### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Method
- 3. Result
- 4. Summary and Discussion
- Acknowledgments
- References

[1] Sea surface temperature (SST) data of one year from Advanced Microwave Scanning Radiometer for EOS (AMSR-E) are used to estimate statistically spatial and temporal scales of the global SST field. Using anomalies from the climatological annual SST variation, correlation coefficients in the horizontal space and time are calculated. Decorrelation scales, defined as an *e*-folding scale of SST anomalies, and signal-to-noise ratio are derived as functions of regional positions and calendar months. We assumed that the autocorrelation function of SST anomaly has anisotropic Gaussian characteristics in space-time domain. We evaluated the space-time scales and statistical errors in the SST data by fitting Gaussian function to the correlation coefficients using a least square method. Resultant zonal, meridional and temporal decorrelation scales range 1.5–3.0 degree, 1.2–2.0 degree and 1.5–3 day, respectively. The scales show geographical and seasonal differences, which means that dominant SST variability in the global oceans depends on regions and seasons.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Method
- 3. Result
- 4. Summary and Discussion
- Acknowledgments
- References

[2] Requirements for spatial and temporal resolutions of near-real-time sea surface temperature(SST) product are 100 km and 1 day for numerical weather prediction (WMO World Weather Watch 4th Long Term Plan, 1996–2005) and 10 km and less than 1 day (diurnal cycle resolved) for ocean data assimilation [*Le Traon et al.*, 2001].

[3] Satellite observations offer great advantages, especially in terms of spatial and temporal coverage, to develop SST products suitable to the above requirements. Using microwave and infrared SST measurements, *Guan and Kawamura* [2004] produced, through an objective analysis, a test product of high-resolution cloud-free SST, which is called New Generation SST version 1.0 (hereafter NGSST ver. 1.0).

[4] Objective mapping or optimal interpolation was first introduced by [*Gandin*, 1963] to produce a systematic procedure for the production of gridded maps of meteorological parameters. Oceanographic application of this method was provided by *Bretherton et al.* [1976]. The method has been widely used for mapping of water temperature fields [e.g., *Reynolds and Smith*, 1994; *White*, 1995], sea surface height anomaly [e.g., *Le Traon et al.*, 1998; *Ducet et al.*, 2000]. If the covariance used in the objective mapping is that of the data field, then it is optimal in the sense that it minimizes the mean square error of the objective estimates.

[5] The method requires knowledge of the signal and noise variance and of the spatial-temporal autocorrelation function for the fields of interest. Because early efforts to estimate these statistics of SST and subsurface temperature fields [*Reynolds and Smith*, 1994; *White*, 1995] specifically addressed relatively long-term variability (annual to interannual), the spatial and temporal scales they obtained are larger than 500 km and a few months. Adequate statistics of SST fields that address short-term variability (intra-seasonal) should be used for production of a high-resolution SST dataset. For producing the NGSST ver. 1.0, *Guan and Kawamura* [2004] used a homogeneous and isotropic autocorrelation function for all seasons and regions from trial and error. Since their definition is only a technical solution and does not have theoretical basis, it is necessary to derive the autocorrelation function from data. In addition, it is expected that the SST variability depends on thermal conditions in the upper layer of ocean and on the oceanic and atmospheric disturbances, which changes their features seasonally and regionally. Therefore, it is necessary to discuss seasonality and regionality of the statistics of SST. We have estimated the decorrelation scale of SST variability in the Kuroshio region south of Japan (K. Hosoda and H. Kawamura, Seasonal variation of space/time statistics of short-term sea surface temperature variability in the Kuroshio region, submitted to *Journal of Oceanography*, 2004, hereinafter referred to as Hosoda and Kawamura, submitted manuscript, 2004), identifying the regional and seasonal change of scales. Here, we extend the analysis of decorrelation scale globally, using SST data observed by Advanced Microwave Scanning Radiometer for EOS (AMSR-E) aboard Aqua. In this study, it is assumed that climatological SST is used as the first guess of the optimum interpolation using the statistics derived here.

[6] AMSR-E is a multi-frequency microwave radiometer that detects microwave emissions from the earth's surface and atmosphere. Microwaves penetrate clouds with little attenuation, giving an uninterrupted view of the ocean surface such as SST-cooling produced by hurricanes observed by Tropical Rainfall Measuring Mission/TRMM Microwave Imager (TRMM/TMI) [*Wentz et al.*, 2000]. Therefore, microwave measurements provides a high-availability SST data compared with the infrared measurements which are limited by cloud presence [*Guan and Kawamura*, 2003]. *Shibata et al.* [1999] pointed out that TRMM/TMI has a problem for low temperature observation since its measurements at 10 GHz has low sensitivity toward SST if it is less than 10°C. Since 6 GHz measurements of AMSR-E improve the SST estimation at low temperature, it is appropriate for estimating statistics of SST globally. A. Shibata (SST algorithm developments—Removal of ocean wind effect, submitted to *Italian Journal of Remote Sensing*, 2004) described the algorithm of deriving SST from AMSR-E data and showed that root mean square of difference between buoy observation and AMSR-derived SSTs is 0.59 K. While the spatial resolution of microwave measurements is sparse, our previous study on the decorrelation scales in the Kuroshio region (Hosoda and Kawamura, submitted manuscript, 2004) revealed that the scales are mainly determined by large-scale atmospheric forcings. Therefore, it is expected that the seasonal/regional characteristics could be derived from the analysis using AMSR-E.

### 2. Data and Method

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Method
- 3. Result
- 4. Summary and Discussion
- Acknowledgments
- References

[7] We use AMSR-E SST data from June 1, 2002 to May 31, 2003 to derive the decorrelation scales globally. The spatial and temporal resolution is 0.25° × 0.25° and 1 day. Before the calculation of correlations, the optimal interpolation is used for filling the gap between the orbit. The correlation function used in the interpolation is the Gaussian function with decorrelation scales of 100 km and 1 day.

[8] Figure 1a shows an example of SST field. The annual signal, with spatial scales as large as 1000 km, is the most significant in the SST variation. It is necessary to eliminate influences of the annual large-scale SST change, because we focus on the small-scale variations of SST. Therefore, we calculate SST anomaly (SSTA) from annual signal:

In this study, we use Reynolds climatological SST (daily long term mean data are available from http://www.cdc.noaa.gov/cdc/data.reynolds_sst.html) [*Reynolds and Smith*, 1994] as annual signal, whose resolution is 1° × 1° and 1 day. Figure 1b is an example of SSTA fields calculated from Figure 1a. Figure 1c shows the geographical distribution of SSTA variance in all the analyzed period.

[9] The auto-correlation matrices are calculated using SSTA at each 2.5° × 2.5° (latitude × longitude) grid as a function of position **x** = (*x*, *y*, *t*) and relative position **x**_{l} = (*x*_{l}, *y*_{l}, *t*_{l}), where *x* and *y* are the longitude and latitude, *t* is the month, *x*_{l} and *y*_{l} are the longitudinal and latitudinal distances, and *t*_{l} is the temporal difference. Ranges of spatial and temporal differences are ±7.5° × ±10° (latitude × longitude) and ±5 days, respectively.

[10] We introduce the following assumption to calculate the SSTA decorrelation scale. For the period in which the correlation matrices are calculated, mean of the error at a position is assumed to be zero and to be a random noise. Then the correlation coefficients of the error are zero, if the temporal difference and/or spatial distance are not zero. In order to estimate the decorrelation scale of SSTA variation, the correlation matrix of observed SSTA variation is assumed to be anisotropic Gaussian as a function of a relative position **x**_{l}:

where *a*_{j} = *a*_{j}(**x**) (*j* = 1,.,7) are the coefficients, which are derived as a function of a position **x**, using least-mean-square method. Since the function, which is used in *Kuragano and Kamachi* [2000], can describe anisotropy, we adopt it as the first guess in this study. Including the coefficient *a*_{6} in equation (2) allows the major axes of the ellipse on *x* − *y* plane not to be forced to lie along the x and y axes. The coefficients *a*_{4} and *a*_{5} describes the migration of peak correlation. Decorrelation scales in this manuscript are defined as so-called *e*-folding scale, where the correlation function at the scale reaches a value of exp(−1):

Signal-to-noise ratio (SNR) is estimated from equation (2) as,

Note that we define the SNR as a ratio of standard deviation, not a ratio of variance in equation (4).

[11] Figure 2 shows the correlation coefficient matrix of the SSTA and the fitted function at 35°N, 215°E, as an example. The fitted Gaussian function shows a good approximation to the feature of the coefficient matrix. The zonal and meridional spatial scales at this point are about 2.35° and 1.47°, respectively. The temporal scale is 2.93 days. With the coefficients *a*_{4}, *a*_{5} and *a*_{6}, the fitted function can describe the tilt of axes, which means anisotropy and propagation of phenomena.

### 3. Result

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Method
- 3. Result
- 4. Summary and Discussion
- Acknowledgments
- References

[12] Figure 3 shows an example of the spatial decorrelation scales as the elliptic function: *a*_{1}*x*_{l}^{2} + *a*_{2}*y*_{l}^{2} + *a*_{6}*x*_{l}*y*_{l} = 1. This function means the 1/*e* contour of the fitted function at zero temporal lag plane if *a*_{7} = 0. Figure 3 indicates that the spatial scales are anisotropic and inhomogeneous. The global distributions of zonal and meridional decorrelation scales are given in Figures 4a and 4b, respectively. For clarifying the seasonal change, we select a month from each season: June, September, December and March. Although the intra-seasonal change is also found, it is weaker than the seasonal change.

[13] The zonal scale is in the range of 1.5–3.0 degrees, while the meridional scale is 1.2–2.0 degrees. In the most region, the zonal scales are longer than the meridional scales. In contrast, the zonal scale in the tropical region is smaller than those in the other regions. In the eastern tropical Pacific and the tropical Atlantic, the zonal scale is as small as 1.5 degrees for almost all season. Seasonal and regional variability of the zonal scale is high, while that of the meridional scale is relatively weak. Seasonal change of the zonal scale is the most significant in the Antarctic Circumpolar Current (ACC) region, where it is as large as 3.0 degree in summer (December). In the western boundary regions, the zonal scales tend to be small in winter (east of Argentina in June, the Gulf stream and the Kuroshio regions in December).

[14] In general,the temporal scale ranges from 1.5 to 3.0 days. Its regional and seasonal variability is not so high as that of the zonal scale. Longer temporal scales are found at the eastern tropical Pacific, where the zonal scale is small. In the ACC region in summer, where the zonal scale is longer than 2.5 degree, the temporal scale is as small as 1.0 days. Therefore, it is suggested that the smaller the zonal scale is, the longer the temporal scale is.

[15] The geographical distribution of SNR of SSTA variation is given in Figure 4d. The values are as small as 0.5–1.0, which is same order as the results by *White* [1995], who estimated the statistics for surface and subsurface temperature variability. The large SNRs are found, in summer of each hemisphere, at the mid-latitude accompanied by the longer zonal scales. The SNRs are larger in the regions where the spatial decorrelation scales are larger because of the greater intensity of signals.

[16] In order to investigate overall seasonal features of statistics, latitudinally-averaged scales and SNR are shown in Figure 5. In the low-latitude regions, the spatial scales are small and temporal scale becomes longer in the winter in the northern hemisphere. The zonal scales become long in the warming season in the mid-latitude regions. Maxima of the zonal scale in south hemisphere are longer than those in the northern hemisphere, since the zonal scales in the ACC region are large as mentioned-above. The seasonal dependency of meridional and temporal scales is smaller than that of zonal scales. The temporal scales are longer when the zonal scales becomes smaller in the mid-latitude regions. The variability of SNR is similar to that of the zonal scales, as mentioned-above.

### 4. Summary and Discussion

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Method
- 3. Result
- 4. Summary and Discussion
- Acknowledgments
- References

[17] The global decorrelation scales and SNR of SST variation are estimated from one-year AMSR-E data. The zonal scale is in the range of 1.5–3.0 degrees, while the meridional scale is 1.2–2.0 degrees. The temporal scale is 1.5–3.0 days. The SNR is in the range of 0.5–1.0. The seasonal and regional variabilities are strong in the zonal scale and SNR, while those of the meridional and temporal scales are not so much. The zonal scale becomes larger in warm season at mid-latitude.

[18] In this paper we used one-year SST data derived from AMSR-E to examine the statistical features of SST variation, since it can observe SST fields globally including the ares under clouds. The further analysis using multi-year data is needed for discussions on interannual variability. To consider the influence of ENSO-scale variability, the length of data should be as long as a decade. Although the observation range is limited in the low-latitude region, TRMM/TMI data may be useful for discussion of interannual variation of the decorrelation scales. Another problem is that the filling process is used in this study to avoid the influence of availability of data according to the satellite orbit. Another solution to fill the gaps is to use multi-satellite observations. Moreover, the analysis using a longer time series could also provide discussions on the statistical significance of the result given in this paper. The discussions are important since it is possible that the seasonal and regional variabilities have less statistical significance. The results in this study need to be viewed with caution until a longer time series is available to properly assess the statistical significance.

[19] It is necessary to study the mechanisms behind seasonal/regional variabilities in the decorrelation scales derived in this study. The variations of SST in short-term periods are dominated by the atmospheric forcings and oceanic turbulence, understanding of which may be essential for producing the high-resolution satellite-based SSTs and predicting the short-term SST variations using them.