-
Four ocean reanalyses are selected in this study. In alphabetical order, they are the Ocean Data Assimilation system of the Geophysical Fluid Dynamics Laboratory (GFDL) (Zhang et al., 2007), the Global Ocean Data Assimilation System (GODAS) of the National Centers for Environmental Prediction (Behringer and Xue, 2004), the Ocean Reanalysis System 4 (ORAs4) of the European Centre for Medium-Range Weather Forecasts (Balmaseda et al., 2013), and the Simple Ocean Data Assimilation (SODA) version 2.2.4 of the Department of Atmospheric and Oceanic Science at the University of Maryland and the Department of Oceanography at Texas A&M University (Carton and Giese, 2008). These reanalysis products are selected because of their frequent use in ENSO studies. Only monthly data are used. The NOAA Extended Reconstructed Sea Surface Temperature V3b (ERSST; Xue et al., 2003) is used to calculate sea surface temperature anomalies (SSTAs) in the Niño-3.4 region (5°S−5°N, 190°−240°E) as an index of ENSO magnitude.
The study domain is (140°E to 90°W, 10°S to 10°N). As mentioned above, rather than focusing only on the narrow equatorial Pacific, this study also covers off-equatorial regions because of their role in ENSO variability (Hu et al., 2014; Hua and Yu, 2015). Subsequently, this study domain will be further divided into inner-equatorial (±5°N) and off-equatorial regions (5°–10°N and 5°–10°S). The study period is from January 1980 to December 2008, which is the common temporal coverage of selected ocean reanalyses at the time of this study.
In this study, ocean heat content (HC) is defined by the following equation:
where h is the depth below the sea surface where the vertical integration ends, ρ is the density of seawater, cp is the specific heat capacity of seawater, and T is the temperature of seawater. The ending depth of the integration (h) is chosen to be 300 m below the sea surface, which is the same as that used by Xue et al. (2012) and Hu et al. (2014). Other studies have used different integrating depths for HC ranging from 350 m to 400 m or more (e.g., Wang et al., 1999; Zhou and Chan, 2007). However, as HC anomalies are dominated by temperature variations along the thermocline between 50 m and 250 m below the sea surface (Fig. 1), adding extra integrating depth below the thermocline in the computation will not significantly affect the findings. Different ocean reanalyses have different climatological mean states as well as variability in ocean temperature (Xue et al., 2012). In order to account for these differences in the comparison, standardized anomalies are used. This standardization is done in each grid cell. Let x denote the raw values of ocean heat content in a certain grid cell, which itself is a time series with n time steps. The standardized anomaly of ocean heat content, denoted by
$\left\langle{x}\right\rangle $ , isFigure 1. The top 350 meters of ocean temperature variability of different ocean reanalyses in the equatorial Pacific Ocean (140°E to 90°W, meridional average from 10°S to 10°N) A 7-year high-pass filter was applied for the whole study period. The magenta dashed line in each plot marks the 300-meter level. All ocean reanalyses show that ocean temperature varies the most in the top 300 meters of the ocean.
where
Very short, high-amplitude waves are found in some ocean reanalysis products. Figure 2 shows a snapshot of HC300A averaged from January to March 2008 from SODA. In this figure, short waves can still be observed in the off-equatorial central Pacific even though a three-month moving average has already been applied. These waves are considered not irrelevant to ENSO. To provide information relevant to ENSO studies, a set of data pretreatment procedures is employed to filter out such signals from the raw data. Details of the filtering procedure are as follows:
Figure 2. The three-month moving average of standardized HC300A in February 2008 derived using SODA. Despite the use of the three-month moving average, short waves can still be observed (here, in the off-equatorial central Pacific). These waves are irrelevant to ENSO and are filtered out to reduce their influence on the dissimilarity measurement.
First, to remove high-frequency (sub-seasonal) signals, a three-month moving average is performed. Second, to remove the strong short waves seen in the raw data, an area filtering technique is applied. The HC300A field is linearly re-gridded into a coarse 2° (latitude) × 5° (longitude) data grid. Individual signals with a size of less than four grid boxes are removed.
The HC300A field is then ranked according to the magnitude in each grid (Table 1). The ranking is made to reduce the influence of the magnitude difference in the re-created HC300A among reanalyses on the measure of dissimilarity. As a result, the analysis will be influenced to a greater extent by differences in the HC300A signal distribution, which is of interest in this study.
Rank number Description Range of standardized HC300A −2 Strong cold signal HC300A ≤ −2 −1 Cold signal −2 < HC300A ≤ −1 0 No signal −1 < HC300A < +1 1 Warm signal +1 ≤ HC300A < +2 2 Strong warm signal HC300A ≥ +2 Table 1. Ranks of signal strength and rank numbers
Figure 3 shows a snapshot of HC300A after the treatment in April 1998, the decay phase of the 1997−98 El Niño. In general, a large area of positive HC300A (anomalously deep thermocline) can be observed in the east. In the west, the thermocline is anomalously shallow, shown as a large patch of negative HC300A on the plot. It is evident that the use of different ocean reanalyses to generate HC300A can yield different results.
Figure 3. Ranked HC300A in April 1998 after data pretreatments for each of the four reanalysis products. Signals irrelevant to ENSO (see the text) are filtered out.
The dissimilarity in HC300A of one ocean reanalysis to the others is defined as the average of the sum of the absolute difference in the ranked HC300A of the reanalysis to the others as shown in Eq. (5). For instance, the dissimilarity in HC300A between GODAS and the other three reanalysis products at a certain time step is computed according to the following methods: First, compute the sum of the absolute difference in the ranked HC300A between GODAS and the others in all grids within the domain. Second, average the three sums to get the dissimilarity of GODAS for the time step. Repeat these processes for all four reanalyses at all time steps to acquire four dissimilarity time series. Equation (5) shows the definition of the dissimilarity of reanalysis Aj to the others at time t:
where HCA is the ranked HC300A field and x and y are the coordinates in the field. The dissimilarity measuring technique is a simple differencing technique similar to root mean square differencing, except for the use of a ranking system and absolute value.
There are many ways to measure dissimilarity between two patterns. These methods can be loosely categorized into two groups, based on either simple differencing or relative difference. Pattern correlation is an example of the latter and is not suitable for this purpose. It is noted that there are periods with very weak signals in the study domain. In such periods, the relative difference–based dissimilarity-measuring techniques yield a very high dissimilarity for even a few small differences between two patterns. Such subtle differences are likely to be ignored in qualitative studies. To avoid this undesirable property, a simple differencing technique is employed. However, this technique is also sensitive to differences in magnitude rather than simply the distribution of signals. The ranking system reduces this sensitivity in the measurement so that the results align with our objectives.
The three-month average of Niño-3.4 SSTA from December, January, and February (DJF) in subsequent years is used to classify warm and cold years at the end of the developing year. Periods of time in the developing year are marked by (0), while (1) signifies periods of time in the subsequent year. The pointwise spread of HC300A is defined as the range of HC300A among the ocean reanalysis data sets (that is, the maximum minus the minimum). Growth and decay rate are measured by their rate of change, which is defined as the slope of six-month running least square linear regression. The six-month running window is selected because it approximates the typical time required for an ENSO event to grow and decay. Changing the length of the running window to three months does not affect the result significantly.
Rank number | Description | Range of standardized HC300A |
−2 | Strong cold signal | HC300A ≤ −2 |
−1 | Cold signal | −2 < HC300A ≤ −1 |
0 | No signal | −1 < HC300A < +1 |
1 | Warm signal | +1 ≤ HC300A < +2 |
2 | Strong warm signal | HC300A ≥ +2 |