv. Horiz. tidal advection of tracers
v. Forcing for free-surface HOPS
KT =  ||uT||2 and K=max(KS, KT)
 =CD ||uS+ uT || uS
 (Reyn. stresses averaged over own T)
½ free surface
full free surface
Two 6-day
model runs
No-tides
Tidal effects
• Vert. Reyn.
Stress
• Horiz.
Momentum
Stress
Temp. at 10 m
T section across Monterey-Bay
Post-Cruise Surface CHL forecast (Hindcast)
• Starts from
zeroth-order
dynamically
balanced IC
on Aug 4
• Then, 13 days
of physical
DA
CHL
Aug 20
CHL
Aug 21
• Forecast of 35 days
afterwards
CHL
Aug 22
CHL
Aug 20,
20:00 GMT