Reconstruction and analysis of long-term satellite-derived sea surface temperature for the South China Sea

Abstract

Sea surface temperature (SST) is one of the key variables often used to investigate ocean dynamics, ocean-atmosphere interaction, and climate change. Unfortunately, the SST data sources in the South China Sea (SCS) are not abundant due to sparse measurements of in situ SST and a high percentage of missing data in the satellite-derived SST. Therefore, SST data sets with low resolution and/or a short-term period have often been used in previous researches. Here we used Data INterpolating Empirical Orthogonal Functions, a self-consistent and parameter-free method for filling in missing data, to reconstruct the daily nighttime 4-km AVHRR Pathfinder SST for the long-term period spanning from 1989 to 2009. In addition to the reconstructed field, we also estimated the local error map for each reconstructed image. Comparisons between the reconstructed and other data sets (satellite-derived microwave and in situ SSTs) show that the results are reliable for use in many different researches, such as validating numerical models, or identifying and tracking meso-scale oceanic features. Moreover, the Empirical Orthogonal Function (EOF) analysis of the reconstructed SST and the reconstructed SST anomalies clearly shows the subseasonal, seasonal, and interannual variability of SST under the influence of monsoon and El Niño-Southern Oscillation (ENSO), as well as reveals some oceanic features that could not be captured well in previous EOF analyses. The SCS SST often lags ENSO by about half a year. However, in this study, we see that the time lag changes with the frequencies of the SST variability, from 1 to 6 months.

Appendix

When using the reconstructed SST, perhaps the users would also like to know the local error map associated with each reconstructed image. Therefore, we will concisely present the method and parameters that were used to compute the error field. For more detailed descriptions, please refer to Beckers et al. (2006).

Beckers et al. (2006) proved that a very efficient least-square fit of EOF amplitudes to an observed subset of data is equivalent to optimal interpolation (OI) if the filtered covariance matrix of DINEOF is used as the ad hoc covariance of OI. Hence the error estimates of OI can be used as a proxy for the error fields of DINEOF. To calculate the error field, a method similar to the least-square fit, instead of an equivalent standard OI error calculation, is applied due to its reduced calculation cost.

In standard OI, the covariance matrix between data points is the sum of the observational error-covariance matrix R and the target field-covariance matrix B. The observational errors and target field are assumed to be uncorrelated. We can use the covariance matrix based on SVD decomposition from DINEOF, with the N-retained significant EOFs ($N = 33$), in an OI approach. If we define scaled spatial EOFs

$$\begin{aligned} {\mathbf{L }} = \frac{1}{\sqrt{n}}{\mathbf{U }}^N{\mathbf{S }}^N \end{aligned}$$

(3)

where L is a matrix with N columns, each of which is the scaled spatial EOF, this leads to the field covariance

$$\begin{aligned} {\mathbf{B }} = \frac{1}{n}{\mathbf{X }}^N{{\mathbf{X }}^N}^{\mathrm{T}} = {\mathbf{L }}{\mathbf{L }}^{\mathrm{T}} \end{aligned}$$

(4)

DINEOF cannot for certain separate noise from signal. It can only say via the cross-validation technique used, that with the amount of data available, no more useful information can be extracted and kept in the retained EOFs. Therefore, if we consider that the N-retained EOFs contain signals and the remaining EOFs contain noise, then the noise can be estimated as the difference between the original values x and the reconstructed ones $x^r$

$$\begin{aligned} {\mu }^2 = \frac{1}{m_{\mathrm{p}}}\sum _{x_{ij}\;{\mathrm{present}}} (x_{ij}^2 - {x_{ij}^r}^2) \end{aligned}$$

(5)

with $m_{\mathrm{p}}$ being present pixels. We can use this equation to estimate the error variance from the variance filtered by the EOF reconstruction. Assuming the observational error uncorrelated, the error-covariance matrix R has the diagonal form

$$\begin{aligned} {\mathbf{R }} = {\mu }^2{\mathbf{I }} \end{aligned}$$

(6)

where I is the identity matrix.

The covariance matrix can be calculated for a given image

$$\begin{aligned} {\mathbf{C }} = {\mu }^2({\mathbf{L }}_{\mathrm{p}}^{\mathrm{T}} {\mathbf{L }}_{\mathrm{p}} + {\mu }^2{\mathbf{I }}_{N})^{-1} \end{aligned}$$

(7)

where ${\mathbf{L }}_{\mathrm{p}}$ are the EOF values of points for which data are available.

For satellite data, atmospheric corrections and associated errors are likely to contain spatial correlations. Therefore, ${\mu _{\mathrm{eff}}}^2$ is used instead of ${\mu }^2$

$$\begin{aligned} {\mu _{\mathrm{eff}}}^2 = {\mu }^2L^2/(\Delta x \Delta y) \end{aligned}$$

(8)

where L is the correlation length of the observational error, $\Delta x$ and $\Delta y$ are the zonal and meridional resolution, respectively. Different values L were used until the error fields from the analysis gave on average a value of 0.46 °C under the clouded regions. Here we chose $L = 88$ km.

The error variance in each grid point as the quadratic form is then calculated

$$\begin{aligned} {\epsilon }^2 ={\mathbf{i }}^{\mathrm{T}} {\mathbf C} i \end{aligned}$$

(9)

where i is column array of dimension $N\times 1$ containing the values of the N scaled EOFs at grid point i (irrespectively of whether or not the data are missing).

A sample of error map is shown in Fig. 20.

Fig. 20

An example of error map of the reconstructed SST on 30 June 2009: a the original AVHRR SST, b the reconstructed AVHRR SST, and c the error map of the reconstructed SST