Restoration of data on water temperature in the Kola Section in 2016–2017
2. The use of multiple linear regressions and data from other standard sections. The principle of the method is to carry out a regression analysis of time-series from the Kola Section and from
other nearby sections to develop regression models to calculate data from the Kola Section (predicant) using data from the neighboring sections (predictors).
The time-series from the Norwegian Fugløya–Bjørnøya and Vardø–North Sections from 1977 to 2017, kindly provided by the Institute of Marine Research, Bergen, Norway, were used as predictors. The time-series in January, March, April–May, August–September and October in the Fugløya–Bjørnøya Section and in January, March and August–September in the Vardø–North Section were used to develop regression models. Regression equations were developed in the Statistica 13.3 package by Stepwise regression Method: forward selection, enter: 0.05, P-to-remove: 0.05, separately for each month, i.e. the interannual variability was examined, so there was no need to exclude a seasonal cycle from the time-series. In total, 132 equations were formulated for 12 months, 3 (or 4) layers, and 3 parts of the Kola Section: 3 layers in the inner part of the section and 4 layers in the central and outer parts.
The coefficients of determination of the models developed are indicative of a rather high degree of correspondence of calculated and observed data for all the layers and parts of the Kola Section, excluding July–September in the 0–50 m layer in the outer part of the Kola Section (Stations 8–10) (Table 2). Thus, data calculated using the developed regression equations adequately describe interannual and seasonal variability of water temperature in the Kola Section.
Table 2. Coefficients of determination (R2) for regression models of water temperature in the Kola Section.
A part of the Kola Figure 4 shows one of the best (R2=84.6) and one of the worst (R2=55.0) models for the central Kola Section as an example. Similar results of consistency between calculated and observed data were obtained for other layers and parts of the section. The best models were obtained for a summer-and-autumn period and deeper layers. The model quality deteriorates in wintertime as well as in the surface layer and in the inner Kola Section (Stations 1–3). This is most probably associated with a higher variability of temperature conditions here as well as with synoptic processes having an impact on deeper layers in wintertime.
Figure 5 shows an example of restored data in the Kola Section using the above approach. The largest discrepancies between observed and calculated temperatures were recorded for 2012 when record-high temperature anomalies were observed (González-Pola et al., 2018).
Figure 4. Distribution of observed and calculated temperatures in the central Kola Section (Stations 3–7) in the 0–
200 m layer in June (left) and in the 0–50 m layer in July (right) from 1977 to 2017 (black circles show temperatures calculated using an independent data set).
Figure 5. Long-term mean (dashed line), observed (black line) and calculated with regression equations (grey line) water temperatures in the 0–200 m layer in the central Kola Section (Stations 3–7).
3. The use of NEMO ocean model. Under this approach, modelled data from the multi-layer high resolution model NEMO (Madec et al., 2008) taken from the Copernicus website (http://marine.copernicus.eu) were used to restore data gaps.
The model has a 9 km horizontal resolution at the Equator, the 50-level vertical discretization, monthly and daily data. When restoring the data gaps, the monthly (from January 2007 to December 2017) modelled data on temperature at standard depths within the coordinates of standard stations in the Kola Section were used. The mean temperatures in the 0–50, 0–200, 50–200 and 150–200 m layers in the inner (Stations 1–3), central (Stations 3–7) and outer (Stations 8–10) parts of the Kola Section were calculated for each month based on the selected data. Then a regression analysis of modelled data obtained and the available observed data on water temperature was carried out. The regression equations between the modelled and observed data developed for
each layer and part of the section were used to restore the gaps. Temperature anomalies were used in calculations to exclude a seasonal cycle.
As an example, Figure 6 shows the distribution of observed and modelled temperature anomalies in the 0–200 m layer in the central Kola Section (Stations 3–7). As can be seen in this figure, the relationship between these two series is statistically significant and rather close (R2 = 0.73, n = 96).
The highest deviations from the regression line are recorded in the area of large positive anomalies.
Similar results of consistency between modelled and observed data were obtained for other layers and parts of the section (Table 3). Worst of all, the model describes the variability of temperature anomalies in the 50–200 m layer in the inner Kola Section (Stations 1–3) (R2 = 0.46), although the relationship between modelled and observed data here remains to be statistically significant. This is most probably associated with a complex nature of hydrophysical and hydrodynamical processes in the coastal zone.
Figure 6. Distribution of observed and modelled water temperature anomalies in the 0–200 m layer in the central Kola Section (Stations 3–7) from January 2007 to December 2014 (dashed line shows a linear trend).
Table 3. Coefficients of determination (R2) of regression equations used to calculate water temperature anomalies in the Kola Section.
Based on the temperature anomalies calculated using regression equations for the period of missing data, absolute values of temperature were calculated. Figure 7 shows an example of data restoration in the Kola Section using the above approach. Relatively large discrepancies between the observed
and modelled temperatures were mainly recorded in 2012 when record-high temperatures were observed (González-Pola et al., 2018).
Figure 7. Long-term mean (dashed line), observed (black line) and calculated (grey line) with a model water temperatures in the 0–200 m layer in the central Kola Section (Stations 3–7).
In general, the model results closely describe interannual and seasonal variability of water temperature in the Kola Section and can be used for restoring gaps in time-series with a rather sufficient degree of reliability.
Results and discussion
To evaluate the quality of the proposed approaches for restoring data in the Kola Section and to select the most appropriate one, absolute errors were calculated, namely modules of differences between the observed and modelled temperatures. Then, mean absolute errors, maximum absolute errors and 2.5σ (σ – standard deviation) were calculated based on those values (Table 4). The 2.5σ means that about 99% of all the absolute errors are less than 2.5σ.
Table 4. Absolute error statistics for various approaches applied to restore data in the Kola Section by the example of the central Kola Section (Stations 3–7) and the 0–200 m layer from 2007 to 2017: 1 – the use of internal structure of time-series from the Kola Section; 2 – the use of multiple linear regressions and data from other standard sections; and 3 – the use of the NEMO model.
Absolute error statistics, °C No. of approach
1 2 3
Mean absolute error 0.10 0.35 0.13
2.5σ (σ – standard deviation) 0.40 1.32 0.42
Maximum absolute error 1.02 2.54 0.54
Table 4 shows that the best results were obtained using modelled data from the Copernicus website (NEMO model). The highest absolute errors were recorded when using multiple linear regressions and data from other standard sections. As far as the first approach is concerned (the use of internal structure of time-series from the Kola Section), the mean absolute error was consistent with that for the third approach. The maximum absolute error, however, was twice as much. Moreover, the first
approach provides good results on dependent data. However, when independent data were used (that is exactly what needed for data restoring), the error increases considerably (Figure 3). This is explained by the fact that when the series is being split into quasi-periodic components, they, in the aggregate, describe the series very well. However, when providing a prediction, i.e. when restoring data gaps, the results get worse, especially when there are abnormal situations like, for example, similar to that observed in 2016 when record-high temperatures were observed in the Barents Sea (González-Pola et al., 2018). The data restored with the first approach seem to be underestimated.
Firstly, in August–September 2016 during the annual ecosystem survey in the Barents Sea, the temperature anomalies nearby the Kola Section were about two times higher than the restored data.
Secondly, observations carried out in the Kola Section in November and December 2017 showed that observed temperature anomalies (0.70 and 0.90°С respectively) were well above the restored ones (–0.05°С and –0.12°С respectively).
Eventually, a decision was taken to use the third approach for restoring data on temperature in the Kola Section, namely using modelled data obtained with the NEMO ocean model. The restored data on temperature are given in Table 5.
Table 5. Mean water temperatures (°C) in the Kola Section in 2016 and 2017 (restored data are in bold).
Year Month
1 2 3 4 5 6 7 8 9 10 11 12
Stations 1–3 (Coastal Murman Current, 0–50 m layer
2016 4.84 4.02 3.58 3.57 4.47 5.39 7.19 8.37 8.74 8.13 7.26 6.03 2017 5.11 4.39 3.90 3.56 3.89 4.82 6.71 8.35 8.55 7.62 6.79 5.87
Stations 1–3 (Coastal Murman Current), 0–200 m layer
2016 5.06 4.26 3.80 3.68 4.13 4.35 5.10 5.62 6.16 6.84 7.00 5.94 2017 5.07 4.37 3.92 3.53 3.68 4.19 5.04 5.90 6.43 6.38 6.36 5.87
Stations 1–3 (Coastal Murman Current), 50–200 m layer
2016 5.18 4.49 3.94 3.75 4.01 3.86 4.17 4.42 5.08 6.37 6.92 5.91 2017 5.06 4.35 3.93 3.52 3.59 3.96 4.25 4.81 5.53 5.87 6.26 5.87
Stations 3–7 (Murman Current), 0–50 m layer
2016 4.91 4.40 4.33 4.39 4.85 5.78 7.68 8.72 8.30 7.54 6.45 5.65 2017 5.09 4.68 4.40 4.14 4.40 4.90 6.80 7.98 8.09 7.35 6.18 5.61
Stations 3–7 (Murman Current), 0–200 m layer
2016 5.23 4.84 4.68 4.55 4.50 5.05 5.56 5.83 5.92 6.08 5.98 5.64 2017 5.25 4.94 4.70 4.36 4.52 4.49 5.13 5.54 5.82 5.92 5.65 5.44
Stations 3–7 (Murman Current), 50–200 m layer
2016 5.33 4.99 4.80 4.62 4.36 4.66 4.72 4.73 4.98 5.44 5.70 5.50 2017 5.17 4.87 4.66 4.30 4.42 4.35 4.57 4.73 5.07 5.44 5.45 5.39
Stations 3–7 (Murman Current), 150–200 m layer
2016 5.28 5.11 4.87 4.55 4.01 4.55 4.60 4.46 4.56 4.85 5.00 5.09 2017 5.02 4.88 4.79 4.40 4.49 4.17 4.24 4.36 4.53 4.80 4.94 5.13
Stations 8–10 (Central branch of the North Cape Current), 0–50 m layer
2016 4.51 4.15 3.94 3.88 4.40 5.33 6.97 8.12 7.59 6.93 5.68 4.93 2017 4.30 4.04 4.04 3.88 4.02 4.48 5.84 7.04 7.19 6.53 5.37 4.75
Stations 8–10 (Central branch of the North Cape Current), 0–200 m layer
2016 4.48 4.07 3.84 3.68 3.85 4.28 4.92 5.38 5.62 5.73 5.26 4.74 2017 4.15 3.89 3.89 3.69 3.81 3.85 4.48 4.89 5.19 5.13 5.15 4.54
Stations 8–10 (Central branch of the North Cape Current), 50–200 m layer
2016 4.47 4.04 3.81 3.61 3.66 3.98 4.25 4.46 4.96 5.34 5.12 4.69 2017 4.11 3.85 3.85 3.64 3.75 3.63 4.02 4.17 4.51 4.66 5.05 4.48
Stations 8–10 (Central branch of the North Cape Current), 150–200 m layer
2016 4.36 3.92 3.65 3.40 3.31 3.56 3.78 3.89 4.18 4.67 4.47 4.43 2017 4.02 3.75 3.65 3.35 3.46 3.28 3.51 3.64 3.82 3.84 4.51 4.20
Conclusions
Three approaches to restoring gaps in data on water temperature in the Kola Section were examined and implemented, based on the use of the following: (1) internal structure of time-series from the Kola Section; (2) multiple linear regressions and data from other standard sections; and (3) modelled data from the Copernicus website
The use of modelled data from the Copernicus website (NEMO ocean model) for restoring data gaps showed the best results and this approach was applied for the final restoration of missing data.
Mean water temperatures were restored for each month from June 2016 to May 2017 in the 0–50, 0–200, 50–200 and 150–200 m layers in the inner, central and outer parts of the Kola Section.
There is an intention to conduct similar exercise for restoring data on salinity.
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