1. Introduction
Water temperature is regarded as the most important environmental and ecological (E&E) factor in coastal seas. This factor is highly expected to change in the long term owing to climate change. In-depth analysis of water temperature change patterns is essential to understand E&E change patterns. However, such analysis usually depends on air temperature change patterns because air temperature data are more abundant than water temperature data.
Although air and water temperatures are of relatively high importance compared to other E&E parameters, the distribution shape and change patterns show considerable differences owing to the typical hysteresis and density difference (Cho & Lee, 2012). In this study, it is suggested that E&E change estimation based only on air temperatures has basic limitations by making a comparison and analysis of the change pattern and distribution shape between air and water temperatures. In general, the overall occurrence distribution shape of air and water temperatures does not show a normal distribution but rather a multimodal or skewed distribution (Toth and Szentimery, 1990; Grace and Curran, 1993; Harmel et al., 2002; Jeong et al., 2013; Jeong et al., 2014). This is why the distribution shape and change pattern analysis is somewhat limited in the case of meanonly estimation. The distribution shape can be used as a reference to understand the changes of the shift-pattern, the modal locations, and the tail shapes in the probability density distribution of the air and water temperatures. Donat and Alexander(2012) examined the shifting probability distributions of global temperatures.
2. Air and water temperature data
The current level of monitoring of air and water temperature data is sufficient, but the simultaneously measured data sets are slightly limited. In this study, four representative data sets collected in 2009 supported by the KHOA (Korea Hydrographic and Oceanographic Administration) are selected to consider the diverse coastal characteristics at the sites Incheon (strong-tide, N 37-27, E 126-35), Mokpo (N 34-46, E 126-22, Gadeokdo (N 35-01, E 128-48), and Mukho (weak-tide, N 37-33, E 129-07) shown in Fig. 1. The data are taken at 1-min intervals. To reduce the data size and utilize the reference data, the raw data are transformed to hourly data through a 1-hour median filter. This data transformation does not change the overall distribution shapes even though the wiggles (small fluctuating patterns) disappear. Outliers are removed by using the efficient outlier detection method by Cho et al. (2014). The basic statistical information is arranged in Table 1. As shown in Table 1, the mean air and water temperatures are highly dependent on the latitude of the stations. Moreover, the dispersion indicators, such as standard deviation, are closely related to the tidal conditions. As the tide strength decreases in a particular order-namely, Incheon, Mokpo, Gadeokdo, and Mukho stations, the dispersion indicators decrease significantly.
3. Results and discussion
3.1. Relationship between air and water temperatures
Fig. 2 shows the time series plots and scatterplots of the air-water temperature data. The upper panels show the time series plots of the data. The fluctuations of air temperature are stronger than those of water temperature, as expected. The mild increase and steep decrease patterns also represent clear typical temporal changes. In the scatterplots in the lower panels, the water temperature barriers (WTB) are shown in the lower and higher regions, which are defined as nearly constant water temperature periods. In this region, the water temperature does not increase any further, even though the air temperature increases. Based on the rough graphical estimation, the lower WTBs in Incheon, Mokpo, Gadeokdo, and Mukho, are approximately 2, 4, 8, and 8℃, respectively. The WTBs in the western coast are much lower than those in the eastern coast because of the physical environment of the seas. In addition, the Incheon WTB is much lower than the Mokpo WTB because Incheon is located at higher latitude than Mokpo. The WTB differences are attributed to the flow and location characteristics. The WTB can be used as a key indicator of the water temperatures for long-term climate change even though in-depth analysis is needed using more temperature data sets in many locations.
3.2 Comparison of the distribution shapes between air and water temperatures
Estimation methods for the distribution function can be classified as parametric and nonparametric methods. Jeong et al. (2013, 2014) suggested that the Gaussian mixture model (order = 2) is more suitable than the normal distribution to fit the air and water temperature data distribution. The model parameters are estimated using the least-square methods in Jeong's study. Another typical parameter estimation method is an EM (expectation-maximization) algorithm (Bishop, 2006), which is available using R-packages (“mixtools”, “mclust”), Matlab function “gmdistribution.fit,” and others. This is the typical parametric method. In this study, the kernel distribution functions are compared with the Gaussian mixture models whose parameters are estimated by a typical EM algorithm. However, the Gaussian model shows relatively poor fitting results in the tail areas and multi-peaks. In order to reduce these limitations, the nonparametric method using kernel functions is used in this study. This method is regarded as a very powerful and flexible method (Silverman, 1998). The bandwidth parameter of the kernel function can be estimated using the following formula, as shown in Eq. (1):
in which hopt = optimal bandwidth parameter, σ ^
Another typical nonparametric method is the histogram. This has been a widely used method even though it shows a discontinuous distribution shape and is sensitive to the bin width (i.e., bin numbers) and data starting point. Moreover, the kernel distribution is continuous and has only one parameter. The histogram method is not used in this study because of these drawbacks.
Fig. 3 shows the comparison plot of the probability distribution function between air and water temperatures. As shown in Fig. 3, all distribution shapes exhibit obvious double peaks. The longer-tailed shapes and asymmetric patterns are shown in each air temperature distribution. With regard to the air temperature distribution shape, the peak probability of the lower temperature is smaller than that of the higher temperature, whereas the peak probability of the higher water temperature becomes smaller than that of the lower water temperature. The probability change pattern between peaks is also different between the air and water temperatures. Even though the distribution shapes using Gaussian mixture model exhibit double peaks and roughly similar shapes suggested by Jeong et al. (2014), the location and probability of the peaks and the gradient of tail regions show considerable differences.
Fig. 4 shows the comparison plot of the cumulative distribution between air and water temperatures. In this figure, the difference in the lower temperature region can be detected with ease. This means that the dominant temperature difference derived in the lower temperature regions because the water temperature scarcely decreases as the air temperature decreases. The water temperature maintains nearly constant values as already shown in the scatterplot (Fig. 2), corresponding to the newly suggested temperature barrier in this study. This value can be regarded as the characteristic value in the coastal zone, which is dependent on the coastal environmental conditions, such as the latitude, tidal strength, water depth (and/or mixing layer thickness), and other seawater properties.
4. Conclusions and recommendations
The information from the probability distribution function (or occurrence frequency) is useful to quantify the contribution of the air and water temperature changes from climate change. All air and water temperature data show similar change patterns because of the dominant annual components. However, there is a large difference between the local change pattern and occurrence distribution because of the difference in the air and water temperature change drivers. Therefore, rough E&E parameter estimation based only on air temperature might be reasonable. Conversely, estimation based on long-term small changes, such as water temperature change due to climate change, could lead to the erroneous conclusions. Thus, it is unreasonable to estimate the water temperature and E&E parameters using air temperature change patterns due to climate change. The E&E parameters in the coastal zone should be estimated using water temperature change patterns.
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