Based on the simple ocean data assimilation (SODA) data, this study analyzes and forecasts the monthly sea surface height anomaly (SSHA) averaged over South China Sea (SCS). The approach to perform the analysis is a time series decomposition method, which decomposes monthly SSHAs in SCS to the following three parts: interannual, seasonal, and residual terms. Analysis results demonstrate that the SODA SSHA time series are significantly correlated to the AVISO SSHA time series in SCS. To investigate the predictability of SCS SSHA, an exponential smoothing approach and an autoregressive integrated moving average approach are first used to fit the interannual and residual terms of SCS SSHA while keeping the seasonal part invariant. Then, an array of forecast experiments with the start time spanning from June 1977 to June 2007 is performed based on the prediction model which integrates the above two models and the time-independent seasonal term. Results indicate that the valid forecast time of SCS SSHA of the statistical model is about 7 months, and the predictability of SCS SSHA in Spring and Autumn is stronger than that in Summer and Winter. In addition, the prediction skill of SCS SSHA has remarkable decadal variability, with better phase forecast in 1997–2007.
Study on the variation of the sea surface height anomaly (SSHA) is an important issue in physical oceanography and meteorological science. Changes in SSHA will influence the frequency and impact of extreme sea level events which engender lots of negative impact [
Analysis and forecast are two crucial aspects of SCS SSHA. As far, most attentions have been paid to the analysis of the SSHA in SCS, like the annual variability [
The remainder of this study is organized as follows: the data, the time series decomposition method, and the statistical model construction are introduced in Section
An ocean reanalysis product, namely, simple ocean data assimilation (SODA), is used in this study, which is based on the Parallel Ocean Program ocean model with an average horizontal resolution of
A merged gridded product of Maps of Sea Level Anomaly produced by AVISO (Archivage Validation et Interpretation des donnees des Satellites Oceanographiques) based on TOPEN/Poseidon, Janson 1, ERS-1, and ERS-2 satellite data is used for evaluating the correctness of SODA data. This product provides SSHAs from January 1993 to December 2007, which consists of maps produced every day on a
In this section, we briefly introduce the time series decomposition method, that is, the centralized moving average scheme. This method partitions a monthly time series into the following three components: the interannual component
According to the time scales of
To investigate the statistical predictability of SSHA in SCS, the statistical forecast model is first constructed in this section.
For the forecast of
For the fitness model, the determination process of the parameters is described as follows. First, the values of
Given that the fitness model has been determined, the
Affected by various factors, such as solar radiation, evaporation and precipitation, monsoon, and El Niño and Southern Oscillation (ENSO), the SCS SSHA has significant characteristics on different time scales. In this section, we roughly analyze the time variability of SCS SSHA with the time series decomposition method (Section
Before applying the time series decomposition to the SCS SSHA derived from the SODA product, the correctness of this dataset should be first verified. Figure
Time series of monthly SCS SSHA (cm) derived from AVISO (black) and SODA (red).
To detect the significant periods of these two datasets, we perform the power spectrum analysis. Figure
The power spectrums of SCS SSHA for the AVISO (blue) and SODA (black). The dashed curves represent the 95% confidence upper limit.
Due to the limited length of AVISO SSHA data, we cannot systematically verify the correctness of the whole time series of SCS SSHA derived from SODA data. However, based on the above analysis, it is reasonable to assume that the quality of the time series of SCS SSHA from SODA data is reliable.
Given that the correctness of the SODA SSHA data has been validated by AVISO data, we apply the time series composition to the monthly SCS SSHA from SODA with a 60-year length. Figure
Time series (1948–1977 in (a); 1978–2007 in (b)) of three components (unit: cm) of SSHA in SCS, including the interannual term (black), the seasonal term (blue), and the residual term (red).
Before performing the forecast experiments of SSHA, the forecast model of SCS SSHA should be first established. Note that the SSHAs from now on indicate the SSHA anomalies. Due to the invariant property of the seasonal term, the forecast model is divided into two parts: the Holt-Winters model for the interannual term and the ARIMA model for the residual term. Given the time series of SCS SSHA, the fitness models for the interannual term and the residual term are first, respectively, constructed and then used to forecast these two quantities. Finally the forecasted interannual term and the residual term are added together to form the forecasted anomaly of SCS SSHA. In this section, we examine the qualities of fitness for the interannual and residual terms.
Figures
Time series of fitted (red curve) and SODA’s (blue curve) interannual term (a) and residual term (b) of SSHA in South China Sea as well as the total SSHA (c). (d) presents the time series of the biases (computed as the difference between the fitted value and the observed value) of the fitted interannual term (black curve), residual term (blue dashed curve), and total SCS SSHA (red curve).
The last 30 years’ analysis results are used to perform the forecast experiment which is similar to the dynamical forecast of physical processes (like ENSO [
The schematic diagram of the forecast experiments.
Based on the forecast results, we investigate the predictability of SCS SSHA from the following three aspects.
We first totally examine the prediction skill of SSHA in SCS with the anomaly correlation coefficient (ACC) and the root-mean-square error (RMSE) relative to the SODA data. The ACC and RMSE are defined as follows:
Figures
Variations of RMSE (a, c, and e) and ACC (b, d, and f) of forecasted SCS SSHA anomaly (a, b), forecasted interannual term (c, d), and forecasted residual term (e, f) with respect to lead time (in month) and start month. The solid curve in (a, c, and e) [b, d, f] is (1.0-contour) [0.6-contour]. Note that RMSEs in (a, c, and e) have been normalized by the climatological standard deviations of SCS SSHA anomaly, interannual term, and residual term, respectively.
To further investigate the contributions of the interannual term and residual term to the total quantity, we separately analyze the predictabilities of the interannual term and the residual term. Figures
To figure out the possible reason causing the prediction skill of the interannual term, we calculate the number of extreme (including maximum and minimum) values of the interannual term (decomposed from the SODA SCS SSHA time series between July 1977 and June 2007) that happens in each month (Figure
The number of extreme (including maximum and minimum) values of the interannual term (decomposed from the SODA SCS SSHA time series between July 1977 and June 2007) happens in each month.
According to the analysis in last section, the valid forecast time of SCS SSHA is about 7 months. We now assess the seasonal forecasts in this section. Figure
Time series of SODA data (blue curve) and forecasted (red curve) SCS SSHA anomaly with 6 (a) and 9 (b) lead months.
To investigate the decadal variability of the prediction skill of SCS SSHA, we divide 361 forecast experiments into three arrays, corresponding to three decades. Figure
Variations of RMSE (black curve) and ACC (blue curve) of the forecasted SSHA anomaly in SCS with respect to the forecast lead time (in months). The dotted line indicates the 0.6-ACC.
In this study, we first simply contrast the time series of monthly SSHAs calculated from SODA and AVISO datasets in SCS to verify the correctness of the SODA SCS SSHA which is used to construct the forecast model of SCS SSHA. Results show that SODA well correlates with AVISO data. Afterwards, we use the long-term time series from 1948 to 2007 of SODA SCS SSHA to establish the statistical forecast model. A time series decomposition method is used to decompose the monthly time series of SCS SSHA into the following three parts: interannual term, seasonal term, and residual term. Then we, respectively, use the Holt-Winters and ARIMA models to fit the interannual and residual terms of SSHA in SCS, aiming to construct the forecast models of these two parts. Results of fitting demonstrate that the Holt-Winters model can exactly track the trajectory of SODA counterpart while the ARIMA can well simulate the phase of the residual term. Finally, we perform an array of forecast experiments based on the above two models. Results show that the valid forecast time of SCS SSHA is about 7 months. The predictability of SCS SSHA in Spring and Autumn is stronger than that in Summer and Winter, and the forecast skill of the anomaly of SCS SSHA is mainly contributed by the counterpart of the interannual term and more or less reduced by the bad prediction skill of the residual term. In addition, the prediction skill of SCS SSHA has remarkable decadal variability.
In the future studies, we will focus on the following three aspects. First, the statistical method used in this study can be applied to each grid to investigate the spatial distribution of the predictability of SSHA in SCS. Second, the results produced by this statistical model should be compared to other statistical models or dynamical models. Third, the physical mechanism causing the decadal variability of the prediction skill of SCS SSHA should be further investigated.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to express their gratitude to two reviewers for their helpful comments and suggestions, which contributed to greatly improve the original manuscript. This research was jointly supported by grants of National Basic Research Program (2013CB430304), National Natural Science Foundation (41176003, 41206178, 41376013, 41376015, and 41306006), National High-Tech R&D Program (2013AA09A505), and Global Change and Air-Sea Interaction (GASI-01-01-12) of China.