# Product Tutorial on Sea Surface Temperature (SST)

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## Chapter V: Infrared measured SST-Algorithms

### Table of Contents

- Infrared measured SST-Algorithms

### Infrared measured SST-Algorithms

SST products are derived from radiometric observations at wavelengths of ~3.7 μm and/or near 10.0 μm. Though the 3.7 μm channel is more sensitive to SST, it is primarily used only for night-time measurements because of the relatively strong reflection of solar irradiation in this wavelength region, which contaminates the retrieved radiation. Both bands are sensitive to the presence of clouds and to scattering of both aerosols and atmospheric water vapor. For this reason, thermal infrared measurements of SST first require atmospheric correction of the retrieved signal and can only be made for cloud-free pixels. Thus, maps of SST compiled from thermal infrared measurements are often weekly or monthly composites which allow enough time to capture cloud-free pixels over a region.

To be able to derive SST, Eq. 7 must be solved. The solving of Eq. 7 can be divided into several methods:

#### Linear algorithms

Single channel methods

These methods are currently not widely used. They are based on a simple inversion of the radiative transfer equation (RTE), already presented (Eq. 7, chapter IV).

Lλ atm and τλ are estimated from radiative transfer models (e.g. MODTRAN (Berk et al., 2014)), using atmospheric profiles as inputs (that may be given by either satellite soundings or by conventional radiosondes). Lλ represents the radiance measured at the satellite sensor. This method assumes only one unknown (SST), that is obtained by inverting the Planck function (Bλ).

Multichannel Sea Surface Temperature (MCSST) methods

This type of algorithm relies on the linearisation of the RTE with respect to the temperature or the wavelength.

In MCSST methods there are two unknows: the SST and the atmospheric water vapor content.

One of the most popular MCSST methods uses two channels centered at about 11.0 μm and 12.0 μm to account for the atmospheric effect. The difference in TOA radiances measured in channels near the Thermal IR (TIR) wavelengths and with distinct atmospheric transmissivities, gives an estimate of the atmospheric water vapor content. A typical linear SW algorithm can be written as:

SST = a0 + a1Ti + a2(Ti - Tj), (Eq.9)

where ak (k=0, 1, and 2) are coefficients that depend on the spectral response function of the two channels (i and j), water vapor content, and the satellite's viewing zenith angle (VZA).

The MCSST (McClain et al., 1985) is typically used with three bands centered at 3.7, 11.0, and 12.0 μm, at night-time only.

During the daytime, the 3.7 μm band is contaminated by reflected solar radiance which limits its use.

Table I summarises the main differences between the three MCSST methods:

Algorithm | Thermal bands used | Day/night usage
--- | --- | ---
Dual Window | 3.7 and 11.0 μm | Daytime
Split Window | 11.0 and 12.0 μm | Day and Night
Triple Window | 3.7, 11.0 and 12.0 μm | Daytime

Table I - main differences between the three MCSST methods. 3.7μm < 11.0 μm < 12.0 μm in terms of water vapor absorption.

#### Non-linear algorithms

When more than 2 TIR channels are available, the SST can be estimated from a linear or non-linear combination of the TOA brightness temperatures in those channels using methods similar to the Split Window (SW) algorithms. Although MCSST assume that the water vapor absorption is a constant, the water vapor absorption is in fact a non-linear function of temperature. This leads to problems in dry polar regions and dry hot regions. Moreover, the radiative transfer equation is non-linear with respect to high amounts of water vapor. The "Non-linear" SST (NLSST) [Walton et al., 1998] exploits the two split-window bands centered at 11.0 and 12.0 μm.

NLSST equations

- NLSST (triple):
  - SST = f(Tj, Tguess, Ti - Tk, (1-secθ)) (Eq. 10)
- NLSST (SPLIT):
  - SST = f(Ti, (Ti-Tj) Tguess, (Ti-Tj)(1-secθ)) (Eq. 11)

Where Ti and Tj refer to brightness temperatures in channels centered at 11.0 and 12.0 μm and θ is the satellite's viewing zenith angle. Tguess can be climatological, modeled, or from the MCSST equation.

#### Bayesian retrieval of SST

Summary:

- Performs a simultaneous retrieval of skin temperature and Total Column Water Vapour (TCWV).
- Uses Bayesian statistical methods and radiative transfer models for each SST measurement.

This approach of making specific use of the atmospheric conditions was pioneered by Merchant et al. (2008b) using an Optimal Estimation (OE) approach in which a first guess of SST is prescribed, as well as the expected variance state variables (Total Precipitable Water (TWV) and SST) and the error variance of each channel. The prior information about the expected state of the system is represented by a state vector xa = (SSTskin, TWV). Vector xa constitutes an input to a forward model F to simulate "prior observations" ya = F(xa). The model F is generally a radiative transfer model and the prior observations are calculated radiances in the satellite radiometer channels. These simulated radiances are then adjusted to match the measured channel radiance within uncertainties determined by the radiometer characteristics. The adjustment is an inverse problem. The a priori values of SSTskin and TWV can be taken from a number of sources, including weather forecast models, or reanalysis fields such as from ECMWF.

A great disadvantage of this method is that it is highly sensitive to the tuning parameters (error variances and state variances) and to the first guess estimate of SST.