# Optimal Estimation of Sea Surface Temperature from AMSR-E

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## Abstract

**:**

## 1. Introduction

^{−1}. SMMR suffered from significant calibration problems (solar contamination of the hot-load calibration target) that resulted in large errors in the retrieved SST, limiting its usefulness [10].

## 2. Materials and Methods

#### 2.1. Data

#### 2.1.1. AMSR-E Brightness Temperatures

#### 2.1.2. In Situ Observations

#### 2.1.3. Ancillary Data Fields

#### 2.2. Matchup Database

#### 2.2.1. ESA-CCI Multi-Sensor Matchup Dataset

#### 2.2.2. Data Filtering Methods

^{−1}then the matchup was flagged. All these flags have been combined into a gross error flag, which in total removes 13.1% of the drifter matchups.

^{−1}were flagged (8.0%). Rain contamination was accounted for by flagging data if the brightness temperature of the 18V channel >240 K (0.4%). Applying all these checks at once leads to an elimination of 41.1% of the total drifter matchups.

#### 2.3. Optimal Estimation Development

**y**=

**F**(

**x**) + e,

**y**is the measurement vector (observed microwave brightness temperatures);

**F**(

**x**) is the non-linear forward model approximating the physics of the measurement, including the surface emissivity and the radiative transfer through the atmosphere [54];

**x**is the state vector containing the relevant geophysical properties of the ocean and atmosphere; and e is a residual uncertainty term containing uncertainties due to the measurement noise and uncertainties in the forward model.

**x**) of the ocean and atmosphere. The forward model used in this study is based on the physical surface emissivity and Radiative Transfer Model (RTM) described in Wentz et al. [54]. The RTM consists of an atmospheric absorption model for oxygen, water vapor and cloud liquid water and a sea surface emissivity model that determines the emissivity as a function of SST, SSS, sea surface wind speed and direction. Some components have been adjusted with respect to Wentz et al. [54]. These include the wind directional signal of sea surface emissivity, which has been suppressed as it did not improve the retrievals; and the fact that we only use the V- and H-polarizations for the 5 lower frequencies: 6.9, 10.7, 18.7, 23.8, 36.5 GHz.

**x**that can reproduce the observed microwave brightness temperatures,

**y**. In this study, the inversion approach follows the OE technique by Rodgers [53] and we broadly follow his conventions.

**x**can be found by minimizing the cost function,

**J**:

**S**

**is a covariance matrix for the measurement and forward model uncertainties,**

_{ϵ}**S**

**is the covariances of the a priori state**

_{a}**x**

**(the a priori guess of the ocean and atmospheric state**

_{a}**x**). The cost function is a measure of the goodness of the fit to both the measurements (first term on the right) and the a priori state (second term on the right) balanced by the inverse of their relative uncertainties (

**S**

**and**

_{ϵ}**S**).

_{a}**J**. Using Newtonian iteration, the state

**x**that minimizes the cost function can be found by:

**S**

**is the error covariance matrix of the retrieved parameters:**

_{x}**K**expresses the sensitivity of the forward model to a perturbation in the retrieved parameters, i.e., it is a matrix consisting of the partial derivatives of the brightness temperatures in a particular channel with respect to each parameter of the state vector. Due to non-linearity, these partial derivatives need to be computed at each iteration (state).

#### 2.3.1. Initial OE Setup

**y**, used in our forward model consists of dual polarization observations (v-pol and h-pol) at the 5 lower frequencies: 6.9, 10.7, 18.7, 23.8, 36.5 GHz. Four geophysical parameters are considered to be the leading terms controlling the observed microwave brightness temperatures in the measurement situation (considering open-ocean only):

**x**= [WS, TCWV, TCLW, SST],

**x**is fixed to:

^{−1}, ${e}_{TCWV}\text{}$ = 0.9 mm, ${e}_{TCLW\text{}}$ = 1 mm and ${e}_{SST}\text{}$ = 0.50 K. The uncertainties on the WS, TCVW and TCLW are best estimates based upon published validation results (see e.g., [47,55,56,57,58]). The SST uncertainty is derived from a comparison against Argo drifting buoys, using the MMD (see Section 3.3). The measurement covariance matrix,

**S**

**is initially set to a diagonal matrix with all diagonal elements equal to 0.1 K [54]. The retrieved state vector is obtained by performing the Newtonian iteration, as described in Equation (3).**

_{ϵ}#### 2.3.2. Testing for Convergence

_{TB}):

_{calc}fit the observed ones, TB

_{obs}. The RMSE

_{TB}criteria is chosen here over e.g., χ

^{2}as it provides an almost linear relationship with the performance of the OE, which will be shown in Section 3. Figure 4a illustrates the mean RMSE

_{TB}difference for each iteration using a subset of the drifter MMD. The uncertainty bars mark one standard deviation. A strong reduction in RMSE

_{TB}and standard deviation is found by performing the first iteration. The second iteration similarly leads to a decrease in RMSE

_{TB}and standard deviation, while the following iterations show no significant improvement on the mean RMSE

_{TB}. The usefulness of RMSE

_{TB}as a confidence indicator will be further illustrated in Section 3.

#### 2.3.3. Improving the Forward Model

_{calc}with TB

_{obs}. If we assume optimal forward model input variables and unbiased TB

_{obs}, we can regard the TB

_{obs}–TB

_{calc}differences as inefficiencies in the forward model that we would like to correct for. In other words, we want to use the best available input variables. Therefore, retrieved WS, TCWV and TCLW and in situ SST values are used in the forward model calculations, to bring us as close to true oceanic and atmospheric conditions as possible. The retrieved variables are obtained by running the initial optimal estimator for a subset of 37,242 matchups. These input variables are used to run the forward model once and the difference TB

_{obs}–TB

_{calc}is calculated for each channel. Part of the observed channel biases may be a result of the difference between the RTM used here and the one used in calibration of the RSS L2A product [60]. In addition, the RTM used here, does not include wind directional effects. Following Merchant et al. [25] cells with TB

_{obs}–TB

_{calc}differences falling outside the range given by the median ±3 robust standard deviations (RSD) in any of our 10 channels are discarded. Furthermore, only matchups that have passed the convergence test (Section 2.3.2) are included. The derived average TB

_{obs}–TB

_{calc}differences of the 10 channels range from −0.75 K on 10 GHz H to 0.62 K on 18.7 GHz V and are subsequently used as a constant bias correction of the forward model. In addition to the constant bias correction, an updated error covariance matrix

**S**

**is calculated from the TB**

_{ϵ}_{obs}–TB

_{calc}subset. The updated

**S**

**used in the following has an average of square root diagonals of 0.20 K, smallest for 10.7 GHz H and 36.5 GHz H (0.09 K) and largest for 6.9 GHz H (0.31 K).**

_{ϵ}_{calc}–TB

_{obs}to analytic functions of in situ SST, retrieved WS and NWP wind direction relative to the azimuthal look, ${\mathsf{\phi}}_{\mathrm{r}}$. The fitting is done on averaged TB

_{calc}–TB

_{obs}values for binned data with respect to SST, WS and ${\mathsf{\phi}}_{\mathrm{r}}$ and with binning intervals of: 1 °C, 2 m·s

^{−1}and 15°, respectively. Only average values from bins with more than 50 members are used when the regression coefficients are determined. Four sinusoidal terms were found to be the most optimal in representing the wind direction biases. The optimal regression model used for the forward model residuals is:

_{calc}–TB

_{obs}(final iteration) for all channels, and all matchups during 2010, before (black) and after (blue) the empirical bias correction scheme has been applied. Figure 5a indicates a positive bias at high latitudes, no bias at mid-latitudes and a slightly positive bias at the equatorial regions before the empirical bias correction has been applied. The black line of Figure 5b shows an almost linear trend in bias ranging from a positive bias of about 0.5 K in cold waters, no bias at temperatures ~20–25 °C and a slightly positive bias for warmer waters, which is in good agreement with Figure 5a. Figure 5c also reveals a systematic bias in the TB

_{calc}–TB

_{obs}difference with the NWP WS before the empirical bias correction is applied. At low wind speeds little bias is present but with increasing wind speeds the bias rapidly becomes larger. Also, the binned ${\mathsf{\phi}}_{\mathrm{r}}$ statistics reveal a dependency with a positive bias around $\text{}{\mathsf{\phi}}_{\mathrm{r}}=250$° that might be related to wind direction effects not included in the forward model. The bottom plots show the number of matchups in each bin (blue curve) and the cumulative percentage of matchups (red curve).

_{calc}for all channels, each time the forward model is called. The application of the empirical bias correction improves the behavior of the residuals against each of the four factors by flattening their bias curves and bringing them closer to zero. The standard deviation of the TB

_{calc}–TB

_{obs}difference also decreases with the application of the empirical bias correction scheme.

^{−1}, −0.04 mm and $7.19\times {10}^{-4}$ mm for WS, TCWV and TCLW, respectively.

**S**

_{ϵ,}S**and $\varepsilon $ values, where $\varepsilon $ is the perturbation used to calculate the Jacobians. The observation loop is started for each satellite observation pixel or matchup by reading the observed brightness temperatures and the first guess values. Thereafter, the iteration process is initiated. For each iteration, the forward model is used to calculate the simulated brightness temperature from the state vector (in the first step: state vector = first guess). Moreover, the Jacobians (**

_{a}**K**), cost function (

**J**), uncertainty (

**S**) and sensitivity (

_{x}**A**, Section 3.1) are calculated. The change in the cost function between two iterations is used to test for convergence and a maximum of 10 iterations are allowed. Until convergence is met, the state vector is updated for each iteration step and the iteration continues. When the iteration process is stopped the state vector is saved together with the uncertainties, corresponding averaging kernels and simulated brightness temperatures.

## 3. Results

^{−1}; and (3) retrieved cloud liquid water outside the range: 0–1.5 kg/kg (mass of condensate/mass of moist air). Applying this gross error check removes 9% of the retrievals and reduces the standard deviation to 0.54 K. Another approach is to check that the retrieval is consistent with the satellite observations by evaluating the RMSE

_{TB}value as described in Section 2.3.2. The practical usefulness of the quality indicator, RMSE

_{TB}, is shown in Figure 7. All retrievals that have passed the convergence test have been binned with respect to RMSE

_{TB}with a bin size of 0.1 K. The number of members in each bin is shown in the bottom plot (blue curve) together with the cumulative percentage (red curve). The middle plot displays the binned distribution of OE SST minus drifter SST (with bin size of 1 K) as a function of binned RMSE

_{TB}, where the color bar is the number of matchups in each bin. The top plot shows the mean (solid) and standard deviation (dashed) of OE SST minus drifter SST as a function of the binned RMSE

_{TB}statistic. We notice a large increase in scatter as RMSE

_{TB}increases. This makes the RMSE

_{TB}-value an efficient indicator of the quality of the OE SST retrieval. Limiting RMSE

_{TB}to 1 K removes only 8% of the converged retrievals and leaves the remaining 92% with a bias of 0.02 K and standard deviation of 0.51 K. These results reflect that the RMSE

_{TB}quality indicator provides a better discrimination of quality compared to the gross error check.

_{TB}value below 0.5 K and a corresponding bias of 0.02 K and standard deviation of 0.47 K, while 42% have a RMSE

_{TB}-value less than 0.35 K and a corresponding bias of 0.02 K and standard deviation of 0.45 K. The validation results of the NWP SSTs are included here for reference, but note that drifting buoy observations and PMW observations have already been included in the generation of the NWP fields, as explained earlier. In the following we will only consider the 64% “good” retrievals, which have a corresponding RMSE

_{TB}< 0.5 K.

_{TB}< 0.5 K. The geographical distribution of the mean OE SST minus drifter SST reveals a dependency on latitude, with positive bias at mid-latitudes and negative bias in high latitudes and the equatorial region, likely linked to surface emissivity issues (dependent on wind speed and direction) and atmospheric effects. We notice areas with high standard deviations in e.g., the Gulf Stream Extension, the Kuroshio Current and the Aghulas Retroflection areas. These western boundary current regions are known to be very dynamical with high mesoscale activity and large SST gradients over smaller scales [61,62]. The mesoscale SST gradients will result in enhanced differences when the large (64 × 32 km native instantaneous field of view at 6.9 GHz) satellite footprints are compared with in situ observations. The elevated variability in these regions is therefore not related to the quality of the OE SST retrieval.

_{TB}< 0.5 K, as a function of binned drifter SST and NWP WS, respectively. The OE SST displays a warm bias for drifter SSTs in the range of 15–25 °C and similar for the small fraction of very high (>28 °C) SSTs. Figure 9b shows that the OE SST has a bias dependency on the NWP WS with a warm bias for low (<6 m·s

^{−1}) wind speeds and a cold bias for higher wind speeds.

#### 3.1. SST Sensitivity

**A**, which contains the sensitivities of the retrieved parameters to the true state on its diagonal (and cross-sensitivities between parameters on the off-diagonals):

^{t}is the true state. If the averaging kernel was equal to the identity matrix the a priori state would have no influence on the retrieved state, which instead would be obtained purely from the information content of the measured brightness temperatures. The mean SST sensitivity for all drifter matchups during 2010 is found to be 0.50 with above OE setup and Figure 10a shows the geographical distribution of SST sensitivity. The SST sensitivity is lowest in high latitudes and increases towards the equatorial region, which is consistent with the fact that $\partial $ TB/ $\partial $ SST is smaller for cold waters (especially for X-band 10.65 GHz channels) [63]. The equatorial region reveals sensitivities of ~0.6 while high latitudes have sensitivities around 0.4. Sensitivities from 0.39 to 0.65 were reported in Gentemann et al. [64] for 0 °C and 30 °C SST, respectively, for an AMSR-E regression type retrieval. In addition, Prigent et al. [63] used simulations to derive channel sensitivities $\partial $ TB/ $\partial $ SST of ~0.3 to 0.6 for the 6 GHz V. These results are in good agreement with the sensitivities obtained here.

#### 3.2. Retrieval Uncertainty

**S**

_{x}_{,}due to uncertainties in the measurements, forward model, and in the a priori state vector (see Equation (4)). Considering all converged drifter matchups during 2010, the global mean uncertainty is 0.35 K. From Figure 7, it is evident that the quality of the SST retrieval is closely connected to the RMSE

_{TB}value from the retrieval. For that reason, we have set up an additional uncertainty indicator based on a scaled RMSE

_{TB}value, using a scaling factor of 0.55. Figure 11 shows the validation results for the uncertainties of the converged matchups, where the actual SST retrieval differences against drifter observations are displayed versus the theoretical uncertainties obtained from the RMSE

_{TB}values. The dashed line represents the ideal uncertainty under the assumptions that drifting buoys have a total uncertainty of 0.2 K and that the sampling uncertainty is 0.3 K. The point to satellite footprint sampling difference is estimated based on the results in Høyer et al. [44]. It is evident from the figure that there is a good agreement between the observed uncertainty and the modeled uncertainty estimates that are based on the RMSE

_{TB}and an integrated part of every OE retrieval. The mean modeled uncertainty is estimated to 0.48 K including the in situ and sampling uncertainty. Figure 10b shows the geographical distribution of RMSE

_{TB}considering the best 64% retrievals with a corresponding RMSE

_{TB}< 0.5 K.

#### 3.3. Validation against Independent Argo Floats

_{TB}and the quality of the OE retrieval, and the highest quality OE retrievals performing better than the NWP SSTs. Note that the standard deviation of differences also includes the point to footprint sampling effects that are larger for the OE retrievals than for the NWP, which has an original spatial resolution of 0.05 degrees in latitude and longitude.

**S**has an average value of 0.35 K, while the modeled estimate has an uncertainty of 0.47 K. The modeled uncertainty is calculated using a scaled RMSE

_{x}_{TB}with a scaling factor of 0.65. The modeled uncertainty has been evaluated for the Argo matchups and the result is shown in Figure 12. The dashed lines represent the ideal uncertainty under the assumptions that Argo floats have an accuracy of 0.002 K [42] and that the sampling uncertainty is 0.3 K [44].

#### 3.4. OE vs. NWP Latitudinal Performance

## 4. Discussion

_{TB}for the first two iterations. This approach resembles what is used for OE sea ice concentration retrieval [30,31] but differs from the OE IR SST retrievals, where one inversion is typically performed [24,25]. The need for several iterations is probably a result of the non-linear behavior of the forward model.

## 5. Conclusions

**S**and the

_{a}**S**

**statistical parameters, as these are key parameters in the retrieval process. Alternative forward models could be tested in the retrieval process, but few accurate forward models exist at present that are suitable for use in an OE context. More work should therefore be put into improving the forward models with the aim of PMW OE SST retrievals. In addition, more work could be done on assessing the role of the first guess values and the impact of these observations on the retrieved SSTs. In the present work, we have disregarded observations in the vicinity of sea ice, but considering the results obtained within the ESA-CCI Sea Ice project, a future development could include the development of an integrated ocean and sea ice OE processor, that is able to estimate the sea ice concentration and SST at the same time and thus allowing for PMW SSTs closer to the marginal ice zone.**

_{ϵ}- That the future 6–7 GHz frequency wide swath imaging capability currently provided by GCOM-W AMSR-2 is sustained by flying a new mission. This implies immediate initiation of satellite development for a potential launch in 2025.
- That the spatial resolution of the 6–7 GHz frequency channels is significantly improved to provide a ~10 km native instantaneous spatial resolution (which may imply using a large 6–9 m rotating deployable mesh antenna). This is required to minimize significant loss of data in the coastal zone and marginal sea ice zone due to side lobe contamination, currently there are no valid measurements within 100 km of these areas.
- That the radiometric quality of future satellite microwave radiometers is significantly improved over current capability. This is required because in many areas imaging microwave radiometer measurements are the only measurements available for the SST climate data record in areas characterized by quasi-permanent cloud cover that confounds thermal IR satellite SST retrievals.
- That appropriate combination with one or more higher-frequency channels (10, 18, 37 GHz) is provided in order to resolve the ambiguities in the microwave measurements if too few channels are available.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Vázquez-Cuervo, J.; Armstrong, E.M.; Harris, A. The effect of aerosols and clouds on the retrieval of infrared sea surface temperatures. J. Clim.
**2004**, 17, 3921–3933. [Google Scholar] [CrossRef] - Reynolds, R.W. Impact of mount pinatubo aerosols on satellite-derived sea surface temperatures. J. Clim.
**1993**, 6, 768–774. [Google Scholar] [CrossRef] - Reynolds, R.W.; Rayner, N.A.; Smith, T.M.; Stokes, D.C.; Wang, W. An improved in situ and satellite sst analysis for climate. J. Clim.
**2002**, 15, 1609–1625. [Google Scholar] [CrossRef] - Donlon, C.; Rayner, N.; Robinson, I.; Poulter, D.J.S.; Casey, K.S.; Vazquez-Cuervo, J.; Armstrong, E.; Bingham, A.; Arino, O.; Gentemann, C.; et al. The global ocean data assimilation experiment high-resolution sea surface temperature pilot project. Bull. Am. Meteorol. Soc.
**2007**, 88, 1197–1213. [Google Scholar] [CrossRef] - Donlon, C.J.; Casey, K.S.; Gentemann, C.L.; Harris, A. Successes and challenges for the modern sea surface temperature observing system. In Proceeding of OceanObs’09: Sustained Ocean Observations and Information for Society; Hall, J., Harrison, D.E., Stammer, D., Eds.; ESA Publication WPP-306: Venice, Italy, 2010; Volume 2. [Google Scholar]
- Wentz, F.J.; Gentemann, C.; Smith, D.; Chelton, D.B. Satellite measurements of sea surface temperature through clouds. Science
**2000**, 288, 847–850. [Google Scholar] [CrossRef] [PubMed] - Chelton, D.B.; Wentz, F.J. Global microwave satellite observations of sea surface temperature for numerical weather prediction and climate research. Bull. Am. Meteorol. Soc.
**2005**, 86, 1097–1115. [Google Scholar] [CrossRef] - Wilheit, T.T.; Chang, A.T.C. An algorithm for retrieval of ocean surface and atmospheric parameters from the observations of the scanning multichannel microwave radiometer. Radio Sci.
**1980**, 15, 525–544. [Google Scholar] [CrossRef] - Lipes, R.G. Description of SEASAT radiometer status and results. J. Geophys. Res.
**1982**, 87. [Google Scholar] [CrossRef] - Milman, A.S.; Wilheit, T.T. Sea surface temperatures from the scanning multichannel microwave radiometer on Nimbus 7. J. Geophys. Res.
**1985**, 90. [Google Scholar] [CrossRef] - Maeda, T.; Taniguchi, Y.; Imaoka, K. GCOM-W1 AMSR2 Level 1R Product: Dataset of brightness temperature modified using the antenna pattern matching technique. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 770–782. [Google Scholar] [CrossRef] - Gaiser, P.W.; St Germain, K.M.; Twarog, E.M.; Poe, G.A.; Purdy, W.; Richardson, D.; Grossman, W.; Jones, W.L.; Spencer, D.; Golba, G.; et al. The WindSat spaceborne polarimetric microwave radiometer: Sensor description and early orbit performance. IEEE Trans. Geosci. Remote Sens.
**2004**, 42, 2347–2361. [Google Scholar] [CrossRef] - Xie, S.-P. Satellite observations of cool ocean—Atmosphere interaction*. Bull. Am. Meteorol. Soc.
**2004**, 85, 195–208. [Google Scholar] [CrossRef] - Shibata, A. Calibration of AMSR-E SST toward a monitoring of global warming. In Proceedings of the 2005 IEEE International Geoscience and Remote Sensing Symposium, Seoul, Korea, 29 July 2005. [Google Scholar]
- Shibata, A. Features of ocean microwave emission changed by wind at 6 GHz. J. Oceanogr.
**2006**, 62, 321–330. [Google Scholar] [CrossRef] - Wentz, F.J.; Meissner, T. AMSR_E Ocean Algorithms; Remote Sensing Systems: Santa Rosa, CA, USA, 2007; p. 6. [Google Scholar]
- Hosoda, K.; Murakami, H.; Shibata, A.; Sakaida, F.; Kawamura, H. Difference characteristics of sea surface temperature observed by GLI and AMSR aboard ADEOS-II. J. Oceanogr.
**2006**, 62, 339–350. [Google Scholar] [CrossRef] - Gentemann, C.L. Three way validation of MODIS and AMSR-E sea surface temperatures. J. Geophys. Res. Oceans
**2014**, 119, 2583–2598. [Google Scholar] [CrossRef] - Donlon, C.J.; Martin, M.; Stark, J.; Roberts-Jones, J.; Fiedler, E.; Wimmer, W. The Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) system. Remote Sens. Environ.
**2012**, 116, 140–158. [Google Scholar] [CrossRef] - Hosoda, K.; Kawamura, H.; Sakaida, F. Improvement of New Generation Sea Surface Temperature for Open ocean (NGSST-O): A new sub-sampling method of blending microwave observations. J. Oceanogr.
**2015**, 71, 205–220. [Google Scholar] [CrossRef] - Stark, J.D.; Donlon, C.J.; Martin, M.J.; McCulloch, M.E. OSTIA : An operational, high resolution, real time, global sea surface temperature analysis system. In Proceedings of the OCEANS, Aberdeen, UK, 18–21 June 2007; pp. 1–4. [Google Scholar]
- Reynolds, R.W.; Smith, T.M.; Liu, C.; Chelton, D.B.; Casey, K.S.; Schlax, M.G. Daily high-resolution-blended analyses for sea surface temperature. J. Clim.
**2007**, 20, 5473–5496. [Google Scholar] [CrossRef] - Donlon, C.; Casey, K.; Robinson, I.; Gentemann, C.; Reynolds, R.; Barton, I.; Arino, O.; Stark, J.; Rayner, N.; LeBorgne, P.; et al. The GODAE high-resolution sea surface temperature pilot project. Oceanography
**2009**, 22, 34–45. [Google Scholar] [CrossRef] - Merchant, C.J.; Le Borgne, P.; Marsouin, A.; Roquet, H. Optimal estimation of sea surface temperature from split-window observations. Remote Sens. Environ.
**2008**, 112, 2469–2484. [Google Scholar] [CrossRef] - Merchant, C.J.; Le Borgne, P.; Roquet, H.; Marsouin, A. Sea surface temperature from a geostationary satellite by optimal estimation. Remote Sens. Environ.
**2009**, 113, 445–457. [Google Scholar] [CrossRef] - Merchant, C.J.; Embury, O. Simulation and Inversion of Satellite Thermal Measurements. In Experimental Methods in the Physical Sciences; Elsevier: Amsterdam, The Netherlands, 2014; Volume 47, pp. 489–526. ISBN 978-0-12-417011-7. [Google Scholar]
- Merchant, C.J.; Embury, O.; Roberts-Jones, J.; Fiedler, E.; Bulgin, C.E.; Corlett, G.K.; Good, S.; McLaren, A.; Rayner, N.; Morak-Bozzo, S.; et al. Sea surface temperature datasets for climate applications from Phase 1 of the European Space Agency Climate Change Initiative (SST CCI). Geosci. Data J.
**2014**, 1, 179–191. [Google Scholar] [CrossRef] - Merchant, C.J.; Le Borgne, P.; Roquet, H.; Legendre, G. Extended optimal estimation techniques for sea surface temperature from the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI). Remote Sens. Environ.
**2013**, 131, 287–297. [Google Scholar] [CrossRef] - Pedersen, L.T. Merging microwave radiometer data and meteorological data for improved sea ice concentrations. EARSeL Adv. Remote Sens.
**1994**, 3, 81–89. [Google Scholar] - Melsheimer, C.; Heygster, G.; Mathew, N.; Toudal Pedersen, L. Retrieval of sea ice emissivity and integrated retrieval of surface and atmospheric parameters over the Arctic from AMSR-E data. J. Remote Sens. Soc. Jpn.
**2009**, 29, 236–241. [Google Scholar] - Scarlat, R.C.; Heygster, G.; Pedersen, L.T. Experiences with an Optimal estimation algorithm for surface and atmospheric parameter retrieval from passive microwave data in the arctic. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2017**, 10, 3934–3947. [Google Scholar] [CrossRef] - Bettenhausen, M.H.; Smith, C.K.; Bevilacqua, R.M.; Wang, N.Y.; Gaiser, P.W.; Cox, S. A nonlinear optimization algorithm for WindSat wind vector retrievals. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 597–610. [Google Scholar] [CrossRef] - Ashcroft, P.; Wentz, F.J. AMSR-E/Aqua L2A Global Swath Spatially-Resampled Brightness Temperatures (Tb), Version 3. 2013. Available online: https://cmr.earthdata.nasa.gov/search/concepts/C190757121-NSIDC_ECS.html (accessed on 30 July 2016).
- Wentz, F.J. SSM/I Version-7 Calibration Report; Remote Sensing Systems: Santa Rosa, CA, USA; 2013; p. 46. [Google Scholar]
- Woodruff, S.D.; Worley, S.J.; Lubker, S.J.; Ji, Z.; Eric Freeman, J.; Berry, D.I.; Brohan, P.; Kent, E.C.; Reynolds, R.W.; Smith, S.R.; et al. ICOADS Release 2.5: Extensions and enhancements to the surface marine meteorological archive. Int. J. Climatol.
**2011**, 31, 951–967. [Google Scholar] [CrossRef] - Good, S.A.; Martin, M.J.; Rayner, N.A. EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates: THE EN4 DATA SET. J. Geophys. Res. Oceans
**2013**, 118, 6704–6716. [Google Scholar] [CrossRef] - O’Carroll, A.G.; Eyre, J.R.; Saunders, R.W. Three-Way Error Analysis between AATSR, AMSR-E, and In Situ sea surface temperature observations. J. Atmos. Ocean. Technol.
**2008**, 25, 1197–1207. [Google Scholar] [CrossRef] - Atkinson, C.P.; Rayner, N.A.; Kennedy, J.J.; Good, S.A. An integrated database of ocean temperature and salinity observations. J. Geophys. Res. Oceans
**2014**, 119, 7139–7163. [Google Scholar] [CrossRef] - Roemmich, D.; Johnson, G.; Riser, S.; Davis, R.; Gilson, J.; Owens, W.B.; Garzoli, S.; Schmid, C.; Ignaszewski, M. The Argo Program: Observing the Global Oceans with Profiling Floats. Oceanography
**2009**, 22, 34–43. [Google Scholar] [CrossRef] - Gille, S.T. Decadal-Scale Temperature Trends in the Southern Hemisphere Ocean. J. Clim.
**2008**, 21, 4749–4765. [Google Scholar] [CrossRef] - Kennedy, J.J. A review of uncertainty in in situ measurements and data sets of sea surface temperature: In situ sst uncertainty. Rev. Geophys.
**2014**, 52, 1–32. [Google Scholar] [CrossRef] - Abraham, J.P.; Baringer, M.; Bindoff, N.L.; Boyer, T.; Cheng, L.J.; Church, J.A.; Conroy, J.L.; Domingues, C.M.; Fasullo, J.T.; Gilson, J.; et al. A review of global ocean temperature observations: Implications for ocean heat content estimates and climate change: Review of ocean observations. Rev. Geophys.
**2013**, 51, 450–483. [Google Scholar] [CrossRef] - Embury, O.; Merchant, C.J.; Corlett, G.K. A reprocessing for climate of sea surface temperature from the along-track scanning radiometers: Initial validation, accounting for skin and diurnal variability effects. Remote Sens. Environ.
**2012**, 116, 62–78. [Google Scholar] [CrossRef] - Høyer, J.L.; Karagali, I.; Dybkjær, G.; Tonboe, R. Multi sensor validation and error characteristics of Arctic satellite sea surface temperature observations. Remote Sens. Environ.
**2012**, 121, 335–346. [Google Scholar] [CrossRef] - Merchant, C.J.; Embury, O.; Rayner, N.A.; Berry, D.I.; Corlett, G.K.; Lean, K.; Veal, K.L.; Kent, E.C.; Llewellyn-Jones, D.T.; Remedios, J.J.; et al. A 20 year independent record of sea surface temperature for climate from Along-Track Scanning Radiometers: SST for climate from atsrs. J. Geophys. Res. Oceans
**2012**, 117. [Google Scholar] [CrossRef] - Udaya Bhaskar, T.V.S.; Rahman, S.H.; Pavan, I.D.; Ravichandran, M.; Nayak, S. Comparison of AMSR-E and TMI sea surface temperature with Argo near-surface temperature over the Indian Ocean. Int. J. Remote Sens.
**2009**, 30, 2669–2684. [Google Scholar] [CrossRef] - Dee, D.P.; Uppala, S.M.; Simmons, A.J.; Berrisford, P.; Poli, P.; Kobayashi, S.; Andrae, U.; Balmaseda, M.A.; Balsamo, G.; Bauer, P.; et al. The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc.
**2011**, 137, 553–597. [Google Scholar] [CrossRef] - Zweng, M.M.; Reagan, J.R.; Antonov, J.I.; Seidov, D.; Biddle, M.M. World Ocean Atlas 2013, Volume 2, Salinity. 2013. Available online: https://repository.library.noaa.gov/view/noaa/14848 (accessed on 26 June 2017).
- Boyer, T.P.; Antonov, J.I.; Baranova, O.K.; Garcia, H.E.; Johnson, D.R.; Mishonov, A.V.; O’Brien, T.D.; Seidov, D.; Smolyar, I.; Zweng, M.M.; et al. World Ocean Database 2013; NOAA Printing Office: Silver Spring, MD, USA, 2013; 208p. [Google Scholar]
- Block, T.; Embacher, S.; Merchant, C.J.; Donlon, C. High performance software framework for the calculation of satellite-to-satellite data matchups (MMS version 1.2). Geosci. Model Dev. Discuss.
**2017**, 1–15. [Google Scholar] [CrossRef] - Schulzweida, U.; Kornblueh, L.; Quast, R. CDO User’s Guide—Climate Data Operators; Max Planck Institute for Meteorology: Hamburg, Germany, 2010; pp. 1–173. [Google Scholar]
- Gentemann, C.L.; Hilburn, K.A. In situ validation of sea surface temperatures from the GCOM-W1 AMSR2 RSS calibrated brightness temperatures: Validation of RSS GCOM-W1 SST. J. Geophys. Res. Oceans
**2015**, 120, 3567–3585. [Google Scholar] [CrossRef] - Rodgers, C.D. Inverse Methods for Atmospheric Sounding—Theory and Practice; Series on Atmospheric Ocanic and Planetary Physics; World Scientific Publishing Co. Pte. Ltd.: Singapore, 2000; Volume 2, ISBN 978-981-281-371-8. [Google Scholar]
- Wentz, F.J.; Meissner, T. AMSR Ocean Algorithm. Algorithm Theoretical Basis Document; Remote Sensing Systems: Santa Rosa, CA, USA, 2000. [Google Scholar]
- Chelton, D.B.; Freilich, M.H. Scatterometer-based assessment of 10-m wind analyses from the operational ECMWF and NCEP Numerical weather prediction models. Mon. Weather Rev.
**2005**, 133, 409–429. [Google Scholar] [CrossRef] - Jakobson, E.; Vihma, T.; Palo, T.; Jakobson, L.; Keernik, H.; Jaagus, J. Validation of atmospheric reanalyses over the central Arctic Ocean: Tara reanalyses validation. Geophys. Res. Lett.
**2012**, 39. [Google Scholar] [CrossRef] - Li, J.-L.F.; Waliser, D.; Woods, C.; Teixeira, J.; Bacmeister, J.; Chern, J.; Shen, B.-W.; Tompkins, A.; Tao, W.-K.; Köhler, M. Comparisons of satellites liquid water estimates to ECMWF and GMAO analyses, 20th century IPCC AR4 climate simulations, and GCM simulations. Geophys. Res. Lett.
**2008**, 35. [Google Scholar] [CrossRef] - Jiang, J.H.; Su, H.; Zhai, C.; Perun, V.S.; Del Genio, A.; Nazarenko, L.S.; Donner, L.J.; Horowitz, L.; Seman, C.; Cole, J.; et al. Evaluation of cloud and water vapor simulations in CMIP5 climate models using NASA “A-Train” satellite observations: Evaluation of IPCC Ar5 model simulations. J. Geophys. Res. Amospheres
**2012**, 117. [Google Scholar] [CrossRef] - Donlon, C.J.; Minnett, P.J.; Gentemann, C.; Nightingale, T.J.; Barton, I.J.; Ward, B.; Murray, M.J. Toward improved validation of satellite sea surface skin temperature measurements for climate research. J. Clim.
**2002**, 15, 353–369. [Google Scholar] [CrossRef] - Meissner, T.; Wentz, F.J. The emissivity of the ocean surface between 6 and 90 GHz over a large range of wind speeds and earth incidence angles. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3004–3026. [Google Scholar] [CrossRef] - Pascual, A.; Faugère, Y.; Larnicol, G.; Le Traon, P.-Y. Improved description of the ocean mesoscale variability by combining four satellite altimeters. Geophys. Res. Lett.
**2006**, 33. [Google Scholar] [CrossRef] - Legeckis, R. A survey of worldwide sea surface temperature fronts detected by environmental satellites. J. Geophys. Res.
**1978**, 83. [Google Scholar] [CrossRef] - Prigent, C.; Aires, F.; Bernardo, F.; Orlhac, J.-C.; Goutoule, J.-M.; Roquet, H.; Donlon, C. Analysis of the potential and limitations of microwave radiometry for the retrieval of sea surface temperature: Definition of MICROWAT, a new mission concept: Sea Temperature from Microwaves. J. Geophys. Res. Oceans
**2013**, 118, 3074–3086. [Google Scholar] [CrossRef] - Gentemann, C.L.; Meissner, T.; Wentz, F.J. Accuracy of satellite sea surface temperatures at 7 and 11 GHz. IEEE Trans. Geosci. Remote Sens.
**2010**, 48, 1009–1018. [Google Scholar] [CrossRef] - Merchant, C.J.; Harris, A.R.; Roquet, H.; Le Borgne, P. Retrieval characteristics of non-linear sea surface temperature from the advanced very high resolution radiometer. Geophys. Res. Lett.
**2009**, 36. [Google Scholar] [CrossRef] - Castro, S.L.; Wick, G.A.; Jackson, D.L.; Emery, W.J. Error characterization of infrared and microwave satellite sea surface temperature products for merging and analysis. J. Geophys. Res.
**2008**, 113. [Google Scholar] [CrossRef] - Dong, S.; Gille, S.T.; Sprintall, J.; Gentemann, C. Validation of the advanced microwave scanning radiometer for the earth observing system (AMSR-E) sea surface temperature in the southern ocean. J. Geophys. Res.
**2006**, 111. [Google Scholar] [CrossRef]

**Figure 2.**(

**a**) Geographical distribution of drifter matchups per square kilometer during 2010; (

**b**) the latitudinal distribution of drifter matchups before and after the number of matchups have been evened out by latitude. The red line denotes the maximum allowed matchups per latitude.

**Figure 3.**(

**a**) Geographical distribution of Argo matchups per square kilometer during 2009–2011; (

**b**) the latitudinal distribution of Argo matchups.

**Figure 4.**(

**a**) The mean RMSE

_{TB}for all channels is plotted for each iteration number. Uncertainty bars show one standard deviation; (

**b**) number of iterations performed for all drifter matchups during 2010.

**Figure 5.**Mean simulated minus observed brightness temperatures for all channels against (

**a**) Latitude; (

**b**) Drifter SST; (

**c**) NWP WS; (

**d**) NWP wind direction relative to azimuthal satellite look. Dashed lines are standard deviations and solid lines are biases. The black and blue colors denote differences before/after the empirical bias correction has been applied. The bottom plots show the number of matchups (blue) and the cumulative percentage of matchups (red) for each data bin.

**Figure 7.**OE SST minus drifter SST as a function of binned RMSE

_{TB}. The dashed line is standard deviation while the solid line is bias in the upper figure. The surface plot in the middle figure shows the number of matchups in each bin, while the bottom plot shows the number of matchups (blue) and the cumulative percentage of matchups (red) in each RMSE

_{TB}bin.

**Figure 8.**(

**a**) Mean OE SST minus drifter SST; (

**b**) Mean standard deviation of the OE retrieved minus drifter SST difference. Only retrievals with a corresponding RMSE

_{TB}< 0.5 K are plotted in the figures.

**Figure 9.**OE SST minus drifter SST as a function of binned (

**a**) Drifter SST; (

**b**) NWP WS. Solid lines are bias and dashed lines are standard deviation in the upper figures. The surface plots in middle figures show the number of matchups in each bin, while the bottom plots show the total number of matchups (blue) and the cumulative percentage of matchups (red) in each drifter SST and NWP WS bin, respectively. Only retrievals with a corresponding RMSE

_{TB}< 0.5 K are plotted in the figures.

**Figure 10.**Gridded statistics of (

**a**) mean sensitivity and (

**b**) mean RMSE

_{TB}. Only retrievals with a corresponding RMSE

_{TB}< 0.5 K are plotted.

**Figure 11.**OE SST uncertainty validation with respect to drifter SST. Dashed lines show the ideal uncertainty model accounting for uncertainties in drifter SST and the sampling error. Solid black lines show one standard deviation of the retrieved minus drifter differences for each 0.1 K bin and the red symbols mark the mean bias. The bottom plot shows number of matchups (blue) and the cumulative percentage of matchups for each bin (red).

**Figure 12.**OE SST uncertainty validation with respect to Argo SSTs. Dashed lines show the ideal uncertainty model accounting for uncertainties in Argo SST and the sampling error. Solid black lines show one standard deviation of the retrieved minus Argo differences for each 0.1 K bin and the red symbols mark the mean bias. The bottom plot shows number of matchups (blue) and the cumulative percentage of matchups (red) for each bin.

**Figure 13.**The latitudinal difference in standard deviations of OE and NWP SST compared against in situ SST. The blue curve is the comparison against drifters, while the red curve shows the comparison against Argo floats.

Flagging | N | % Removed |
---|---|---|

All matchups | 7,278,035 | |

Gross error flag | 6,323,288 | 13.1 |

- -
- Land/ice mask
^{1}
| 13.1 | |

- -
- Sun glitter
^{1}
| 9.6 | |

- -
- RFI
^{1}
| 6.5 | |

- -
- Diurnal warming
^{1}
| 8.0 | |

- -
- Rain
^{1}
| 0.4 | |

All above checks | 4,286,354 | 41.1 |

Even out by latitude | 3,764,798 | 12.2 |

Total | 3,764,798 | 48.3 |

^{1}Percentage of gross error checked matchups removed by applying each filter individually.

Aspect of Optimal Estimator | Configuration |
---|---|

Initial forward model, iF(x) | Modified from Wentz et al. [54] (Section 2.3.1) |

Channels used in retrieval | 6.9, 10.7, 18.7, 23.8, 36.5 GHz (V/H) |

First guess fields, x_{a} | NWP (Section 2.1.3) |

Prior error covariance for SST, ${e}_{SST}$ | 0.5 K |

Error covariance of observations and model, S_{ϵ} | Full matrix (Section 2.3.2) |

Convergence criterion | $\mathsf{\u2206}\mathrm{J}={\mathrm{J}}_{\mathrm{i}}-{\mathrm{J}}_{\mathrm{i}+1}<0.1$. (Section 2.3.2) |

IterationsImproved forward model, F(x) | Max iterations = 10iF(x) + corrections (Section 2.3.3) |

Filter | Bias/K OE-Drifter | std/K OE-Drifter | Bias/K NWP-Drifter | std/K NWP-Drifter | N (10^{6}) | |
---|---|---|---|---|---|---|

Convergence test passed | 0.02 | 0.57 | −0.04 | 0.50 | 3.7429 | =100% |

Gross error check | 0.04 | 0.54 | −0.04 | 0.50 | 3.4071 | =91% |

RMSE_{TB} < 1 K | 0.02 | 0.51 | −0.04 | 0.50 | 3.4329 | =92% |

RMSE_{TB} < 0.50 K | 0.02 | 0.47 | −0.04 | 0.48 | 2.3953 | =64% |

RMSE_{TB} < 0.35 K | 0.02 | 0.45 | −0.04 | 0.47 | 1.5681 | =42% |

Filter | Bias/K OE-Argo | std/K OE-Argo | Bias/K NWP-Argo | std/K NWP-Argo | N | |
---|---|---|---|---|---|---|

Convergence test passed | 0.01 | 0.61 | −0.05 | 0.55 | 57789 | =100% |

Gross error check | 0.03 | 0.58 | −0.05 | 0.54 | 51846 | =90% |

RMSE_{TB} < 1 K | 0.01 | 0.55 | −0.06 | 0.54 | 53150 | =92% |

RMSE_{TB} < 0.50 K | 0.01 | 0.50 | −0.06 | 0.51 | 36639 | =63% |

RMSE_{TB} < 0.35 K | 0.01 | 0.49 | −0.05 | 0.50 | 23410 | =41% |

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## Share and Cite

**MDPI and ACS Style**

Nielsen-Englyst, P.; L. Høyer, J.; Toudal Pedersen, L.; L. Gentemann, C.; Alerskans, E.; Block, T.; Donlon, C.
Optimal Estimation of Sea Surface Temperature from AMSR-E. *Remote Sens.* **2018**, *10*, 229.
https://doi.org/10.3390/rs10020229

**AMA Style**

Nielsen-Englyst P, L. Høyer J, Toudal Pedersen L, L. Gentemann C, Alerskans E, Block T, Donlon C.
Optimal Estimation of Sea Surface Temperature from AMSR-E. *Remote Sensing*. 2018; 10(2):229.
https://doi.org/10.3390/rs10020229

**Chicago/Turabian Style**

Nielsen-Englyst, Pia, Jacob L. Høyer, Leif Toudal Pedersen, Chelle L. Gentemann, Emy Alerskans, Tom Block, and Craig Donlon.
2018. "Optimal Estimation of Sea Surface Temperature from AMSR-E" *Remote Sensing* 10, no. 2: 229.
https://doi.org/10.3390/rs10020229