estimating ecosystem model uncertainties in pan-regional syntheses and climate change impacts on...
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Estimating Ecosystem Model Uncertainties in Pan-Regional Synthesesand Climate Change Impacts on
Coastal Domains of the North Pacific Ocean
Jerome FiechterAndrew M. MooreOcean Science, UCSC
Thomas M. “Zack” PowellIntegrative Biology, Cal
Christopher K. WikleMevin HootenStatistics, U. Missouri Utah State
Ralph F. MilliffJeremiah BrownNWRA, CoRA Div.
US GLOBEC PIs and Co-Is:
Emanuele Di LorenzoEarth Sci, Ga Tech
L. Mark BerlinerStatistics, Ohio State
William G. LargeNCAR, CGD
Bernard MegreyNOAA, NMFS
Project Advisory Panel:
3rd US GLOBEC PRS Workshop, 17-20 Feb 2009, Boulder
1D relocatable BHM; Data Stage Inputs – Regional Obs, Regional ROMS output Process Model Stage – NPZD, NEMURO, Error Models, dynamics
Climate Scale Calculations (1D BHM) Data Stage Inputs – Pac Boundary Ecosystem Climate Project (Di Lorenzo et al.) NCAR OGCM, ROMS-Pacific Basin
3D Coastal Domain BHM “Forest” of statistically-linked 1D BHM Conventional 3D
Goals:
Estimate ocean ecosystem model parameters, and quantify parameter uncertainty for coastal domains spanning the North Pacific Ocean
Demonstrate the feasibility and advantages of Bayesian Hierarchical Models (BHM)for large state-space ocean ecosystems
Quantify impacts of climate-scale variability on coastal ocean ecosystems
Objectives:
Bayesian Estimation Cartoon:
Model for Process of Interest: e.g. Phytoplankton Abundance
mmolN m-3
mmolN m-3
Measurement Error Model: e.g. estimates based on fluorometer readings
Bayesian Estimation Cartoon:
Posterior Distribution: Prior updated by Observation distribution (normalized)
Bayesian Estimation Cartoon:
mmolN m-3
Process Model Stage Distribution“Prior”, “(approximate) Balance Eqns”, “Basis Functions”, ...1D and 3D NEMURO+Fe and NPZD+Fe discretizationsplus error (test sophisticated error models)
Parameter Distributionsstructured vs. vaguesome “random”, some “fixed”, model validation tool
Posterior Distribution“posterior mean”, “spread quantifies uncertainty”estimate via sampling; e.g. Markov Chain Monte Carlo (MCMC) posterior distributions on parameters
Bayes Theorem
Data Stage Distribution “Likelihood” “Measurement Error Model”Station obs, transects, satellite obs; i.e. with error estimatesROMS-NEMURO+Fe output with error estimates
What is a Bayesian Hierarchical Model (BHM)?
Use hierarchies of distributions to facilitate modelling, multi-platform data, ...
WPAC
CGOA
CCS
WPAC
Data Stage Distribution “Likelihood” “Measurement Error Model”Station obs, transects, satellite obs; i.e. with error estimatesROMS-NEMURO+Fe output with error estimates
Process Model Stage Distribution“Prior”, “(approximate) Balance Eqns”, “Basis Functions”, ...1D and 3D NEMURO+Fe and NPZD+Fe discretizationsplus error (test sophisticated error models)
Parameter Distributionsstructured vs. vaguesome “random”, some “fixed”, model validation tool
Posterior Distribution“posterior mean”, “spread quantifies uncertainty”estimate via sampling; e.g. Markov Chain Monte Carlo (MCMC) posterior distributions on parameters
Bayes Theorem
Data Stage Distribution “Likelihood” “Measurement Error Model”Station obs, transects, satellite obs; i.e. with error estimatesROMS-NEMURO+Fe output with error estimates
What is a Bayesian Hierarchical Model (BHM)?
Use hierarchies of distributions to facilitate modelling, multi-platform data, ...
Process Model Stage Distribution“Prior”, “(approximate) Balance Eqns”, “Basis Functions”, ...1D and 3D NEMURO+Fe and NPZD+Fe discretizationsplus error (test sophisticated error models)
Process Model Stage Distribution“Prior”, “(approximate) Balance Eqns”, “Basis Functions”, ...1D and 3D NEMURO+Fe and NPZD+Fe discretizationsplus error (test sophisticated error models)
Parameter Distributionsstructured vs. vaguesome “random”, some “fixed”, model validation tool
Posterior Distribution“posterior mean”, “spread quantifies uncertainty”estimate via sampling; e.g. Markov Chain Monte Carlo (MCMC) posterior distributions on parameters
Bayes Theorem
Data Stage Distribution “Likelihood” “Measurement Error Model”Station obs, transects, satellite obs; i.e. with error estimatesROMS-NEMURO+Fe output with error estimates
What is a Bayesian Hierarchical Model (BHM)?
Use hierarchies of distributions to facilitate modelling, multi-platform data, ...
Parameter Distributionsstructured vs. vaguesome “random”, some “fixed”, model validation tool
AttSW
Vm_NO3
PhyMRDZooGR
ZooMRDDetRR
wDet
T_Fe
FeRR
K_NO3
K_FeC
Unif (0.04,0.4)
Unif (0.2,2.0)
Unif (0.02,0.2)Unif (0.1,1.0)
Unif (0.02,0.2)Unif (0.1,1.0)Unif (0,50)
Unif (1,10)
Unif (0.1,1.0)
Unif (0.3,3.0)
Unif (3,30)
Process Model Stage Distribution“Prior”, “(approximate) Balance Eqns”, “Basis Functions”, ...1D and 3D NEMURO+Fe and NPZD+Fe discretizationsplus error (test sophisticated error models)
Parameter Distributionsstructured vs. vaguesome “random”, some “fixed”, model validation tool
Posterior Distribution“posterior mean”, “spread quantifies uncertainty”estimate via sampling; e.g. Markov Chain Monte Carlo (MCMC) posterior distributions on parameters
Bayes Theorem
Data Stage Distribution “Likelihood” “Measurement Error Model”Station obs, transects, satellite obs; i.e. with error estimatesROMS-NEMURO+Fe output with error estimates
What is a Bayesian Hierarchical Model (BHM)?
Use hierarchies of distributions to facilitate modelling, multi-platform data, ...
Posterior Distribution“posterior mean”, “spread quantifies uncertainty”estimate via sampling; e.g. Markov Chain Monte Carlo (MCMC) posterior distributions on parameters
Zooplankton Grazing Rate Posterior Distribution
day-1
What do we get from a BHM?
Distributions mode is “most likely state”, distribution (“spread”) is uncertainty animations of “posterior mean”, “uncertainty maps”, summary fields
parameter posterior distributions are the model parameters “identifiable” given the data? partition uncertainty; i.e. biological components vs. physics
Conditional Probabilities diagnose/compare dependencies (i.e. “top-down/bottom-up”, “webs”) multi-platform (disparate) data stages “borrowed support” from well-known distributions to less well-known
Model and Array Design identify next “most explanatory” term identify next “most informative” observation
WPAC
CGOA
CCS
ROMS-NPZD+Fe: Sea Surface Height Annual Average
New WPAC ROMS-Nemuro+Fe and ROMS-NPZD+Fe implemented by J. Fiechter and A. Moore
CCS dynamical model from C. Edwardsand M. VenezianiBiology implemented by J. Fiechter
CGOA and WPAC physical boundary conditions from N. Pacific ROMS due toJAMSTEC; E. Curchitser and E. Di Lorenzo
CCS
ROMS-NPZD-Fe: Surface Chlorophyll Annual Average (sample data stage inputs)
CGOA
WPAC
SEAWIFS Chlorophyll: 2001 Annual Mean (use comparison with ROMS-NPZD+Fe to estimate error)
WPAC
CGOA
CCS
WPAC
Data Stage Input Choices: Compare ROMS-NPZD, ROMS-NEMURO, SeaWIFS
inner shelf mid shelf outer shelf
Zmax 61.2 m 162.4 m 915.4 m 10 levels
109-203 107-195 105-198 dt = 1 d 94 d 88 d 93 d
days
1D-NPZD+Fe BHM: Initial Experiments CGOA
x,t domain:
data stage inputs:
NO3, P, Z, D, Fe dissolved, Fe P-assoc, SW rad
GLOBEC data: GAK line station data
NO3, SiOH4, P_total, P_small, P_large
ROMS-NPZD output
BHM solution procedure:
Markov Chain Monte Carlo(Metropolis Hastings)
22K iterations, 2K burn-invalidate with 30K repeat
1D NPZD+Fe BHM:
Process Model development
3D NPZD fr PowellFe limitation fr Fiechterf90 fr ROMS-NPZD+Fe
Semi-implicit, 3D»1DMatlab fr BrownBHM by Wikle
1. Random params2. Random dependent vars3. Error Models
AttSW
Vm_NO3
PhyMRDZooGR
ZooMRDDetRR
wDet
T_Fe
FeRR
K_NO3
K_FeC
Unif (0.04,0.4)
Unif (0.2,2.0)
Unif (0.02,0.2)Unif (0.1,1.0)
Unif (0.02,0.2)Unif (0.1,1.0)Unif (0,50)
Unif (1,10)
Unif (0.1,1.0)
Unif (0.3,3.0)
Unif (3,30)
1D NPZD+Fe BHM: Initial Experiments CGOA Random Parameters and Hyperprior Distributions
BHM Params
BHM Initial Val
BHM Initial Dist
inner shelf
mid shelf
outer shelf
T_Fe k_FeC FeRR
1D NPZD+Fe BHM: CGOA Initial Results GLOBEC GAK line data only Fe limitation vs. offshore position
1D NPZD+Fe BHM: CGOA Initial Results GLOBEC GAK line data only Data Influence on Posterior Mean Trace
Forward integration of Process Model (no Bayesian estimation)
Mean of posterior distribution from 1D NPZD+Fe BHM at one level on inner shelf profile
* Observed N concentration at 19.375m on GAK line (inner shelf)
BHM for 1D-NPZDFe using data from obs + ROMS
Preliminary runs exhibit Bayesian learning and “mixing”
BHM to be validated via sequence of 1D calculations: NPZDFe, NPZD, NPZ, NP, N, P
Test issues of uniqueness in solutions
Summary
IssuesIssuesData Stage
Process Model
• Incl. vertical adv. and vertical mixing• Identify correlated parameters• Fixed vs. random parameters
• Data volume• Data importance (uncertainty)• Data timing
EXTRAS
1D NPZD+Fe BHM: CGOA Initial Results ROMS-NPZD+Fe data only Fe limitation vs. offshore position
inner shelf
mid shelf
outer shelf
T_Fe k_FeC FeRR
1D NPZD+Fe BHM: CGOA Initial Results GLOBEC GAK line data only Vm_NO3 convergence vs. offshore position
inner shelf
mid shelf
outer shelf
Vm_NO3 MCMC iteration trace
22K iterationsPhytoplankton Nitrate Uptake Rate
inner shelf
mid shelf
outer shelf
Vm_NO3 MCMC iteration trace
22K iterationsPhytoplankton Nitrate Uptake Rate
1D NPZD+Fe BHM: CGOA Initial Results ROMS-NPZD+Fe data only Vm_NO3 convergence vs. offshore position