# Sea Surface Temperature Analysis for Fengyun-3C Data Using Oriented Elliptic Correlation Scales

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Methods

#### 2.2.1. Oriented Elliptic Correlation Scale

#### 2.2.2. Estimation of SST Observation Error

**R**is a vector of regressors obtained from $M{D}_{local}$, $\langle \xb7\rangle $,which denotes averaging of the vector, superscript T stands for the transpose of a vector, and ${D}_{local}$ is a covariance matrix of regressors. After calculating the parameter of ${\rho}_{i,j}$ with Equation (3),$\left\{{\rho}_{local}\right\}$ is the collection of ${\rho}_{i,j}$ for each pixel in the local window that can be obtained, and the $M{D}_{optimal}$ can be chosen when the difference between the centered estimated standard deviation ${\rho}_{i,j}$ and $\left\{{\rho}_{local}\right\}$ is smaller than a finite value S. The initial S is 0.5, and it increases by 0.1 until the number of optimal matchup samples $({N}_{optimal})$ is larger than 100. Finally, the error standard deviation estimation, $S{D}_{est}$, of VIRRD and VIRRN can be obtained using the matched datasets of in situ SST and ${T}_{s,i,j}$ from $M{D}_{optimal}$.

#### 2.2.3. Estimation of SST Background Error

## 3. Results

#### 3.1. Comparison of 2016 SST Analysis Results

#### 3.2. Validation of Two Sets of Daily SST Analysis Results

## 4. Discussion

#### 4.1. Error Analysis for SST Analysis Methods

#### 4.2. Error Analysis for SST Observations

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Thomas, A. Evaluation of Indian Summer Monsoon Rainfall Using the NCEP Global Model: An SST Impact Study. Pure Appl. Geophys.
**2019**, 176, 3697–3715. [Google Scholar] [CrossRef] - Barnett, T.P.; Graham, N.; Pazan, S.; White, W.; Latif, M.; Flügel, M. ENSO and ENSO-related predictability. Part I: Prediction of equatorial Pacific sea surface temperature with a hybrid coupled ocean-atmosphere model. J. Clim.
**1993**, 6, 1545–1566. [Google Scholar] [CrossRef] [Green Version] - Brasnett, B. A global analysis of sea surface temperature for numerical weather prediction. J. Atmos. Ocean. Technol.
**1997**, 14, 925–937. [Google Scholar] [CrossRef] - Ruela, R.; Sousa, M.C.; de Castro, M.; Dias, J.M. Global and regional evolution of sea surface temperature under climate change. Glob. Planet. Chang.
**2020**, 190, 103190. [Google Scholar] [CrossRef] - Xu, Y.; Li, J.; Sun, C.; Lin, X.; Liu, H.; Wang, L.; Liang, Y.; Wang, Q.; Zhang, Y.; Hou, Z.; et al. Contribution of SST change to multidecadal global and continental surface air temperature trends between 1910 and 2013. Clim. Dyn.
**2020**, 54, 1295–1313. [Google Scholar] [CrossRef] [Green Version] - Banzon, V.F.; Reynolds, R.W.; Stokes, D.; Xue, Y. A 1/4°-Spatial-Resolution Daily Sea Surface Temperature Climatology Based on a Blended Satellite and in situ Analysis. J. Clim.
**2014**, 27, 8221–8228. [Google Scholar] [CrossRef] - Martin, M.; Dash, P.; Ignatov, A.; Banzon, V.; Beggs, H.; Brasnett, B.; Cayula, J.F.; Cummings, J.; Donlon, C.; Gentemann, C.; et al. Group for High Resolution Sea Surface temperature (GHRSST) analysis fields inter-comparisons. Part 1: A GHRSST multi-product ensemble (GMPE). Deep. Sea Res. Part II Top. Stud. Oceanogr.
**2012**, 77–80, 21–30. [Google Scholar] [CrossRef] - 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.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] - Park, K.A.; Chung, J.Y. Spatial and temporal scale variations of sea surface temperature in the East Sea using NOAA/AVHRR data. J. Oceanogr.
**1999**, 55, 271–288. [Google Scholar] [CrossRef] - Gohin, F.; Langlois, G. Using geostatistics to merge in situ measurements and remotely-sensed observations of sea surface temperature. Int. J. Remote Sens.
**1993**, 14, 9–19. [Google Scholar] [CrossRef] - Doney, S.C.; Glover, D.M.; McCue, S.J.; Fuentes, M. Mesoscale variability of Sea-viewing Wide Field-of-view Sensor (SeaWiFS) satellite ocean color: Global patterns and spatial scales. J. Geophys. Res. Ocean.
**2003**, 108, 3024–3038. [Google Scholar] [CrossRef] - Liao, Z.; Xu, B.; Zhang, L.; Gu, J.; Shi, C. Optimum interpolation analysis for Fengyun-3C sea surface temperature data using oriented elliptic correlation scales. Remote Sens. Lett.
**2021**, 12, 585–593. [Google Scholar] [CrossRef] - Tandeo, P.; Autret, E.; Chapron, B.; Fablet, R.; Garello, R. SST spatial anisotropic covariances from METOP-AVHRR data. Remote Sens. Environ.
**2014**, 141, 144–148. [Google Scholar] [CrossRef] [Green Version] - Liu, N.; Xu, L.; Xu, Y.; Wang, J. SST fusion analysis based on Kalman Filter and Spatiotemporal dimension. In Proceedings of the Fifth International Conference on Machine Vision (ICMV 12); SPIE: Bellingham, WA, USA, 2013; Volume 8783. [Google Scholar]
- Reynolds, R.W.; Chelton, D.B. Comparisons of Daily Sea Surface Temperature Analyses for 2007–08. J. Clim.
**2010**, 23, 3545–3562. [Google Scholar] [CrossRef] [Green Version] - Alaka, M.A.; Elvander, R.C. Optimum interpolation from observations of mixed quality. Mon. Weather Rev.
**1972**, 100, 12–624. [Google Scholar] [CrossRef] - Gentemann, C.L.; Wentz, F.J.; DeMaria, M. Near real time global optimum interpolated microwave SSTs: Applications to hurricane intensity forecasting. In Proceedings of the 27th Conference on Hurricanes and Tropical Meteorology, Monterey, CA, USA, 24–26 April 2006. [Google Scholar]
- Reynolds, R.W.; Smith, T.M. Improved global sea surface temperature analyses using optimum interpolation. J. Clim.
**1994**, 7, 929–948. [Google Scholar] [CrossRef] [Green Version] - Tanimoto, Y.; Hanawa, K.; Toba, Y.; Iwasaka, N. Characteristic Variations of Sea Surface Temperature with Multiple Time Scales in the North Pacific. J. Clim.
**1993**, 6, 1153–1160. [Google Scholar] [CrossRef] [Green Version] - Trishchenko, A.P.; Cihlar, J.; Li, Z. Effects of spectral response function on surface reflectance and NDVI measured with moderate resolution satellite sensors. Remote Sens. Environ.
**2002**, 81, 1–18. [Google Scholar] [CrossRef] - Yan, Y.; Barth, A.; Beckers, J.M.; Candille, G.; Brankart, J.M.; Brasseur, P. Comparison of different assimilation schemes in an operational assimilation system with Ensemble Kalman Filter. In Proceedings of the EGU General Assembly Conference Abstracts, Vienna, Austria, 17–22 April 2016. [Google Scholar]
- Kalman, R.E.; Bucy, R.S. New Results in Linear Filtering and Prediction Theory. J. Basic Eng.
**1961**, 83, 95–108. [Google Scholar] [CrossRef] - Tang, Y.Q.; Zhang, J.S.; Wang, J.S. FY-3 Meteorological Satellites and the Applications. Space Sci. Act. China
**2014**, 34, 703–709. [Google Scholar] - Wang, S.; Cui, P.; Zhang, P.; Ran, M.; Lu, F.; Wang, W. FY-3C/VIRR SST algorithm and cal/val activities at NSMC/CMA. In SPIE Asia Pacific Remote Sensing; International Society for Optics and Photonics: Beijing, China, 2014. [Google Scholar]
- Yang, Z.; Lu, N.; Shi, J.; Zhang, P.; Dong, C.; Yang, J. Overview of FY-3 payload and ground application system. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 4846–4853. [Google Scholar] [CrossRef] - Liao, Z.; Dong, Q.; Xue, C. A Bias Correction Method for FY-3C VIRR SST Data. Remote Sens. Lett.
**2017**, 8, 429–437. [Google Scholar] [CrossRef] - Xu, F.; Ignatov, A. In situ SST quality monitor (i quam). J. Atmos. Ocean. Technol.
**2014**, 31, 164–180. [Google Scholar] [CrossRef] - Xu, F.; Ignatov, A. Error characterization in iQuam SSTs using triple collocations with satellite measurements. Geophys. Res. Lett.
**2016**, 43, 10826–10834. [Google Scholar] [CrossRef] - Dash, P.; Ignatov, A.; Martin, M.; Donlon, C.; Brasnett, B.; Reynolds, R.W.; Banzon, V.; Beggs, H.; Cayula, J.F.; Chao, Y.; et al. Group for High Resolution Sea Surface Temperature (GHRSST) analysis fields inter-comparisons—Part 2: Near real time web-based level 4 SST Quality Monitor (L4-SQUAM). Deep. Sea Res. Part II Top. Stud. Oceanogr.
**2012**, 77, 31–43. [Google Scholar] [CrossRef] [Green Version] - Petrenko, B.; Ignatov, A.; Kihai, Y.; Dash, P. Sensor-specific error statistics for SST in the Advanced Clear-Sky Processor for Oceans. J. Atmos. Ocean. Technol.
**2016**, 33, 345–359. [Google Scholar] [CrossRef] - Wang, H.; Guan, L.; Chen, G. Evaluation of Sea Surface Temperature From FY-3C VIRR Data in the Arctic. IEEE Geosci. Remote Sens. Lett.
**2016**, 13, 292–296. [Google Scholar] [CrossRef] - McClain, E.P.; Pichel, W.G.; Walton, C.C. Comparative performance of AVHRR-based multichannel sea surface temperatures. J. Geophys. Res. Ocean.
**1985**, 90, 11587–11601. [Google Scholar] [CrossRef] - Liao, Z.; Dong, Q.; Xue, C. Evaluation of sea surface temperature from FY-3C data. Int. J. Remote Sens.
**2017**, 38, 4954–4973. [Google Scholar] [CrossRef] - Pryamitsyn, V.; Ignatov, A.; Petrenko, B.; Jonasson, O.; Kihai, Y. Evaluation of the initial NOAA AVHRR GAC SST reanalysis version 2 (RAN2 B01). In SPIE Defense + Commercial Sensing; SPIE: Bellingham, WA, USA, 2020; Volume 11420. [Google Scholar]

**Figure 1.**Global distribution of the ${L}_{max}$ parameter estimated using the optimum interpolation (OI) analysis results of 2015 [13].

**Figure 2.**Global distribution of the ${L}_{min}$ parameter estimated using the optimum interpolation (OI) analysis results of 2015 [13].

**Figure 3.**Global distribution of the $\phi $ parameter estimated using the optimum interpolation (OI) analysis results of 2015 [13].

**Figure 4.**Schematic diagram of the error standard deviation estimation $S{D}_{est}$ using the optimal matched datasets ($M{D}_{optimal}$) for visible and infrared radiometer (VIRR) surface sea temperature (SST) products. ${T}_{s,i,j}$,${T}_{c,i,j}$, ${\mathsf{\theta}}_{i,j}$, and ${\rho}_{i,j}$ separately stand for the original VIRR SST, climatology SST, view zenith angle, and estimated standard deviation in the position of SST matrix ($i,j$), respectively.

**Figure 8.**Comparison of the average bias (BIAS) and standard deviation (SD) from 2016 from (

**a**,

**b**) OI, (

**c**,

**d**) Kalman and (

**e**,

**f**) OISST results in global 10° × 10° grids.

**Figure 10.**Time series of (

**a**) root-mean-square error (RMSE), (

**b**) standard deviation (SD), (

**c**) correlation coefficient (R), and (

**d**) signal-to-noise ratio (SNR) from OI, Kalman and OISST results for 2016.

**Figure 11.**Daily sea surface temperature (SST) analysis results from (

**a**) 1 May 2016, and (

**b**) 1 October 2016, obtained by the Kalman filtering method with oriented elliptic correlation scales.

**Figure 12.**Difference distributions of the OI results (

**a**,

**c**) and Kalman results (

**b**,

**d**) with the OISST products from 1 May and 1 October 2016 respectively.

**Figure 13.**Comparison of the OI, Kalman, and OISST results with the in situ SSTs from (

**a**) 1 May 2016 and (

**b**) 1 October 2016 using Taylor diagrams.

RMSE (°C) | SD (°C) | R | SNR | NUM | |
---|---|---|---|---|---|

OI | 0.3911 | 0.2539 | 0.9989 | 22.41 | 82,441 |

Kalman | 0.3243 | 0.2214 | 0.9993 | 26.64 | 82,441 |

OISST | 0.2897 | 0.2140 | 0.9994 | 29.31 | 82,441 |

**Table 2.**Error Statistics of the in situ SST, OI, Kalman, and OISST results from 1 May and 1 October 2016.

1 May | 1 October | |||||||
---|---|---|---|---|---|---|---|---|

R | SST SD | ubRMSE | NUM | R | SST SD | ubRMSE | NUM | |

In situ | 1 | 8.7775 | 0 | 268 | 1 | 8.3529 | 0 | 260 |

OI | 0.9985 | 8.7005 | 0.4779 | 268 | 0.9989 | 8.3659 | 0.3986 | 260 |

Kalman | 0.9990 | 8.7576 | 0.4001 | 268 | 0.9993 | 8.3719 | 0.3207 | 260 |

OISST | 0.9992 | 8.7452 | 0.3413 | 268 | 0.9992 | 8.2884 | 0.3302 | 260 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liao, Z.; Xu, B.; Gu, J.; Shi, C.
Sea Surface Temperature Analysis for Fengyun-3C Data Using Oriented Elliptic Correlation Scales. *Sensors* **2021**, *21*, 8067.
https://doi.org/10.3390/s21238067

**AMA Style**

Liao Z, Xu B, Gu J, Shi C.
Sea Surface Temperature Analysis for Fengyun-3C Data Using Oriented Elliptic Correlation Scales. *Sensors*. 2021; 21(23):8067.
https://doi.org/10.3390/s21238067

**Chicago/Turabian Style**

Liao, Zhihong, Bin Xu, Junxia Gu, and Chunxiang Shi.
2021. "Sea Surface Temperature Analysis for Fengyun-3C Data Using Oriented Elliptic Correlation Scales" *Sensors* 21, no. 23: 8067.
https://doi.org/10.3390/s21238067