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A systematic method of parameterisation estimation using data assimilation Cover

A systematic method of parameterisation estimation using data assimilation

Volume 68 (2016): Issue 1

By: Matthew Lang, Peter Jan Van Leeuwen and Philip Browne

Open Access

|Dec 2016

Figures & tables

Figures & Tables

A single timestep from the data assimilation trajectory from timestep t−1 to t. Step 3 defines $\tilde{x}$ as a single model timestep from the data assimilation trajectory at timestep t−1 using the model f with the prior parameterisation G ^b.

Estimated parameter values from state augmentation, for the parameters described in eq. (38).

Table 1. Analysis parameterisations from parameterisation estimation method for different observation densities

Observations at all space-time points

G^{a} = (- 1.5101 \pm 0.0408) \frac{\partial x}{\partial s} + (1.0313 \pm 0.0741) x \frac{\partial x}{\partial s}

Observations at every three gridpoints and every timestep

G^{a} = (- 1.5216 \pm 0.0555) \frac{\partial x}{\partial s} + (0.9783 \pm 0.0902) x \frac{\partial x}{\partial s} + (0.0074 \pm 0.0967) \frac{\partial^{2} x}{\partial s^{2}} + (- 0.0048 \pm 0.1695) x^{2} \frac{\partial^{2} x}{\partial s^{2}}

Observations at every gridpoint and every three timesteps

G^{a} = (- 1.4146 \pm 0.0484) \frac{\partial x}{\partial s} + (0.8492 \pm 0.0872) x \frac{\partial x}{\partial s}

Observations at every three gridpoints and every three timesteps

G^{a} = (- 1.4683 \pm 0.0541) \frac{\partial x}{\partial s} + (1.0149 \pm 0.1129) x \frac{\partial x}{\partial s} + (0.0035 \pm 0.1148) x \frac{\partial^{2} x}{\partial s^{2}}

Table 2. Analysis parameterisations from parameterisation estimation method for different magnitudes of observation error relative to model error

R=0.005²I such that Q=4R

G^{a} = (- 1.5101 \pm 0.0408) \frac{\partial x}{\partial s} + (1.0313 \pm 0.0741) x \frac{\partial x}{\partial s}

R=0.01²I such that Q=R

G^{a} = (- 1.4651 \pm 0.0423) \frac{\partial x}{\partial s} + (1.0217 \pm 0.0778) x \frac{\partial x}{\partial s}

R=0.02²I such that Q = 0.25R

G^{a} = (- 1.4472 \pm 0.0481) \frac{\partial x}{\partial s} + (1.0055 \pm 0.0847) x \frac{\partial x}{\partial s} + (- 0.0023 \pm 0.0742) \frac{\partial^{2} x}{\partial s^{2}}

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DOI: https://doi.org/10.3402/tellusa.v68.29012 | Journal eISSN: 3035-9554

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Language: English

Page range: 29012 - 29012

Submitted on: Jun 30, 2015

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Accepted on: Jan 11, 2016

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Published on: Dec 1, 2016

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

Keywords:

data assimilation,

parameterisation estimation,

parameter estimation

© 2016 Matthew Lang, Peter Jan Van Leeuwen, Philip Browne, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

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