Ensemble uncertainty of inherent optical properties.

We present a method to evaluate the combined accuracy of ocean color models and the parameterizations of inherent optical proprieties (IOPs), or model-parametrization setup. The method estimates the ensemble (collective) uncertainty of derived IOPs relative to the radiometric error and is directly applicable to ocean color products without the need for inversion. Validation shows a very good fit between derived and known values for synthetic data, with R(2) > 0.95 and mean absolute difference (MADi) <0.25 m(-1). Due to the influence of observation errors, these values deteriorate to 0.45 < R(2) < 0.5 and 0.65 < MADi < 0.9 for in-situ and ocean color matchup data. The method is also used to estimate the maximum accuracy that could be achieved by a specific model-parametrization setup, which represents the optimum accuracy that should be targeted when deriving IOPs. Application to time series of ocean color global products collected between 1997-2007 shows few areas with increasing annual trends of ensemble uncertainty, up to 8 sr m(-1) decade(-1). This value is translated to an error of 0.04 m(-1) decade(-1) in the sum of derived absorption and backscattering coefficients at the blue wavelength 440 nm. As such, the developed method can be used as a tool for assessing the reliability of model-parametrization setups for specific biophysical conditions and for identifying hot-spots for which the model-parametrization setup should be reconsidered.

Stochastic inversion of ocean color data using the cross-entropy method.

Improving the inversion of ocean color data is an ever continuing effort to increase the accuracy of derived inherent optical properties. In this paper we present a stochastic inversion algorithm to derive inherent optical properties from ocean color, ship and space borne data. The inversion algorithm is based on the cross-entropy method where sets of inherent optical properties are generated and converged to the optimal set using iterative process. The algorithm is validated against four data sets: simulated, noisy simulated in-situ measured and satellite match-up data sets. Statistical analysis of validation results is based on model-II regression using five goodness-of-fit indicators; only R2 and root mean square of error (RMSE) are mentioned hereafter. Accurate values of total absorption coefficient are derived with R2 > 0.91 and RMSE, of log transformed data, less than 0.55. Reliable values of the total backscattering coefficient are also obtained with R2 > 0.7 (after removing outliers) and RMSE < 0.37. The developed algorithm has the ability to derive reliable results from noisy data with R2 above 0.96 for the total absorption and above 0.84 for the backscattering coefficients. The algorithm is self contained and easy to implement and modify to derive the variability of chlorophyll-a absorption that may correspond to different phytoplankton species. It gives consistently accurate results and is therefore worth considering for ocean color global products.

Bayesian model for matching the radiometric measurements of aerospace and field ocean color sensors.

A Bayesian model is developed to match aerospace ocean color observation to field measurements and derive the spatial variability of match-up sites. The performance of the model is tested against populations of synthesized spectra and full and reduced resolutions of MERIS data. The model derived the scale difference between synthesized satellite pixel and point measurements with R(2) > 0.88 and relative error < 21% in the spectral range from 400 nm to 695 nm. The sub-pixel variabilities of reduced resolution MERIS image are derived with less than 12% of relative errors in heterogeneous region. The method is generic and applicable to different sensors.

Error decomposition and estimation of inherent optical properties.

We describe a methodology to quantify and separate the errors of inherent optical properties (IOPs) derived from ocean-color model inversion. Their total error is decomposed into three different sources, namely, model approximations and inversion, sensor noise, and atmospheric correction. Prior information on plausible ranges of observation, sensor noise, and inversion goodness-of-fit are employed to derive the posterior probability distribution of the IOPs. The relative contribution of each error component to the total error budget of the IOPs, all being of stochastic nature, is then quantified. The method is validated with the International Ocean Colour Coordinating Group (IOCCG) data set and the NASA bio-Optical Marine Algorithm Data set (NOMAD). The derived errors are close to the known values with correlation coefficients of 60-90% and 67-90% for IOCCG and NOMAD data sets, respectively. Model-induced errors inherent to the derived IOPs are between 10% and 57% of the total error, whereas atmospheric-induced errors are in general above 43% and up to 90% for both data sets. The proposed method is applied to synthesized and in situ measured populations of IOPs. The mean relative errors of the derived values are between 2% and 20%. A specific error table to the Medium Resolution Imaging Spectrometer (MERIS) sensor is constructed. It serves as a benchmark to evaluate the performance of the atmospheric correction method and to compute atmospheric-induced errors. Our method has a better performance and is more appropriate to estimate actual errors of ocean-color derived products than the previously suggested methods. Moreover, it is generic and can be applied to quantify the error of any derived biogeophysical parameter regardless of the used derivation.