We propose a new deterministic approach for remote sensing retrieval, called modified total least squares (MTLS), built upon the total least squares (TLS) technique. MTLS implicitly determines the optimal regularization strength to be applied to the normal equation first-order Newtonian retrieval using all of the noise terms embedded in the residual vector. The TLS technique does not include any constraint to prevent noise enhancement in the state space parameters from the existing noise in measurement space for an inversion with an ill-conditioned Jacobian. To stabilize the noise propagation into parameter space, we introduce an additional empirically derived regularization proportional to the logarithm of the condition number of the Jacobian and inversely proportional to the L2-norm of the residual vector. The derivation, operational advantages and use of the MTLS method are demonstrated by retrieving sea surface temperature from GOES-13 satellite measurements. An analytic equation is derived for the total retrieval error, and is shown to agree well with the observed error. This can also serve as a quality indicator for pixel-level retrievals. We also introduce additional tests from the MTLS solutions to identify contaminated pixels due to residual clouds, error in the water vapor profile and aerosols. Comparison of the performances of our new and other methods, namely, optimal estimation and regression-based retrieval, is performed to understand the relative prospects and problems associated with these methods. This was done using operational match-ups for 42 months of data, and demonstrates a relatively superior temporally consistent performance of the MTLS technique.Index Terms-Condition number of matrix, ill-conditioned inverse methods, regularization, satellite remote sensing, sea surface temperature (SST), total error, total least squares (TLS). I. INTRODUCTIONP ARAMETER estimation from remotely sensed satellite measurements can be broadly categorized into two groups: a) the direct method, which directly correlates the measure-Manuscript

The National Oceanic and Atmospheric Administration’s (NOAA) office of National Environmental Satellite, Data, and Information Service (NESDIS) now generates a daily 0.05° (∼5 km) global high-resolution satellite-based sea surface temperature (SST) analyses on an operational basis. The new analysis combines SST data from U.S., Japanese, and European geostationary infrared imagers, and low-Earth-orbiting infrared (United States and Europe) SST data, into a single high-resolution 5-km product. An earlier version produced a 0.1° (∼11 km) resolution, a resolution chosen to approximate the Nyquist sampling criterion for the midlatitude Rossby radius (∼20 km), in order to preserve mesoscale oceanographic features such as eddies and frontal meanders. Comparison between the two analyses illustrates that the higher-resolution grid spacing has more success in this regard. The analysis employs a rigorous multiscale optimum interpolation (OI) methodology that approximates the Kalman filter, together with a data-adaptive correlation length scale, to ensure a good balance between detail preservation and noise reduction. The product accuracy verified against globally distributed buoys is ∼0.02 K, with a robust standard deviation of ∼0.25 K. The new analysis has proven a significant success even when compared to other products that purport to have a similar resolution. This analysis forms the basis for other operational environmental products such as coral reef bleaching risk and ocean heat content for tropical cyclone prediction. Forthcoming enhancements include the incorporation of microwave SST products from low-Earth-orbiting platforms [e.g., Global Change Observation Mission for Water-1 (GCOM-W1)] in order to improve the resolution of SST features in areas of persistent cloud and correct for diurnal effects via a turbulence model of upper-ocean heating.

Global sea-surface temperatures (SST) from MODIS measured brightness temperatures generated using the regression methods, have been available to users for more than a decade, and are used extensively for a wide range of atmospheric and oceanic studies. However, as evidenced by a number of studies, there are indications that the retrieval quality and cloud detection are somewhat sub-optimal. To improve the performance of both of these aspects, we endorse a new physical deterministic algorithm, based on truncated total least squares (TTLS), using multiple channels and parameters, in conjunction with a hybrid cloud detection scheme using a radiative transfer model atop a functional spectral difference method. The TTLS method is a new addition that improves the information content of the retrieval compared to our previous work using modified total least squares (MTLS), which is feasible because more measurements are available, allowing a larger retrieval vector. A systematic study is conducted to ascertain the appropriate channel selection for SST retrieval from the 16 thermal infrared channels available from the MODIS instrument. Additionally, since atmospheric aerosol is a well-known source of degraded quality of SST retrieval, we include aerosol profiles from numerical weather prediction in the forward simulation and include the total column density of all aerosols in the retrieval vector of our deterministic inverse method. We used a slightly modified version of our earlier reported cloud detection algorithm, namely CEM (cloud and error mask), for this study. Time series analysis of more than a million match-ups shows that our new algorithm (TTLS+CEM) can reduce RMSE by~50% while increasing data coverage by~50% compared to the operationally available MODIS SST.