The Marginal Particle Filter method for ecosystem models · Marginal PF Conclusions The method of the particle lter takes 4 steps: 1 Initial draw of particles from a probability density

IntroductionParticle FilterMarginal PFConclusions

The Marginal Particle Filter method for ecosystemmodels

June 20, 2016

The Marginal Particle Filter method for ecosystem models


Introduction:

We aim to improve consistency and accuracy of theLPJ-GUESS model by incorporating observations

The method of data assimilation we used in this study iscalled the particle filter



Vegetation structure

and composition

Litter

Soil organic matter

NPP

Soil watersoil hydrology

stomatal

regulation

photosynthesis

plant respiration

leaf & root

phenology

microbial

decomposition

biomass allocation

& growth

reproduction

establishment

mortality

fire

disturbance

leaf, root &

bark turnover

ecosystem statedaily processes annual processes

CO2

CO2

CO2

Vegetation structure

and composition

Litter

Soil organic matter

NPP

Soil watersoil hydrology

stomatal

regulation

photosynthesis

plant respiration

leaf & root

phenology

microbial

decomposition

soil hydrology

stomatal

regulation

photosynthesis

plant respiration

leaf & root

phenology

microbial

decomposition

biomass allocation

& growth

reproduction

establishment

mortality

fire

disturbance

leaf, root,

sapwood turnover

ecosystem statedaily processes annual processes

CO2

CO2

H2OH2O

CO2

temperature, precipitation, radiation, CO2

Leaf longevity

Longevity

Est max

αa

αC3

cton sap

cton root

turn root

soil resp min N



LPJ-GUESS

Prior parameter valuesClimate data

Modelled NEP

Cost function

Observed CO2 flux

Posterior parameter values

Particle filter weighting

New parameter values

Minimum

NOTminimum



The method of the particle filter takes 4 steps:1 Initial draw of particles from a probability density function

(pdf)

Each particle is a set of the process parameters we areoptimizing

2 Run the LPJ-GUESS model for each particle

3 Calculate the weights based on the cost function values

4 From the weights, adjust the pdf for each parameter



The traditional Particle filter suffers from the problem of filterdegeneracy

Tempering is a method of slowing the filter degeneracyadequately in order to avoid falling into local minima

The marginal particle filter fixes the problem of filterdegeneracy by finding the equilibrium between the probabilityof the particles given the observation p(x |y) and the likelihoodof the particle from the re-sampled distribution q(x |y , xi−1)



The marginal particle filter uses this new formula for the weights:

w̃i =p(xi |yi )bi

q(xi |yi , xi−1)(1)

where p(xi |yi ) is the probability of the particles given theobservation and q(x |y , xi−1) is the likelihood of the particle fromthe re-sampled distribution q. The weights are normalized beforethe next set of samples are drawn. Set a value for bi , such that∑M

i=1 bi = 1, where M is the number of iterations



Figure: The median and range of particles for four parameters using themarginal particle filter. The red thick line is the twin experiment solutionand the red dotted lines represent the solution uncertainty.



Figure: The max,min and median cost function with each iteration. Thetraditional (left) and marginal (right).



Data assimilation techniques can improve parameter estimateswithin LPJ-GUESS by optimizing against observations.

The traditional particle filter suffers from filter degeneracy andoften finds local minima.

The Marginal particle filter is much more robust at avoidinglocal minima, while still being very efficient.

The results from the marginal particle filter are moreconsistently closer to the correct answer. However, neithermethod can achieve a perfect solution.



Any questions?



Figure: The prior distribution is in blue, the particles and in red and theobservation is in black.



Figure: The prior distribution is in blue, the particles and in red, theposterior distribution is in green and the observation is in black.



Figure: The new prior distribution is in blue, the re-sampled particles andin red and the observation is in black.



Figure: The new prior distribution is in blue, the re-sampled particles andin red, the new posterior distribution is in green and the observation is inblack.



The twin experiment is:

Standard test of the technical setup

Run the particle filter model for the first time

Take the output of this run and call it observations

Perturb the prior values from the run before

Run the particle filter again using the just made observations

The filter should be able to recover the initial parameter values



Figure: The median and range of particles for four parameters using thetraditional particle filter. The red thick line is the twin experimentsolution and the red dotted lines represent the solution uncertainty.



Bayes@Lund 2014 Conference (10th of April)Introduction to faculty (9th of May 2014) - 0.5Norunda field course (10-17 May 2014)LUCCI R3I workshop (31st of March 2014)ICOS-NEON Greenhouse Gas Data training workshop (8-13Sept 2014, Aix-en-Provence)Data Assimilation in Biogeochemical Cycles Autumn school(20-27 Sept 2014, Trieste)Introduction to PhD (January 2015)EGU (European Geosciences Union)LUCCI scientific writing course (27-28 January 2015)Global environmental governanceClimbeco summer workshopClimbeco winter workshopScience communicationParis conferenceResearch visit in Reading



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The Marginal Particle Filter method for ecosystem models · Marginal PF Conclusions The method of the particle lter takes 4 steps: 1 Initial draw of particles from a probability density