how can we improve the infrared atmospheric correction algorithm?

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How can we improve the infrared atmospheric correction algorithm?. Peter J Minnett Meteorology & Physical Oceanography Sareewan Dendamrongvit Miroslav Kubat Department of Electrical & Computer Engineering University of Miami. NLSST. - PowerPoint PPT Presentation

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Remote Sensing of SST Group Meeting

How can we improve the infrared atmospheric correction algorithm? Peter J Minnett

Meteorology & Physical Oceanography

Sareewan DendamrongvitMiroslav Kubat

Department of Electrical & Computer Engineering

University of Miami

SST Science Team Meeting Coconut Grove November 2011NLSSTSST Science Team Meeting Coconut Grove November 2011

The NLSST has been used for over a decade, is very robust, and has been hard to improve upon.

Where next?Use advanced computational techniques: Genetic Algorithm (GA)-based equation discovery to derive alternative forms of the correction algorithm

Regression tree to identify geographic regions with related characteristics

Support Vector Machines (SVM) to minimize error using state-of-the-art non-linear regressionSST Science Team Meeting Coconut Grove November 2011Equation Discovery using Genetic AlgorithmsDarwinian principles are applied to algorithms that mutate between successive generationsThe algorithms are applied to large data bases of related physical variables to find robust relationships between them. Only the fittest algorithms survive to influence the next generation of algorithms.Here we apply the technique to the MODIS matchup-data bases.The survival criterion is the size of the RMSE of the SST retrievals when compared to buoy data. SST Science Team Meeting Coconut Grove November 2011Genetic Mutation of EquationsThe initial population of formulae is created by a generator of random algebraic expressions from a predefined set of variables and operators. For example, the following operators can be used: {+, -, /, , , exp, cos, sin, log}. To the random formulae thus obtained, we can include seeds based on published formulae, such as those already in use.In the recombination step, the system randomly selects two parent formulae, chooses a random subtree in each of them, and swaps these subtrees.The mutation of variables introduces the opportunity to introduce different variables into the formula. In the tree that defines a formula, the variable in a randomly selected leaf is replaced with another variable.

SST Science Team Meeting Coconut Grove November 2011Successive generations of algorithms

The formulae are represented by tree structures; the recombination operator exchanges random subtrees in the parents. Here the parent formulae (yx+z)/log(z) and (x+sin(y))/zy give rise to children formulae (sin(y)+z)/log(z) and (x+yx)/zy. The affected subtrees are indicated by dashed lines.

Subsets of the data set can be defined in any of the available parameter spaces.(From Wickramaratna, K., M. Kubat, and P. Minnett, 2008: Discovering numeric laws, a case study: CO2 fugacity in the ocean. Intelligent Data Analysis, 12, 379-391.)

SST Science Team Meeting Coconut Grove November 2011GA-based equation discovery

SST Science Team Meeting Coconut Grove November 2011And the fittest is.The fittest algorithm takes the form:

where:Ti is the brightness temperature at = i ms is the satellite zenith anglea is the angle on the mirror (a feature of the MODIS paddle-wheel mirror design)

Which looks similar to the NLSST:

SST Science Team Meeting Coconut Grove November 2011Regression treeRegions identified by the regression tree algorithmThe tree is constructed usinginput variables: latitude and longitudeoutput variable: Error in retrieved SSTAlgorithm recursively splits regions to minimize variance within themThe obtained tree is pruned to the smallest tree within one standard error of the minimum-cost subtree, provided a declared minimum number of points is exceeded in each regionLinear regression is applied separately to each resulting region (different coefficients result)

SST Science Team Meeting Coconut Grove November 2011

SST Science Team Meeting Coconut Grove November 2011

SST Science Team Meeting Coconut Grove November 2011Regions Mk 2

Aqua MODIS SST (11, 12 m). Daytime & night-time. Mean difference wrt buoys. Jan-Feb-Mar, 2007.SST Science Team Meeting Coconut Grove November 2011Regions Mk 2

Replicate data longitudinally in an attempt to avoid region boundaries at 180oSST Science Team Meeting Coconut Grove November 2011Regions Mk 2

SST Science Team Meeting Coconut Grove November 2011Regions Mk 2

Aqua MODIS SST (11, 12 m). Daytime & night-time. St. dev about the mean difference wrt buoys. Jan-Feb-Mar, 2007.SST Science Team Meeting Coconut Grove November 2011Genetic Algorithms & Regression Tree SST algorithms. Global uncertainties.Aqua MODISSST - Day & NightSST DaySST nightSST4 nightPopulation*Mean [K]Sdev [K]Mean [K]Sdev [K]Mean [K]Sdev [K]Mean [K]Sdev [K]Q10.50%0.0010.486-0.0020.5100.0000.4500.0030.384Q20.50%0.0010.4920.0000.5190.0020.493-0.0010.376Q30.50%0.0010.486-0.0030.5210.0010.4240.0030.348Q40.50%0.0010.434-0.0010.4520.0000.4060.0000.342Q12.00%-0.0010.496-0.0020.519-0.0010.4610.0000.392Q22.00%0.0010.5220.0000.5360.0020.5090.0010.378Q32.00%0.0000.509-0.0030.5450.0030.4300.0020.356Q42.00%0.0000.443-0.0010.4650.0000.4100.0010.347*Minimum population as fraction of training set. 0.5% is ~100 for day or night; ~200 for day & night.SST Science Team Meeting Coconut Grove November 2011ResultsThe new algorithms with regions give smaller errors than NLSST or SST4 Tsfc term no longer requiredNight-time 4m SSTs give smallest errorsAqua SSTs are more accurate than Terra SSTsRegression-tree induced in one year can be applied to other years without major increase in uncertaintiesSST Science Team Meeting Coconut Grove November 2011Next stepsCan some regions be merged without unacceptable increase in uncertainties?Iterate back to GA for regions different formulations may be more appropriate in different regions.Allow scan-angle term to vary with different channel sets.Introduce regions that are not simply geographical.Suggestions?

SST Science Team Meeting Coconut Grove November 2011Variants of the new algorithms

Note: No TsfcCoefficients are different for each equationSST Science Team Meeting Coconut Grove November 2011MODIS scan mirror effects

Mirror effects: two-sided paddle wheel has a multi-layer coating that renders the reflectivity in the infrared a function of wavelength, angle of incidence and mirror side.

SST Science Team Meeting Coconut Grove November 2011Regression tree (cont.)Example of a regression tree

SST Science Team Meeting Coconut Grove November 2011

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