Improving the Algal Bloom Prediction in the North Sea by Ensemble Kalman Filtering in the GEM ...

133 Pages·2013·4.67 MB·English

Delft University of Technology
Faculty of Electrical Engineering, Mathematics and
Computer Science
Delft Institute of Applied Mathematics
Improving the Algal Bloom Prediction
in the North Sea
by Ensemble Kalman Filtering
in the GEM/BLOOM Model
A thesis submitted to the
Delft Institute of Applied Mathematics
in partial fulfillment of the requirements
for the degree
MASTER OF SCIENCE
in
APPLIED MATHEMATICS
by
Elisabeth Geraldine Rens
Delft, the Netherlands
August 2013
Copyright (cid:13)c 2013 by Elisabeth Geraldine Rens. All rights
reserved.

MSc THESIS APPLIED MATHEMATICS
“Improving the Algal Bloom Prediction in the North Sea by
Ensemble Kalman Filtering in the GEM/BLOOM Model”
Elisabeth Geraldine Rens
Delft University of Technology
Daily supervisor Responsible professor
G.Y.H. El Serafy PHD Prof.dr.ir A.W. Heemink
Other thesis committee members
Prof.dr.ir C. Vuik
August 2013 Delft, the Netherlands

Abstract
The ecological state of the North Sea surface water can be indicated by ocean
variablessuchastheChlorophyll-a(Chlfa)concentration. Chlfa istheprincipal
photosynthetic pigment and is common to all phytoplankton and can therefore
be used as a measure of phytoplankton biomass. The GEM/BLOOM model
developed at Deltares is a generic ecological model that simulates transport of
substancesinawatersystemalongwithvariousecologicalprocesses. Thismodel
is able to estimate the Chlfa concentration. Models are always prone to errors
due to assumptions made in the development and the use of numerical approx-
imations. Such errors can be reduced through the use of data assimilation and
thuscansignificantlyimprovetheforecast. TheensembleKalmanfilter(EnKF)
is a generic data assimilation method which is suited for highly nonlinear mod-
els with a large scale. This filter is validated by the use of twin experiments
on the GEM/BLOOM model. It successfully improves the prediction of Chlfa,
but however shows filter divergence in some grid points. The performance is
furtherimprovedbytheuseoftheEnsembleSquareRootFilter(ESRF)witha
localizedanalysis. Finally,applicationofthisfiltertoassimilatingdailyMERIS
remotesensingimagesisexploredandshowstobepromising,butrequiresmore
tuning before it can operate.
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Acknowledgments
The work for this thesis was done at Deltares, an institute for applied research
in the field of water, subsurface and infrastructure. The thesis was part of the
COBIOSprojectthataimstointegratesatelliteproductsandecologicalmodels
into an operational information service on high biomass blooms in Europes
coastal waters.
ItwasagreatopportunityandapleasuretoundertakeaprojectatDeltares
in the second year of my master’s study. I would like to thank Ghada El
Serafy and Arnold Heemink for their support and useful feedback. Also, a
thank you to Sandra Gaytan for her technical support. Furthermore, I would
liketoexpressmygratitudetoAsiaPelcandMartinVerlaanfortheiradviceon
dataassimilation. Also,athankyoutoPeterWilders,fordiscussingmyreport.
Kees Vuik, I think for being in the thesis committee. I also thank the other
students at Deltares who made my stay very pleasant. Finally, a thank you to
my boyfriend, all my family and friends, for greatly supporting me, but also for
making sure that I made time to relax.
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Contents
1 Introduction 10
2 Problem description 12
3 Thesis outline 14
4 Model description 16
4.1 BLOOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2 Key aspects of the model . . . . . . . . . . . . . . . . . . . . . . 19
4.2.1 Chlorophyll-a concentration . . . . . . . . . . . . . . . . . 19
4.2.2 Diffuse Attenuation Coefficient . . . . . . . . . . . . . . . 20
4.3 The North Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5 Observations 24
5.1 MERIS data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2 In situ measurements . . . . . . . . . . . . . . . . . . . . . . . . . 24
6 Data Assimilation 26
6.1 Standard Linear Kalman Filter . . . . . . . . . . . . . . . . . . . 26
6.2 Ensemble Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . 28
6.2.1 Augmented state . . . . . . . . . . . . . . . . . . . . . . . 29
6.2.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . 31
6.2.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . 32
6.3 Ensemble Square Root Filter . . . . . . . . . . . . . . . . . . . . 33
6.3.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . 35
6.4 Relative error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.5 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
6.5.1 Twin experiment . . . . . . . . . . . . . . . . . . . . . . . 36
6.5.2 RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6.5.3 Innovations . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7 Model of the system noise 40
7.1 Squared exponential correlation function . . . . . . . . . . . . . . 40
7.1.1 Approximation . . . . . . . . . . . . . . . . . . . . . . . . 41
7.2 Interpolation of white noise . . . . . . . . . . . . . . . . . . . . . 42
7.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
7.2.2 Choosing the weights. . . . . . . . . . . . . . . . . . . . . 44
7.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
8 Covariance Localization 52
8.1 Localization function . . . . . . . . . . . . . . . . . . . . . . . . . 52
8.1.1 Issues with the EnKF . . . . . . . . . . . . . . . . . . . . 53
8.1.2 Adapted for ESRF . . . . . . . . . . . . . . . . . . . . . . 55
8.1.3 Issues with the ESRF . . . . . . . . . . . . . . . . . . . . 56
8.2 Localized analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . 56
8.2.1 Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
8.2.2 Define constraints . . . . . . . . . . . . . . . . . . . . . . 58
8.3 Choice of localization method . . . . . . . . . . . . . . . . . . . . 59
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9 Noise propagation 60
9.1 Effect on Chlfa . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
9.2 Effect on Chlfa after one day . . . . . . . . . . . . . . . . . . . . 61
9.3 Defining measurement noise . . . . . . . . . . . . . . . . . . . . . 63
10 Twin experiments 66
10.1 Evaluate EnKF . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
10.2 Comparison EnKF/ESRF . . . . . . . . . . . . . . . . . . . . . . 71
10.3 Comparison model system noise . . . . . . . . . . . . . . . . . . . 74
10.4 Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
10.5 Ensemble size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
11 Application to MERIS data 86
11.1 Compare Model with MERIS . . . . . . . . . . . . . . . . . . . . 86
11.2 Added features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
11.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
12 Discussion 96
13 Conclusion 100
14 Recommendations 102
15 References 104
16 Appendix 108
16.1 Extra figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
16.2 List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
16.3 List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
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