Background Information
The goal of this project is to produce a global hydrographic climatology that
includes a good description of the Arctic Ocean and its environs. We
started with the Levitus climatologies, which provide excellent global coverage
over much of the world ocean. Coverage within the Arctic Ocean itself has been
poor, although it continues to improve. The soon-to-be published Levitus 1998
World Ocean Atlas includes data from some peripheral Arctic seas, but still lacks
coverage of the deep Arctic basins. Recently, historical Russian data from the
Arctic seas have been made
available by the Environmental Working Group (EWG) in the form of an analyzed,
gridded arctic climatology known as the Arctic Ocean Atlas. Our task here has been
to merge these two fields in a satisfactory way.
Description of Data Sets
The
Levitus
Climatology
provides a raw field of data (Temperature,Salinity,etc)
from which specific seasons and years can be extracted.
Data which
contain any of
several documented errors are flagged, so these can be discarded as we
have done when
using the raw data. An analyzed field (interpolated from the raw data
using a
scheme based on Barnes(1973))
for all years and individual seasons is also provided. This method is similar to
our optimal interpolation scheme
in that a correlation length scale is specified, a weighting
function is chosen and a first guess field is used.
Major differences from our scheme are: (i) Levitus uses a
more complicated weighting function;(ii) his background,
or "first-guess field" is a
zonal average of the existing data by individual ocean basins, and (iii) following
the
interpolation, his results are further smoothed by two succesive filters.
The analyzed fields are given on a
1 degree x 1 degree grid. The Levitus
seasons are: Winter (JFM), Spring (AMJ), Summer (JAS) and Fall (OND).
The
EWG
Climatologies (Arctic Ocean Atlas)
provide analyzed fields for each of two
seasons: Winter (DJFMAM), and Summer (JJASON), and statistical fields for
selected months. There are four options
for analysis method for the winter period: Vorontsov, GDEM, OI and Spectral
Objective
Analysis. There are only two methods provided for the summer period: GDEM and Spectral Objective Analysis.
The last, Spectral Analysis is presented as the default field with
the most support in the Climatology; looking through
the other options, it
also appears to yield the most physical results. It was the method we used
for both our
interpolation products. The analyzed
fields are
given on a 50km x 50km grid.
| *There are two directories in the EWG atlas. One has 50Ękm gridded decadal mean temperature and salinity down to 65N using four different interpolation schemes. The other has statistical parameters on a variable grid with 200Ękm resolution within the Arctic Basin and 50Ękm resolution in the Barents and GIN Seas. The statistical variables are not interpolated; they include fields of means, maxima, minima, standard deviations, and higher order moments. |
Surface Temperature
Surface Salinity
References
Environmental Working Group (EWG), Joint U.S.-Russian Atlas of
the
Arctic Ocean for the Winter Period [CD-ROM], Natl. Snow and ice Data Cent., Boulder, Colo.,
1997.
Environmental Working Group (EWG), Joint U.S.-Russian Atlas of the Arctic Ocean for the Summer Period [CD-ROM], Natl. Snow and ice Data Cent., Boulder, Colo., 1998.
Levitus, S. and T. Boyer, NOAA Atlas NESDIS: World Ocean Atlas 1994, US
Dept. of Commerce, NOAA/NESDIS, Washington, DC, 1994.
Contact Information and Acknowledgements
This project was funded by the Office of Naval Research High
Latitude Program,
and by the NASA Sponsored program:
Polar Exchange at the Sea's Surface: Dr. Drew Rothrock, PI
The data set may be referred to as:
M. Steele and R. Morley, The Polar science center Hydrographic Climatology,
available at:
http://psc.apl.washington.edu/Climatology.html, 1999.
Acknowledgements
We would like to thank Axel Schweiger and Mark Ortmeyer for their unfailing
technical and computer support.
Ron Lindsay, Harry Stern, Ignatius Rigor and Roger Colony provided much needed
and appreciated insight into
the workings of optimal interpolation, both
theoretical and practical.
We also sincerely appreciate the
valuable
feedback provided by users of this data set
For more information about these merged data sets,
or their creation and
distribution,
please contact:
General Description of Optimal
Interpolation
Optimal Interpolation works with 4 basic parameters (plus one more we
added).
For each grid-point a weighted
sum of nearby data points is taken, based
on their distance from the point of interest
(in the form of an
exponential function),
and the error associated with each of them. Before the data values
are added,
a background field (bg(j)) is subtracted from each data point. So the sum represents
a deviation or variation from a background mean field; it is a weighted sum of
the difference between each data
value and the background field at the corresponding
geographical location. The final interpolated
value at the
point of interest is this number with the background field at the
output gridpoint location (bg(i))
added back in.
The first parameter involved is the correlation length scale which acts basically as the smoothing length of the field. It is the factor by which the exponential function is scaled, and determines how each point will be weighted (this is referred to as c in the code).
The second parameter is the number of nearest neighbor points to consider in computing the new point. Theoretically, the sum is carried out over the entire field. However, since very distant points will have very small weights (due the correlation length scale parameter, c) they contribute very little. Effectively, then, the weighted sum does not need to be performed for every existing data point. Instead, we specify the maximum number of points for which the computation will be run (this is referred to as n in the code).
The third parameter is an error value or error field associated with the existing data field. This error value (normalized by a variance parameter) is a measure of how much to trust the associated data point, and thus acts as another weighting factor (this is referred to as err in the code).
The fourth parameter is the background field. The interpolated value at the point is added on to this background, and the value of the field is subtracted from each input data point. Naturally, the values chosen for the background field are most important in areas with scant data where the output values will most closely resemble the default first guess or background field. However, the interpolation routine is in general fairly sensitive to the choice of background (this is referred to as bg in the code).
The fifth parameter, which we introduced, can be thought of as a radius of influence. There are cases where, of the n nearest neighbor points being used, some may be quite distant relative to others and relative to c, the correlation length. In those cases it may be desirable to eliminate them from the computation since they may possibly cause errors due to their very small weighting factor, and the fact that they represent data far distant and thus possible far different. And so, aside from c, if any of the n points fall outside the radius of influence (md), they will not be used. Thus, in some cases, in fact fewer than n points will be computed in the weighted sum.
For a more technical, matrix representation of OI, click Here (downloadable pdf file).
This gridded hydrographic data set is recommended for use by Arctic and global modelers for the purposes of initialization, climate restoring, and validation. The OI algorithm is performed using as inputs two data sets that are already gridded, analyzed fields: (i) the Levitus (1994) global data set (spanning the years 1900-1992) and (ii) the EWG (1997,1998) Arctic data sets (spanning the years 1950-1989). The result is a global analyzed gridded hydrography that closely reproduces Levitus south of the Arctic, and closely reproduces EWG within the Arctic.
| Polar science center Hydrographic Climatology Product 1 | Polar science center Hydrographic Climatology Product 2 | ||
|---|---|---|---|
| Geographical Extent | Global | Same | |
| Input Fields | EWG Analyzed;Levitus Analyzed (Winter & Summer) | Levitus:monthly; Synthetic EWG monthly fields | |
| Produced Fields | Summer,Winter: 1900-1992 mean | Monthly: 1900-1992 mean | |
| OI Parameters | c=1000km; md=1000km; n=20 points;
bg=zonal average of combined data input fields to which is first applied a 15-pt median smoother, and then a 15-pt mean smoother, both applied along each meridian from 90N to 90S; lev_err=.0001*variance of the combined field, for Levitus points below 65 N; .01*var, above 65 N; ewg_err= .00005*var of the field everywhere | Same |
To avoid the inclusion of spurious data, we discarded points in the Levitus Analyzed Field north of 65N that corresponded to a 1 degree x 1 degree pixel in which fewer than two raw profiles were taken. South of 65N no points in the analyzed Levitus fields were discarded, in order to provide a better match with the original.
In order to ensure good agreement with the existing Levitus Analyzed Field, the error value for Levitus points below 65 N latitude was made very small. However, to ensure that EWG values were trusted in their domain, a much larger value for Levitus errors was used above that same latitude. EWG error was the same value everywhere.
Since EWG field depths did not always correspond exactly to Levitus field depths, the EWG fields were linearly interpolated (using a canned IDL routine) onto the Levitus depths.
A value of n=20 points was used. The variance was taken as a single number which is the variance of the two fields taken together (EWG,Levitus). The background is taken as a zonal average of the combined field which is smoothed with a 15-pt median filter, and then a 15-pt mean filter along each meridian from 90N to 90S. This removes any longitudinal banding effects from the field. So far, this interpolation is only done 2-dimensionally for each depth; there is no vertical smoothing, and no physical parameters to eliminate interpolation artifacts like static instabilities (such as observed in the EWG and Levitus data sets), although this is a focus of current research at NODC.
After all of the above manipulations, there were several points in the Canadian Archipelago which contained values below the freezing point. This is a result of the very poor data coverage in this region in both EWG and Levitus data sets. To eliminate this problem, we followed the procedure used by Levitus, i.e., setting below-freezing values back to freezing. The formula that we use is given in the back of A. Gill's book: Tf = -.0575*S + 0.001710523*S^1.5 - 0.0002154996*S^2 - 0.000753*z, where Tf is in degrees celsius, S is in ppt, and z is depth in meters (positive downwards, e.g., 100 m depth is positive). Reference: Millero, F.J. (1978) Freezing point of seawater, In "Eighth report of the joint panel on oceanographic tables and standards, UNESCO Tech. Pap. Mar. Sci. No. 28, Annex 6. UNESCO, Paris.
The effects with varying the radius of influence, md, were similar. A too-large radius of influence can lead to errors, and far distant data points having an undesirable influence in the algorithm. Whereas, if md is taken to be too small, the bullseye effects of an undersmoothed field are likely to recur.
A graphical representation of these
results for Temperature:
A graphical representation of these results for Salinity:
In essence, the Error Field should reflect the existing variability in the data field. We decided to assign a single value, based on a percentage of the variance of the combined field (a value by which the error is normalized in any case). The important thing, it seems, is to maintain the correct proportions, between the Error Fields and the variance, and between the Levitus associated Error and the EWG associated Error. Since we expect the error of the gridded EWG fields to be smaller than that of the gridded Levitus fields in the Arctic domain, we trust EWG more when there is a choice between the two. The actual numerical values are much less significant.
Ultimately, the background field was chosen as a zonal average (ignoring regional/basin distinctions) to provide a more accurate representation. To avoid banding effects and inconsistencies across latitudinal boundaries, this field was smoothed first with a 15-point median filter to remove anomalous points, and then with a 15 point mean filter for smoothing along each meridian from 90N to 90S. The filters were applied on a 1 degree x 1 degree pixel point. This result was more satisfactory, we felt, than applying a smoothing filter after the fact to the produced OI field.
Final Product: c= 1000km,md=1000km.
Representative plots of Summer Temperature (0,100) north down to 20 N:
Representative plots of Winter Salinity (0,100,500,1000) north down to 20 N:
Representative plots of Summer Salinity (0,100) north down to 20 N:
Explanation of Format
For each season there are two files, one for temperature and one for salinity.
These files are structured
and named to be exactly analogous with the format of the Levitus Analyzed CD data. Each of
these files
contains all 33 level depths starting with the surface. The data points begin at -89.5 S and
are arranged on a matrix which runs
first over longitude, then over latitude, ending with 89.5 N. There
are 33 of these matrices, corresponding to each of the ocean
depths. There are 10 entries per line, and
there are 8 significant figures, 4 after the decimal point (10f8.4). Since the EWG CD
contains no
readings deeper than 4400 m, the last three depths in the files (4500,5000,5500) are optimally interpolated
Levitus
Analyzed data alone, included simply for consistency in file format.
(1) The Levitus (1994) analyzed monthly fields. These are treated similarly to the Product 1 fields, i.e., 1 x 1 lat/lon pixels north of 65 degN are discarded if they contain fewer than 2 actual profiles.
(2) Fitted EWG monthly fields. These fields are provided on the CD's as seasonal products only. To create a monthly field, we fit each point in the grid to an analytical function of matched cosine curves, one for summer and another for winter. We assume that the winter (DJFMAM) & summer (JJASON) EWG fields represent conditions roughly at the mid-points of their seasons, i.e., winter = conditions on April 1 and summer = conditions on August 15. (We shifted the winter data a bit later than the mid-point because much of the data on the winter CD are from the last three months, ie MAM. The summer data are also slightly biased, so we shifted the value to mid-August.) The result is a relatively rapid temperature increase (salinity decrease) from April 1 to August 15, followed by a slower temperature decrease (salinity increase) from the second half of August through the end of March.
The summer function applies for 4.5 months and is given by:
Y1 = -(A/2)*cos( pi*(t - tw)/delts) + D, for tw <= t < ts
The winter function applies for 7.5 months and is given by:
Y2 = (A/2)*cos( pi*(t - t')/deltw) + D,
where t' = ts for ts <= t (Aug.15 - Dec.31)
and t' = ts - 365.25 for 0 <= t < tw (Jan.1 - Mar.31)
where "t" is time and "Y" represents T or S. Values are computed at the monthly mid-points, e.g., Jan 16. The 2 curves match in value and (zero) derivative on April 1 and August 15.
tw = April 1 = Day 90.25
ts = August 15 = Day 226.25
delts = April 1 through August 14 = 136 days
deltw = August 15 through March 31 = 229.25 days
A = Ys - Yw
D = (Ys + Yw)/2
where:
Ys = T or S on Aug.15
Yw = T or S on Apr.1
Representative Plots of Fitted Monthly EWG
Representative
plots
of monthly fitted EWG surface Temperature and Salinity:
Representative Plots of Results
Representative plots of monthly surface Temperature north down to 20 N:
Representative plots of monthly surface Salinity north down to 20 N:
Explanation of Format
For each month there are two files, one for temperature and one for salinity, for a total of 24 files.
These files are structured
and named to be exactly analogous with the format of the Levitus Analyzed
CD data. Each of
these files contains all 19 monthly level depths starting with the surface.
The data points begin at -89.5 S and
are arranged on a matrix which runs first over longitude, then
over latitude, ending with 89.5 N. There
are 33 of these matrices, corresponding to each of the ocean
depths. There are 10 entries per line, and
there are 8 significant figures, 4 after the decimal point
(10f8.4).
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