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