Torsten Seifert, Franz Tauber, Bernd Kayser
Baltic Sea Science Congress, November 2529, 2001, Stockholm, Sweden, Poster 147.
A high resolution spherical grid topography of the Baltic Sea  revised edition
Motivation
The use of numerical models and geographic information systems is nowadays state of the art in oceanography. These research tools require highly resolved digitised bathymetric maps as a basic input. The gridded bathymetric data sets of the Baltic Sea and the Belt Sea made available by SEIFERT & KAYSER (1995), have been applied by many scientists around the Baltic and elsewhere. The great number of data requests showed that there is a common need for such data. Motivated by the widespread application and by the revelation of some local errors (which are due to the sea charts used) we felt the need to update the data sets.
The aim of this data compilation is to provide an improved digital topography of the Baltic Sea. Available data sets of water depths and land heights were mapped onto a regular spherical grid covering the area 9°31°E and 53°30'66°N with a resolution of 2' in geographical longitude and 1' in latitude. For the Belt Sea region 9°15°10'E and 53°30'56°30' a subgrid with a higher resolution of 1' in longitude and 30" in latitude is given. The longitudes x_{i} and the latitudes y_{j} pointing to the centre of the grid cell (i,j) are specified by the following equations:
Belt Sea grid:  xi = 9°E + ( i  ½ ) * Dx1,  Dx1 = 1’,  i = 1 … 370,  (1) 
yj = 53°30’N + ( j  ½ ) * Dy1,  Dy1 = 30",  j = 1 … 360.  
Baltic Sea grid:  xi = 9°E + ( i  ½ ) * Dx2,  Dx2 = 2’,  i = 1 … 660,  (2) 
yj = 53°30’N + ( j  ½ ) * Dy2,  Dy2 = 1',  j = 1 … 750. 
The geographic coverage of the data grids is shown in Fig. 1 and Fig. 2. The resulting data set for the Belt Sea grid will be called iowtopo1, and iowtopo2 for the Baltic Sea grid, resp.
Available Data
The data given by SEIFERT & KAYSER (1995) were sampled as local water depth from available sea charts. According to the resolution of the sea charts the depths values were estimated in steps of 1 m, 5 m, and 10 m within the depth intervals 050 m, 50150 m, and below 150 m the sampling points were located at the edges of the grid cells specified by Eqs. (1) and (2).
A substantial progress was possible after a series of new data sets had become available.
During the MASTII project DYNOCS a 1 nautical mile bathymetry for the whole region of the North Sea and the Baltic Sea was compiled by DHI (Danish Hydraulic Institute) on an UTM32 grid, which included the IOW data and Danish sea charts, WEIERGANG & JOENSSON (1996). Moreover, DHI provided Belt Sea bathymetry data, JENSEN et al. (2000), with a high spatial resolution of 207 m. Both Danish data sets include also digitised soundings.
The German territorial waters are covered by the data compiled by LEIMER (1999). Additional local high resolution data were sampled by HARFF & MEYER (2001).
A highly detailed sea chart of the central Baltic was published by Swedish and Lithuanian institutes in the framework of the GEOBALT project, GELUMBAUSKAITE et al. (1999). The isolines were resampled with a spacing of about 500 m. The accompanying set of local water depths was completed by IOW data referring to the depth at the monitoring stations.
Bathymetry data which rely on recent shipborne measurements were published by REISSMANN (1999). In the framework of the MESODYN project the central parts of the Arkona Basin, the Bornholm Sea and the Stolpe Furrow, as well as the Eastern Gotland Basin were sampled several times on nearly regular grids of 2.5 nautical miles resolution. The measurements were checked by statistical methods resulting in mean water depths supplemented with estimates of the errors in depths and positioning.
Land heights were adapted from the GTOPO30 data set which has a resolution of 0.5 minutes in longitude and latitude.
Table I gives an overview of the main characteristics of all data sets used. For the following it is important to realise the differences between the data:
 Data sources: The data sets rely on different sources. Most of the data were sampled from sea charts of different scales. Some include digitised soundings, only REISSMANN (1999) relies on direct measurements.
 Resolution: There are gridded data sets which differ in spatial density between 207 m and approximately 2.5 nautical miles. Resampling of the isolines of the GEOBALT chart lead to polygon data with an inhomogenous spatial density. The local depths represent irregularly distributed data.
 Reliability: The data have to be taken "as is", since no additional information about the accuracy of the water depths and/or measurement locations is accessible (except REISSMANN 1999).
Table I: List of applied data sets
BSH (Bundesamt für Seeschiffahrt und Hydrografie, Hamburg), DHI (Danish Hydraulic Institute Hoersholm, Danmark), DYNOS (MASTII project MAS2CT940088), IOW (Institute of Baltic Research Warnemünde, Germany), MESODYN (GermanRussian contribution to the BASYS project).
data set  region  grid & resolution  source & reference  remarks 

bsh2excl.dat  German Baltic coast  768 x 319 spherical grid 25" x 12" (» 400 m), 0.1 m 
BSH, LEIMER 1999 
land data removed 
dhi207noland.dat  Belt Sea  1801 x 1401 UTM32 207 m, 0.1 m 
DYNOCS, DHI, sea charts, ablade soundings JENSEN et al. 2000 
land data removed 
dk0excl0.dat  North Sea and Baltic Sea 
1051 x 951 UTM32 1852 m, 0.1m 
DYNOCS, DHI, sea charts, IOW data, EUROCOAST data WEIERGANG, JOENSSON 1996 
land data removed 
geobalt_iso.dat  Central Baltic  isoline data 
GEOBALT sea chart GELUMBAUSKAITE et al. 1999 
sampled with approx. 500m 
geobalt_z.dat  ditto  93 local depths, 1m  ditto  
E020N90ij.dat, W020N90ij.dat 
20W  40 E 30N  90 N 
7200 x 7200 spherical grid approx. 0.5' x 0.5', 1 m 
GTOPO30 www.cr.usgs.gov/landdaac/gtopo30 
only land heights 
iow1excl0.dat  Belt Sea  321 x 301 spherical grid 1' x 0.5' (ca. 1 km), 1 m 
IOW, sea charts SEIFERT,KAYSER 1995 
land data removed 
iow2excl3.dat  Baltic Sea  741 x 641 spherical grid 2' x 1' (ca. 1 km), 1 m 
IOW, sea charts SEIFERT,KAYSER 1995 
land data, Belt Sea and error in Gotland basin removed 
tfstat.dat  Baltic Sea  147 local depths, 1 m  IOW, Monitoring stations  
mesodyn_bathy_xyz.dat  Arkona, Bornholm and Eastern Gotland Basin, Stolpe Furrow 
890 points on 4 nearly regular grids » 2.5 nautical miles, 1 m 
IOW, MESODYN, repeated soundings REISSMANN 1999 
used as reference data sets 
mesodyn_bathy_tri.dat  ditto  17280 points on 4 regular spherical grids 1' x 0.5' (» 1 km), 0.1 m 
ditto  interpolated by linear triangulation to Belt Sea grid 
oderexcl.dat  Oder bight and lagoon  1' x 0.5' (» 1 km), 1 m  IOW, sea charts  land data removed 
trave_wismar_salzhaff.dat  German coastal regions  4116 points, irregular grids  HARFF, MEYER 2001 
The resampling procedure
With respect to the amount of data and their different characteristics the data were resampled to the target grids by evaluating a representative mean value for each grid cell by the following procedure:

All data sets are reformatted to ascii files specifying longitude, latitude and land height/water depth by positive/negative values for each datum line by line. Artificial blank values (for instance a constant land height) and regions containing obvious data errors are filtered out.

A weighting factor w_{set} is specified for each of the input data sets (default is an equal weight of w_{set}=1).

The data are sequentially read and directly allocated to the corresponding cells of the target grid. An overlap of 1% of the cell size is applied in order to allocate data located just on cell edges to all of the neighbouring cells, see Fig. 3.

For each grid cell the weighted mean and the Gaussian sums (Sz^{n}) up to the 4^{th} order are evaluated. Moreover, the minimal and the maximal data values are saved as well as the distance and the value of the datum nearest to the centre of the grid cell. The number of matching data is counted separately for land heights and water depths.

Empty grid cells (which are not occupied by any data) may be filled up by averaging over neighbours containing data. (There must be at least two occupied neighbours, one of it directly adjoining to the target grid cell, see Fig. 4.) Greater holes are closed by repeated averaging.

The results are saved in netCDF files which contain all information (including the grid axes) and may be processed and visualised by many tools like Ferret, Matlab, Grads etc.
The sequential processing allows to process an
arbitrary amount of data (at the moment approx. 1.7 million water
depths and 2.9 million land heights). The data basis may be extended by
adding new input files.
The weighting factors have been applied to compensate for the different
spatial data density and to emphasise selected data sets, see below.
The overlap option assures that the point samples of SEIFERT & KAYSER (1995)
are resampled with a (2by2) averaging. Otherwise occupation numbers
between 0 to 4 may occur because of rounding errors in the data
coordinates, see
Fig. 3.
Since the result is the weighted mean
of all N data allocated to a grid cell (i,j), the standard deviation is calculated as
z_stdev^{(i,j)}  = sqrt{S_{k}^{N}(z_wgt^{(i,j)}  z_{k}^{(i,j)})^{2} / (N1)}  (4) 
= sqrt{(N z_wgt^{(i,j)}  2 z_wgt^{(i,j)} [z]^{(i,j)} + [z^{2}]^{(i,j)}) / (N1)}. 
On the basis of the weighted sum Eq. (3) and the Gaussian sums
[z^{n}] = S_{k}^{N}z_{k}^{n}the
standard deviation and higher moments of the data distribution as the
skewness (n=3) and the excess (n=4) can be calculated after all data
have been processed.
The resampling procedure (without the filling option) was first applied to the individual data sets. Thus an intercomparison on the basis of the target grids was carried out, see Table III below. Because of the quality control the data of REISSMANN (1999) were considered as reference data. In order to get a continous coverage, these data were interpolated onto the fine resolution Belt Sea grid by linear triangulation. Moreover, two firstguess topographies were evaluated: A total (equally weighted) average of all data, and an average where the spatial density of the data sets is approximately equalised. The relative weighting factors were derived from the mean occupation numbers of the data sets. Singular depths and data coarser than the target grids were weighted with unity. Note, that some data sets have been emphasised by an enhancing factor > 1, see Table II.
Table II: Relative data set weights derived from mean grid cell occupation numbers
(entries correspond to: relative weight / enhancing factor / mean number of data in grid cells)
data set  Baltic Sea grid  Belt Sea grid 

bsh2excl.dat  0.0500 / 1 / 20  0.0125 / 1 / 8 
dhi207noland.dat  0.0125 / 1 / 80  0.0500 / 1 / 20 
dk0excl0.dat  1 / 1 / 1   /  /  
geobalt_iso.dat  0.0500 / 1 / 20  0.2000 / 1 / 5 
geobalt_z.dat  1 / 1 / 1  1 / 1 / 1 
iow1excl0.dat  0.1250 / 1 / 8  0.2500 / 1 / 4 
iow2excl2.dat  1 / 4 / 4   /  /  
mesodyn_bathy_tri.dat  25 / 100 / 4  10 / 10 / 1 
oderexcl.dat  0.1250 / 1 / 8  0.2500 / 1 / 4 
trave_wismar_salzhaff.dat  0.0333 / 1 / 30  0.1000 / 1 / 10 
tfstat.dat  1 / 1 / 1  1 / 1 / 1 
On the basis of the target grids the bathymetric data sets were intercompared by evaluating mean differences and the spatial cross correlation, see Table III. The mean differences show the offset between the data sets. The root mean square differences measure the average variation of data between grid cells and the maxima are achieved at locations of maximum bottom gradient. The peak correlation was found within ± 1 grid cell (otherwise the data set would not have been taken into account). These parameters allow only rough estimates since they are related to the intersection between data sets of different spatial coverage. However, a general tendency is clearly indicated: Within Belt Sea a good agreement between all data sets is found, but from the Bornholm Basin to the northern Baltic Sea increasing deviations occur. These are obviously coupled to the increasing roughness of the bottom relief. The left panel of Fig. 5 shows the gradient of the sea bottom derived by central differencing from the weighted average water depth. At Landsort Deep (approx. 18°E and 59°N) gradients of more then 50 m/km occur which explain maximum differences of ± 100 m within one cell of the Baltic Sea grid, where D(x,y) » 1.8 km, Eq. (2). The right panel of Fig. 5 shows that half the range of variation of data in each grid cell (z_maxz_min)/2 is approximately equal to the local bottom gradient. It is not possible to estimate to what a degree the data variation is influenced by subgrid scale gradients since the original data sets covering the full Baltic Sea are of nearly the same resolution as the target grid, see Table I.
Table III: Typical range of differences between the bathymetric data sets
region  mean differences  root mean square diff.  maximum differences  peak correlation  reference data  target grid 

Arkona Basin  ± 0.5 m  ± 1.5 m  ± 10 m  >95%  MESODYN  both grids 
Bornholm Basin Stolpe Furrow 
± 2.5 m  ± 3.5 m  ± 15 m  >95%  MESODYN  Baltic Sea 
Gotland Basin GEOBALT 
± 2 m  ± 7.5 m  ± 40 m  >95%  MESODYN  Baltic Sea 
Belt Sea  ± 0.5 m  ± 1.5 m  ± 20 m  >98%  weighted average  Belt Sea 
Baltic Sea  ± 1.5 m  ± 5 m  ± 100 m  >98%  weighted average  Baltic Sea 
Belt Sea total average 
± 0 m  ± 0.7 m  ± 13 m  >99.9%  weighted average  Belt Sea 
Baltic Sea total average 
± 0.1 m  ± 1.9 m  ± 70 m  >99.9%  weighted average  Baltic Sea 
MESODYN triangulated. 
± 0 m  ± 0.4 m  ± 2 m  >99.8%  MESODYN  Belt Sea 
MESODYN triangulated 
0.1 m  ± 0.7 m  ± 5 m  >99.4%  MESODYN  Baltic Sea 
The lower rows of Table III show that the deviations introduced by the linear triangulation of the MESODYN data and the mapping onto different grid scales are fairly small compared with the uncertainties in the data sets. Checking some regions with strong bottom gradients in detail revealed that there are considerable local differences between the data sets despite of the high overall correlation. The worst case was found at Landsort Deep, see Table IV:
Table IV: Location of the maximum water depth at Landsort Deep from different data sets resampled to the Baltic Sea grid Eq. (1).
The sounding was taken during IOW Monitoring cruise 11/01/01 (r/v Gauss 374a). z_wgt and z_min refer to the weighted average of data and the maximum data water depth.
data set  parameter  depth (m)  Baltic grid cell  location error  

i  j  di  dj  
dk0excl0.dat  z_wgt = z_min   396  283  312  +5  +7 
iow2excl3.dat  z_wgt z_min 
 420  460 
279, 281 277, 278 
309, 311 304, 305 
+1, +3 1, 0 
+4, +6 1, 0 
geobalt_iso.dat  z_wgt z_min 
 433.3  450 
279 278, 279 
310 309, 310 
+1 0, +1 
+5 +4, +5 
geobalt_z.dat  z_wgt = z_min   463  278  309  0  +4 
tfstat.dat  z_wgt = z_min   459  277,278  304,305  1, 0  1, 0 
sounding   455.5  278  305 
Table IV shows that local subgrid scale structures may be lost by averaging all data allocated to a grid cell. But singular depths or heights are saved in the auxiliary parameters z_min and z_max. Nevertheless, the original data show substantial differences in location of Landsort Deep (one grid step corresponds to approximately 1 nautical mile).
The visualisation of the two firstguess topographies revealed that the equalised spatial density average yields a smoother result. Therefore the final compilation was run as follows:
 The water depths and the land heights were resampled separately.

The bathymetric data sets were weighted as shown in Table II.
 The MESODYN data set was emphasised by an enhancing factor of 10 for the Belt Sea grid and a factor of 100 for the Baltic Sea grid in order to suppress distortions by other data.
 The Baltic Sea data (dk0excl0.dat and iow2excl3.dat) were used with the same relative weight of unity.
 The fine resolution Belt Sea bathymetry was inserted into the Baltic grid by using it as an additional data set with a relative weight factor of 100.
 A composite topography was established by overlaying the average bathymetry and land heights with a prescribed landmask. If there was no data average available for grid cells redefined by the landmask, these cells were filled with a minimum value of ± 0.1 m and indicated by an error flag (+1 for land, 1 for water).
The separate resampling and the extra landmasks were introduced because no satisfying landwater distribution could be obtained by processing all data simultaneously. The relative weights between land and bathymetry data were varied from 0.01 to 100, but in any case the results were not satisfying. The coastlines appear distorted even by errors of ± 1 to ± 2 grid cells as shown in the upper panel of Fig. 6. The landmasks were derived from the high resolution shoreline data of WESSEL & SMITH (1996), and FEISTEL (1999). Neglecting closed polygons which are smaller than half a grid step in extent the shorelines were overlaid to the target grids. On this basis the corrections were made to restore or eliminate small coastal structures like islands, sounds or estuaries, see lower panel of Fig. 6.
Evidently the composite topography using the prescribed landmasks is nearer to reality. But on the other hand, the corrections introduce a certain degree of arbitrariness since ± 1 grid cells are free choice at the limit of resolution. However, the compiled data sets contain the necessary information to make own decisions: Besides the composite topography and the landmask, the weighted averages and the occupation numbers of water depths and land heights are given for each grid cell. The statistical parameters (unweighted mean value, minimum and maximum data value, standard deviation, nearest datum and distance, error flag) correspond to the composite.
Skewness and excess have not been included into the published output files. A reasonable estimate was possible only for the water depth in the Belt Sea grid covered by dense bathymetric data sets leading to N^{(i,j)}>10. Both parameters show a very noisy distribution on small scales , see Fig. 7. Within central Arkona Basin, which is dominated by the MESODYN data triangulated to the high resolution Belt Sea grid, Eq. (1), the skewness varies on somewhat larger scales with slightly enhanced amplitudes. However, in the average, skewness and excess have a smaller range of variation for the weighted average bathymetry confirming our choice of resampling the data. (The skewness varies within ± 2 , and the excess within ± 3 in 99 % of grid cells.)
The resulting data sets are finally characterised by the hypsographic
curves, i. e. the surface area and the enclosed water volume in
dependency from the water depth, and the possible errors in volume
caused by the data variation within grid cells.
The left panel of Fig. 8a
shows the hypsography of the data set iowtopo1 resampled to the high
resolution Belt Sea grid Eq. (1). In the right panel the relative error
in the average water volume is estimated from the data variance (red)
and from the the minimum and maximum values (blue) in each grid cell.
Down to 60 m water depth the probable errors are ± 10 %, or ± 20 % at maximum. At 75 m the error might be ± 50 % but this refers to a remaining volume of 1 km^{3} only. Below the uncertainity is increasing rapidly since the reference volume approaches zero.
Fig. 8b
displays the Belt Sea hypsography for the data resampled to the Baltic
Sea grid. It turns out, that area and volume of the water body are in
close agreement, but the errors double in accordance with the
coarsening in grid resolution.
The volume curve of the data set iowtopo2 derived for the Baltic Sea grid shows three regions in the semilogarithmic plot, see Fig. 8c.
The Volume decays nearly linear between 0100 m and 150450 m, and
asymptotically below 500 m. The depth dependency of the area looks
similar.
Errors are limited to ± 20 %; down to 450 m water depth.
Things are rather different if subregions are considered. Fig. 8d displays smooth hypsographic curves for the southern Baltic Proper 1622.5°E, 5457°N. The errors exeed ± 50 % below 160 m where only 10 km^{3}
of water are enclosed.
In the northern Baltic Proper 1622.5°E, 5760.5°N, both area and
volume show a sudden change in slope at 240 m. Greater depths occur
mainly in two regions, the Landsort Deep and the Aland trench (19°E,
60.5°N) where the original data show considerable shifts in location.
The data for these regions also introduce the asymmetry in relative
errors tending to overestimate the amount of bottom water. It is not
satisfying that 300 km^{3} below 150 m are probably in error by ± 50 % and more, see Fig. 8e.
The hypsography of the Botten Sea (above 60.5°N) and the Gulf of
Finland (east off 22.5°E) show similar uncertainities. For the
subbasins, filled with the quality controlled MESODYN data, reliable
hypsographic estimates are evaluated, see for instance Fig. 8f. The uncertainty is mainly caused by subgrid scale bottom gradients there.
The data sets iowtopo1 and iowtopo2 are available from the web site: www.iowarnemuende.de/iowtopo.
Summary
By inclusion of new data the digitised Baltic bathymetry could be substantially improved:
 The Belt Sea and the Central Baltic are now covered by several dense data sets. This allows an statistical estimate of probable errors.
 The MESODYN data introduced a quality checked bathymetry of 3 important basins and the Stolpe Furrow.
 The water depths are averaged without using a coarsening vertical grid.
However, the result is not completely satisfying:
 There are considerable local deviations between the data sets as was shown for the example of the Landsort Deep.
 Estimates for the amount of water eclosed within the deeper basins are probably in error by ± 50% or more.
Every contribution and/or cooperation leading to a further improvement of the data basis and the derived digitised Baltic Bathymetry is welcome.
Acknowledgements
The assistance of all persons and institutions who made their data available is greatly acknowledged. The resampling procedure uses some code from the MOM3 model, PACANOWSKI & GRIFFIES (1999). The postprocessing of netCDF data was done with Ferret.
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