DATA ASSIMILATION AND MODEL ERROR ESTIMATION Dusanka Zupanski Cooperative Institute for Research in...
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DATA ASSIMILATION AND DATA ASSIMILATION AND MODEL ERROR ESTIMATION MODEL ERROR ESTIMATION Dusanka Zupanski Dusanka Zupanski Cooperative Institute for Research in the Cooperative Institute for Research in the Atmosphere Atmosphere Colorado State University Colorado State University Fort Collins, CO 80523-1375 Fort Collins, CO 80523-1375 Oregon State University Physical Oceanography Seminar Series 27 April 2004 ftp://ftp.cira.colostate.edu/Zupanski/presentations ftp://ftp.cira.colostate.edu/Zupanski/manuscripts
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Transcript of DATA ASSIMILATION AND MODEL ERROR ESTIMATION Dusanka Zupanski Cooperative Institute for Research in...
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DATA ASSIMILATION AND MODEL ERROR ESTIMATION
Dusanka ZupanskiCooperative Institute for Research in the AtmosphereColorado State University Fort Collins, CO 80523-1375Oregon State University Physical Oceanography Seminar Series27 April 2004ftp://ftp.cira.colostate.edu/Zupanski/presentationsftp://ftp.cira.colostate.edu/Zupanski/manuscripts
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OUTLINE:
Data assimilation research pursued at CIRA
Approaches: variational and ensemble (EnsDA)
Model error estimation
Experimental results
Summary and future work
Dusanka Zupanski, CIRA/[email protected]
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DATA ASSIMILATION RELATED RESEARCH
Basic development of data assimilation- Variational methods (T.Vukicevic, M. Zupanski, D. Zupanski)- Ensemble (EnsDA) methods (M. Zupanski, D. Zupanski)- Non-Gaussian probability distributions (M. Zupanski) - Model error estimation (D. Zupanski)
Specific applications- 4DVAR cloud state estimation (T.Vukicevic, M. Sengupta)- 4DVAR soil moisture estimation (A. Jones, T. Vukicevic)- 4DVAR carbon cycle studies (T. Vukicevic; D. Ojima CSU/NREL; D. Schimel NCAR; S. Denning CSU/ATS; D. Zupanski)- EnsDA application to NCEPs global (GFS) model (M. Zupanski) - EnsDA application in GOES-R risk reduction (M. DeMaria, D. Zupanski)- EnsDA application to NASAs GEOS model (D. Zupanski)
Dusanka Zupanski, CIRA/[email protected]
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DATA ASSIMILATION RELATED RESEARCH
Research funding- DoD (CG/AR), NOAA (NESDIS, JCSDA, THORPEX), NSF, NASA
-----------------------Data assimilation research at CIOSS and COAS- (A. Bennett, R. Miller, G. Egbert, B. Chua, A. Kurapov)
Dusanka Zupanski, CIRA/[email protected]
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OUTLINE:
Data assimilation research pursued at CIRA
Approaches: variational and ensemble (EnsDA)
Model error estimation
Experimental results
Summary and future work
Dusanka Zupanski, CIRA/[email protected]
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DATA ASSIMILATION APPROACHES
Variational- Weak constraint 4DVAR (including model bias estimation)- RAMS mesoscale atmospheric model- Developed after NCEPs Eta model 4DVAR- WRF 3DVAR observation operators for conventional atmospheric observations- GOES visible and IR radiances (all weather)- Non-linear operators (M, H) are usedEnsDA- Maximum Likelihood Ensemble Filter (MLEF)- Model error estimation (model bias, empirical parameters)- Optimal solution obtained by minimizing a cost function- KdVB model, NASAs GEOS column model- Adjoint model not needed (non-linear and discontinuous processes handled well)- Non-linear operators (M, H) are usedDusanka Zupanski, CIRA/[email protected](MLEF is described in M. Zupanski, submitted to MWR, 2004)
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(KF)(MLEF) (4DVAR and MLEF)
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OUTLINE:
Data assimilation research pursued at CIRA
Approaches: variational and ensemble (EnsDA)
Model error estimation
Experimental results
Summary and future work
Dusanka Zupanski, CIRA/[email protected]
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Model error estimationDusanka Zupanski, CIRA/[email protected] estimation is a special case of state augmentation approach!x0 initial conditions ; bk model biasn model time step; k analysis cycle; a - constant State augmentation approach (following Zupanski, MWR 1997)
- model state (x ) augmented to include model error ( )- estimate optimal initial conditions and a serially correlated model error (boundary conditions error is a part of model error) Assimilation of real observations
- model error cannot be neglected- use information from observations to learn about model error(Assumption: 0 = bk-1)
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Relation between of first order Markov process variable and the time decorrelation length L*t, for time separation k*tFor =0.80:k=10 L=22.6k=20 L=60k=30 L=101.2For =0.70:k=10 L=18.86k=20 L=45.1k=30 L=72.38With assuming n 1:
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OUTLINE:
Data assimilation research pursued at CIRA
Approaches: variational and ensemble (EnsDA)
Model error estimation
Experimental results (4DVAR method)
Summary and future work
Dusanka Zupanski, CIRA/[email protected]
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DATA ASSIMILATION APPROACHES
Variational- Weak constraint 4DVAR (including model bias estimation)- RAMS mesoscale atmospheric model- Developed after NCEPs Eta model 4DVAR- WRF 3DVAR observation operators for conventional atmospheric observations- GOES visible and IR radiances (all weather)- Non-linear operators (M, H) are usedEnsDA- Maximum Likelihood Ensemble Filter (MLEF)- Model error estimation (model bias, empirical parameters)- Optimal solution obtained by minimizing a cost function- KdVB model, NASAs GEOS column model- Adjoint model not needed (non-linear and discontinuous processes handled well)- Non-linear operators (M, H) are usedDusanka Zupanski, CIRA/[email protected](MLEF is described in M. Zupanski, submitted to MWR, 2004)
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Dusanka Zupanski, CIRA/[email protected] 4DVAR: Surface pressure model error time evolution(every 2-h over a 12-h data assimilation interval) From Zupanski et al. 2004 (submitted to QJRMS)
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Dusanka Zupanski, CIRA/[email protected] 4DVAR: Exner function model error time evolution (lev=5km), every 2-h From Zupanski et al. 2004 (submitted to QJRMS)
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Sample of results from 4DVAR cirrus cloud study(21 March 2000, RAMS model resolution 6km/84layers, 1-h assimilation window)Tomislava Vukicevic, CIRA/[email protected](Vukicevic et al., submitted to MWR 2004)
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BRIGHTNESS TEMPERATURE AT 10.7
Model after assimilation
GOES 10 observations
Model before assimilation
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Comparison with independent data: ARM sounding of TGood convergenceModel domain bias eliminated Error variance significantly reduced TemperatureTemperatureIteration numberIteration numberTomislava Vukicevic, CIRA/[email protected]
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COST FUNCTIONS
DOMAIN AVERAGE TB ERRORS (K)
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observations
model
Temperature
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Vertical extent of cirrus cloud and radar reflectivity values in good agreement with the observations within 1 h window of assimilation Tomislava Vukicevic, CIRA/[email protected]
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dz~5 km
dz~5 km
1 h assimilation window
COMPARISON WITH ARM RADAR
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Andy Jones, CIRA/[email protected](Jones et al., J. Hydrometeor., 2004)
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Objective: Measure and Predict Deep Soil Moisture
Satellite
Data Assimilation and ModelingPhysically linksthe systemtogether inspace and time
Soil Moisture
Physical Hydrological Models
1DVAR Water Vapor Profiling
Channel Flow / Erosion / Deposition
Emissivity
Energy and Mass Flux
SpatialDataFilters
The Deep Soil Moisture Problem
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Andy Jones, CIRA/[email protected](Jones et al., J. Hydrometeor., 2004)
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MWLSM Observational Operator
The passive microwave observational operator (including the adjoint) is completeMicrowave Land Surface Model (MWLSM)Based on 6 and 10 GHz passive microwave dataAfter Njoku (1999) (AMSR land algorithms)Applicable to a new generation of passive microwave imagers: AQUAs AMSR-E (launched May 4, 2002)ADEOS-IIs AMSR (launched Dec. 14, 2002)WindSat (launched Jan. 6, 2003)NPOESS C1 CMIS (~ 2009)
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OUTLINE:
Data assimilation research pursued at CIRA
Approaches: variational and ensemble (EnsDA)
Model error estimation
Experimental results (EnsDA method)
Summary and future work
Dusanka Zupanski, CIRA/[email protected]
-
DATA ASSIMILATION APPROACHES
Variational- Weak constraint 4DVAR (including model bias estimation)- RAMS mesoscale atmospheric model- Developed after NCEPs Eta model 4DVAR- WRF 3DVAR observation operators for conventional atmospheric observations- GOES visible and IR radiances (all weather)- Non-linear operators (M, H) are usedEnsDA- Maximum Likelihood Ensemble Filter (MLEF)- Model error estimation (model bias, empirical parameters)- Optimal solution obtained by minimizing a cost function- KdVB model, NASAs GEOS column model- Adjoint model not needed (non-linear and discontinuous processes handled well)- Non-linear operators (M, H) are usedDusanka Zupanski, CIRA/[email protected](MLEF is described in M. Zupanski, submitted to MWR, 2004)
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Maximum Likelihood Ensemble Filter (MLEF) Data assimilation with KdVB model (quadratic obs operator, 10 ensembles, 10 obs)Impact of assimilationAnalysis error covarianceNO OBSMLEFModel dynamics helps in localization of analysis error covariance !H(x)=x2(M. Zupanski, submitted to MWR, 2004)
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Cycle 1
Cycle 4
Chart7
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0.0537930920.0087595491
0.053138390.0088351622
Analysis cycle
RMS error
IMPACT OF MLEF ASSIMILATION(quadratic observation operator - 10 obs)
Sheet1
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Sheet1
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Analysis cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - 10 obs)
Sheet2
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00
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00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Analysis cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - 10 obs)
Sheet3
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
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00
00
00
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00
00
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00
00
00
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00
00
00
00
00
00
00
00
00
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00
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00
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00
00
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00
00
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00
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00
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00
00
00
00
00
00
00
00
00
00
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00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Analysis cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - 5 obs)
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
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00
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00
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00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Assimilation cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - in-situ)
-
MLEF data assimilation with KdVB model Impact of minimizationCost function minimization reduces RMS errorNO MINIMIZATIONMLEFAnalysis statistics is adequate in both algorithms, analysis quality differs
Chart1
0.0484229950.064137988
0.0404536680.026752706
0.0304223970.023376229
0.037938070.018404556
0.039595480.017404816
0.0360433580.015223663
0.0286418390.014906229
0.0240367170.014914598
0.0225677970.015680101
0.0279478360.012393903
0.0327213430.012583977
0.034757490.015594674
0.0363861920.017688023
0.037560570.016313773
0.0385411830.015531515
0.0387652280.014807823
0.0383679120.014799669
0.0390245930.013992457
0.038695750.016112672
0.0379771450.015992675
0.037886140.016043963
0.0384745740.016468597
0.0385026650.017527988
0.0381640860.018408885
0.0373965050.016942574
0.0364387490.017955713
0.0361410740.017427483
0.0363328270.018292562
0.0366005750.018372096
0.0367409320.018957219
0.036820130.017692797
0.0367698670.017250376
0.0364782380.0152072
0.0360376410.014008548
0.0355161450.013623545
0.0350396610.012454848
0.0345747040.01163782
0.0343647360.01166286
0.0342271380.012080718
0.0340981340.012146825
0.0339327450.012811118
0.0337602230.01264528
0.0336143370.012923679
0.0334772730.01284966
0.0333040480.012753474
0.0331696560.012822807
0.0329516290.01296764
0.0327751020.013139354
0.0326291750.013417727
0.0325163870.013497626
0.0324723150.01322355
0.0322700860.013201417
0.0318877430.013522995
0.0314424660.013571249
0.0310071440.012355702
0.030732350.011764309
0.0304198310.011536763
0.0300120450.011460035
0.0295710090.011556734
0.0290856250.011547076
0.0285379840.011822649
0.0280959490.011992046
0.0276158190.011972337
0.0271715350.011787844
0.0268507360.011772965
0.0266566320.011527584
0.0264583110.011730461
0.0261547370.011689939
0.0259175560.01132517
0.0258083060.011130161
0.0256170650.011137977
0.0254249690.011098058
0.0252639960.010909302
0.0250912380.010526047
0.0249016140.010371106
0.0246983580.010371389
0.0244810870.010864973
0.024271240.010601288
0.0240568660.01029098
0.0238355660.010344033
0.0236191890.010204922
0.0233978560.010249643
0.0231711030.0098870239
0.0229528280.0098223915
0.0227290990.0096520844
0.0225010420.0099581871
0.0222868230.0098845749
0.022082360.0095531645
0.0218839550.0095514393
0.0216903020.0096297379
0.0215160970.0095017862
0.0213540510.0093603725
0.0212047080.0092445679
0.0210655710.0092765579
0.0209333320.0092260122
0.0207784030.0090771551
0.0206651350.0089301834
0.0205798170.0088611546
0.0204574890.0087595491
0.0203551410.0088351622
Analysis cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - 10 obs)
Sheet1
8.08E-024.84E-026.41E-025.92E-024.81E-024.84E-024.34E-02
9.61E-024.05E-022.68E-025.61E-025.13E-026.33E-024.54E-02
1.05E-013.04E-022.34E-025.93E-023.46E-025.36E-023.79E-02
1.05E-013.79E-021.84E-026.53E-024.57E-025.69E-025.04E-02
1.12E-013.96E-021.74E-024.70E-023.62E-026.77E-026.09E-02
1.31E-013.60E-021.52E-025.31E-023.08E-028.25E-026.82E-02
1.52E-012.86E-021.49E-024.69E-023.33E-028.76E-026.74E-02
1.59E-012.40E-021.49E-023.80E-022.67E-028.71E-026.69E-02
1.66E-012.26E-021.57E-024.77E-022.64E-028.96E-026.84E-02
1.73E-012.79E-021.24E-023.96E-023.19E-028.98E-026.77E-02
1.73E-013.27E-021.26E-023.71E-022.16E-028.82E-026.89E-02
1.72E-013.48E-021.56E-023.34E-022.02E-028.92E-027.16E-02
1.68E-013.64E-021.77E-022.91E-022.52E-028.78E-027.29E-02
1.65E-013.76E-021.63E-022.90E-022.42E-028.70E-027.37E-02
1.61E-013.85E-021.55E-022.71E-022.31E-028.54E-027.37E-02
1.56E-013.88E-021.48E-022.74E-021.81E-027.42E-026.21E-02
1.51E-013.84E-021.48E-023.18E-021.87E-026.98E-026.06E-02
1.48E-013.90E-021.40E-023.22E-021.87E-025.80E-025.93E-02
1.45E-013.87E-021.61E-023.27E-022.16E-025.51E-026.00E-02
1.40E-013.80E-021.60E-023.22E-022.35E-025.51E-026.16E-02
1.36E-013.79E-021.60E-023.42E-022.37E-025.41E-026.12E-02
1.34E-013.85E-021.65E-023.29E-022.30E-025.45E-026.09E-02
1.33E-013.85E-021.75E-023.27E-022.49E-025.53E-026.14E-02
1.31E-013.82E-021.84E-023.16E-022.53E-025.55E-026.16E-02
1.28E-013.74E-021.69E-023.19E-022.73E-025.50E-026.09E-02
1.24E-013.64E-021.80E-023.37E-022.81E-025.41E-025.96E-02
1.21E-013.61E-021.74E-023.40E-022.67E-025.34E-025.82E-02
1.19E-013.63E-021.83E-023.40E-022.65E-025.33E-025.76E-02
1.18E-013.66E-021.84E-023.30E-022.67E-025.36E-025.68E-02
1.17E-013.67E-021.90E-023.16E-022.74E-025.42E-025.67E-02
1.17E-013.68E-021.77E-022.89E-022.65E-025.47E-025.67E-02
1.17E-013.68E-021.73E-022.85E-022.74E-025.52E-025.62E-02
1.16E-013.65E-021.52E-022.78E-022.66E-025.53E-025.58E-02
1.15E-013.60E-021.40E-022.75E-022.51E-025.57E-025.50E-02
1.13E-013.55E-021.36E-022.89E-022.49E-025.58E-025.42E-02
1.11E-013.50E-021.25E-022.91E-022.37E-025.51E-025.34E-02
1.09E-013.46E-021.16E-023.03E-022.43E-025.44E-025.28E-02
1.07E-013.44E-021.17E-023.14E-022.53E-025.43E-025.20E-02
1.06E-013.42E-021.21E-023.05E-022.47E-025.46E-025.14E-02
1.04E-013.41E-021.21E-023.08E-022.62E-025.47E-025.12E-02
1.03E-013.39E-021.28E-023.00E-022.64E-025.49E-025.11E-02
1.01E-013.38E-021.26E-022.96E-022.67E-025.47E-025.11E-02
9.99E-023.36E-021.29E-022.91E-022.67E-025.40E-025.10E-02
9.84E-023.35E-021.28E-022.88E-022.67E-025.43E-025.10E-02
9.69E-023.33E-021.28E-022.92E-022.69E-025.15E-025.07E-02
9.55E-023.32E-021.28E-022.96E-022.68E-025.16E-025.08E-02
9.43E-023.30E-021.30E-022.96E-022.67E-025.07E-025.05E-02
9.32E-023.28E-021.31E-023.01E-022.69E-024.95E-024.97E-02
9.22E-023.26E-021.34E-023.00E-022.70E-024.93E-024.99E-02
9.13E-023.25E-021.35E-022.97E-022.71E-024.79E-024.96E-02
9.04E-023.25E-021.32E-022.99E-022.74E-024.73E-024.94E-02
8.95E-023.23E-021.32E-023.04E-022.78E-024.68E-024.91E-02
8.84E-023.19E-021.35E-023.12E-022.88E-024.61E-024.89E-02
8.74E-023.14E-021.36E-023.14E-022.88E-024.61E-024.89E-02
8.62E-023.10E-021.24E-023.17E-022.86E-024.58E-024.87E-02
8.51E-023.07E-021.18E-023.19E-022.82E-024.54E-024.84E-02
8.39E-023.04E-021.15E-023.19E-022.81E-024.50E-024.81E-02
8.27E-023.00E-021.15E-023.19E-022.77E-024.46E-024.76E-02
8.16E-022.96E-021.16E-023.15E-022.73E-024.41E-024.72E-02
8.06E-022.91E-021.15E-023.17E-022.71E-024.36E-024.69E-02
7.96E-022.85E-021.18E-023.16E-022.72E-024.32E-024.65E-02
7.86E-022.81E-021.20E-023.14E-022.71E-024.28E-024.61E-02
7.78E-022.76E-021.20E-023.07E-022.73E-024.24E-024.57E-02
7.69E-022.72E-021.18E-023.08E-022.77E-024.22E-024.55E-02
7.61E-022.69E-021.18E-023.06E-022.81E-024.19E-024.52E-02
7.54E-022.67E-021.15E-023.04E-022.87E-024.16E-024.48E-02
7.47E-022.65E-021.17E-023.02E-022.90E-024.13E-024.44E-02
7.40E-022.62E-021.17E-022.98E-022.92E-024.13E-024.45E-02
7.33E-022.59E-021.13E-022.95E-022.90E-024.09E-024.43E-02
7.27E-022.58E-021.11E-022.97E-022.97E-024.02E-024.31E-02
7.21E-022.56E-021.11E-022.96E-022.99E-023.99E-024.32E-02
7.15E-022.54E-021.11E-022.93E-022.96E-023.97E-024.36E-02
7.09E-022.53E-021.09E-022.89E-022.91E-023.97E-024.34E-02
7.03E-022.51E-021.05E-022.91E-022.91E-023.91E-024.35E-02
6.97E-022.49E-021.04E-022.92E-022.91E-023.86E-024.29E-02
6.90E-022.47E-021.04E-022.94E-022.91E-023.77E-024.16E-02
6.84E-022.45E-021.09E-022.95E-022.90E-023.73E-024.11E-02
6.77E-022.43E-021.06E-022.98E-022.90E-023.70E-024.11E-02
6.70E-022.41E-021.03E-022.98E-022.90E-023.69E-024.10E-02
6.64E-022.38E-021.03E-022.99E-022.90E-023.63E-024.05E-02
6.57E-022.36E-021.02E-023.00E-022.90E-023.60E-024.02E-02
6.50E-022.34E-021.02E-023.00E-022.89E-023.56E-023.97E-02
6.43E-022.32E-029.89E-032.99E-022.89E-023.50E-023.90E-02
6.36E-022.30E-029.82E-032.98E-022.88E-023.48E-023.91E-02
6.29E-022.27E-029.65E-032.96E-022.87E-023.44E-023.87E-02
6.22E-022.25E-029.96E-032.95E-022.87E-023.41E-023.84E-02
6.15E-022.23E-029.88E-032.94E-022.88E-023.37E-023.80E-02
6.09E-022.21E-029.55E-032.91E-022.86E-023.33E-023.75E-02
6.02E-022.19E-029.55E-032.87E-022.84E-023.29E-023.72E-02
5.96E-022.17E-029.63E-032.85E-022.84E-023.26E-023.69E-02
5.89E-022.15E-029.50E-032.83E-022.84E-023.23E-023.66E-02
5.83E-022.14E-029.36E-032.80E-022.82E-023.21E-023.64E-02
5.77E-022.12E-029.24E-032.76E-022.80E-023.18E-023.62E-02
5.70E-022.11E-029.28E-032.73E-022.79E-023.16E-023.60E-02
5.64E-022.09E-029.23E-032.72E-022.80E-023.13E-023.58E-02
5.58E-022.08E-029.08E-032.71E-022.79E-023.11E-023.56E-02
5.51E-022.07E-028.93E-032.68E-022.77E-023.09E-023.54E-02
5.44E-022.06E-028.86E-032.68E-022.77E-023.07E-023.51E-02
5.38E-022.05E-028.76E-032.65E-022.73E-023.05E-023.50E-02
5.31E-022.04E-028.84E-032.64E-022.72E-023.03E-023.48E-02
Sheet1
Analysis cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - 10 obs)
Sheet2
Analysis cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - 10 obs)
Sheet3
Analysis cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - 5 obs)
Assimilation cycle
RMS error
IMPACT OF MINIMIZATION(quadratic observation operator - in-situ)
-
WITH MINIMIZATION
WITHOUT MINIMIZATION
Chart1
0.86670361
0.97027597
0.62969151
0.78396111
0.73052359
0.91867819
0.82639322
1.0477682
0.96907196
1.1541603
0.640407090.96304188
1.05997550.99592609
0.702469250.98805437
1.15300321.0118017
0.801769161.0342535
1.06783561.0556139
1.01721931.0520256
1.2833371.0417601
0.828920941.0375098
0.926767441.0402831
0.88190681.0326647
1.5243871.0507648
0.812842181.0459299
1.10463891.0619204
1.2329941.0697919
1.15773031.0803025
0.846912191.0893719
0.621085171.096189
0.962762071.0673462
1.02453611.0596133
1.00179151.0568584
1.00241241.0589327
0.963277911.0192856
1.02227831.0087295
1.3104330.98836832
1.01198160.98849735
1.24922390.99093122
1.15356310.98277836
0.706479981.0021175
0.674262621.0207072
0.871669861.0203385
0.923388581.0039814
0.731443981.021404
0.601722291.0264205
0.697416971.029195
1.23557411.0143019
1.20640721.0264537
0.683854531.0007818
1.00786840.98873005
1.33455661.0097835
1.01716171.0292978
0.674648711.0342903
1.35086641.0357469
1.06360471.0553051
1.07777111.076269
1.01257281.0970346
1.25501741.0765915
0.735785441.0647923
0.912528421.0805978
1.12754891.076061
1.06455061.038546
0.971518991.0357383
0.952520081.0459856
1.12260531.0409114
1.02100171.0475429
1.11272861.0508976
0.826711651.0424861
0.970424461.038267
0.999963381.0482174
0.917133711.0458254
0.584253881.0292622
0.961009791.0299439
0.879595471.0599216
1.24938241.0670848
1.19623581.0599345
1.1448651.0631802
0.844339181.0542327
1.17063671.0571914
0.934791661.0573226
0.864689641.0762106
0.796286541.1009463
1.07818681.1275409
1.57107191.1148722
1.09578511.1075162
0.979595951.0750153
1.08591651.061643
0.933776281.0541902
0.885885811.0689025
0.973050591.0615562
1.37772121.0671631
1.41184881.0239285
1.11614850.98411427
0.70763388
0.73247271
0.5993679
0.92878923
0.99580975
1.1385863
1.0237093
1.0469282
Analysis cycle
INNOVATION c2 TEST(quadratic obs operator + minimization)
Sheet1
8.67E-01
9.70E-01
6.30E-01
7.84E-01
7.31E-01
9.19E-01
8.26E-01
1.05E+00
9.69E-01
1.15E+00
6.40E-019.63E-01
1.06E+009.96E-01
7.02E-019.88E-01
1.15E+001.01E+00
8.02E-011.03E+00
1.07E+001.06E+00
1.02E+001.05E+00
1.28E+001.04E+00
8.29E-011.04E+00
9.27E-011.04E+00
8.82E-011.03E+00
1.52E+001.05E+00
8.13E-011.05E+00
1.10E+001.06E+00
1.23E+001.07E+00
1.16E+001.08E+00
8.47E-011.09E+00
6.21E-011.10E+00
9.63E-011.07E+00
1.02E+001.06E+00
1.00E+001.06E+00
1.00E+001.06E+00
9.63E-011.02E+00
1.02E+001.01E+00
1.31E+009.88E-01
1.01E+009.88E-01
1.25E+009.91E-01
1.15E+009.83E-01
7.06E-011.00E+00
6.74E-011.02E+00
8.72E-011.02E+00
9.23E-011.00E+00
7.31E-011.02E+00
6.02E-011.03E+00
6.97E-011.03E+00
1.24E+001.01E+00
1.21E+001.03E+00
6.84E-011.00E+00
1.01E+009.89E-01
1.33E+001.01E+00
1.02E+001.03E+00
6.75E-011.03E+00
1.35E+001.04E+00
1.06E+001.06E+00
1.08E+001.08E+00
1.01E+001.10E+00
1.26E+001.08E+00
7.36E-011.06E+00
9.13E-011.08E+00
1.13E+001.08E+00
1.06E+001.04E+00
9.72E-011.04E+00
9.53E-011.05E+00
1.12E+001.04E+00
1.02E+001.05E+00
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Innovation c2 test(quadratic observation operator + MLEF)
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PDF
INNOVATION HISTOGRAM(quadratic obs operator + minimization)
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PDF
Innovation histogram(quadratic observation operator + MLEF)
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PDF
INNOVATION HISTOGRAM(quadratic obs operator + NO minimization)
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PDF
INNOVATION HISTOGRAM
Sheet2
Sheet3
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Analysis cycle
INNOVATION c2 TEST(quadratic obs operator + NO minimization)
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Analysis cycle
INNOVATION c2 TEST(quadratic obs operator + NO minimization)
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Sheet3
-
EnsDA Experiments with KdVB model (PARAMETER estimation impact)10 obs101 obsINCORRECTDIFFUSIONCORRECTDIFFUSIONPARAMETERESTIMATION
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PDF
Innovation histogram(Parameter etimation 10 ens, 10 obs)
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PDF
Innovation histogram(Parameter etimation 10 ens, 10 obs)
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PDF
Innovation histogram(Incorrect diffusion, 10 ens, 101 obs)
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PDF
Innovation histogram(Incorrect diffusion, 10 ens, 101 obs)
Sheet2
Sheet3
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0.0175327530.034653468
0.0224002170.040594058
0.0283342170.036633663
0.0354835870.046534653
0.0439947320.055445547
0.0540046310.064356441
0.065632410.073267326
0.0789701370.0960396
0.0940728760.10792079
0.110948920.15445543
0.129550390.13762376
0.149765390.17425742
0.171411990.18613862
0.194235250.21584158
0.217907380.24059405
0.242032070.23564358
0.266152720.26930692
0.289764980.25643563
0.312333110.27920792
0.333309130.33366337
0.352154590.34950495
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0.381484510.34851484
0.391141870.40693069
0.397053190.40198021
0.399043450.35049505
0.397053190.3841584
0.391141870.34455445
0.381484510.35841584
0.368363520.34356437
0.352154590.3049505
0.333309130.29801979
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0.217907380.1980198
0.194235250.1990099
0.171411990.13861387
0.149765390.14851485
0.129550390.11881188
0.110948920.087128716
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Category bins
PDF
Innovation histogram(Parameter estimation, 10 ens, 101 obs)
Sheet1
1.49E-061.98E-03-5
2.44E-061.98E-03-4.9
3.96E-060.00E+00-4.8
6.37E-060.00E+00-4.7
1.01E-050.00E+00-4.6
1.60E-051.98E-03-4.5
2.49E-050.00E+00-4.4
3.85E-059.90E-04-4.3
5.90E-052.97E-03-4.2
8.93E-051.98E-03-4.1
1.34E-041.98E-03-4
1.99E-040.00E+00-3.9
2.92E-049.90E-04-3.8
4.25E-041.98E-03-3.7
6.12E-049.90E-04-3.6
8.73E-046.93E-03-3.5
1.23E-034.95E-03-3.4
1.72E-037.92E-03-3.3
2.38E-031.09E-02-3.2
3.27E-035.94E-03-3.1
4.43E-031.58E-02-3
5.95E-037.92E-03-2.9
7.92E-032.18E-02-2.8
1.04E-022.77E-02-2.7
1.36E-023.07E-02-2.6
1.75E-023.47E-02-2.5
2.24E-024.06E-02-2.4
2.83E-023.66E-02-2.3
3.55E-024.65E-02-2.2
4.40E-025.54E-02-2.1
5.40E-026.44E-02-2
6.56E-027.33E-02-1.9
7.90E-029.60E-02-1.8
9.41E-021.08E-01-1.7
1.11E-011.54E-01-1.6
1.30E-011.38E-01-1.5
1.50E-011.74E-01-1.4
1.71E-011.86E-01-1.3
1.94E-012.16E-01-1.2
2.18E-012.41E-01-1.1
2.42E-012.36E-01-1
2.66E-012.69E-01-0.9
2.90E-012.56E-01-0.8
3.12E-012.79E-01-0.7
3.33E-013.34E-01-0.6
3.52E-013.50E-01-0.5
3.68E-013.63E-01-0.4
3.81E-013.49E-01-0.3
3.91E-014.07E-01-0.2
3.97E-014.02E-01-0.1
3.99E-013.50E-010
3.97E-013.84E-010.1
3.91E-013.45E-010.2
3.81E-013.58E-010.3
3.68E-013.44E-010.4
3.52E-013.05E-010.5
3.33E-012.98E-010.6
3.12E-013.16E-010.7
2.90E-012.82E-010.8
2.66E-012.44E-010.9
2.42E-012.41E-011
2.18E-011.98E-011.1
1.94E-011.99E-011.2
1.71E-011.39E-011.3
1.50E-011.49E-011.4
1.30E-011.19E-011.5
1.11E-018.71E-021.6
9.41E-021.08E-011.7
7.90E-026.34E-021.8
6.56E-028.12E-021.9
5.40E-026.24E-022
4.40E-024.36E-022.1
3.55E-025.84E-022.2
2.83E-023.37E-022.3
2.24E-023.07E-022.4
1.75E-022.67E-022.5
1.36E-021.49E-022.6
1.04E-021.29E-022.7
7.92E-031.09E-022.8
5.95E-031.09E-022.9
4.43E-035.94E-033
3.27E-032.97E-033.1
2.38E-039.90E-043.1
1.72E-039.90E-043.3
1.23E-032.97E-033.4
8.73E-040.00E+003.5
6.12E-041.98E-033.6
4.25E-049.90E-043.7
2.92E-049.90E-043.8
1.99E-040.00E+003.9
1.34E-040.00E+004
8.93E-050.00E+004.1
5.90E-050.00E+004.2
3.85E-059.90E-044.3
2.49E-050.00E+004.4
1.60E-050.00E+004.5
1.01E-050.00E+004.6
6.37E-060.00E+004.7
3.96E-060.00E+004.8
2.44E-060.00E+004.9
1.49E-060.00E+005
Sheet1
Category bins
PDF
Innovation histogram(Parameter estimation, 10 ens, 101 obs)
Sheet2
Sheet3
Chart1
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0.010423590.0079207926
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0.391141870.42277231
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0.397053190.36831684
0.391141870.4108911
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0.368363520.36138616
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0.129550390.13069307
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Category bins
PDF
Innovation histogram(Correct diffusion, 10 ens, 101 obs)
Sheet1
1.49E-060.00E+00-5
2.44E-060.00E+00-4.9
3.96E-060.00E+00-4.8
6.37E-060.00E+00-4.7
1.01E-050.00E+00-4.6
1.60E-050.00E+00-4.5
2.49E-050.00E+00-4.4
3.85E-050.00E+00-4.3
5.90E-050.00E+00-4.2
8.93E-050.00E+00-4.1
1.34E-040.00E+00-4
1.99E-040.00E+00-3.9
2.92E-040.00E+00-3.8
4.25E-040.00E+00-3.7
6.12E-040.00E+00-3.6
8.73E-040.00E+00-3.5
1.23E-030.00E+00-3.4
1.72E-030.00E+00-3.3
2.38E-030.00E+00-3.2
3.27E-039.90E-04-3.1
4.43E-031.98E-03-3
5.95E-036.93E-03-2.9
7.92E-038.91E-03-2.8
1.04E-027.92E-03-2.7
1.36E-022.08E-02-2.6
1.75E-021.49E-02-2.5
2.24E-022.28E-02-2.4
2.83E-022.38E-02-2.3
3.55E-023.27E-02-2.2
4.40E-026.73E-02-2.1
5.40E-025.84E-02-2
6.56E-026.34E-02-1.9
7.90E-027.23E-02-1.8
9.41E-027.92E-02-1.7
1.11E-019.41E-02-1.6
1.30E-011.46E-01-1.5
1.50E-011.42E-01-1.4
1.71E-011.77E-01-1.3
1.94E-011.91E-01-1.2
2.18E-012.24E-01-1.1
2.42E-012.49E-01-1
2.66E-012.94E-01-0.9
2.90E-012.89E-01-0.8
3.12E-012.97E-01-0.7
3.33E-013.25E-01-0.6
3.52E-013.47E-01-0.5
3.68E-013.61E-01-0.4
3.81E-014.06E-01-0.3
3.91E-014.23E-01-0.2
3.97E-014.30E-01-0.1
3.99E-014.03E-010
3.97E-013.68E-010.1
3.91E-014.11E-010.2
3.81E-013.72E-010.3
3.68E-013.61E-010.4
3.52E-013.49E-010.5
3.33E-013.01E-010.6
3.12E-013.38E-010.7
2.90E-013.07E-010.8
2.66E-012.59E-010.9
2.42E-012.38E-011
2.18E-012.22E-011.1
1.94E-011.81E-011.2
1.71E-011.87E-011.3
1.50E-011.50E-011.4
1.30E-011.31E-011.5
1.11E-019.11E-021.6
9.41E-028.22E-021.7
7.90E-028.51E-021.8
6.56E-026.24E-021.9
5.40E-024.65E-022
4.40E-023.96E-022.1
3.55E-023.37E-022.2
2.83E-023.17E-022.3
2.24E-021.78E-022.4
1.75E-021.98E-022.5
1.36E-021.98E-022.6
1.04E-025.94E-032.7
7.92E-034.95E-032.8
5.95E-034.95E-032.9
4.43E-039.90E-043
3.27E-030.00E+003.1
2.38E-030.00E+003.1
1.72E-030.00E+003.3
1.23E-030.00E+003.4
8.73E-040.00E+003.5
6.12E-040.00E+003.6
4.25E-040.00E+003.7
2.92E-040.00E+003.8
1.99E-040.00E+003.9
1.34E-040.00E+004
8.93E-050.00E+004.1
5.90E-050.00E+004.2
3.85E-050.00E+004.3
2.49E-050.00E+004.4
1.60E-050.00E+004.5
1.01E-050.00E+004.6
6.37E-060.00E+004.7
3.96E-060.00E+004.8
2.44E-060.00E+004.9
1.49E-060.00E+005
Sheet1
Category bins
PDF
Innovation histogram(Correct diffusion, 10 ens, 101 obs)
Sheet2
Sheet3
Chart1
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Category bins
PDF
Innovation histogram(Correct diffusion 10 ens, 10 obs)
Sheet1
1.49E-060.00E+00-5
2.44E-060.00E+00-4.9
3.96E-060.00E+00-4.8
6.37E-060.00E+00-4.7
1.01E-050.00E+00-4.6
1.60E-050.00E+00-4.5
2.49E-050.00E+00-4.4
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8.93E-050.00E+00-4.1
1.34E-040.00E+00-4
1.99E-040.00E+00-3.9
2.92E-040.00E+00-3.8
4.25E-040.00E+00-3.7
6.12E-040.00E+00-3.6
8.73E-040.00E+00-3.5
1.23E-030.00E+00-3.4
1.72E-030.00E+00-3.3
2.38E-030.00E+00-3.2
3.27E-030.00E+00-3.1
4.43E-031.11E-02-3
5.95E-030.00E+00-2.9
7.92E-031.11E-02-2.8
1.04E-021.11E-02-2.7
1.36E-020.00E+00-2.6
1.75E-022.22E-02-2.5
2.24E-021.11E-02-2.4
2.83E-022.22E-02-2.3
3.55E-027.78E-02-2.2
4.40E-025.56E-02-2.1
5.40E-023.33E-02-2
6.56E-028.89E-02-1.9
7.90E-028.89E-02-1.8
9.41E-021.11E-01-1.7
1.11E-011.33E-01-1.6
1.30E-011.56E-01-1.5
1.50E-011.22E-01-1.4
1.71E-011.56E-01-1.3
1.94E-012.67E-01-1.2
2.18E-012.22E-01-1.1
2.42E-012.78E-01-1
2.66E-012.89E-01-0.9
2.90E-012.67E-01-0.8
3.12E-012.67E-01-0.7
3.33E-012.56E-01-0.6
3.52E-013.44E-01-0.5
3.68E-013.00E-01-0.4
3.81E-013.44E-01-0.3
3.91E-013.33E-01-0.2
3.97E-013.44E-01-0.1
3.99E-014.44E-010
3.97E-014.67E-010.1
3.91E-014.44E-010.2
3.81E-013.67E-010.3
3.68E-013.67E-010.4
3.52E-014.67E-010.5
3.33E-013.78E-010.6
3.12E-011.78E-010.7
2.90E-012.56E-010.8
2.66E-013.44E-010.9
2.42E-012.89E-011
2.18E-012.00E-011.1
1.94E-011.44E-011.2
1.71E-011.78E-011.3
1.50E-011.22E-011.4
1.30E-011.67E-011.5
1.11E-011.11E-011.6
9.41E-021.33E-011.7
7.90E-024.44E-021.8
6.56E-024.44E-021.9
5.40E-027.78E-022
4.40E-022.22E-022.1
3.55E-024.44E-022.2
2.83E-024.44E-022.3
2.24E-020.00E+002.4
1.75E-022.22E-022.5
1.36E-021.11E-022.6
1.04E-020.00E+002.7
7.92E-031.11E-022.8
5.95E-030.00E+002.9
4.43E-030.00E+003
3.27E-030.00E+003.1
2.38E-030.00E+003.1
1.72E-030.00E+003.3
1.23E-030.00E+003.4
8.73E-040.00E+003.5
6.12E-040.00E+003.6
4.25E-040.00E+003.7
2.92E-040.00E+003.8
1.99E-040.00E+003.9
1.34E-040.00E+004
8.93E-050.00E+004.1
5.90E-050.00E+004.2
3.85E-050.00E+004.3
2.49E-050.00E+004.4
1.60E-050.00E+004.5
1.01E-050.00E+004.6
6.37E-060.00E+004.7
3.96E-060.00E+004.8
2.44E-060.00E+004.9
1.49E-060.00E+005
Sheet1
Category bins
PDF
Innovation histogram(Correct diffusion 10 ens, 10 obs)
Sheet2
Sheet3
Chart1
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0.0001987070.011111112
0.00029202260.033333335
0.00042489010.011111112
0.00061206010.011111112
0.00087290760.022222223
0.00123253630.077777777
0.00172301160.022222223
0.00238469980.077777777
0.00326765540.055555558
0.00443298050.06666667
0.00595405340.011111112
0.007917470.044444447
0.010423590.088888893
0.0135864260.033333335
0.0175327530.1
0.0224002170.06666667
0.0283342170.17777778
0.0354835870.14444446
0.0439947320.15555556
0.0540046310.16666667
0.065632410.1
0.0789701370.2
0.0940728760.18888889
0.110948920.26666667
0.129550390.21111112
0.149765390.17777778
0.171411990.2
0.194235250.32222223
0.217907380.14444446
0.242032070.23333333
0.266152720.23333333
0.289764980.26666667
0.312333110.36666667
0.333309130.26666667
0.352154590.32222223
0.368363520.23333333
0.381484510.3
0.391141870.35555556
0.397053190.28888891
0.399043450.34444447
0.397053190.21111112
0.391141870.21111112
0.381484510.17777778
0.368363520.25555558
0.352154590.28888891
0.333309130.2
0.312333110.22222223
0.289764980.24444444
0.266152720.14444446
0.242032070.14444446
0.217907380.22222223
0.194235250.055555558
0.171411990.14444446
0.149765390.12222222
0.129550390.088888893
0.110948920.088888893
0.0940728760.088888893
0.0789701370.044444447
0.065632410.1
0.0540046310.055555558
0.0439947320.088888893
0.0354835870
0.0283342170.033333335
0.0224002170.077777777
0.0175327530.022222223
0.0135864260
0.010423590.022222223
0.007917470.011111112
0.00595405340.022222223
0.00443298050
0.00326765540.011111112
0.00238469980.011111112
0.00172301160
0.00123253630.022222223
0.00087290760.011111112
0.00061206010
0.00042489010
0.00029202260
0.0001987070
0.00013386510
0.00008928480.011111112
0.00005895840
0.00003854530
0.0000249490
0.00001598790
0.00001014350
0.00000637150
0.00000396230
0.00000243960.011111112
0.00000148710
Category bins
PDF
Innovation histogram(Incorrect diffusion, 10 ens, 10 obs)
Sheet1
1.49E-065.56E-02-5
2.44E-060.00E+00-4.9
3.96E-060.00E+00-4.8
6.37E-060.00E+00-4.7
1.01E-050.00E+00-4.6
1.60E-050.00E+00-4.5
2.49E-050.00E+00-4.4
3.85E-052.22E-02-4.3
5.90E-050.00E+00-4.2
8.93E-052.22E-02-4.1
1.34E-043.33E-02-4
1.99E-041.11E-02-3.9
2.92E-043.33E-02-3.8
4.25E-041.11E-02-3.7
6.12E-041.11E-02-3.6
8.73E-042.22E-02-3.5
1.23E-037.78E-02-3.4
1.72E-032.22E-02-3.3
2.38E-037.78E-02-3.2
3.27E-035.56E-02-3.1
4.43E-036.67E-02-3
5.95E-031.11E-02-2.9
7.92E-034.44E-02-2.8
1.04E-028.89E-02-2.7
1.36E-023.33E-02-2.6
1.75E-021.00E-01-
