An Efficient Ensemble Data Assimilation Approach To Deal With Range Limited Observation

Transcription

1 An Efficient Ensemble Data Assimilation Approach To Deal With Range Limited Observation A. Shah 1,2, M. E. Gharamti 1, L. Bertino 1 1 Nansen Environmental and Remote Sensing Center 2 University of Bergen 11 th International EnKF Workshop June 2, 216 1

2 Outline Motivation Range Limited Observations (RLO): Methodology and Algorithm Numerical Experiments Conclusion 2

3 Motivation Many available measurement in environmental systems are defined within certain interval. To use the qualitative information available from the range limited observations. Very few studies carried out dealing this issue Borup et. al., (215) 3

4 Range limited Observations Photo : Earth Imaging Journal 4

5 Methodology and Algorithm Bayesian Rule p( x y) = p ( x )p( y x) p( y) Borup et. al., (215): Ensemble Partial Updating (EnPU) for RLO EnPU will allow us to use qualitative information about data i.e., the posterior will be p( x k y quant, y ) qual where y quant and y qual are quantitative and qualitative observation respectively 5

6 Figure : (Borup et. al., 215) With and without partial updating when the measurement gauge has lower observation limit 6

7 Partial Ensemble Kalman Filter (PEnKF) OR-observation Create virtual observation at threshold limit Data likelihood for perturbing observations Two Piece Gaussian distribution (Fechner s Kollektivmasslehre, 1897) One of the observation variance in 2-piece Gaussian s or = p* ( Hx f ) where p is positive real number 7

8 Probability Probability Cont.. Posterior when the prior is in-range ï ( ) µ p(x k)p(y quant x k ) í p x k y quant, y qualit ì îï p(x k )p(y qualit x k ) Bayesian Representation Prior Obs. Likelihood Prior Obs. Prior Likelihood Posterior Threshold State value 8

9 Check if y isout of range No Update x i f as it isdoneinenkf Yes Check if Hx i f is within range No Updatethe X i f settinginnovationtozero Yes UpdateX i f with perturb observation generated from 2-piece Gaussian Repeat from the step 2 for all all the members Repeat from the step 2 for all the members 9

10 Numerical Experiments EnKF, PEnKF and EnKF-ignored DA methods are tested under the framework of twin experiment. Model Lorenz 96 with configuration as below Number of Ensemble 1 dt -.5 (~6 hours) Total time of integration is 5 Years Model error introduced by using wrong forcing s obs =1 1

11 Cont.. Experiments for Sensitivity to Number of observation Observation frequency Threshold limit Model error Diagnostics tools: Root Mean Square Error Average Ensemble Spread Observation Influence Rank Histograms 11

12 RMSE RMSE and Avg. Ensemble Spread RMSE-Analysis for EnKF, PEnKF and EnKF-Ignored with full obs. network EnKF PEnKF EnKF-ignored % of observations are out of range on an average for total time of integration12

13 RMSE Avg. RMSE for EnKF, PEnKF and EnKF-Ignored for different observation frequency 2.5 EnKF PEnKF EnKF-Ignored Observation frequency (Time step) 13

14 RMS and AESP AESP Average Ensemble Spread Analysis for PEnKF and EnKF-(Ignored) Snap-shot of time series of RMSE and AESP of Analysis AESP-PEnKF AESP-EnKF(Ign) RMSE-PEnKF AESP-PEnKF RMSE-EnKF(Ign) AESP-EnKF(Ign) Time Time 14

15 tr(kh) T /No.of obs Observation Influence.45.4 Average Observation influence in PEnkF All Observation OR-Observation Time 15

16 P(rank) P(rank) P(rank) P(rank) P(rank) P(rank) Rank Histogram(Reliability).6 PEnKF-all observation.1 PEnKF- Half observation.6 PEnKF- 13 observations Rank Rank Rank.6 EnKF(Ignored) all observation.1 EnKF(Ignored) - Half observation.6 EnKF(Ign)-13 observations Rank Rank Rank 16

17 RMSE Sensitivity-Model Error 3.5 RMSE Analysis for strong model error PEnKF EnKF-Ignored Time 17

18 Conclusion and future work Adding qualitative information with PEnKF Improve quality of forecast Reduce uncertainty Improves reliability of forecast Adding strong model error deteriorates the performance of the proposed DA scheme Implementation with some real world model and data set To investigate further for some possible improvement if possible 18

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