Advances in Meteorology

Volume 2015, Article ID 907313, 9 pages

http://dx.doi.org/10.1155/2015/907313

## Statistical Prediction of the South China Sea Surface Height Anomaly

^{1}National University of Defense Technology, Changsha, Hunan 410073, China^{2}Key Laboratory of Marine Environmental Information Technology, SOA, National Marine Data and Information Service, Tianjin 300171, China

Received 16 December 2014; Revised 8 February 2015; Accepted 26 February 2015

Academic Editor: Shaoqing Zhang

Copyright © 2015 Caixia Shao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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.

#### 1. Introduction

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 [1, 2]. Previous studies found that the regional SSHA variability at the interannual time scale dominated by ocean variability is much larger than the global SSHA [3–5]. As the largest marginal sea in Western Pacific, South China Sea (SCS) is a crucial link between Pacific and Indian Ocean, and it has significant impacts on human activities and the sustainable development of coastal economy and society.

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 [6, 7], interannual variability [8, 9], seasonal variability [10], the rising rate [11, 12], the forcing of the variations [13–16], and the variability associated with El Niño and Southern Oscillation (ENSO) [8, 9, 16, 17]. For the forecast of SCS SSHA, the forecast model of SCS SSHA, mainly, includes the dynamical models and statistical methods. Now the 3D dynamical prediction system of the SCS SSHA has been improved [18, 19]. For example, Wei et al. [18] use a fine-grid dynamical model covering SCS to produce monthly and annual mean SSHA of the SCS from 1992 to 2000, and the model-produced data is in good agreement with altimeter measurements. While the dynamical approaches have been studied widely [1, 20, 21], little attentions have been paid to the statistical forecast of SSHA in SCS, which is simple and feasible in practice. The Pacific ENSO Applications Climate (PEAC) Centre at the National Oceanographic and Atmospheric Administration (NOAA) uses a statistical model to calculate site-specific seasonal sea level outlooks, and the results indicated that the statistical model is potentially useful in predicting seasonal sea level variations in the U.S.-affiliated Pacific Islands (USAPI) [22]. Imani et al. [23] used the Holt-Winters exponential smoothing technique to analyze and forecast Caspian Sea level anomalies from 15-year altimetry data from 1993 to 2008 and found that the modeling results of a 3-year forecasting time span (2005–2008) agree well with the observed time series. As far as we know, no literature on the statistical prediction of SCS SSHA has been documented. Also it is feasible to use the statistical models to implement the forecast of the SCS SSHA compared with the complicated dynamical models. In this study, based on the long-term monthly time series of SCS SSHA derived from the Simple Ocean Data Analysis (SODA), we first use a time series decomposition method to analyze the variability of monthly SCS SSHA. Then, a statistical model is constructed to fit the monthly SCS SSHA and used to perform an array of forecast experiments. Finally, the statistical prediction skill of SCS SSHA is investigated.

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 2. Section 3 presents the analysis results of SSHA in SCS while the forecast results are shown in Section 4. Summary and discussion are given in Section 5.

#### 2. Methodology

##### 2.1. Data

###### 2.1.1. SODA

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 and with 40 vertical levels during January 1948 to December 2007 [24]. SODA data is downloaded from web site at http://dsrs.atmos.umd.edu/DATA/soda_2.2.4/. For our study, we first calculate the monthly mean values of SSH so as to derive the monthly SSHA. Then, we average the monthly SSHA over the South China Sea (5°N–25°N, 105°E–121°E) to form the basic datasets used in this study.

###### 2.1.2. AVISO

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 Cartesian grid. The monthly SSHA in AVISO is first computed and then used to derive the monthly SCS SSHA.

##### 2.2. Statistical Methods for Modeling and Forecasting

###### 2.2.1. Decomposition Method

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 , the seasonal component , and the residual component as follows:where represents the monthly value at time . The computational processes of , , and are listed as follows.

*(a) Interannual Component*. A simple centralized moving average technique with 12-month time scale is used to obtain the interannual term aswhere represents the length of . Apparently, with the smoothing-scale being set to 12 months, filters the short time scale (less than 12 months) information of and keeps the interannual variations. Thus, describes the interannual variabilities of . Note that the valid period of is from July 1948 to June 2007. The following decomposition and analysis as well as the forecast experiments will be also based on during the same period.

*(b) Seasonal Component*. After the interannual term of has been computed with the above method, we first subtract from to get the remaining term. In this study, the seasonal term () corresponds to the climatology of the remaining term. Thus, although the length of is the same as , the period of is 12 months.

*(c) Residual Component*. With the interannual term () and the seasonal term () being determined, the residual term of is directly computed by

According to the time scales of and , it is easy to derive that reflects the variability of whose time scale is interseasonal or smaller. As the resolution of is monthly, it is expected that is noise-dominant. In addition, the summation of and represents the anomaly of . Due to the static nature of , the forecasting of mainly depends on the prediction of the anomaly of which consists of and . Because of the different time scales of and , different statistical models are used to fit and forecast and .

###### 2.2.2. Models for Fitting and Forecasting

To investigate the statistical predictability of SSHA in SCS, the statistical forecast model is first constructed in this section.

*(a) The Model for Interannual Term*. Due to the simplicity and robustness [23, 25], Holt’s linear exponential smoothing technique is widely used to handle nonseasonal time series by introducing smoothing parameters [26], like the precipitation prediction [27] and the maxima and minima air temperature prediction [28]. In this study, we also use Holt’s linear exponential smoothing technique to fit and forecast . The fit formula of iswhereHere and denote the smoothing parameters. The initial values of and are usually set to 0. Given preset values (i.e., first guesses) of * α* and

*, the fitness of (denoted as , , ) can be calculated sequentially with known . Note that 7 is the starting index of (see (2)) and . Then a cost function between and is established. Taking and as the control variables to be optimized, an optimization algorithm, like the L-BFGS-B algorithm [29], is used to obtain the optimum and . In addition, to avoid the overflow of and , the bound is applied to these two parameters during the optimizing process.*

*β*For the forecast of , a linear function of the lead time is constructed as follows:Here is the lead time in month.

*(b) The Model for Residual Term*. Due to the noise-dominant nature of , we use an auto-regression integrated moving average model (denoted as ARIMA [30, 31]) to construct the fit model of . Here represents the order of the autoregression model (i.e., AR); is the order of time differential of ; indicates the order of the moving average model. The model can be formulated aswhere represents the time series of -order time differentiate of , is the time, are coefficients of the autoregressive integrated model, are coefficients of the moving average model, and is a white noise time series [32].

For the fitness model, the determination process of the parameters is described as follows. First, the values of , , and are automatically determined by auto.arima libiary in R software, according to statistic tests. The value of is selected based on successive KPSS unit-root tests and then and are chosen based on the approach of Akaike’s Information Criterion (AIC) [33]. Then there are a total of parameters to be determined. Taking as an example, according to (7), given the previous fitted , can be computed accordingly. Then a cost function is established between and to determine the optimized parameters with an optimization algorithm.

Given that the fitness model has been determined, the is integrated by , and the same values of parameters are consistently used to perform the forecast experiment.

#### 3. Modeling Construction

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 2.2.1) based on the SODA product.

##### 3.1. Verification of SODA SSHA

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 1 shows the time series of the monthly SCS SSHA derived from SODA (red) and AVISO (black). It can be seen that the most prominent signal is the seasonality in both products. The correlation coefficient between two time series reaches 0.89 with the significance level above 95%. The root-mean-square error between two time series is 2.56 cm. The SODA product can well capture the temporal variability of SCS SSHA.