Transcript Heuristic models in research: iterative failure = learning

“Modeling”
In the Narragansett Bay
CHRP Project
Dan Codiga, Jim Kremer, Mark Brush,
Chris Kincaid, Deanna Bergondo
Hypoxia in Narragansett Bay
Workshop Oct 2006
Does the word “Model” have meaning?
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Hydrodynamic
Ecological
Research vs Applied
Prognostic vs Diagnostic
Heuristic, Theoretical, Conceptual, Empirical,
Statistical, Probabilistic, Numerical, Analytic
• Idealized/Process-Oriented vs Realistic
• Kinematic vs Dynamic
• Forecast vs hindcast
CHRP Program Goals
(selected excerpts from RFP)
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Predictive/modeling tools for decision makers
Models that predict susceptibility to hypoxia
Better understanding and parameterizations
Transferability of results across systems
Data to calibrate and verify models
 Following two presentations
Our approaches
• Hybrid Ecological-Hydrodynamic Modeling
– Ecological model: simple
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Few processes, few parameters
Parameters that can be constrained by measurements
Few spatial domains (~20), as appropriate to measurements available
Net exchanges between spatial domains: from hydrodynamic model
– Hydrodynamic model: full physics and forcing of ROMS
• realistic configuration; forced by observed winds, rivers, tides, surface fluxes
• Applied across entire Bay, and beyond, at high resolution
• Passive tracers used to determine net exchanges between larger domains of
ecological model
• Empirical-Statistical Modeling
– Input-output relations, emphasis on empirical fit more than mechanisms
– Development of indices for stratification, hypoxia susceptibility
– Learn from hindcasts, ultimately apply toward forecasting
Heuristic models in research:
iterative failure = learning
Conceptual
Model
Processes
Formulations
Runs that
fall short
Parameter values
But for management models:
• Heuristic goal less impt
• Accurate even if not precise
• Well constrained coefs
• Simple (?) (at least understandable)
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≠ Research models
A paradox -“Realism” = many parameters
weakly constrained
limited data to corroborate
i.e. “Over-parameterized”
(many ways to get similar results)
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Accuracy is unknown.
(often unknowable)
An alternative approach?
4 state variables, 5 processes
Processes of the model
(excluding macroalgae...)
Temp, Light,
Boundary Conditions
Chl, N, P, Salinity
O2 coupled
stoichiometrically
Productivity
Phytoplankton
Photic zone
heterotrophy
Atmospheric
deposition
N
Surface layer
DO2
mixing
- -flushing
-------
Flux to
bottom
.
N P
Deep layer
Sediment
organics
Land-use
NP
Physics
Benthic
heterotrophy
--------Denitrification
.
Bottom
sediment
Shallow test
sites
(MA, RI, CT)
Corroboration:
“Strength in numbers”
Deep test sites
(MA, RI, CT,
VA, MD)
Narragansett Bay
Chesapeake Bay
Long Island Sound
Long Island
Sound -Hypoxia
August 20
Hydrodynamic Model
Equations
Momentum balance x & y directions:
u + vu – fv = f + Fu + Du
t
x
v + vv + fu = f + Fv + Dv
t
y
Potential temperature and salinity :
T + vT = FT + DT
t
S + v S = FS + DS
t
The equation of state:
r= r (T, S, P)
Vertical momentum:
f = - r g
z
ro
Continuity equation:
u + v + w = 0
x y z
Initial Conditions
Forcing Conditions
ROMS Model
Regional Ocean
Modeling System
Output
Hydrodynamic Model
Grid Resolution: 100 m
Grid Size: 1024 x 512
Vertical Layers: 20
River Flow: USGS
Winds: NCDC
Tidal Forcing: ADCIRC
Open Boundary
This project: Mid-Bay focus
Narragansett Bay Commission: Providence & Seekonk Rivers
Mt. Hope
Bay circulation/exchange
Extent
of counter
/mixing study. ADCP, tide gauges
(Deleo, 2001)
Summer, 07: 4 month deployment (Outflow pathways)
Bay-RIS exchange study (98-02)
This project: Mid-Bay focus
Narragansett Bay Commission: Providence & Seekonk Rivers
Mt. Hope
Bay circulation/exchange
Extent
of counter
/mixing study. ADCP, tide gauges
(Deleo, 2001)
Summer, 08: Deep return flow processes
Bay-RIS exchange study (98-02)
Model-Data Comparison
Salinity - Phillipsdale
Salinity (ppt)
Model
Data
Time (days)
Model-Data Comparison
Bottom-model
Shallows: North-South Component
0.15
150
0.05
50
-0.05
-50
-0.15
-150
-0.25
-250
10
15
Observed Velocity
(mm/s)
Model Velocity
(m/s)
Bottom
20
Time
Channel: North-South Component
0.25
250
0.15
150
0.05
50
-0.05
-50
-0.15
-150
-0.25
-250
10
15
Time (days)
20
Obsevered
Velocity (m/s)
Model Velocity
(m/s)
Bottom-model
Bottom
Hybrid: Driving Ecological model with Hydrodynamic Model:
Lookup Table of Daily Exchanges (k)
dP1/dt = P1(G-R) - k1,2P1V1 + k2,1P2V2 ...
Modeling Exchange Between
Ecological Model Domains
DYE_01
DYE_02
DYE_03
DYE_06
DYE_07
DYE DYE
04
05
DYE_08
DYE_09
Passive Tracer Experiment
Passive Tracer Experiment
Passive Tracer Experiment
Long-term Aims:
Hybrid Ecological-Physical Model
• Increased spatial resolution of ecology:
approach TMDL applicability
• Scenario evaluation
– Nutrient load changes
– Climatic changes
• Alternative to mechanistic coupled
hydrodynamic/ecological modeling
Empirical/Statistical Modeling
Overall Goals
• Data-oriented—complements Hybrid– less mechanistic
• Synthesize DO variability
– Spatial (Large-scale CTD; towed body)
– Temporal (Fixed-site buoys)
• Develop indices
– Stratification
– Hypoxia vulnerability
• First: Hindcasts to understand relationship between
forcing (physical and biological) and DO responses
• Long-term: Predictive capability for forecasting and
scenario evaluation
• Candidate predictors for DO
– Biological
• Chlorophyll
• Temperature & solar input
• Nutrient inputs (Rivers, WWTF, Estuarine
exchange)
• Others
– Physical
• River runoff, WWTF water transports
• Tidal range cubed (energy available for mixing)
• Windspeed cubed (energy available for mixing)
• Others (Wind direction; Precip; Surface heat flux)
Strategy: start simple & develop method
• Start with Bullock Reach timeseries
– 5 yrs at fixed single point (no spatial information)
• Investigate stratification (not DO-- yet)
– Target variable: strat = [sigt(deep) – sigt(shallow)]
– Include 3 candidate predictor variables:
• River runoff (sum over 5 rivers)
• Tidal range cubed (energy available for mixing)
• Windspeed cubed (energy available for mixing)
2001
Visually apparent features
• Stratification reacts to ‘events’ in each of:
– River inputs
– Winds
– Tidal stage
• Stratification ‘events’ appear to be
– Triggered irregularly by each process
– Lagged by varying amounts from each process
Low-pass and subsample to 12 hrs…
Compare techniques
• Multiple Linear Regression (MLR)
– No lags
– Optimal lags – determined individually
• Static Neural Network
– No lags
– Lags from MLR analysis
• [coming soon] Dynamic Neural Network
– Varying lags
– Multiple interacting inputs
Stratification
Dst [kg m-3]
Observed
Model
Multiple Linear Regression
No lags
r2=0.42 (River alone: 0.36)
MLR with lags
River 2 days Wind 1 day Tide 3.5 days
r2=0.51 (River alone: 0.48)
Static Neural Net
No lags
r2=0.55 (River alone: 0.41)
Static Neural Net
Lags from MLR
r2=0.59 (River alone: 0.52)
Advantages/Disadvantages
of Neural Networks
• Advantages
– Nonlinear, can achieve better accuracy
– Excels with multiple interacting predictors;
– Dynamic NN: input delays capture lags
• Varying lags from multiple interacting inputs
– Transferable; conveniently applied to other/new data
– Easy to use (surprise!!)
• Main disadvantage
– opaque “black-box” can be difficult to interpret;
ameliorated by: complementary linear analysis,
sensitivity studies, isolating/combining predictors
Next steps
• Stratification
– Consider additional predictors:
• Surface heat flux; precipitation; WWTF volume flux
– Different sites (North Prudence, etc)
– Treat spatially-averaged regions
• Apply similar approach to DO
– Finish gathering forcing function data
• Chl; solar inputs; WWTF nutrients
– Corroborate Hybrid Ecological-Hydrodynamic Model