Untitled Document

3. Data Processing

| 3.1. Hydrochemical Information
| 3.1.1. Data Sources
| 3.1.2. Spatial and Temporal Distribution of Observations
| 3.2. Control of Hydrochemical Measurements
| 3.2.1. Data Input
| 3.2.2. Formal Data Control in the Hydrochemical Database.
| 3.2.2.1. Control of Station Passports.
| 3.2.2.2. Control of Maximum Station Observation Depths.
| 3.2.3. Regional control
| 3.2.4. Control of Variability Limits.
| 3.2.5. Expert Control.
| 3.3. Statistical Characteristics.
| 3.4. Objective Analysis
| 3.5. References to Section 3.

3.1. Hydrochemical Information

3.1.1. Data Sources

Observations carried out by expeditions on drift ice, icebreakers in ice and research vessels on open water in the water area of the Arctic Ocean (Fig. 3.1) formed a data set of initial hydrochemical measurements. Period of observations was chosen since 1948 till 2000.

Fig. 3.1. Water areas for which data of hydrochemical measurements were collected for the years 1948-2000.

Data of the AARI and of the National Oceanographic Data Center- World Data Center - A(NODC) were used for creation of the complete historical data set of Russian and western observations. The NODC data set was collected from different sources including the Russian ones (See Appendix 2).

Significant part of the AARI hydrochemical information was stored on paper. Therefore, the data typing was organized first of all.

The collected data were united in a data set of initial measurements (See Section 4.1.). The data set included 21.264 stations with 163.127 observation depths. Structure of hydrochemical information was non-uniform. Observation data were presented in different formats, different measurement units of hydrochemical characteristics were used, indices of expeditions and vessels were often changed, there was duplication of data.

The data set of initial measurements was subjected to analysis for the data duplication. Presence of duplicated data is a serious problem of oceanographic databases, collected from different sources, because the present-day system of information collection and exchange allows repeated data input in data sets.

Check and exclusion of duplicated stations from the database was realized in two ways: using automatic check of data coincidence, during the expert control of hydrochemical information.

The automatic control provides data scan for coincidence of coordinates (with accuracy of 0.5' of latitude and longitude), date and time of station performance, and information at the first standard depths. If coordinates and time of stations coincide, or, in the absence of time, information at the first standard depth coincides, then station with more useful information (time of observation, station depth, greater number of parameters at greater number of observation depths, presence of temperature and salinity measurements at the first observation depth, etc.) is selected for further processing and analysis. This method rather quickly allows to get rid of duplicating oceanographic stations (BarKode, 1999), however, there is a danger of a loss of some useful information.

Additional check for duplicates was made by the expert method. Data samplings were made for that purpose, these data were obtained by different expeditions at different time in specific regions of the Arctic Ocean. In presence of duplicated data, they were compared using the expert method. The most reliable and complete data sets were left in the database, and the questionable and incomplete duplicated data sets were eliminated.

The data set of initial measurements has reduced for 18.52% after preliminary analysis and duplicated data elimination. The obtained data set was used for description of specific features of spatial and temporal distribution of hydrochemical observations.

Metadata are given in Appendix 2.

3.1.2. Spatial and Temporal Distribution of Observations

Information on amount of stations for the years 1948-1993 in the joint database is given in Section 3. Location of oceanographic stations, where measurements of hydrochemical characteristics were carried out, is shown in Fig. 3.2-3.8. Fig. 3.9 and 3.10 demonstrte distribution of stations with element determination for different years.

Scale of temporal averaging for the Arctic Basin was chosen as follows. Seasonal variations of oceanographic characteristics in the Arctic Basin manifest themselves in the upper 200 m layer. Winter season lasts for 9 months, beginning in September and finishing in the end of May. Ice thickness growth and salinity increase in the upper layer are observed in the central part of the ocean till June. Therefore, May can be considered as the last month of the winter period.

In the southern parts of Arctic seas duration of the winter season is somewhat shorter. Transition to spring processes happens in river mouths and separate fiords in the second half of May.

a | b

Fig. 3.2. Location of stations with oxygen observations in the Arctic Basin and Arctic seas for the years 1948-2000: a) winter (November- May) - 3017 stations; b) summer (July-September) - 8748 stations.

a | b

Fig. 3.3. Location of stations with silicate observations in the Arctic Basin and Arctic seas for the years 1948-2000: a) winter (November- May) - 4430 stations; b) summer (July-September) - 6966 stations.

a | b

Fig. 3.4. Location of stations with phosphate observations in the Arctic Basin and Arctic seas for the years 1948-2000: a) winter (November- May) - 1626 stations; b) summer (July-September) - 3284 stations.

a | b

Fig. 3.5. Location of stations with nitrite observations in the Arctic Basin and Arctic seas for the years 1948-2000: a) winter (November- May) - 1423 stations; b) summer (July-September) - 2553 stations.

a | b

Fig. 3.6. Location of stations with nitrate observations in the Arctic Basin and Arctic seas for the years 1948-2000: a) winter (November- May) - 256 stations; b) summer (July-September) - 1461 stations.

a | b

Fig. 3.7. Location of stations with pHB observations in the Arctic Basin and Arctic seas for the years 1948-2000: a) winter (November- May) - 2247 stations; b) summer (July-September) - 6848 stations.

a | b

Fig. 3.8. Location of stations with alkalinity observations in the Arctic Basin and Arctic seas for the years 1948-2000: a) winter (November- May) - 1420 stations; b) summer (July-September) - 1567 stations.

Fig. 3.9. Number of stations in the working base of hydrochemical determinations in the Arctic Ocean for different years (1948-2000) of concentration: a) dissolved oxygen, b) silicate, c) phosphate, d) nitrite

Fig. 3.10. Number of stations in the working base of hydrochemical determinations in the Arctic Ocean for different years (1948-2000) of concentration: a) nitrate, b) pHB, c) alkalinity

3.2. Control of Hydrochemical Measurements

3.2.1. Data Input

Data from the primary paper sources were placed in computer and added the files already containing station passport, meteorological and ice information, water temperature and salinity at observation depths.

The following permissible ranges of values variations were accepted by the first computer-aided control:

a) station passport

- station number should be positive,
- coordinates should change within the limits from 0 to 90° and from 0 to 59' for latitude, from 0 to 360° and from 0 to 59' for longitude; symbols S or N are given to latitude, and symbols E and W are given to longitude (longitude greater, than 180°, was later converted to the western one),
- use of a field of the "data" type realizes full control of date appropriateness up to the control of a leap-year in case typing "29 February", time: hours - from 0 to 23, minutes - from 0 to 59;
- sea depth should exceed zero;
- air temperature should vary from -55 to +50° C;
- wind speed should vary from 0 to 40 m/sec, wind direction - from 0 to 360°;
- atmospheric pressure should vary from 800 to 1200 mb;
- ice concentration should be within the limits from 0 to 10 conventional units, direction to the ice edge - from 0 to 360°, and distance to it should not be negative.

b) oceanographic data:

- · observation depth should be less or equal sea depth in the station passport,
- · water temperature - from -2.20 to + 30° C,
- · salinity - from 0 to 36 psu,
- · oxygen - from 0 to 20 ml/l,
- · pHB - from 7 to 9 conventional units
- · alkalinity - from 0 to 9.999 mg-eq/l,
- · phosphate - from 0 to 99.9 µg/l,
- · silicate - from 0 to 7000 µg/l,
- · nitrite - from 0 to 30 µg/l,
- · nitrate - from 0 to 700 µg/l.

Collation of the typed data with the primary paper sources was carried out after their input. One specialist typed the data, and the other one collated the input data with the primary paper sources.

After load, all the oceanographic information was subjected to a more strict computer-aided control. In the process of control system elaboration, notions were used outlined in different publications (Belkin, 1991; Boyer & Levitus, 1994; BarKode, 1999) and some other additional provisions. Control was carried out using 14 criteria: station coordinates, date and time of observations, correspondence of depths, correspondence of input data to general distribution regularities of temperature, salinity and hydrochemical parameters in the World Ocean and in the Arctic Ocean, in particular.

Questionable records were not eliminated from the database, but marked with special symbols. A system of quality flags was used for this procedure.

3.2.2. Formal Data Control in the Hydrochemical Database.

3.2.2.1. Control of Station Passports.

Station coordinates. According to this control, the stations with latitude exceeding 90° and longitude beyond the limits of the range -180° 180° , or with coordinate minutes equal or greater 60 are marked with flag 23, and they are not used for further work. Such stations were not revealed in the result of this control.

3.2.2.2. Control of Maximum Station Observation Depths.

Control of observation depths. According to this control, the stations with observation depths exceeding sea depth taken from reference array of the Arctic Ocean depths are marked with flag 25, and they are not used for further work. The nearest to this station point from the depth array was chosen, but not far than 14.1 km. If the observation depth significantly exceeds sea depth in this point (for 120% for depth range 0-100 m, for 40% for depths greater than 100 m), location of the station is questionable. Formally, 1085 stations should have been marked according to this control. Location of the stations that did not pass the control was studied before station marking with flag 25 (Fig. 3.11).This location analysis showed that these stations were located in deepwater regions mainly over the continental slope or in places with strongly broken relief; in shallow regions, they were located mainly near shore. Taking into account, that depth interval in places with strongly broken relief at the distance of 14.1 km is significant, and grid spacing of the depth array in shallow waters (coastal water areas, estuaries, bays) did not guarantee necessary representativity, the stations in these regions were not marked with flag 25 and were used in further calculations. Group of the stations located over relatively flat region in the northern part of the Chukchi Sea was performed in the "Sever" expeditions. Depths at these stations in these expeditions could have been determined with insufficient accuracy. Taking into account results of this analysis and, first and foremost, significance of each station with hydrochemical observations in the Arctic Ocean, poorly covered by observations, these stations were not marked by flag 25 and were used for further calculations.

3.2.3. Regional control

Regional control included check of correctness of station coordinates. It was done at different stages of joint data set preparation. Because the main part of the data was placed in computer as separate files, each of these files contained data of a specific cruise of research vessel, airborne expedition or coastal observations at observatories, regional control was carried out before file input in the joint database. The Ocean Data View software (Schlitzer, 2001) gives an opportunity to scan operatively data of separate expeditions to make sure that vessel route coincides with schemes of its movement given in expedition reports. False station coordinates were corrected, and after this correction data input in the database was performed.

Some problem arose by data check for the data obtained from other sources and not from the AARI archives. Cruise or expedition reports were inaccessible. Check technique in these cases consisted of comparison of research vessel route with time of station performance. Succession of station performance in time was checked in condition that vessel speed did not exceed 15 knots. Oceanographic stations falling out of reasonable schedule of vessel movement at transects were marked as questionable.

Fig. 3.11. Location of stations that did not pass formally control of maximum station observation depths (flag 25).

+ stations in deepwater regions, observation depths at these stations exceeded depths from the reference depth array for 40%

stations in shallow regions, observation depths at these stations exceeded depths from the reference depth array for 120%.

3.2.4. Control of Variability Limits.

Primary computer-aided control of the station passports and variability limits of the parameters was carried out both by data input and by loading of data obtained from different sources. Permissible ranges of different attributes of the station passports and values of the hydrochemical elements were described above in Section 3.2.1. Values beyond the limits of these permissible ranges were not eliminated by loading of data from files with hydrochemical information, but marked with the according flags of quality and reliability as questionable or rejected. The hydrochemical parameters vary over a wide range in the Arctic Ocean, therefore, criteria of control and data estimate for ranges of their variability in deepwater regions differs from that in shallow regions. Use of automatic methods of control recommended in other papers (Belkin, 1991; BarKode, 1999) does not give good results. That is why, only those data were rejected that were beyond the reasonable limits of variability of the hydrochemical parameters typical for the entire World Ocean. Expert data control was carried out afterwards.

3.2.5. Expert Control.

Expert control is initial and final phase of the procedure of quality estimate of hydrochemical measurements. Its importance in assessment of accuracy and representativity of observations in different parts of water area is specially great by insufficient number of observations and /or their non-uniform distribution in time and space. It is typical for this Atlas. The expert control was the most labor-consuming and minute part of the data set check. In the process of control, the base was divided into several parts according to regional indications: the Arctic Basin, the Kara Sea, the Laptev Sea and the region uniting the East Siberian Sea, the Chukchi Sea and the Beaufort Sea. These samples include all the available data for the region.

Four different experts did the control. Each of them controlled the data for his region. Cruise scan of the data was carried out using the Ocean Data View software (Schlitzer, 2001). In this process, station coordinates, dates and time of their conduction, correspondence of depths given in the station passports to bottom relief were checked. Distribution of the hydrochemical parameters at each station was analyzed, and it was compared with mean distributions of the same parameters in same region of seas or the Arctic Basin in the same period of the year. Correspondence of the loaded hydrochemical information with general regularities of distribution of the hydrochemical parameters in the Arctic Ocean and in the Arctic seas, in particular (Rusanov et al., 1979).

Results beyond the limits of tolerance were rejected, i.e. they were marked as bad data. Abnormal values of the hydrochemical parameters within the reasonable limits of hydrochemical element variability, but not corresponding to our notion of hydrochemical structure of a specific region, were marked as the questionable data. Number of rejected and questionable data revealed in the result of the expert control is given in Table 3.1.

Some problems, that arose by the data expert control, should be mentioned. First, it is complicated to check the data in such poorly studied regions as, for example, the East Siberian Sea or the north-eastern part of the Kara Sea. Second, the Arctic seas are characterized by complex vertical structure and inlaid distribution of the hydrochemical parameters, both on the surface, at the standard depths and, especially, at the near-bottom depths. Reference literature on structure of water column and variability of the hydrochemical parameters in shallow regions of the Arctic seas (shelf zone) is limited and contradictory. All this makes impossible to use unit criteria of data quality estimates not only for all the Arctic seas, but for separate regions of each of these seas.

Table 3.1.

Number of data marked as questionable and rejected at the first stage in the joint data set.

Parameter | Total | Questionable | Quest., % | Rejected | Rejected,% | Quest..+Rej., %
Oxygen | 111127 | 1116 | 1,00 | 737 | 0,66 | 1,67
Phosphate | 43132 | 976 | 2,26 | 1593 | 3,69 | 5,96
Silicate | 102750 | 1305 | 1,27 | 2334 | 2,27 | 3,54
Nitrite | 26465 | 184 | 0,70 | 1507 | 5,69 | 6,39
Nitrate | 16201 | 239 | 1,48 | 1240 | 7,65 | 9,13
pH | 74730 | 562 | 0,75 | 321 | 0,43 | 1,18
Alkalinity | 19442 | 124 | 0,64 | 203 | 1,04 | 1,68

The expert control was carried out using C-code specially elaborated for this project by AARI specialists, accounting for knowledge of hydrological and hydrochemical conditions of the Arctic Ocean.

Program of the expert control provided performance of the following procedures:

1. Control of correspondence of extreme values of the hydrochemical elements determined at all the stations with actual hydrological and hydrochemical conditions.
2. Construction of display plots of vertical distribution (profiles) of the elements and determination of those values that form extremes that cannot be caused by real processes.
3. Drawing of experimental maps of gridded distribution of the hydrochemical elements of different scale using statistical characteristics.
4. Check of extreme mean values of the elements on the gridded maps constructed with the help of objective analysis of observations for their correspondence to temporal series in the adjacent grid cells.
5. Interpolation of separate values of the elements in grid nodes not covered by observations.
6. Output of final data for map drawing of hydrochemical element distribution.

In the process of the expert control, the experts decide, what "quality flag" should be given to distributions. This information is placed and stored in the archive of distributions.

Therefore, the expert control was carried out after the statistical control and after gridding of the results of hydrochemical distributions by the objective analysis. Results of the control were put on maps, and plots of vertical distribution were constructed only after repeated performance of the expert control.

3.3. Statistical Characteristics.

Linear interpolation of values of the hydrochemical elements to the standard depths was carried out before calculation of statistical characteristics and after the formal and expert control: 0, 5, 10, 15, 25, 50, 75, 100, 150, 200, 250, 300, 400, 500, 750, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500 meters (Fig. 3.12).

Number of oceanographic stations with the hydrochemical observations was analyzed. This analysis revealed that the standard depths were the best covered by observations. If observations at some station were conducted at other depths, linear interpolation of the hydrochemical elements to the standard depths was carried out. This interpolation was conducted only in the case, when number of the standard depths between the observations did not exceed one. If the interpolation was prohibited according to this criterion, and difference between the observation depth and the nearest standard depth did not exceed 5% of the layer thickness between the neighboring standard depths and the observation, then values of the hydrochemical elements were transferred ("dragged") to the nearest standard depth. For example, if the upper observation depth was 210 m, and the next one was 305 m, then the interpolation was not conducted for the "mixed" standard depths 250 and 300 m, because their number (two) exceeded the chosen criterion (one). However, value from 305 m was "dragged" (transferred) to the standard depth 300 m in this case. This procedure was not carried out for the observation depth 210 m. Values of the standard depths and upper and lower limits for the procedure of transfer are given in Table 3.2.

Statistical characteristics of the hydrochemical elements were calculated after the interpolation and transfer of values to the standard depths for all the standard depths from 0 up to 400 m separately for two seasons: winter (November-May) and summer (July-September). Winter and summer values of the hydrochemical elements were used together for calculations of statistical characteristics at the standard depths from 400 to 4500 m.

Final calculation of statistical characteristics of the hydrochemical elements after all the types of control was carried out at the standard depths in the winter season in squares 200x200 km, in the summer season - in squares 200x200 km for the Arctic Basin and 100x100 km for the Arctic seas (Fig. 3.13). Grid of the squares coincides with the location of the squares for which statistical characteristics of temperature and salinity were calculated in the Hydrographic Atlas of the Arctic Ocean (1997, 1998).

Coordinates of the squares are given as the Cartesian coordinates of the Lambert equigraphic azimuth projection calculated using the formulas:

here is supplement of latitude, is longitude, R=6371.116 radius of the sphere having the same surface as the Earth ellipsoid, X, Y are grid coordinates. X-axis is oriented along meridian 0-180° , Y-axis is oriented along meridian 270-90° . Center of the coordinate system is located in the Pole. All the maps given in the Atlas are constructed in this coordinate system. X and Y axes are subscribed in tens of kilometers.

Fig. 3.12. Distribution of number of oceanographic stations with the hydrochemical observations for the years 1948-2000 (a - in the layer 0-110 m, b- in the layer 110-310 m, c - in the layer 310-4500 m) in the working base after the formal and expert control.

Fig.3.13. Grid used for calculation of statistical characteristics of the hydrochemical elements: a- grid 200x200 km for the winter season (November-May); b - 200x200 km (in the Arctic Basin) and 100x100 km (in the Arctic seas) for the summer season (July-September).

Table. 3.2.

Standard depths and upper and lower limits for the procedure of transfer of observational depth to the standard depth

Standard depth (m) | Upper limit for the procedure of transfer of observational depth to the standard depth (m) | Lower limit for the procedure of transfer of observational depth to the standard depth (m)
5 | 4.75 | 5.25
10 | 9.75 | 10.75
25 | 24.25 | 26.25
50 | 48.75 | 51.25
75 | 73.75 | 76.25
100 | 98.75 | 102.5
150 | 147.5 | 152.5
200 | 197.5 | 202.5
250 | 247.5 | 252.5
300 | 297.5 | 305
400 | 395 | 405
500 | 495 | 512.5
750 | 737.5 | 762.5
1000 | 987.5 | 1025
1500 | 1475 | 1525
2000 | 1975 | 2025
2500 | 2475 | 2525
3000 | 2975 | 3025
3500 | 3475 | 3525
4000 | 3975 | 4025
4500 | 4475 | 4525

Calculation of the following statistical characteristics was conducted using the formulas:

here X is the parameter mean value, Xi is the parameter observed value, N is the number of observations in a square, is the parameter dispersion, S is the root-mean deviation, As is the asymmetry (skewness), Ex is the excess µ2,µ3,µ4, are the central moments of the second, third and fourth order, respectively.

Of course, calculation of the first three statistical characteristics has a sense only in the case, when number of measurements exceeds three (then corresponding estimates can be carried out using the Student criterion). However, these corresponding statistical characteristics can be reliably obtained in some points of coastal observations (located in estuaries and estuary seashores of Ob, Yenisei, Lena, Khatanga).

The parameter mean value in a square was calculated taking into account preliminary averaging for each year. Extreme values were chosen, and the other statistical characteristics were calculated using the whole series of observations in this square.

Besides, the equation of mean square regression plane was calculated using the least square method, scatter of observation points near this surface is the minimum one, if compared with other surfaces. Equation of this surface is as follows:

Z = Ax + By + C,

here Z is the parameter value (in corresponding units of measurement for this hydrochemical element), x and y are coordinates (in tens of kilometers).

Examples of fields of the statistical characteristics (mean values and mean-root deviations) at 5 m depth are shown in Fig. 3.14-3.17 for two elements: dissolved oxygen with the best coverage by observations and nitrite with the worst coverage.

The Cartesian coordinates of the square angles (in tens of kilometers) and values of the statistical characteristics of the hydrochemical elements are given in the ASCII- files ("Statistics\Txt" subdirectory) on CD-ROM. Mask of names of the ASCII- files looks as follows:

SSN_ELE_1948-2000_HHHH.TXT,

here SSN is the season, (WIN - winter, SUM - summer); ELE is the hydrochemical element (OXY - dissolved oxygen, SIL - silicate, PO4 - phosphate, NO2 - nitrite, NO3 - nitrate, PHB - pHB, ALK - alkalinity); 1948-2000 - period of observations; HHHH is the standard depth (m); TXT is the file name extension.

The characteristics demonstrated in Table 3.3. are given in columns of the files (in order from left to right).

Fig. 3.14. Mean concentration of dissolved oxygen (ml/l) and its mean-root deviation in the Arctic Basin and the Arctic seas (according to data in the squares 200x200 km) in winter (November-May) for the years 1948-2000 at 5 m depth.

Fig. 3.15. Mean concentration of dissolved oxygen (ml/l) and its mean-root deviation in the Arctic Basin (squares 200x200 km) and the Arctic seas (squares 100x100 km) in summer (July-September) for the years 1948-2000 at 5 m depth.

Fig. 3.16. Mean nitrite concentration ( µmol/l) and its mean-root deviation in the Arctic Basin and the Arctic seas (according to data in the squares 200x200 km) in winter (November-May) for the years 1948-2000 at 5 m depth.

Fig. 3.16. Mean nitrite concentration (µ mol/l) and its mean-root deviation in the Arctic Basin and the Arctic seas (according to data in the squares 200x200 km) in winter (November-May) for the years 1948-2000 at 5 m depth.

Table 3.3.

Information given in the ASCII-files ("Statistics" Directory) with calculated statistical characteristics of the hydrochemical elements (in order from left to right).

Name of the column | Characteristics | Column format in notation SDF ("System Data Format")
Initial and final position in line | Length
XMIN | Minimum value of X-coordinate (tens of km) for this square | 1-10 | 10
XMAX | Maximum value of X-coordinate (tens of km) for this square | 11-19 | 9
YMIN | Minimum value of Y-coordinate (tens of km) for this square | 20-28 | 9
YMAX | Maximum value of Y-coordinate (tens of km) for this square | 29-37 | 9
NUM_VALUES | Number of actual, interpolated and "dragged" values of observations for this hydrochemical element in the corresponding* season in this square at this depth | 38-48 | 11
NUM_YEARS | Number of years with observations for this hydrochemical element in the corresponding* season in this square at this depth | 49-58 | 10
MIN_VALUE | Minimum value for this hydrochemical element in the corresponding* season in this square at this depth | 59-68 | 10
MEAN_VALUE | Mean value for this hydrochemical element in the corresponding* season in this square at this depth (taking into account preliminary averaging for each year) | 69-79 | 11
MAX_VALUE | Maximum value for this hydrochemical element in the corresponding* season in this square at this depth | 80-89 | 10
STAND_DEV | Mean-root (standard) deviation | 90-99 | 10
VARIANCE | Dispersion (variance) | 100-108 | 9
SKEWNESS | Coefficient of skewness (asymmetry) ** | 109-117 | 9
EXCESS | Coefficient of excess ** | 118-125 | 8
COEF_A | Coefficient A of the equation of mean square regression plane ** | 126-139 | 14
COEF_B | Coefficient B of the equation of mean square regression plane ** | 140-153 | 14
COEF_C | Coefficient C of the equation of mean square regression plane ** | 154-167 | 14

> > NOTE: * STATISTICAL CHARACTERISTICS WERE CALCULATED AT THE

> > STANDARD DEPTHS FROM 0 TO 400 M FOR EACH SEASON AND FOR THE

> > STANDARD DEPTHS FROM 500 TO 4500 M BOTH WINTER AND

> > SUMMER VALUES OF THE HYDROCHEMICAL ELEMENTS WERE USED TOGETHER;

> > ** VALUE .NULL. IN THE DATA COLUMN OF THE ASCII-FILES MEANS

> > ABSENCE OF THE CALCULATED STATISTICAL CHARACTERISTICS FOR THIS SQUARE

> > > 3.4. Objective Analysis

The spectral method of objective analysis, developed by Pokrovsky (1984), was used as the basic method for construction of decadal climatic fields of temperature and salinity by realizing of the US-Russian Oceanographic Atlas of the Arctic Ocean (1997, 1998). The spectral method of objective analysis has shown the best results in terms of reconstruction of temperature and salinity characteristics if compared with the other methods used in the Oceanographic Atlas of the Arctic Ocean. Moreover, only this method has been capable to reconstruct oceanographic fields using observations in the summer period in the absence of data on significant part of the central Arctic Basin. This method has also given the opportunity to obtain fields of reconstruction errors. The mentioned advantages of this method were determined by the fact that it was based on simultaneous spatial and temporal analysis of observational data by decomposition of these fields with the help of a combination of empirical spatial and temporal components. This method combines analytical approach and statistical interpretation of estimation results.

The essence of the method is as follows: measured values of hydrochemical characteristics z(t, x) are considered as a random function of temporal (t) and spatial (x) coordinates. The observed values z(t, x) are presented as a sum of a true value of a hydrochemical parameter and an observation error e(t,x). We postulate presence of spatial correlation for characteristics of , absence of a systematic error and correlation between the observation errors ei and hydrochemical characteristics , spatial and temporal independence of the observation error and presence of standard deviation . This totality of postulates is reduced to the following model of statistical structure of the analyzed characteristics.

The problem of estimation is formulated for anomalies of the hydrochemical characteristics , i.e. deviations z of the corresponding mean values . The mean values were obtained by temporal averaging and spatial smoothing. Taking into account, we shall further consider only the above-mentioned deviations, and they will be marked as z.

In order to take into account spatial and temporal connections of observational data, Pokrovsky (1984) proposed to use a biorthogonal decomposition of a hydrochemical parameter z as follows:

here is the spatial EOF, is the estimated coefficient that is usually called the n-th principal component. xi can be an irregular grid, and values of measured hydrochemical parameters are given in its nodes.

There are two versions of the spectral analysis (SA). The first variant of the method supposes interpolation of the spatial EOF in nodes of a regular grid xi , where values of characteristics under consideration will be estimated. The second variant is based on EOF approximation with the help of a linear combination:

of appropriate analytical functions (polynomials, splines, trigonometric functions, etc.) Pl(xi). In this case, we obtain the following modification of the biorthogonal decomposition (2):

There are no differences of principle between these mentioned approaches based on the formulas (2) and (4). In both cases, our problem is in estimation of a totality of coefficients of the spectral decomposition Therefore, we shall further consider only the version based on notion (2) without loss of generality. We shall rewrite formula (2) in the following matrix form:

Let us introduce designations for the following covariance matrices:

The system of linear equations (5) in respect to unknown coefficients can be solved on the basis of a priori statistical information (1) using methods of statistical estimation. A formula for the estimation of the matrix of unknown coefficients C was obtained in () on the basis of ():

here and are the back and transposed matrices in respect to A, and • is the sign of matrix multiplication. The matrix of covariance errors of the decomposition coefficients Kc is a diagonal matrix composed of the eigenvalues of the covariance matrix Kz :

The matrix F is formed by the EOF values, and the matrix Z is composed of a totality of measurement data in the network of observations xi.

In order to obtain an estimate of a hydrochemical characteristics in the nodes of a regular grid xi, it is necessary to interpolate the EOF in appropriate nodes of the grid and to obtain a new matrix F of the EOF. Using the obtained matrix F and the estimates of coefficients C, formula (6) and matrix correlation

we shall obtain the estimate of our parameters in the nodes of the regular grid. Covariance matrices of estimate errors can be obtained simultaneously with hydrochemical fields using the following formulas:

here Ke is the covariance matrix of observation error extended on the regular grid.

The described procedure of hydrochemical field restoration is a combination of the well-known method of singular decompositions (SVD - singular value decomposition in the original) and statistical regularization (Pokrovsky 1984).

Practical realization of the SA method includes several main stages. The first stage is an optimal choice of a grid cell (grid spacing and distribution). Aim of this choice is to cover general spatial regions (for the time period under consideration), where observations were carried out. This stage is the basis for EOF calculation of a maximum dimensionality.

The next stage is a reconstruction of fields in the cells without observations. Dual character of the coefficients in formula (2) (in respect to spatial and temporal dependencies) is the basis for estimate of unknown geophysical parameters in the "empty cells" without observational data. The described approach was realized not only in spatial regions with low spatial data density, but also by restoration of the whole temporal series of observational data for each cell with observations for at least in one year. In order to realize this idea more effectively, we have proposed to perform a preliminary division into districts of the region under consideration. For that purpose, the analyzed region was divided into information-uniform zones (IUZ) on the basis of the previously elaborated method (Pokrovsky & Piatigorsky, 1995). Time interval of the analysis was divided into uniform sub-intervals. Values of hydrochemical parameters were statistically interconnected in each of these sub-intervals. For example, several first EOF's did not change their signs with the aim that the time correlation function also did not change its sign within these IUZ's. In the same time, sign could be changed at the boundaries of the IUZ's and corresponding uniform intervals at time axis.

The principal temporal modes (the first terms of decomposition (2)) were used for calculation of mean values in the "empty" grid cells. Mean values of a hydrochemical parameter can be estimated in each grid cell with at least one observation for the time period under consideration, having these temporal modes.

The next stage of the calculation procedure is interpolation of the fields for one or several years in the given spatial grid. It is necessary now to interpolate the EOF in the given spatial grid and then to calculate the coefficients in decomposition (2). The described procedure should be applied to each year for the time period under consideration.

The next stage is calculation of mean climatic fields for several years. Such mean values were calculated in each grid cell on the basis of the described reconstruction method or by interpolation. In particular, it is possible to calculate decomposition coefficients using the EOF even in the case, when there is only one observation in each IUZ, while having spatial structure of the uniform zones.

3.5. References to Section 3.

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- Joint US-Russian Atlas of the Arctic Ocean, Oceanography Atlas for the Winter Period. Ed. by F. Tanis, L. Timokhov. Environmental Working Group, University of Colorado, Boulder, CD-ROM, 1997.
- Joint US-Russian Atlas of the Arctic Ocean, Oceanography Atlas for the Summer Period. Ed. by F. Tanis, L. Timokhov. Environmental Working Group, University of Colorado, Boulder, CD-ROM, 1998.
- Smith T., Reynolds R., Livezey R., Stokes D.: Reconstruction of historical sea surface temperatures using empirical orthogonal functions. - J. of Climate, 1996, v. 9, pp. 1403-1420.