Neural Network uncertain/es. Roland Doerffer & Carsten Brockmann Brockmann Consult GmbH Germany

Transcription

1 Neural Network uncertain/es Roland Doerffer & Carsten Brockmann Brockmann Consult GmbH Germany

2 Content General uncertain:es of Case 2 water remote sensing using inverse modelling Specific uncertain:es of neural network algorithms Present NN calcula:ons of uncertain:es for MERIS and OLCI (and other sensors) Realisa:on in SNAP using the C2RCC (Carsten)

3 General uncertain/es of Case 2 water remote sensing using inverse modelling We have an under determined system, i.e. informa:on content of TOA spectra is less than the number of variables, which determine the spectra Our bio-op:cal model has to reduce the natural variability to a few components Masking and satura/on effects An inverse modelling algorithm has a certain scope: measured spectra may be out of scope defini/on of case 2 water: more than 1 water cons:tuent have to be used to explain the variability of water reflectance spectra

4 What determines the radiance spectrum at TOA TOA Radiance Spectra Radiance (Wm-2 sr-1 µm-1) North Sea wavelength (nm) Pin 1 Pin 2 Pin 3 Pin 4 Pin 5 Pin 6 air molecules different aerosols thin clouds contrails Sky reflectance Sun glint foam floating material Suspended particles dissolved organic matter Vertical distribution chlorophyll Bottom reflection different phytoplankton species

5 Uncertain/es of case 1 water phytoplankton fotos by M. Rademaker c by A. Morel NOMAD data: log(apig 443) vs log(chl) log(chl) = a +b*log(r445/r555)

6 The bio-op/cal model phytoplankton pigments apig Chl.a absorption by organic matter ad ag adg at 443 m-1 scattering by particles bp TSM g m-3 IOPs of water constituents IOP components of bio-optical model all at 443 nm conversion factors MERIS products

7 Variability of spectral proper/es nomad_ phytoplankton pigments slope s detritus absorp:on coefficient ad_443 [m-1] nomad_ nomad_ slope s CDOM absorp:on coefficient slope s par:cle sca_ering coefficient ag_443 [m-1] bbp_443 [m-1] Variability the rela,ve absorp,on/sca4ering from the NOMAD data set (NASA)

8 Satura/on and masking effects RLw [sr -1 ] RLw for MERIS bands 1 (412 nm), 6 (560 nm), 10 (708 nm) band 1 = 412 nm band 5 = 560 nm band 9 = 708 nm a_gelb_440: 0.2, a_part_440: SPM/25, pig: 2 mg m SPM [g m -3 ] Sensitivity of the reflectance at a spectral band depends on the concentration To cover a large concentration range many bands from the blue to NIR range are necessary Rsr (sr-1) 9.00E E E E E E E-003 Remote Sensing reflectance TSM 1 Chl. 5/10 mg m-3 TSM 1 g m-3 ays(443) 0.1 m-1 Rsr 5_01_1 Rsr 10_01_1 Rsr (sr-1) 6.00E E E E E-002 Remote Sensing reflectance TSM 100 Chl. 5/10 mg m-3 TSM 100 g m-3 ays(443) 0.1 m-1 Rsr 5_01_100 Rsr 10_01_ E E E E wavelength (nm) 0.00E wavelength (nm)

9 Specific uncertain/es of neural network algorithms Training of a NN means to minimize the difference between the modelled result of the training data set and the corresponding outcome of the NN over all training cases: cases my be under represented Gaps in the training data set have to be interpolated by the NN, but this may lead to amplitudes between points (such as a polynomial of high degree)-> overtraining The quality of a NN depends on: the bio-op/cal model and model of the atmosphere and its scope the number of data points and the range and frequency distribu/on of all components of the training data set the co-variances between the variables introduced expected uncertain/es in the training data set the architecture of the NN, the training algorithm, control of training process

10 Simplified scheme of NN Algorithm Input layer: reflectances and angles R 1 Hidden layer Output layer: concentrations Chlorophyll training progress rw-> 5 iops (OLCI) R 2 R 3 W Susp. Matter dev. Gelbstoff number of training loops X 1 ox= 2 s( bias + w i x i ) X 3 X 4 3 W i X i incominglinks y = s( d + w s( c + v s( b + u x ))) l l kl k jk j ij i k = 1 j= 1 i= 1 s: sigmoid func:on, u,v,w: weight, b,c,d: bias 5 4 o trainings samples: points test samples: points #planes=5: 17, 97, 77, 37, 5 average of residues: training = test = ra:o avg.train/avg.test=

11 Sensi/vity Tests of NNs Test of a_pig, no additional error Test of adg, no additional error Test of a_pig with an extra random error with a standard deviation of 3% Test of adg with an extra random error with a standard deviation of 3%

12 Present NN uncertain/es calcula/ons for MERIS and OLCI Iden:fica:on of out of scope spectra Es:ma:on of uncertain:es of IOPs

13 Overview

14 Detec/on of out of scope condi/ons using an aann Important to detect toa radiance specta which are not in the simulated training data set These are out of scope of the atmospheric correc:on algorithm Autoassocia:ve neural network with a bo_le neck layer Functions also as nonlinear PCA i.e. bottle neck number of neurons Provide estimate of Independent components Input layer Hidden 1 Bottleneck Hidden 3 output layer For the GAC training data Set of ~ 1Mio. Cases Bottleneck minimum was 4-5

15 Detec/on of out of scope condi/ons aann: example for L1 (TOA) data High SPM Sun glint Transect

16 Detec/on of out of scope condi/ons aann: example AutoNN test 12x5x12 Yellow Sea transect, MERIS band 7, nm AutoNN test 12x5x12 Yellow Sea transect, MERIS band 7, nm rltoa rltoa_ann difference ratio rel. deviation RLtoa longitude AutoNN test Yellow Sea transect 12x5x12, MERIS band 7, nm longitude significant deviation in area with high SPM concentrations, but not in sun glint area rel. frequency Histogram of deviations shows 2 maxima, around 1 in sun glint 0.9 in high SPM area, which out of scope rel. radiance reflectance ratio to true

17 Uncertain/es due to ambigui/es, masking and satura/on for different concentra/on mixtures 10 2 case 2 water chlorophyll retrieval with NN 10 2 Pigment in North Sea Water (gelb < 0.2 m-1, MSM < 5 mg/ 10 1 chlorophyll 10 1 chlorophyll nn-derived µg/l nn µg/l mg m model chlorophyll µg/l All cases of turbid water model chlorophyll µg/l Typical North Sea coastal water: ay_443: < 0.2 m-1, TSM < 5 mg /l Using a lookup-table from these tests we can train a NN with the 5 IOPs as input and the uncertain:es for the 5 IOPs as output

18 Uncertainty NN measured IOPs with uncertain:es bio-op:cal model IOP table freq. distr. radia:ve transfer model reflectances Test Data base rho_w / IOPs rhow->iop NN result IOPs compute difference table IOPs / diff IOPs train unc. NN uncertainty NN uncertainty 5 IOPs 5 IOP uncertain:es NN

19 Helgoland transect C Rtosa Rpath aann

20 Helgoland transect C atotal_443 TSM

21 Helgoland transect C apig_443 and uncertainty chlorophyll

22 Valida/on: Test of NN based on measurements for chlorophyll Log10 scale, red: 1 by 1 line NOMAD data set

23 Comparison of histograms: measured, NN computed

24 Valida/on of uncertain/es: Error due to masking and ambigui/es simulated reflectance test error 0.01 stdev RLw [sr-1] wavelength [nm] rlw_true rlw_err rlw_retr True spectrum simulated measured spectrum = true * random error Retrieved spectrum when LM has found solution

25 Comparison of es/mated and true uncertain/es using simula/ons Results and errors of retrieval Variable conc true conc retr. stdev of log_conc err. estimated % err true % chlorophyll [mg m-3] detritus [g m-3] gelbstoff a443 [m-1] min. SPM [g m-3] kdmin_true: kdmin_ret: error: % kd490_true: kd490_ret: error: -1.04%

26 Summay and Conclusions number of factors, which determine the reflectance spectra at top of atmosphere, >> number of factors we can retrieve -> ambigui:es, uncertain:es our model has to reduce the natural variability to a few components natural variability of conversion factors op:cal components > mass concentra:on causes uncertain:es satura/on and masking effects leads to variable uncertain:es, which may change from pixel to pixel spectra may be out of scope of the algorithm design of the training data set extremely cri/cal for quality of the NN model, range and number of training points, frequency distribu:on for each component and overall absorp:on and sca_ering coefficient, co-varia:on, introduced error 5 steps to reduce and determine uncertain/es: proper design of the model and training data set adapta:on to local or regional condi:ons (opt. proper:es, range, covariances) test of out of scope condi:ons, e.g. using an aann determina:on of uncertainty using an uncertainty NN valida:on of results and uncertain:es

27 Adria/c Sea, chlorophyll

28 chlorophyll

29 MERIS Top of atmosphere radiance reflectance RLtoa RGB New York

30 Water leaving radiance reflectance RLw MERIS band 5 (560 nm)

31 Chlorophyll

32 Thank you for listening!

33 Searching for minimum: principle, 1D case Search for minimum: Deviation between measured and simulated spectrum deviation Acceptance level deviation Acceptance level Independent variable Independent variable Width can be estimated from the 2nd order derivative (Hessean matrix)

34 Detec/on of out of scope condi/ons (MERIS processor) r g Reflectance spectrum r g invnn r, r log of reflectances c log of concentrations g geometry information q quality indicator c IOPs or concentrations forwnn r NN input NN output q c q c Comparator to trigger out of scope flag C: log(b_tot) log(a_ys+a_btsm) log(a_pig) All at 443 nm Out of scope flag Angles: Sun zenith View nadir Azimuth diff If RLw < , RLw = ( ρ 0.003) Reflectance spectrum Output of NN flag PCD1_16,17 q true if sum (r(i) / r (i)) > 4.0 courtesy of H. Schiller