**5. Periodic fluctuations**

If you look closely at the graph of the course of the mean monthly SST (**Figure 7** [11]), then in addition to seasonal fluctuations, you can notice interannual variations. They are especially pronounced in August, when the mean monthly water temperature reaches its maximum value, and are expressed in the modulation of the annual harmonic. Moreover, these oscillations are of a quasiperiodic nature, most likely associated with certain phenomena in the atmosphere and hydrosphere.

Any periodic oscillations can be described by knowing their amplitude, phase and period. Using the least squares method, you can find the corresponding amplitude and phase for each selected period. Thus, it is possible to establish a kind of "influence zones" of harmonics with a certain period, i.e. areas in which the amplitude of one or another harmonic exceeds a certain threshold value. And in order not to interfere in the calculations with long-term components (the period of which exceeds half the length of the series), the trend obtained according to the method described in the previous section was subtracted from the initial data.

The distribution of the amplitudes of temperature fluctuations in the studied region is rather complex. Having determined in each spatial cell the period corresponding to the largest amplitude and displaying the obtained data on the screen, we have established several main periods that play a significant role in interannual SST variations in most cases. For a series of 21 years, it is not entirely correct to calculate fluctuations with a period exceeding 11 years. Short-period fluctuations are unstable and generally have little information. Thus, the spatial distributions of harmonic amplitudes with a period from 3 to 11 years were considered in detail.

In most of the studied water area, the main role was played by variations with a period of about 5.5–6 years (on the graphs for points 2, 5 and 8 in **Figure 8**, you can see that the largest amplitude at these points corresponds to a period of 66–68 months), the spatial distribution of the amplitude with a period of 6 years is shown in **Figure 9** [12]. The zone of its influence is the most extensive and occupies

**Figure 7.**

*Annual variation of average monthly temperature (left) and average temperature in august (right) [11].*

#### *Analysis of Spatiotemporal Variability of Surface Temperature of Okhotsk Sea and Adjacent… DOI: http://dx.doi.org/10.5772/intechopen.94918*

the southern half of the Sea of Okhotsk and the northern part of the Sea of Japan, up to the Amur estuary. The amplitude of this harmonic in the zone of its influence ranges from 1 to 2°C. In the vicinity of the Kuril Islands, off the western coast of about. Hokkaido, off the northeastern coast of about. Sakhalin, the amplitude is slightly lower (from 0.5 to 1°C). Further to the north, starting from 52 N, its influence decreases and practically disappears.

In [8], based on the EOF decomposition of the sea surface temperature in the North Pacific Ocean, it was shown that an oscillation with a similar period is characteristic of the entire region influenced by the Kuroshio Current and its branch, the warm Tsushima Current. This is evidenced by the large amplitudes in the zone of the indicated currents and in **Figure 9**. Consequently, as a result of this study, it was possible to estimate the boundaries of the influence of this component in the Sea of Okhotsk, which runs parallel to the islands of the Kuril ridge and divides this basin into two practically equal parts. The entire northern Sea of Japan is significantly affected by this cycle.

As seen from **Figure 8**, at most points, one can also note peaks in the range of periods from two to three years. The highest values of the amplitude of the 3-year harmonic can be noted in the northwestern part of the Sea of Okhotsk, at a distance from the coast, as well as near the northwestern coast of Kamchatka and in the strip from 47 to 490 N. and from 147 to 1490 E. in the area of the Kuril deep-water basin and in the northwestern part of the Pacific Ocean. However, the amplitudes of these oscillations are somewhat lower than those of the six-year harmonic (from 1 to 1.5°C). At a distance from these regions, the amplitude gradually decreases to zero.

The spatial distribution of the amplitudes of the cyclic component with a period of 5 years differs markedly from that considered above for a period of 6 years. The zone of its influence is noticeably narrower, it is concentrated mainly on the northern shelf of Hokkaido, in the region of the South Kuril Islands (vast waters both on

#### **Figure 8.**

*Examples of graphs of the dependence of the amplitude of the harmonic (in °C) from its period (in months). The location of the points is shown in Figure 9 [12].*

#### **Figure 9.**

*Distribution of amplitudes (in °C) of interannual fluctuations in the mean monthly sea surface temperature (august) with a certain period (indicated in years in the upper left corner of the image) [12].*

the Sea of Okhotsk and on the ocean sides), and, surprisingly, on the northeastern shelf of Sakhalin, where the influence of a lower frequency component was not noted. In the Tatar Strait, its role is also noticeable, but expressed to a lesser extent than the 6-year harmonic.

In the western part of the Sea of Okhotsk and the northwestern part of the Pacific Ocean, a cyclical component with a period of about 8 years is significantly manifested. The zone of influence of the Amur river runoff in summer is clearly distinguished in the spatial distribution - the Amur estuary, the southern and eastern parts of the Sakhalin Bay, the area between the Schmidt Peninsula and the Kashevarov Bank [13]. It is interesting that in the area of the Kuroshio Current manifestation, this component has large amplitudes, in the Tsushima Current zone in the Sea of Japan - insignificant, while on the northern shelf of Hokkaido and on the Sea of Okhotsk side of the Southern Kuril Islands, where the warming effect of the Soya Current affects, the amplitudes are significantly.

The lowest frequency of the considered harmonics with a period of 11 years is manifested in the northern part of the Sea of Okhotsk; in other parts of the study area, its role is insignificant. It is rather difficult to put forward a reasonable hypothesis that could explain such significant differences in the very long-term variations in SST in different parts of the same basin. It can only be assumed that

*Analysis of Spatiotemporal Variability of Surface Temperature of Okhotsk Sea and Adjacent… DOI: http://dx.doi.org/10.5772/intechopen.94918*

due to the comparative shallowness of the northern region, the effect of the winds of the southern rumba and the greater number of sunny days than in the southern part, due to the lesser influence of cloudiness, the influence of the solar cycle is more noticeable here.

Attention is drawn to the fact how the zones of manifestation of harmonics shift with a period of 5 to 11 years. If the zone of influence of the 5-year harmonic is focused near the islands of Sakhalin, Hokkaido and the Southern Kuriles, then with an increase in the period, the region with the highest amplitude shifts clockwise (towards the northeastern coast of Sakhalin and further to the northern part of the Sea of Okhotsk). This interesting fact is also difficult to give a reasonable explanation, it requires additional study.

In work [8], a method was developed for predicting thermal conditions for a year in advance in certain areas of the studied water area (this method was also used to recover data gaps associated with the influence of cloudiness or technical reasons), which consisted in calculating the temperature in a given square in time t according to the formula:

$$T\left(t\right) = at + b + \sum\_{k=1}^{N} c\_k \cos\left(\phi\_k t - \phi\_k\right) \tag{1}$$

where a and b are the parameters of the linear trend, are the amplitudes, and are the phases of the cyclic components (harmonics) of sea surface temperature variations. An essential feature of the method is the fact that the amplitudes and phases of the main cyclical components are calculated by the least squares method, with their periods ranging from 18 to 144 months with a step of 1 month. For each cell, a set of 3–4 harmonics was determined, which make the largest contribution to the interannual variations in SST. Since they are not orthogonal, for forecasting using formula (1), it is necessary to subtract the calculated wave from the initial series before determining the parameters of the next one in order to avoid double inclusion of coherent components (in [14, 15]) such a technique was called "Sequential spectra method").

Based on the parameters of the obtained cyclic components, a retrospective forecast of thermal conditions for the summer of 2018 was carried out (observational data for 1998–2017 were used to calculate the parameters of harmonics and a linear trend). The calculation was carried out for each spatial cell according to formula ( 1 ), taking into account the trend and four harmonic components with the highest amplitudes. For the forecast, periods from 18 to 144 months were covered. The calculation results are presented in **Figure 8** in the form of graphs of forecast curves and real variations in sea surface temperature, including the predicted values that took place in the summer of 2018. **Figure 10** shows the spatial distribution of the difference between the predicted and actual temperatures for August 2017 and 2018. The forecast was built for a year ahead along the entire previous series.

The curves, which are the sum of the trend and the first four harmonics, generally repeat the actual interannual temperature fluctuations. The correlation coefficient of the initial and predicted series at the selected points exceeds 90%. Note that even the first two harmonics in many cases provide a correlation coefficient of more than 70%. Despite the fact that 2018 was anomalous in terms of thermal conditions (the Tsushima Current and its Okhotsk branch of the Soya Current were weakened, a heat deficit was felt in the zone of influence of the Amur River runoff), and in some other areas, even in such water areas, the forecast can be considered acceptable. An example of a similar situation is given for the Tatar Strait, where the predicted value was higher than the actual one, but the general course was predicted correctly, and the error was not so great. For the northern part of the Sea of Okhotsk, the northeastern shelf of Sakhalin Island, and a number of other areas,

**Figure 10.**

*Examples of temperature forecast graphs (in °C) for the next year. The dashed line shows the prognostic curve. The forecast is carried out for the period from 1998 to 2017. The actual temperature in 2018 is marked with a cross [11].*

good agreement was observed between the calculated and real values of the surface layer temperature.

Let us consider some of the parameters of the graphs below. The standard deviation of the initial and predicted series correspond to each other and range from 1.5°C (Tatar Strait) to 2°C (South Kuriles). The average displacement of the predicted series relative to the initial one ranges from 0.4 to 0.6°C. The forecast error is 1.7°C in the Tatar Strait, 1.3°C near the Southern Kuriles, 0.3–0.4°C in the northern part of the studied water area.

More detailed studies devoted to predictability and the limits of applicability of the approach used will be carried out later. However, we can already say that for a significant part of the Sea of Okhotsk regions and adjacent water areas, the forecast of the surface layer temperature with a one-year lead time is quite successful, although the abnormally cold temperatures that took place in a number of areas in 2018 are rather difficult to predict.

Let us take a closer look at **Figure 11**. The forecast for August 2017 turned out to be quite successful, the discrepancy between the actual and predicted temperatures in most of the water area does not exceed ±2°C, with a standard deviation of SST of about 1.5-2°C (only in the northwestern part of the Pacific Ocean is the standard SST deviation is within 2-4°C). At the same time, the forecast for August 2018 contains a large area within which the temperature estimate was greatly overestimated (over 4°C). The map of SST anomalies for August 2018 [16] also contains areas of low temperatures (3-4°C lower than the average multiyear norm), which coincide in space with areas of unsuccessful forecast. This area is located in the zone of influence of the Tsushima Current, and the forecast inaccuracies are due to the fact that the weakening of this current occurred two years earlier than the expected date. Indeed, in **Figure 8**, we see that in the Tatar Strait and the Southern Kuriles, the distance between two neighboring SST minimums decreased to 3–4 years, while its quasiperiodic oscillations with a period of about 6 years are described in the literature [17].

As a result of the analysis of the data set on the surface temperature of the Sea of Okhotsk and adjacent waters, the main cyclical components responsible for the interannual variations of this parameter and the "zones of influence" of each

*Analysis of Spatiotemporal Variability of Surface Temperature of Okhotsk Sea and Adjacent… DOI: http://dx.doi.org/10.5772/intechopen.94918*

**Figure 11.** *Difference between predicted and actual temperatures [11].*

harmonic were determined. It is shown that the main contribution to these variations comes from components with a period of about 6 years, as well as 3, 5, 8, and 11 years.

The zone of influence of the fundamental harmonic is the most extensive and occupies the southern half of the Sea of Okhotsk and the entire northern part of the Sea of Japan; its amplitude is within 1–2°C. In the vicinity of the Kuril Islands, off the western coast of Hokkaido Island, off the northeastern coast of Sakhalin Island, the amplitude is slightly lower (0.5–1°C), and in the northern part of the Sea of Okhotsk its influence is insignificant. Most likely, this component is associated with fluctuations in the Kuroshio Current and its branch, the Tsushima Current [17].

The highest values of the amplitude of the 3-year harmonic (1–1.5°C) can be noted in the northwestern part of the Sea of Okhotsk, at a distance from the coast, as well as off the northwestern coast of Kamchatka, in the region of the Kuril deepwater basin and in the northwestern parts of the Pacific Ocean.

The area of manifestation of the component with a period of 5 years is noticeably narrower, it is concentrated mainly on the northern shelf of Hokkaido, in the region of the South Kuril Islands (both from the Sea of Okhotsk and the ocean side), and on the northeastern shelf of Sakhalin. In the Tatar Strait, its role is also noticeable, but expressed to a lesser extent than the 6-year harmonic.

In the western part of the Sea of Okhotsk, in the zone of influence of the Amur River runoff, as well as in the northwestern part of the Pacific Ocean, a cyclical component with a period of about 8 years is significantly manifested.

The lowest frequency of the considered harmonics with a period of 11 years is manifested in the northern part of the Sea of Okhotsk; in other parts of the study area, its role is insignificant.

Together with the parameters of the linear trend [9], the amplitudes and phases of the main cyclical components (in each spatial cell, 4 harmonics with the highest amplitudes were used) can be used to predict thermal conditions for the next summer. The retrospective calculation for 2018 gave generally satisfactory results, despite the abnormally cold conditions of this year, noted in a number of areas of the studied water area. The possibility of predicting thermal conditions is of practical importance, primarily for assessing the conditions for the approach of Pacific salmon to spawning. And the results obtained show that in some areas of the water area, one can count on a fairly accurate forecast even for such an unstable parameter as the ocean surface temperature.

In general, the success of the forecast is influenced by how pronounced the cyclical components with a certain period in a given area. Identification of the zone of influence of various harmonics allows you to determine the boundaries of the regions in which the applicability of this method can be expected. As for the

accuracy of the forecast, one should pay attention to the presence of large areas in which the modulus of the difference between the predicted temperature and the actual one was of the order of two standard deviations. This fact shows that this method does not guarantee the success of the forecast in cases where strong temperature anomalies are observed. It can only be used to obtain a primary estimate of the ocean surface temperature (or another parameter that experiences quasiperiodic oscillations) based on a sufficiently long series. The 21-year series is not enough to estimate low-frequency components (with a period of 30–50 years), which could also affect the quality of the forecast. For a better forecast, you can combine this method with an assessment of the current conditions, adjusting the forecast in the direction of increasing or decreasing temperature, depending on the current meteorological conditions.
