Skewed Occurrence Frequency of Water Temperature and Salinity in the Subarctic Regions

Journal of Oceanography, Vol. 59, pp. 9 to 99, 3 Skewed Occurrence Frequency of Water Temperature and Salinity in the Subarctic Regions SACHIKO OGUMA *, TORU SUZUKI, SYDNEY LEVITUS and YUTAKA NAGATA Marine Information Research Center, JHA, 7-5- Ginza, Chuo-ku, Tokyo -, Japan World Data Center for Oceanography, NODC/NOAA, Silver Spring, MD 9-3, U.S.A. (Received May 3; in revised form August 3; accepted 9 August 3) In a previous paper (Oguma and Nagata, ), it was shown that frequency distributions of temperature and salinity in the sea off Sanriku Coast, Japan are skewed, and sometimes observed values exceed m + 5σ (m = mean, σ = standard deviation). This means that, if we apply a 3σ criterion for a range check, many real data would be lost. We have expanded our analysis to the subarctic North Pacific, the subarctic North Atlantic and their surrounding areas, by computing the distributions of skewness and kurtosis. It is found that the region of high positive skewness extends in an eastnorth-east direction in the Mixed Water Region from off Sanriku, and reaches to about 55 E. A high negative skewness zone is recognized along the southern margin of the Kuroshio Extension. These are thought to be generated by the breaking of the meander of the Kuroshio Extension and subsequent ejection of warm and cold eddies to the north and south, respectively. Other high positive skewness areas are found to the south of Kuril Islands and in the Japan Sea. These are generated due to very sharp vertical gradients of temperature and salinity. The situation in the North Atlantic is very similar to the North Pacific, though the detailed nature is changed due to differences of oceanographic condition. The effect of grid size on the skewed nature of the distribution is also discussed. Keywords: Subarctic region, skewed occurrence frequency, quality control, range check, water intrusion.. Introduction By analyzing the data obtained by the Iwate Fisheries Technology Center in the sea off Sanriku Coast, Japan, we found that frequency distributions of observed temperature and salinity in the Mixed Water Region between the Kuroshio and Oyashio Fronts are very skewed, and the usual techniques of quality control, such as a range check, are hard to apply (Oguma and Nagata, ). For example, some of the temperature values observed at 3 m depth exceed m + 5σ (m is the mean and σ the standard deviation), as shown in Fig.. Though the frequency of high temperature values is low, they are shown to be real. These extreme values were found when pure, unmodified Kuroshio Water intrudes into the region due to very specific events such as the approach of Large Warm Eddies or an abnormal northward intrusion of the Kuroshio along the Sanriku Coast (Oguma and Nagata, ). * Corresponding author. E-mail: oguma@mirc.jha.or.jp Copyright The Oceanographic Society of Japan. Therefore, if we apply a 3σ criterion, and delete the data which lie outside of the range m ± 3σ, many of the real data will be lost. We represent the non-normal nature of observed frequency distributions by using skewness and kurtosis, and expand our region of analysis to the subarctic North Pacific Ocean and subarctic North Atlantic Ocean and their surrounding areas.. Data Used and Representation of Skewed Nature of Frequency Distributions The Marine Information Research Center (MIRC) of the Japan Hydrographic Association conducted detailed quality checks on the oceanic data in the Northwestern North Pacific, and compiled the MIRC Ocean Dataset (MODS-: MIRC, ). This dataset was used for analysis in the Western North Pacific. For the analysis in the North Atlantic Ocean, World Ocean Database (WOD-: Ocean Climate Laboratory, NODC, ) was used. We used data interpolated to standard depths. In WOD-, a range check was done by using a 3σ criterion before the interpolation procedure. As the 9

Fig.. Occurrence frequency distribution of temperature at 3 m depth off Sanriku Coast, Japan. Below the abscissa, two kinds of standard deviation scale are shown: the upper scale is based on the standard deviation calculated directly from the distribution shown, and the lower is based on the converged standard deviation, which was obtained by an iterative procedure in which data lying outside the range m ± 3σ are omitted, and m and σ are recalculated using remaining data (Oguma and Nagata, ). Fig.. Mean temperature distributions at m (upper figure), at m depth (middle figure), and at 3 m depth (lower figure) in the Western North Pacific. Numerals attached to isotherms indicate temperature in C. WOD- dataset draws data from a variety of sources, this process is quite useful to eliminate possible erroneous data. Since this check was made for 5-degree subregions, if we re-analyze these data for -degree sub-regions, some of data may lie outside the range m ± 3σ, which was calculated afresh for the -degree sub-regions. The area analyzed was basically divided into -degree sub-regions. In the case of the North Atlantic, analysis was also done for 5-degree sub-regions, and the results were compared with those for -degree sub-regions. There are few data below m in the subarctic Pacific Ocean, and the results of were used only for a check. There are various methods to represent the skewed nature of a distribution, but we adopted moments of higher orders, skewness and kurtosis. Skewness is defined by (x i m) 3 /(n )σ 3 and kurtosis by (x i m) /(n )σ, where x i is the value of the i-th data point and n the number of data. m is the mean and m = (x i )/n, and σ the standard deviation σ = (x i m) /(n ). For normal distribution, skewness becomes zero, and kurtosis becomes 3. The excess of kurtosis, (x i m) /(n )σ 3 is used as kurtosis in this paper. 3. Mean Temperature Fields and Standard Deviation Fields in the Western North Pacific Mean temperature fields in the Western North Pacific for m, m and 3 m depths are shown in Fig.. The mean temperature decreases monotonically from south to north, and the high gradient zone corresponds to the Mixed Water Region between the Kuroshio and Oyashio Fronts. The densest isotherms are seen at the northern edge of the Mixed Water Region at m depth, and its position shifts southward as the depth increases. Standard deviation fields in the Western North Pacific for m, m and 3 m depths are shown in Fig. 3. The standard deviation shows a high-value band extending in the east-west direction, which corresponds to the highest gradient zone in temperature fields at each depth. These high standard deviation values are thought to be generated by the current path fluctuation of the Kuroshio Extension. The value tends to decrease eastward, as north-south temperature gradient is weakened eastward. 9 S. Oguma et al.

- - - - - -.5.5 - - - - - - - - - - - - - - - - - - -.5 - - -.5 3.5.5 - -.5 - - -.5 - -.5 --.5 - - - - - - - - -.5 - - - -.5.5 3 3.5 - - - - - - - - - - -.5 - -.5 - - -.5 - -.5 - - - -.5 - - - -.5 -.5 - - - - Fig. 3. As in Fig,, except for standard deviation fields. Fig.. As in Fig. except for skewness fields.. Skewness and Kurtosis Fields in the Western North Pacific Skewness and kurtosis fields in the Western North Pacific for m, m and 3 m depths are shown in Figs. and 5, respectively. Kurtosis distribution is a little simpler than skewness distribution, but high kurtosis values are generated in the area where high absolute values of skewness occur. This means that the distribution is not only skewed but also has a sharp peak and/or long tails. In general, kurtosis distributions appear to provide little additional information to skewness distributions, and will not be discussed further in this paper.. Peak area in the Mixed Water Region The skewness distribution at 3 m depth has a high positive value region extending from the sea off Sanriku Coast (39 N, E) towards the east-north-east. This high skewness region is not observed in the distribution at m depth. The distribution at m depth shows relatively high values in the corresponding region, but it is masked by another high value region to the south of Kuril Islands. We selected the -degree sub-region centered at N, 3 E as a representative region, and show frequency distributions of temperature and salinity for various depths ranging from to 5 m in Fig.. The m m 3 m Fig. 5. As in Fig., except for kurtosis fields. Skewed Occurrence Frequency of Water Temperature and Salinity in the Subarctic Regions 93

Fig.. Variations of the occurrence frequency distribution of temperature (left) and salinity (right) with depth in the -degree sub-region centered at N, 3 E. The depth is indicated in the figure. Black triangle attached to abscissa indicates m, and white triangles m ± 3σ. Values of mean, standard deviation, skewness, and kurtosis are shown for each figure. distributions are greatly skewed below m. It appears that the distributions below m are rather symmetric, but available data are very limited for these deeper depths. The vertical changes of the distribution patterns are very similar to those in the sea off Sanriku Coast discussed by Oguma and Nagata () (see figure of their paper). So this skewed nature can be understood in terms of sporadic intrusion of warm eddies ejected by the breaking of meanders of the Kuroshio Extension. The high value region extends eastward to about 55 E near the position of the Shatsky Rise.. Peak area to the south of the Kuroshio Extension A negative high value region extending east-west between 3 N and 35 N is seen in the skewness distributions at m depth and at 3 m depth. Some signature can also be seen in the distribution at m depth. We selected the -degree sub-region centered at 33 N, E, and show the frequency distribution of temperature at m, m, m and 3 m depths in Fig. 7. The distribution pattern is a mirror of the distributions observed in the Mixed Water Region. This skewness is thought to be generated by sporadic ejection of cold water eddies caused by the southward breaking of meanders of the Kuroshio Extension..3 Peak area in shallow layers to the south of the Kuril Islands In the skewness distributions at m and m depths, there is a high value region extending in the eastwest direction to the south of the Kuril Islands. However, no corresponding region can be seen in the distribution at 3 m depth. We selected the -degree sub-region centered at 3 N, 5 E, and show the frequency distri- 9 S. Oguma et al.

Fig. 7. Variations of the occurrence frequency distribution of temperature with depth in the -degree sub-region centered at 33 N, E. The depth is indicated in the figure. Black triangle attached to abscissa indicates m, and white triangles m ± 3σ. Values of mean, standard deviation, skewness, and kurtosis are shown for each figure. bution of temperature at m, 5 m, m and m depths in Fig.. There one can see considerable warm water at the sea surface. This results from the fact that observations there were made mainly in the summer season. This warm water is usually confined to the thin surface layer (e.g. Dodimead, 97; Nagata et al., 99). The maximum temperature value is considerably decreased, and its frequency becomes low at 5 m depth. However, some influence of the surface warm water can be seen down to m depth, and the distribution pattern has a tail on the higher temperature side, resulting in high positive skewness values up to this depth. It is difficult to discuss the nature of downward penetration of the surface warm water using the limited data presently available. Possible causes might be horizontal change of the thickness of the surface layer, internal waves and their breaking, or mixing due to strong storms. The first two cases are associated with high temperature and salinity contrasts in the horizontal direction, and this case is associated with high contrast in the vertical direction. Another high value region is seen inside the Japan Sea. There warm, saline water is influenced by the Tsushima Current in the surface layer, with very homogeneous Japan Sea Proper Water below it. The interface between two waters is generally sharp, and the high Fig.. As in Fig. 7, except for the -degree sub-region centered at 3 N, 5 E. skewness and kurtosis values are due to similar mechanism in the region south of the Kuril Islands. 5. Skewness Fields in the Western North Atlantic Skewness distributions in the Western North Atlantic are calculated for -degree sub-regions, and the skewness distributions are shown in Figs. 9 and for m, and 3 m depths. The skewness values at m depth (Fig. 9) are small except in the region southeast of Newfoundland Island where the Labrador Current Water encounters the Gulf Stream Water. At 3 m depth (Fig. ), the high north-south gradient zone corresponds to the average position of the Gulf Stream. The sign of the skewness changes from positive to negative crossing the stream from north to south. The situation is similar to the case crossing the Kuroshio Extension (see Fig. ). However, the positive ridge along the north edge of the Gulf Stream is not so conspicuous compared with the corresponding ridge in the North Pacific. The warm eddies ejected north from the Gulf Stream generally flow westwards and are re-absorbed into the Gulf Stream, and have a relatively short life time. Most of the warm eddies ejected from the Kuroshio Extension move northward, and are observed to persist for several years. The warm eddies in the North Atlantic have relatively smaller scale than those found in the North Pacific. This would make the positive ridge in the North Atlantic weaker. Skewed Occurrence Frequency of Water Temperature and Salinity in the Subarctic Regions 95

Fig.. Occurrence frequency distributions in the sub-region centers at 3 N, 7 W (left figures: Sub-region A) and in that centered at 7 N, 7 W (right figures: Sub-region B). The distributions at 3 m depth are shown in the upper row, and those at 5 m depth the lower row. Fig. 9. Skewness distribution at m depth in the Western North Atlantic. Fig.. As in Fig. 9, except for 3 m depth. The high negative skewness band along the southern edge of the Gulf Stream is strong, and comparable to that along the Kuroshio Extension. Ejection of cold eddies southward from the meander of the Gulf Stream is often observed, similar to the case of the Kuroshio Extension. This high skewness band extends to about 5 W. Large negative skewness values are found in the 3 m depth (Fig. ) to the east of the Florida Peninsula. There are two peaks at the -degree sub-region centered at 3 N, 7 W (Sub-region A) and at the sub-region centered at 7 N, 7 W (Sub-region B). The occurrence frequency distributions of temperature at 3 m depth (upper figures) and 5 m depth (lower figures) are shown in Fig. for Sub-region A (left figures) and for Subregion B (right figures). In the frequency distribution of Sub-region A, two temperature data lie well below the m-3σ level, both at 3 m and 5 m. These two data were obtained on September 9 at adjacent stations. The observed temperature are 5.9 C at 3 m and.3 C at 5 m at one station, and.33 C at 3 m and 7.9 C at 5 m at the other. In addition to abnormally low temperature values, the vertical temperature gradients between 3 m and 5 m for these data are abnormally high in comparison with the vertical gradient of the main peak value of the distribution. In Sub-region B, the abnormally low temperature values were observed on 3 February 97 both at 3 m depth (. C) and at 5 m depth (. C). These are other questionable temperature values (5. C at 3 m and.9 C at 5 m) which were observed at one station occupied on 3 March 97. These data are well isolated from other data in the distributions, and we feel that these data are erroneous, though more elaborate analysis is necessary to verify this. If we omit these data, the skewness would be much smaller and its sign would be changed for these sub-regions.. Dependence of Sub-Region Scale on Occurrence Frequency Distribution As seen in Fig., number of available data decreases considerably with depth, and the detailed nature of the distribution nature is difficult to discuss below 5 m in the Western North Pacific. For such cases we need to select a broader sub-region. We adopted broader 5-degree sub-regions for the analysis of the 5 m depth surface in 9 S. Oguma et al.

Fig.. As in Fig., except for the 5-degree sub-region centered at 37.5 N, 7 W in the Western North Atlantic. the North Atlantic, and found a conspicuous bi-modal distribution in the vicinity of the Gulf Stream System. As an example, variations of occurrence frequency distributions of temperature and salinity with depth are shown in Fig. for the 5-degree sub-region centered at 37.5 N, 7 W. Both the temperature and salinity distributions show a bi-modal feature below m. In order to understand why such a bi-modal structure occurred, we selected two representative -degree sub-regions to the north of the Gulf Stream centered at 39 N, 7 W and to the south of the Gulf Stream centered at 37 N, 7 W, respectively. The occurrence frequency distributions of temperature in these sub-regions are shown in Fig. 3 for various depths. The distribution patterns below m are much skewed. In the sub-region to the north of the Gulf Stream, the distributions below m depth have tails on the higher temperature side, while in the sub-region to the south of the Gulf Stream the distributions have tails on lower temperature side. It should be noted that the distributions have single a peak, and the bi-modal structure is disappeared. The distribution patterns to the north and south of the Gulf Stream are the same as those seen on the 3 m depth surface to the north and south of the Kuroshio Extension shown in Figs. 7 and, respectively. When the larger 5-degree sub-region is used, it can be shown that a bi-modal structure is also generated in the vicinity of the Kuroshio and the Kuroshio Extension. The horizontal distributions of skewness at 5 m depth based on -degree sub-regions are shown in Fig.. The distributions are almost identical to those at 3 m (Fig. ). The distribution pattern would have multiple peaks if the regions analyzed are wide and contain multiple domains having water masses quite different from each other. So we need to pay special attention to quality con- Skewed Occurrence Frequency of Water Temperature and Salinity in the Subarctic Regions 97

Fig. 3. Occurrence frequency distributions of temperature for various depths in the -degree sub-region centered at 39 N, 7 W (left figure) to the north of the Gulf Stream, and that at 37 N, 7 W (right figure) to the south of the Gulf Stream. The depth is indicated in each figure. Calculated mean, standard deviation, skewness and kurtosis are shown also in each the figure. trol in such regions. Also, the values of skewness might become large in such regions. 7. Concluding Remarks In order to perform high grade quality checks, we need to know the nature of occurrence frequency distributions in the region under consideration. If the distribution is skewed, a 3σ criterion is difficult to apply in the range check procedure. It is shown that large skewness values appear in many regions in the subarctic North Pacific, subarctic North Atlantic and their adjacent regions. However, it should be noted that a skewed occurrence frequency distribution may be found in the seas where large temperature and salinity contrasts exist in the horizontal or vertical direction. For example, we found many skewed salinity distributions in the surface layer in the sea near the mouth of the Amazon River, where the horizontal salinity gradient is considerable. We need to conduct surveys to find where large skewed distributions occur in the world ocean, but it should be recalled that the nature of the distribution may be changed due to the size of the analyzed sub-domains selected. If we use broad sub-regions where sharp fronts exist, the distribution might be bi-modal. Moreover, the skewness value is greatly increased if erroneous extreme values exist in the dataset. In the analysis of the skewed nature of the distribution, we may apply a range check by using a 3σ criterion for sufficiently larger sub-regions at first, in order to exclude such erroneous values. Even so, we should remember that skewness and kurtosis can represent only some aspect of the skewed distribution. We always need to check the original distribution patterns. 9 S. Oguma et al.

Acknowledgements We would like to thank Prof. Kimio Hanawa of Tohoku University for his valuable advice. We thank the Iwate Fisheries Technology Center for providing us with valuable observation data. The works were partly supported by the Science and the Technology Agency (International Cooperative Experiments on North Pacific Subarctic Gyre and Climate Change: SAGE) and by the Nippon Foundation. Fig.. As in Fig. 9, except for 5 m depth. References Dodimead, A. J. (97): Winter oceanographic conditions in the central Subarctic Pacific. Int. North Pacific Comm., Doc. 999,. Marine Information Research Center (): MIRC Ocean Dataset Documentation, MIRC Technical Report No., 9 pp. (in Japanese). Nagata, Y., K. Ohtani and M. Kashiwai (99): Subarctic Gyre in the North Pacific Ocean. Umi no Kenkyu,, 75 (in Japanese). Ocean Climate Laboratory, NODC (): World Ocean Database. National Oeanographic Data Center Internal Report, 37 pp. Oguma, S. and Y. Nagata (): Skewed water temperature occurrence frequency in the sea off Sanriku, Japan, and intrusion of the pure Kuroshio Water. J. Oceanogr., 5, 79 79. Skewed Occurrence Frequency of Water Temperature and Salinity in the Subarctic Regions 99