Transcript Implicit Ocean Biogeochemistry Modeling Eun Young Kwon and Francois Primeau UCI The Ocean Spin-up Problem The approach to equilibrium of the tracer transport equation is controlled by the.

Implicit Ocean
Biogeochemistry
Modeling
Eun Young Kwon and Francois Primeau
UCI
The Ocean Spin-up
Problem
The approach to equilibrium of the
tracer transport equation is
controlled by the decay rate of the
transport operator’s slowest
decaying eigenmode (in models this
decay rate is largely controlled by
the weak background diapycnal
diffusivity)
Spin-up typically takes 3000+ years.
Because of slow spin-up
We can typically only do a few runs
We cannot easily optimize uncertain model
parameters, (especially true for parameters
that interact)
we end up using parameter values that are
suboptimal, this introduces biases in the
model
We cannot easily quantify
the uncertainty of model parameters
the impact of parameter uncertainty on
model predictions
Implicit Ocean Model
3-D transport
operator
biogeochemistry
source-sink term
: biogeochemical state of the model, i.e. 3-D tracer
fields
: biogeochemical model parameters
Equilibrium condition:
System of coupled
nonlinear algebraic
equations
Solve iteratively using Newton’s Method
Newton’s Method
Jacobian matrix
(tangent linear model)
use a sparse linear solver
to factor and invert
Iterate until
Newton’s Method
If method converges it is orders of
magnitude faster than time-stepping
Can always be made to converge by
starting with a good enough initial
guess
Can be generalized to find periodic
steady states (i.e. seasonally
varying solutions)
Example from a 3-D
OGCM
(No seasonal cycle)
The OGCM is run to equilibrium (~6000 yrs)
and time averaged velocity and diffusion
tensor fields are used in an offline model
(Primeau 2005) no seasonal cycle
global model 3.75o x 3.750, 29 vertical levels
KPP and GM mixing scheme
OCMIP-2 ocean biogeochemistry formulation
less than 45 minutes per equilibrium bgc
solution on an already old 1-cpu workstation
Phosphate
Equilibrium solution
OCMIP-2
Observed
Equilibrium solution
Optimized
Automatic parameter
optimization
Minimize cost function
a handful of bgc model parameters
[ phosphate, dissolved inorganic carbon,
alkalinity]
Parameter optimization and
parameter uncertainty: example
phosphate
lifetime of
DOP
Vertical POC flux power law
parameterization exponent
fraction of new
production
allocated to
DOP
Parameter Uncertainty:
example
ALKALINITY
1. rain-ratio: molar ratio of POC to CaCO3
2. vertical POC flux power-law
parameterization exponent
Fraction of the observed
spatial variance
captured by the model
DISSOLVED INORGANIC
CARBON
PHOSPHATE
Parameter
Sensitivity
Implicit function theorem
Jacobian matrix
available in factored
form from Newton
Solver
Phosphate Sensitivity
Parameter Sensitivity
Atmospheric pCO2
Future Work
Proposal with Keith Moore to apply
method to CCSM Ocean model grid
Use Doney et al. (2006)
OCMIP+Iron biogeochemistry
model with prognostic biological
production
Extend method to periodic steady
states i.e. with seasonal cycles.
Example from a periodic column
model (iron replete region)
Spin-up:
Time stepping versus Newton’s
Method