Model Studies of Surface
Waves and Sediment
Resuspension in the Baltic Sea
Anette Jönsson
Linköping Studies in Arts and Science No. 332
Linköping University, Department of Water and Environmental Studies
Linköping 2005
Linköping Studies in Arts and Science • No. 332
At the Faculty of Arts and Science at Linköping University, research and
doctoral studies are carried out within broad problem areas. Research is
organised in interdisciplinary research environments and doctoral studies
mainly in graduate schools. Jointly, they publish the series Linköping
Studies in Arts and Science. This thesis comes form the Department of
Water and Environmental Studies at the Tema Institute.
Distributed by:
Department of Water and Environmental Studies
Linköping University
SE-581 83 Linköping
Sweden
Anette Jönsson
Model Studies of Surface Waves and Sediment Resuspension in the Baltic
Sea
Cover: Waves in Kattegat outside Tylösand. Photo by Lars Meuller.
ISBN 91-85299-94-4
ISSN 0282-9800
Ó Anette Jönsson
Department of Water and Environmental Studies 2005
Printed by UniTryck, Linköping 2005
ii
This thesis is based on the following five papers, referred to by their Roman
numerals (I–V).
I.
A. Jönsson, B. Broman & L. Rahm (2002) Variations in the Baltic
Sea wave fields. Ocean Engineering, 30(1): 107-126.
II.
A. Jönsson, Å. Danielsson & L. Rahm (2005) Bottom type
distribution based on wave friction velocity in the Baltic Sea.
Continental Shelf Research, 25(3): 419-435.
III.
Å. Danielsson, A. Jönsson & L. Rahm (2005) Resuspension patterns
in the Baltic Proper, the Baltic Sea. Manuscript.
IV.
A. Jönsson (2005) Suspended sand due to surface waves during a
winter storm in the Baltic Sea. Submitted.
V.
L. Rahm, A. Jönsson & F. Wulff (2000) Nitrogen fixation in the
Baltic proper: An empirical study. Journal of Marine Systems 25,
239–248.
Papers I, II and V are reprinted with kind permission from the publishers.
iii
iv
Contents
1
INTRODUCTION .......................................................................................... 1
1.1
1.2
2
SURFACE SEDIMENT ................................................................................. 7
2.1
2.2
2.3
3
BED SHEAR-STRESS ................................................................................ 21
RESUSPENSION AND SEDIMENT MOVEMENTS ......................................... 23
SUSPENDED SEDIMENT PROFILE ............................................................. 24
BALTIC SEA WAVES AND SEDIMENT RESUSPENSION ................. 27
5.1
5.2
5.3
5.4
5.5
5.6
6
WAVE MOTIONS ..................................................................................... 11
WAVE FIELDS......................................................................................... 16
THE WAVE MODEL HYPAS.................................................................... 17
WAVE–SEABED INTERACTIONS .......................................................... 21
4.1
4.2
4.3
5
GRAIN SIZES ............................................................................................ 7
BOTTOM TYPES ........................................................................................ 9
FLUFFY LAYERS ..................................................................................... 10
SURFACE GRAVITY WAVES.................................................................. 11
3.1
3.2
3.3
4
OBJECTIVES AND PAPER DESCRIPTIONS.................................................... 2
DESCRIPTIONS OF THE STUDY AREA ......................................................... 4
WIND CLIMATE ...................................................................................... 27
MODELLED WAVES ................................................................................ 29
WAVE FRICTION VELOCITIES.................................................................. 32
RESUSPENSION....................................................................................... 34
IMPLICATIONS ON THE BIOGEOCHEMISTRY ............................................ 35
CONCLUSIONS........................................................................................ 37
FUTURE OUTLOOKS................................................................................ 39
6.1
6.2
6.3
CLIMATE CHANGES ................................................................................ 39
BENTHIC BOUNDARY LAYER MODELS .................................................... 40
SEDIMENT-WATER EXCHANGES ............................................................. 41
7
ACKNOWLEDGEMENT ........................................................................... 43
8
REFERENCES ............................................................................................. 45
v
vi
1 Introduction
The waves in the Baltic Sea can become quite high, steep and difficult, even
if this is a relatively small and shallow sea. The highest significant wave
measured in the Baltic Sea is 7.7 m and the corresponding single wave
height 14 m. These waves were measured 22 December 2004 between the
islands Åland and Hiiumaa in the northern Baltic Proper by a Finnish wave
buoy. On the oceans, waves of this magnitude are frequently occurring, but
also there these heights are considered complicated for ships and if possible
other routes are chosen. The shipping in the Baltic Sea is intense, and is
assumed to increase even more within the next couple of years (Buch and
Dahlin, 2000). Some severe accidents have also occurred in the area where
the waves most likely were an important factor in the event chain. Wave
models are good tools for deciding the wave condition in an area, and
necessary for making wave forecasts and warnings. Small area studies of the
wave climate in the Baltic Sea have been made by e.g. Svensson (1981);
Rugbjerg and Mühlestein (1997); Paplińska (1999); Blomgren et al. (2001)
and Soomere (2001).
Surface waves also influences things below the sea surface. In shallow
regions, for depths less than about half the wavelength, the wave motion will
reach the bottom and give rise to a frictional force on the sediment surface. If
this is large enough, the bottom stress can mobilise the sediment particles
and bring them into suspension. On the continental shelves, waves are
known to resuspend sediments down to considerable depths. Symmetric
sediment ripples have for example been found at 200 m depth outside
Oregon USA (Seibold and Berger, 1982) and movements of quartz grains
have been modelled at depths larger than that (Harris and Coleman, 1998).
When fine particles are resuspended much less energy is needed to keep
them in suspension than for the actual resuspension process (Friedrich et al.,
2000). Consequently, resuspension processes in combination with advective
currents are important for the long-term transport of particulate matter from
1
shallow erosion bottoms to deep accumulation ones. Brydsten (1993)
classified the transport bottoms in the Bothnian Sea and Bothnian Bay from
wave induced resuspension and recently Kuhrts et al. (2004) modelled the
sediment transport due to waves and currents in the south Baltic Proper.
Eutrophication is a large problem in the Baltic Sea, and different remedy
actions have been implemented to decrease the external nitrogen and
phosphorus load from land. However, there are internal sources that are
more difficult to control. Nutrients (and pollutants) are accumulated in the
sediment for long times, but during a resuspension event, the stored material
may be reintroduced into the water mass. This means that nutrients, which
otherwise might have been a limiting factor for the pelagic production may
become available again. There are also indications on the importance of
resuspension as an enhancing factor for degradation of deposited organic
matter (Ståhlberg et al., 2005). In shallow coastal zones like the Baltic Sea,
the sediments therefore play an important role in the annual nutrient
recycling.
Another internal nutrient source is the fixation of gaseous nitrogen by
cyanobacteria. This is a natural phenomenon in the Baltic Sea, but the
frequency, duration and biomass of the blooms have increased due to the
eutrophication (Bianchi et al., 2000). When nitrogen becomes the limiting
nutrient in the pelagic, nitrogen fixating bacteria get a competitive advantage
compared to other algae, which may result in harmful blooms.
1.1
Objectives and paper descriptions
The aims of this thesis are to describe the surface gravity waves and the
sediment dynamics coupled to them in the Baltic Sea. Discussions of
consequences on the biogeochemistry and other internal nutrient sources are
included. Sediment movements not induced by surface waves are excluded
from the studies, and only particulate matters are modelled.
2
Figure 1. The study area with its bathymetry.
The surface waves in the Baltic Sea, Kattegat and Skagerrak have been
modelled for a period of two years (Paper I and this Thesis). The spatial and
temporal variation in the field is shown, and the used model is validated at
measuring sites. These results are used further in three different applications
to study surface wave effects on the seabed. For the first application
(Paper II) the bottom stress was calculated from the wave field without
including any sediment characteristics in the calculation. The spatial
distribution of the bottom stress was compared to a sediment map, which
classify different bottom types according to their dynamics, to test their
correspondence. How the resuspension frequencies and the duration of an
3
event varies in time and space were studied further in Paper III. Here the
grain sizes of the sediments were taken into account in the calculations of
bottom stress. The final wave study analyses how much sediment that is
resuspended into the water mass during a storm passage, i.e. the effect in the
water mass of a large event (Paper IV). That study focused on sandy
sediments for which the vertical suspended sediment concentrations were
calculated. In Paper V, the nitrogen fixation in the Baltic Proper was
calculated from nitrogen and phosphorus changes in the surface layer. Here
we assumed that nitrogen fixation was the only internal source of nitrogen.
The resulting blooms of nitrogen fixating bacteria will in the end deposit and
contribute to the organic matter in the sediments.
1.2
Descriptions of the study area
Our studies are based on modelled waves in the Baltic Sea, Kattegat and
Skagerrak, see Fig. 1. With the exception of Skagerrak, these seas are rather
shallow, which means that water motions set up by the surface wave reach
the bottoms over large areas. Mean and maximum depths in the different
basins can be found in Table 1.
Table 1
Mean and maximum depths from the region (Sjöberg, 1992).
Mean depth [m]
Max depth [m]
Bothnian Bay
43
148
Bothnian Sea
68
293*
Baltic Proper
62
459
Gulf of Finland
37
115
Gulf of Riga
22
56
Kattegat
23
124
Skagerrak
174
711
*
301 m in the Åland Sea.
The Baltic Sea is a semi-enclosed sea and the only connection to the
North Sea is through Skagerrak. The actual sills are in the Öresund and the
two Danish Straights, but the whole of Kattegat can be regarded as a
transition region due to its shallowness. The sills control the water exchange
4
and the density stratification in the Baltic Sea (Stigebrandt, 1987). Another
result of the narrow and shallow entrance is that the tides are more or less
non-existent in the Baltic Sea and an otherwise important energy source to
the benthic boundary layer is excluded (Stigebrandt, 2001).
Since it is an enclosed area the waves in the Baltic Sea are mostly fetch
limited. It is the distance to the shore in the up-wind direction that
determines how high the waves can be, not the duration of the wind as in the
open sea. During wintertime, ice is common in the northern parts, as well as
in the Gulf of Finland and Gulf of Riga, see Fig. 2.
a.
b.
Figure 2. The maximum ice extent during (a) severe and (b) mild winters (SMHI and
Marentutkimuslaitos/Havsforskningsinstitutet, 1982).
The Baltic Proper is the largest and southernmost basin of the Baltic Sea
and three of our studies focus on this area. It has a permanent halocline at
about 60-80 m depth that separates a well mixed surface layer from a
stratified bottom layer. It is mainly through infrequent saltwater intrusions
that the bottom water is refreshed, and large areas below the halocline have
very low oxygen concentrations. In the surface layer, a seasonal thermocline
is formed each spring at about 20 m depth. In the autumn when the days are
getting shorter, the heat inflow is reduced and the autumn storms begin, the
thermocline is destroyed.
5
The Baltic Proper is assumed nitrogen limited with respect to the primary
production (Granéli et al., 1990) and after the spring bloom almost all
dissolved nitrogen is consumed, while there still is some phosphorus left.
This is a condition that is assumed to favour cyanobacteria since these can
utilise gaseous nitrogen found in the water mass. Blooms of nitrogen fixating
bacteria are frequently occurring during the warm half of the year (Sellner,
1997). At the autumn turnover when water is mixed up from below, the
amount of nutrients in the surface layer increases again, while the primary
production ceases due to less light and lower temperatures.
6
2 Surface sediment
The main source of material in the sediments is of mineralogenic origin
(clay, fine sand etc). To this is added organic matter mainly from the pelagic
production. Of the primary production, only a few percent is buried
“permanently” in the sediment, the rest is degraded in some way and/or
recycled (e.g., Danielsson et al., 1998).
The spatial distribution of surface sediments can be described in different
ways. For our calculations in the Baltic Sea, two different descriptions have
been used, which are described below.
2.1
Grain sizes
Sediments can be classified according to their median grain size. However,
the defining size intervals between different sediment types vary slightly
between classifications. The values stated below are from the Wentworth
grain size scale (e.g., Soulsby, 1997). Common for all grain size
classifications are that the smallest size fractions are called clay (<0.004
mm), and with increasing diameter we find silt (0.004-0.063 mm), sand
(0.063-2 mm) and gravel (>2 mm). Clay and silt are collectively called mud.
These fractions are often divided further into sub-fractions such as coarse,
medium and fine sand.
For our studies in Paper III and IV, we used a map of grain sizes by
Repecka and Cato (1998). It covers the Baltic Proper and the Gulf of Riga,
and has been digitised into a resolution of 6x6 km, see Fig. 3 and Table 2.
7
Figure 3. The digitised grain size map from Repecka and Cato (1998).
For sediments with a grain diameter less than 0.06 mm, cohesive factors
between grains can be important. These forces ‘glue’ sediment grains
together making them more resistant to erosion. Hence, cohesive sediments
behave different from non-cohesive ones and other empirical relations are
valid when calculating, e.g., sediment suspension. Therefore, only sediment
grains larger than 0.06 mm is used for the calculations in Paper IV.
8
Table 2
The first columns show the numbers from the legend on the map in Fig. 3, the next columns
show the sediment types and grain size interval as specified in the map by Repecka and Cato
(1998).
No Sediment type
size
[mm]
16 Gyttja clay & clay gyttja (Litorina and postlitorina Sea)
5 Clay of the Baltic Ice Lake, the Yoldia Sea and
the Ancylus Lake
19 Peltic mud
3 Aleurite peltic mud
2 Fine aleuritic mud
1 Coarse silt
18 Coarse aleurite
14 Fine sand
15 Fine sand
7 Glacial deposits (till)
11 Medium sand
8 Mixed sediments
12 Sand
13 Coarse and medium sand
10 Coarse sand
4 Gravel
6 Pebble
9 Sedimentary bedrocks
17 Crystalline bedrock
2.2
<0.01
<0.01
0.05-0.01
0.06-0.02
0.10-0.05
0.20-0.06
0.25-0.10
0.50-0.25
1.0-0.1
2.0-0.2
1.0-0.5
10-1
100-10
-
Bottom types
Another way to describe the sediments is by dividing them into
accumulation, transport and erosion bottoms as suggested by Håkanson and
Jansson (1983). On erosion bottoms there is no accumulation of fine material
(<0.006 mm), while these can be deposited continuously on accumulation
bottoms. Transport bottoms represent an intermediate state between erosion
and accumulation bottoms, which allows for deposition during calm periods
and resuspension during others. In practise, these bottom types are decided
from the measured water content profile in sediment cores. Erosion bottoms
have the lowest water content and accumulation bottoms the highest.
9
65
63
61
Finland
Sweden
59
Estonia
57
Lithuania
Erosion
Transport
Accumulation
55
13
15
17
19
21
23
25
27
29
Figure 4. The digitised bottom type map from Carman and Cederwall (2001).
A map that shows the distribution of accumulation, transport and erosion
bottoms by Carman and Cederwall (2001) was used in Paper II for
comparison with the distribution of modelled bottom stresses. It covers the
whole Baltic Sea and has been digitised into a resolution of 10´x10´, see
Fig. 4.
2.3
Fluffy layers
On top of the sediment, a fluffy layer can be found. This consists of newly
deposited organic rich material such as plankton, bacteria grazing on
decaying organisms, and other organic and inorganic debris that settles to the
sea floor within an hour (Leipe et al., 2000). It has high water content and
‘floats’ above the bottom in a layer that is easily resuspended. Above sand
this layer is easily seen, but above mud there is a more gradual change in the
physical and chemical properties (Emeis et al., 2002).
10
3 Surface gravity waves
Waves at sea are generated by the wind blowing over the sea surface. Small
disturbances in the wind create small ripples on the surface, which then grow
as the wind puts more energy into them. When the waves move away from a
storm the shape of the waves changes from shorter, steeper waves to longer,
smoother waves. These long swell waves can travel far but eventually they
reach shallower water at some coast, where they again transform into
shorter, steeper waves under the influence of bottom friction. In the end, the
remaining wave energy is destroyed by wave breaking in very shallow
waters or at the coastline.
To see the connection between the surface waves and the seabed, some
elements of wave theory is recalled below. A brief description of the used
wave model follows.
3.1
Wave motions
Surface gravity waves are waves that exist at the interface between air and
water, i.e., ‘normal’ waves that we more or less always see on a sea surface.
Their wave frequency is small compared to the Coriolis frequency, and
thereby the waves move unaffected by earth rotation. If we assume that
viscous effects can be neglected outside boundary layers, the flow is
irrotational, and a velocity potential f exist, such that
uº
¶f
¶x
vº
¶f
¶y
wº
¶f
,
¶z
(1)
where u, v and w are the velocities in the x, y and z-directions, z being
positive upwards ( z = 0 at the seabed). Substituting these expressions into
the continuity equation
11
¶u ¶ v ¶ w
+
+
=0
¶x ¶y ¶z
(2)
shows that the velocity potential has to satisfy the Laplace equation
¶ 2f ¶ 2 f ¶ 2f
+
+
=0.
¶x 2 ¶y 2 ¶z 2
(3)
For surface gravity waves this equation can be solved with the boundary
conditions
¶f
=0
at z = 0
(4)
¶z
¶f ¶h
=
at z = D
(5)
¶z ¶t
¶f
= -g h
at z = D
(6)
¶t
where D is the water depth, h the surface displacement around the
undisturbed surface at z = D , g is the acceleration due to gravity, and t is
time. These conditions state that there is no vertical velocity through the sea
bottom, that the vertical velocity at the surface follows the vertical
movement of the water surface, and that the pressure at the surface is equal
to the ambient pressure if surface tension is neglected. To solve this
problem, a surface displacement described by
h (x, t ) = a cos(k x - w t ) ,
(7)
can be assumed. This is the simplest possible form of a wave, where we
assume that the wave propagates only in the x-direction and that the
amplitude a of the wave is small compared to the water depth and the
wavelength. The wave number k and the angular wave frequency w are
given by
2p
2p
and w =
k=
,
(8)
l
T
where T is the period of the wave and the wavelength l is defined
implicitly through
12
Figure 5. Illustration of the hyperbolic functions.
l=
T2 g
æ 2p ö
tanh ç
D÷ .
2p
è l ø
(9)
A more thorough description of the problem and the derivation of it can be
found, e.g., in Kundu (1990), and an illustration of the hyperbolic functions
is found in Fig. 5. The boundary value problem Eqs. 3-7 has the solution
f=
a w cosh (k z )
sin (k x - w t ) ,
k sinh (k D )
(10)
which implies for the two velocity components,
u = aw
cosh (k z )
cos(k x - w t )
sinh (k D )
(11)
w = aw
sinh (k z )
sin (k x - w t ) .
sinh (k D )
(12)
and
13
Figure 6. Equations 11 and 12 illustrated for two different depths and two periods. Left
figures show u and w for T=5 s and right figures for T=10 s, the upper four figures show u
and w for D=5 m and the lower four figures for D=50 m. Wave amplitude are in all cases
a=0.5 m.
These equations and the illustration in Fig. 6 reveal some important
features of surface waves. A water ‘particle’ beneath a surface wave moves
14
in circular or elliptical orbits for which the velocity decreases with depth.
The vertical motion is assumed to be zero at the bottom, but the horizontal
motion depends on depth, wave period and amplitude. If the water is deep
(i.e., D l >> 1 ), the particle motion is circular and the horizontal velocity
tends to zero at the bottom. If the water depth is shallow or intermediate
there is a horizontal motion left at the bottom, which affects the sediment.
The maximum orbital velocity at the bottom becomes
U0 =
pH
T sinh (k D )
(13)
where H = 2 a is the wave height. The maximum amplitude of the
horizontal motion at the bottom is then given by
Ab =
U0
.
w
(14)
So far, the boundary condition regarding the surface pressure (Eq. 6) has
not been used. That in combination with the earlier found solution (Eq. 10)
gives the dispersion relation
w = g k tanh (k D )
(15)
or in terms of the phase speed
c=
w
=
k
g
tanh (k D ) .
k
(16)
The phase speed is dependent on depth and wave number. For deep water
Eq. 16 reduces to
c»
g
k
(17)
that is, in deep water the phase speed is independent of water depth and
longer waves travel faster than shorter waves. Due to this, a first notice of a
distant storm can be long swell waves approaching a shore. For shallow
water (D l << 1) Eq. 16 becomes
c» gD
(18)
15
where the phase speed is dependent only on water depth.
However, when the waves are dispersive, the energy of a wave
component does not propagate with the phase speed. Instead it travels with
the group velocity
dw
,
(19)
cg =
dk
which in deep water becomes approximately equal to half the phase speed.
In the simple one-dimensional case, the angular wave frequency ω have been
assumed to be a function of the wave number k in the direction of
propagation. For higher dimensions, ω is a function of the components of the
wave number vector k, giving that the group velocity
dw
cg =
.
(20)
dk
3.2
Wave fields
A wave field may be described as a number of sinusoidal waves with
different amplitudes and periods travelling in different directions
superimposed. Wave properties for the whole field are described by
statistical parameters derived, e.g., from a wave energy spectrum.
A wave energy spectrum shows the distribution of wave energy over the
frequency ( f = T -1 ) or wave number space. This energy is proportional to
the square of the amplitude ( 12 r g a 2 , where r is the density of water).
Such a wave energy spectrum reveals within which frequency range the
energy is concentrated, as well as the number of peaks and their shape. A
time series of spectra shows how the wave field evolves within different
frequencies. As the waves develop, the energy is passed from the higher
frequencies to the lower. The shape of the spectrum is due to a balance
between atmospheric energy input, non-linear energy transfer between
waves of different frequencies and dissipation of energy.
The wave properties used further in this thesis are mainly the significant
wave height and peak period. Significant wave height corresponds to the
average height of the highest one-third of the waves in the wave field. The
16
origin of this somewhat odd measure is that it has been found more or less
equivalent to the visually observed wave height. From a wave energy
spectrum significant wave height can be derived as
H s = 4 m0 ,
(21)
m 0 = E ( f ) df
(22)
where
ò
is the moment of zero-order of the one-dimensional energy spectrum E ( f ) .
The peak period Tp is the period at the highest peak of the wave energy
spectrum, i.e., where the spectra has the most energy. This period is used
throughout this thesis for resuspension calculations.
3.3
The wave model HYPAS
To study the wave properties in a large area, the wave field needs to be
modelled. For our studies we have chosen the second generation spectral
wave model HYPAS (Hybrid Parametrical Shallow water, Günther and
Rosenthal, 1995). This model was accessible from SMHI (Swedish
Meteorological and Hydrological Institute), where it is set up for the Baltic
Sea with a grid size of 11x11 km. HYPAS is an improvement of an earlier
model (NORSWAM model, Günther et al., 1979) and it has been tested in at
least two large model intercomparison studies in the 80’s (SWAMP Group:
Allender et al., 1985; SWIM Group: Bouws et al., 1985).
The model is based on the spectral energy balance equation (e.g., WMO,
1998)
¶E
¶E
¶E
(23)
+ c gx
+ c gy
=S
¶t
¶x
¶y
where E ( f , Q, x, y, t ) denotes the two-dimensional wave energy spectrum
which depends on frequency f and direction of propagation Q at a specified
position and time. The group velocity components are denoted cgx and cgy,
and the source function S includes all processes that add/remove energy
to/from the spectrum.
17
To solve Eq. 23 some predefined wave energy spectra are posed in
HYPAS. These have earlier been derived from different field experiments.
The PM-spectrum is used for the fully developed sea (Pierson and
Moskowitz, 1964), and is given by
E PM ( f ) =
-4
æ
æ f ö ö÷
ç
÷
exp - 0.74 çç
,
ç
f m ÷ø ÷
f5
è
è
ø
a g2
(2 π )4
(24)
where fm is the peak frequency. The parameter a was originally set to a
constant value of 0.0081, although Hasselmann et al. (1973) later showed
that this parameter varies with fetch
æ
g ö÷
a = 0.0662ç X
ç u 2÷
10 ø
è
-0.2
,
(25)
where X is the fetch and u10 is the wind speed at 10 m altitude.
For a growing sea in fetch-limited conditions the Jonswap spectrum is
assumed (Hasselmann et al., 1973). This spectrum is obtained by multiplying
a PM-spectrum by a ‘peak enhancement’ factor, and it is formulated as
E J ( f ) = E PM ( f ) g
æ ( f - f m )2
exp ç ç 2s 2 f 2
m
è
ö
÷
÷
ø
,
(26)
where the form parameters g =EJmax/EPMmax and s influences the magnitude
and width of the spectral peak. The main difference between the Jonswap
and the PM-spectrum is that the energy at the peak frequency is higher
during the wave growth phase than in the fully developed sea, see Fig. 7.
When a wave field approaches shallow water it is influenced by the
bottom and additional processes such as bottom friction, percolation, and
sediment motion might become present. In this case a third spectrum is used,
the TMA (Texel-Marsen-Arsloe) spectrum, which is a modification of the
Jonswap spectrum (Bouws et al., 1985). A function f that ranges between 0
and 1, and depends on water depth and wave frequency is multiplied by the
Jonswap spectrum so that
18
Figure 7. An example of a PM-spectrum and a Jonswap spectrum (u10=9.15 m/s, fm=0.15 s-1,
X=25 km, g =2 and s =0.01).
E TMA ( f ) = E J ( f )f ( f , D ) .
(27)
In practice the Jonswap spectrum could be replaced with the T MA spectrum
since the latter by definition transforms into the Jonswap spectrum in deep
water. The shape of these spectra is defined by a number of free parameters
(a, fm, sa, sb, g, f and Q) which are determined in the wave model from the
source functions.
A historical problem regarding wave modelling has been the non-linearity
of waves and how to handle these. The exact form of the non-linear wavewave interactions has been described by Hasselmann (1962), but this form is
difficult to apply numerically. The first generation wave models did not
include the non-linear interactions at all. Instead, these models let each
spectral component evolve independently of the other components. Since the
non-linear interactions are mainly important during the growth phase, these
models usually underestimate the wave growth (Khandekar, 1989). The next
generation, of which HYPAS belong, solve the non-linear problem in a
simplified way by parameterizing the wave-wave interactions. Even though
this works rather well, its drawbacks are found in rapidly shifting winds
(e.g., hurricanes, intense small-scale cyclones or fronts) as well as in the
19
transition between wind sea waves and swell waves (e.g., WAMDI Group:
Hasselmann et al., 1988). Most advanced are the third generation wave
models, which still not solve the exact form of the non-linear wave-wave
interaction but use a more complex parameterisation of it. These models are,
however, quite computer intense.
For our studies, HYPAS was forced every third hour with wind data. We
have used analysed wind fields as they improve the wind prognoses slightly
(Häggmark et al., 2000). These analysed fields are formed by MESoscale
wind field ANalysis (MESAN) which is based on an optimal interpolation
technique. The start field of the analysis is adopted from the atmospheric
circulation model HIRLAM (HIgh Resolution Limited Area Model, Källén,
1996) and then modified by wind observations from different weather
stations. Since the HIRLAM field underestimates the winds slightly (SMHI,
1999) the MESAN fields might do the same. If this is the case, our modelled
wave fields might be somewhat underestimated as well.
Ice has not been included in our studies due to lack of gridded ice data.
Therefore, the waves are exaggerated at times when there was an ice cover,
both where the ice was located and down-wind from it, due to the
overestimated fetch. However, the modelled years were rather mild ice
winters why this should not have any large impact on our studies.
In Paper I the model was validated with data from five wave measuring
sites and HYPAS was shown to perform well, even though it underestimated
the higher waves slightly (see Tables 2 and 3 in Paper I). The same is found
in some recent studies where HYPAS was compared with the two third
generation models WAM and SWAN as well. Contrary to HYPAS, the two
latter models sometimes exaggerated the high waves (Höglund, 2004;
Myklebust, 2005).
20
4 Wave–seabed interactions
Waves mainly influence the sediment dynamics through the frictional forces
they exert on the seabed. The size of the frictional force is in its turn
dependent on the roughness of the sediment surface. If the bed is smooth, the
flow can be laminar above the bed, while a rough bed almost always gives
rise to a turbulent flow. The interaction between the waves and the seabed
take place in the wave boundary layer, which is defined as the layer where
the flow is significantly affected by the seabed. Due to the oscillating nature
of a wave, with a constant shift in velocity direction and speed, a wave
boundary layer is in the order of millimetres. A corresponding boundary
layer due to a steady current of the same magnitude would be in the order of
meters. This makes the velocity shear, and thereby the frictional forces,
much larger in a wave bottom boundary layer.
4.1
Bed shear-stress
For waves, the bed shear-stress is oscillatory with a maximum value of
2
t w = 12 r f w U 0 ,
(28)
where fw is the wave friction factor, ρ is the density of water and U0 the
maximum orbital velocity just outside the boundary layer as defined by
Eq. 13. A number of empirical relations have been proposed for the wave
friction factor (Sleath, 1984; Fredsøe and Deigaard, 1992; Nielsen, 1992;
Soulsby, 1997). These relations are based either on the Reynolds number
Re = U 0 Ab n or the relative roughness Ab k N of the bed. Here
n = 1.3 × 10 -6 m2/s is the kinematic viscosity and k N = 2.5 d is the Nikuradse
roughness with d being the sediment grain diameter. Ab is the amplitude of
the horizontal motion as earlier defined by Eq. 14. If the bed is assumed to
21
be smooth ( Ab k N ® ¥ ), the friction factor is only dependent on flow
regimes (laminar, turbulent or transitional). For this type of bottoms
2
ì
ï
Re
ï
-3
f w = í3.34 × 10 + 1.05 × 10 -9 Re
ï
0.024 Re -0.123
ï
î
Re £ 3 × 10 5
3 × 10 5 < Re < 1 × 10 6
1 × 10 6 £ Re
(29)
is chosen (Nielsen, 1992). A linear dependence has been assumed in the
transition region between the laminar and turbulent flow, see Fig. 8a. If the
bed instead is assumed to be rough, and the flow turbulent
æ æA
f w = expç 5.5 çç b
ç
k
è è N
ö
÷÷
ø
-0.2
ö
- 6.3 ÷
÷
ø
(30)
Figure 8. Relation between wave friction factor and (a) Reynolds number and (b) the relative
roughness of the bed.
22
is chosen (Nielsen, 1992), see Fig. 8b. The smooth bottom friction factor
(Eq. 29) is used in Paper II, where we compared the calculated bottom
stresses statistically with the sediment distribution of bottom types. In
Papers III and IV the rough bottom friction factor (Eq. 30) is used, with an
additional maximum value of f w = 0.3 for very rough bottoms
( Ab k N < 1.57 ) in the latter paper.
The bed shear-stress is often expressed in other forms than t w for
mathematical convenience. Bed shear-stress in the form of a virtual velocity,
the wave friction velocity, is used in Papers II and III. This is defined
u* =
tw
.
r
(31)
A dimensionless form of bed shear-stress called the Shields parameter q is
used in Paper IV. Grain properties are then put in relation to the bed shearstress,
tw
.
(32)
q=
g (r s - r ) d
Here ρs is the density of the sediment grains, in our studies taken as
r s = 2650 kg/m3, which is the density of quartz grains.
4.2
Resuspension and sediment movements
To mobilise sediments, a critical limit of bed shear-stress must be exceeded.
This limit is highly dependent on local factors such as the type of sediment,
compactness, bio-fouling etc and it is found empirically. Since we not have
made any measurements of our own, two variants of critical limits have been
used. In Paper III different critical limits for different grain sizes were taken
from the literature. In Paper IV only sand is considered, in which case we
use
0.30
(33)
q cr =
+ 0.055(1 - exp(- 0.020 D* ))
1 + 1.2 D*
to calculate the critical limits of the Shields parameter (Soulsby, 1997). Here
the dimensionless grain size is defined
23
æ g (s - 1) ö
D* = d ç
÷
2
è n
ø
(34)
and s = r s r is the density ratio between sediment and water.
When the critical limit for resuspension is exceeded, sediment grains are
set into motion. If the wave friction velocity is lower than the grain settling
velocity, the grains remain on the bottom and hop (saltate), roll or slide
along it as bed load. When the flow speed is increased and the wave friction
velocity becomes larger than the grain settling velocity, the sediment grains
are suspended. If the bed is rippled, sediment grains are erupted at the crest
of the ripple and moved circularly behind the crest in the downstream
direction, see Fig 9. For even higher flows, the bed becomes flat with the
ripples washed out. In this case there is a large but concentrated sediment
flow close to the bottom, a so called sheet flow.
Sediment ripples can be formed by all types of flows but will have
different shapes and sizes depending on the flow. A ripple formed by waves
is e.g. symmetrical, while a current generated one is asymmetric with a
gentler slope in the upstream direction. The height and length of the bed
forms are important for calculations of suspended sediment, and the ripples
influence the friction caused by the bed.
4.3
Suspended sediment profile
Vertical profiles of suspended sediments are usually described by a reference
sediment concentration at the bed and a function for the vertical distribution.
The expressions for these are based on laboratory or field experiments and
vary slightly. In Paper IV different relations are used for a rippled bed or
sheet flow conditions.
For a rippled bed, the relation is exponential with a reference
concentration by Nielsen (1992):
æ zö
C ( z ) = C 0 R expç - ÷
è lø
3
C 0 R = 0.005q r .
24
q cr £ q £ 0.8 and u * < ws
(35)
(36)
Figure 9. Sediment movements over a rippled bed. The photo is from Nielsen (1992) and is
reproduced with the kind permission of Professor P. Nielsen and World Scientific.
Here C(z) is the volumetric sediment concentration and l the decay length
scale dependent on ripple height Dr , maximum orbital wave velocity at the
bottom U0 and grain settling velocity ws,
U
ì
ï0.075 0 Dr
l=í
ws
ï
D
1
.
4
r
î
U0
< 18
ws
otherwise.
(37)
The decay length scale is always positive. The parameter q r is a
modification of the ordinary Shields number to compensate for the flow
enhancement that occurs near the ripple crest,
qr =
q
(1 - p Dr
lr
)2
(38)
where lr is the ripple length.
For sheet flow conditions, a relation by Soulsby (1997) with the reference
concentration by Zyserman and Fredsøe (1994) is used:
25
C (z ) = C 0 S
æ z
çç
è z0
ö
÷÷
ø
-b
q > 0.8 and u * > ws
0.331(q - 0.045)
.
0.331
1.75
(q - 0.045)
1+
0.46
(39)
1.75
C0 S =
Here
z 0 = 2 .0 d
(40)
is the virtual bed level and the exponent b = w s k u * ,
where ws is the grain settling velocity and k is the von Karman’s constant.
When sediments are suspended, they might dampen the turbulence in the
boundary layer due to the increased density stratification. This effect is not
accounted for in the equations specified above. Therefore the relations may
overestimate the amount of suspended sediment in the water column,
especially for small grain diameters (≤0.2 mm) and sheet flow. A more
thorough discussion of this is found in Paper IV.
26
5 Baltic Sea waves and sediment
resuspension
The waves in the Baltic Sea, Kattegat and Skagerrak have been modelled
with HYPAS and analysed for a period of two years, 1999-2000. These
waves have been used further to calculate the bed shear-stress for various
sediments, and estimates of resuspension have been made for the same
period. Sediment suspension was studied during a period of eight stormy
days. Finally, a separate study of nitrogen fixation in the surface layer has
been made. The main results from these studies are presented in this chapter.
5.1
Wind climate
Most of the temporal variations found for waves and resuspension
parameters originate from the wind fields. The wave height is related to wind
speed, fetch and duration, while the bottom stress and resuspension
parameters in their turn depend on the wave characteristics. Therefore the
temporal variation found in the wind field will be found also in the other
data. Storm frequency can by this be a way of indirectly studying high wave
events (see e.g., Eckhéll et al., 2000).
There is a strong seasonal variation in the wind field with higher wind
speeds during winter and lower during summer, but also between years there
are differences, see Fig. 10. In our study the winter at the turn of the century
exerted higher wind speeds than the other two winter periods. During this
particular winter, five events with wind speeds over 20 m/s occurred. The
storm which passed 3-4 December 1999 is one of the 50 largest storms
during last century (P-O Ganerlöv, SMHI).
27
28
>20 m/s
15-20 m/s
10-15 m/s
26
24
22
Percent of total wind
20
18
16
14
12
10
8
6
4
2
mar-01
jan-01
feb-01
dec-00
okt-00
nov-00
sep-00
jul-00
aug-00
jun-00
apr-00
maj-00
mar-00
jan-00
feb-00
dec-99
okt-99
nov-99
sep-99
jul-99
aug-99
jun-99
apr-99
maj-99
mar-99
jan-99
feb-99
0
Month
Figure 10. Percent of all MESAN winds over the Baltic Sea above 10 m/s from January 1999
to March 2001.
It is not only the winter periods that differ between years, the two
summer periods do as well. The summer 2000 was windier, which might be
due to a number of thunderstorms that summer. As a curiosity, the year 2000
was one of the warmest years in southern Sweden since the 16th century, but
the summer was still slightly colder than average and extremely rainy
(Karlström and Vedin, 2001).
The dominant wind direction in the area is from south and south-west
(see Fig. 11 and Paper II, Fig. 2). This is due to the main low-pressure
passage tracks from west. The highest wind speeds during the two studied
years are found for south-westerly, westerly and southerly winds, in this
order, while the average wind speed is more or less the same from all
directions. The same pattern is found, e.g., by Soomere (2003), but the
increased winds from north found in his study can not be seen in our
material. However, during the years 1999 and 2000 the southerly wind
components were slightly above average in occurrence, and the northerly
components slightly below average (H. Alexandersson SMHI, pers. comm.).
28
30
*
25
*
*
*
20
*
*
*
o
o
o
N
NE
E
*
15
10
5
o
o
o
S
SW
o
o
W
NW
0
SE
Figure 11. Mean (o) and max (-*-) MESAN wind speeds [m/s] as well as percent of total
winds (bars) from different directions. Data is from Baltic Proper area during 1999-2000.
5.2
Modelled waves
It is only the waves from 1999 that is presented in Paper I, but as will be
shown here, there are no large differences compared to the following year.
To describe the actual wave climate in the area, an even longer study is
needed since variations can exist over time-scales of decades or more (see
e.g., Bacon and Carter, 1991).
The temporal variation of significant wave height follows that of the wind
and consequently, the highest waves appear during winter storm events. The
spatial variation depends mainly on water depth and fetch and there are no
large differences in the spatial wave distribution in-between years. The
highest waves were found in the eastern Baltic Proper and in the outer part
of Skagerrak where the longest fetches and the deepest water are found, see
Fig. 12a and b. On average, the waves during 2000 were lower than the year
29
65
65
64
64
63
63
62
62
7m
61
61
6m
60
60
5m
59
59
4m
58
58
3m
57
57
2m
56
56
1m
55
0m
55
1999
10
12
14
16
18
20
22
24
26
28
2000
30
10 12 14 16 18 20 22 24
Lon. E
a.
28
30
b.
65
[m]
[m]
1.0
62
0.5
61
64
0.00
1.5
63
65
0.05
2.0
64
Lat. N
26
Lon. E
0.0
-0.05
63
-0.10
62
-0.15
61
-0.20
60
-0.5
-0.25
59
60
-1.0
-0.30
59
58
-1.5
-0.35
58
57
-2.0
-0.40
57
56
56
Hsmean 55
2000-1999
Hsmax
2000-1999
55
9
11 13 15 17
19 21 23
25 27 29
9
Lon. E
c.
Lat. N
Lat. N
before but the maximum waves showed higher values in Skagerrak and the
Gulf of Bothnia in 2000, see Fig. 12c and d.
11 13 15 17
19 21 23 25
27 29
Lon. E
d.
Figure 12. Yearly maximum significant wave height during (a) 1999 and (b) 2000 is shown,
as well as the differences in this parameter between (c) the yearly max and (d) yearly average.
The 5-meter isoline is made thicker in the upper panels and the 0-difference line in the lower.
The dominant modelled wave heights are in the range 0.5-1.5 m in winter
and less than 1 m in summer. Corresponding modelled zero-downcrossing
periods are 3.5-5.0 s in winter and 2.5-4.5 s in summer. To get waves with a
30
significant wave height larger than 6 m, strong winds (15-20 m/s) must blow
from a favourable direction over deep water for at least 6 hours (Paper I).
Despite some scatter, a spatial pattern with comparably lower peak
periods in Kattegat and higher in Skagerrak is found, see Fig. 13. In the
Baltic Proper there is a clear eastward increase in period while the Gulfs of
Riga and Finland have lower values. In the Gulf of Bothnia, values decrease
with latitude. Also this a reflection of the dominant wind directions and the
fetch limited waves.
Tp [s]
65
64
12
63
62
10
Lat. N
61
8
60
59
6
58
4
57
56
55
10
12
14
16
18
20
22
24
26
28
30
Long. E
Figure 13. Maximum peak period during December 1999.
31
Max u*
[cm/s]
65
64
63
5.0
62
Lat. N
61
2.7
60
59
1.2
58
57
56
55
12
14
16
18
20
22
24
26
28
30
Lon. E
Figure 14. Maximum
5.3
u * during 1999. The 80-m bathyline is included.
Wave friction velocities
From the modelled wave fields, bed shear-stresses expressed as wave
friction velocities u * are calculated. Therefore, the same seasonal pattern
with higher values during winter and lower during summer is found also for
this parameter. However, the spatial distribution is different, and the largest
shear-stresses are found in the shallower areas around the high wave areas,
preferably in the down-wind direction, see Fig. 14. This gives, due to the
dominant wind direction, an east-west asymmetry in the Baltic Proper,
32
which is seen also for peak periods but not for wave heights. The fetch is
important for u * , and for each location the highest u* is modelled when the
wind blows from the direction with the longest fetch, see Fig. 15. In these
cases the wave field has had longer time to evolve, thus getting both higher
waves and longer periods.
Figure 15. Wind directions for the maximum wave friction velocity in each point.
A correlation between u * and bottom type distribution has been found,
where erosion bottoms have higher u * than accumulation bottoms (Paper II).
The distribution of u * due to surface waves can not explain all variations in
the sediment distribution, but this relation shows where the waves are
important and where they are not. Also other processes rework the sediment,
and a longer discussion of these is found in Paper II.
33
Resuspended area [%]
100
80
60
40
Silt (4.0)
F. sand (1.0)
M. Sand (1.4)
20
C. sand (2.3)
0
199901
Gravel (4.0)
199906
199911
200004
200009
Figure 16. Monthly values of the amount of resuspended areas for each grain size during
1999-2000. Values in brackets are the used critical limits for u * .
5.4
Resuspension
Waves are supposed to interact with the seabed down to about half the
wavelength. During storm conditions, wavelengths up to 200 m have been
modelled in the Baltic Sea, which in these cases indicate that waves may
influence the bottoms down to about 100 m depth. On average the
wavelengths during winter is 50-60 m, which would give a wave influence
depth of 25-30 m. In Papers II, III and IV waves have been found to induce
sediment motions down to about 80 m depth. In shallow waters (<20 m)
suspended sediments can be found already for as low winds as 5 m/s
(Paper IV). Comparing these results with a sediment map, it is found that
below 80 m fine material and accumulation bottoms generally are found, and
in shallower waters coarser sediment are found (Repecka and Cato, 1998).
34
Resuspension frequencies and events were only studied in the Baltic
Proper, and for these calculations the grain sizes were taken under
consideration. The seasonal pattern with higher values in winter and lower
values in summer is again seen in the graph, Fig. 16. Besides that, it is
mainly seabeds with fine and medium sand that are resuspended. These
sediment types cover together about 25% of the Baltic Proper area. Silt is
found mainly in the deeper areas and very few of these sediments are
resuspended throughout the year. Depth is another important factor and for
more or less equal winds and waves, shallow areas resuspend more often and
for longer periods, see Fig. 17. Overall, no sediment grains larger than 0.5
mm (i.e., medium sand) were suspended, but some moved as bed load
(Paper IV).
On average sediments are resuspended 4-5 times per month and each
event last about 22 hours. For individual points, the number of events ranges
from 1-19 per month with a duration of up to 15 days in one go.
5.5
Implications on the biogeochemistry
When sediments are resuspended, particulate material enters the water mass
and the associated interstitial water is released. This might supply nutrients
to the water mass and stimulate an increased productivity (e.g., Wainright
and Hopkinson Jr., 1997). During a storm passage from west, the highest
amounts of suspended sediments in the water mass are found along the
eastern side of the Baltic Proper. Then about 2.5 Mton sediment is
suspended and about 0.5 × 106 m3 interstitial water is released (Paper IV).
This is probably an important internal source of nutrients, which is beyond
control by remedy actions. Observed nitrogen concentrations are also about
11 times lower on erosion bottoms than on accumulation bottoms (Carman
and Cederwall, 2001), which probably is due to an increased degradation of
organic matter both in the surficial sediment and in the water mass above
erosion bottoms. Further, Shum and Sundby (1996) have suggested that even
during non-resuspension conditions wave-induced ventilation of porous
sediment might be an important part of the degradation process. As the
highest resuspension frequencies are found during winter, this coincide with
the unproductive time of year and the effect on the biogeochemistry might
35
be somewhat damped. However, also during the productive period
resuspension events occur, and in some shallow areas these are frequent.
24
22
wind [m/s]; Hs [m]; Tp [s]
20
18
16
w ind ; 55 .5N 2 0 .7 E
Hs
Tp
w ind ; 55 .9N 2 0 .7 E
Hs
Tp
14
12
10
8
6
4
2
0
1,2
1
C [kg/m3]
0,8
5 cm, D=52 m
20 cm, D=52 m
40 cm, D=52 m
5 cm, D=35 m
20 cm, D=35 m
40 cm, D=35 m
0,6
0,4
0,2
0
19
19
19
19
19
19
19
19
19
99
99
99
99
99
99
99
99
99
-11
-12
-11
-12
-12
-11
-12
-12
-12
-30
-01
-29
-02
-03
-28
-04
-05
-06
Figure 17. Time series from two positions with fine sand (d=0.1 mm). The upper panel show
wind, significant wave height and peak period, and the lower panel show sediment
concentrations at 5, 20 and 40 cm above bottom.
An important internal source of nitrogen is nitrogen fixation by
cyanobacteria. These are also, through large blooms, a substantial
contributor to the organic matter deposition on the bottoms. In Paper V we
36
calculated the net internal load of nitrogen to 30 - 260 × 10 3 ton/year or
10-130 nmol/l·day during the production period. This calculation was based
on the dissolved inorganic phosphorus (DIP) changes in the water mass
during the period when the available dissolved inorganic nitrogen (DIN)
were below detection limits. The external load of DIN is at the same time
25-75 nmol/l·day, which is less or comparable to the nitrogen fixating rates
per day. One exception is east of Gotland where the nitrogen fixation rate
was always less than the average external load per day. This asymmetry
might be due to a higher nutrient input from the eastern border (Grimvall and
Stålnacke, 2001; Rahm and Danielsson, 2005), and the higher recycling rates
on the eastern side due to wave action.
5.6
Conclusions
This thesis presents the spatial and temporal variations in the surface waves
and its influence on the sediments. There is a strong seasonal signal in all
studied parameters (wind, significant wave height, peak period, resuspension
frequency and duration) with higher values during winter and lower during
summer. This is due to the typical wind pattern in the Baltic Sea area.
The waves normally influence sediments on bottoms down to about
25-30 m depth, but during storms they may reach bottoms down to 80 m
depth. In shallow waters (<20 m), already wind speeds of 5 m/s can give
waves that resuspend sediment.
Our studies suggest that, sediment is resuspended on average 4-5 times
per month with a duration of 22 hours for each event. Areas with fine and
medium sand resuspend more frequently than other areas. These sediment
types cover about 25% of the Baltic Proper. There is an east-west asymmetry
in the resuspension parameters with higher values on the eastern side. Also
this is an effect of the prevailing wind pattern in the area. A similar east-west
asymmetry is found for nitrogen fixation. This is probably due to a
difference in nutrient input, both from land and atmosphere, but might also
be a result of the resuspension frequencies along the eastern side of the
Baltic Proper. The conditions for cyanobacteria blooms are thereby more
favourable along the western side of the Baltic Proper.
37
38
6 Future outlooks
6.1
Climate changes
The Baltic Sea wave field and the parameters derived from that are found to
be quite variable seasonally, but on average the highest values are always
found in more or less the same areas. As said before, this is due to the fact
that the waves in the Baltic Sea are fetch limited and consequently, as long
as the winds remain, the highest waves will occur in the same areas as before
with about the same maximum heights.
In other places, e.g., in the North Atlantic and the North Sea, wave
records show that the waves in these areas have increased during the last 30
years (Bacon and Carter, 1991; Carter and Draper, 1988; Gulev and Hasse,
1999). The same holds for the waves in the north eastern Pacific (Allan and
Komar, 2000). No similar study on waves has been made in the Baltic Sea
region, but studies on the wind climate show that the storm frequency has
increased since the 1960’s to reach a peak around 1990. However, this peak
was not as large as the one in the beginning of 1880’s (Alexandersson et al.,
1998; Alexandersson et al., 2000). Therefore, on a time scale of a century it
looks like there on average has been no significant change in the storm
climate.
Despite this, model scenarios of future climate change in the area for the
period 2071-2100 give that there will be an increase in wind speed of up to
15% compared to the control period 1961-1990 (Meier et al., 2005). Their
results also indicate that there will be an increase in the 90th percentile of
significant wave height with up to 0.5 m. In these cases the largest changes
are found along the eastern side of the Baltic Sea, but increased values are
found also in the Gulf of Bothnia. In Paper I scenarios of possible maximum
wave heights in different areas calculated with constant winds from different
39
directions were analysed. Possibilities for increased wave heights, especially
in the Gulf of Bothnia and in the Bornholm area, were found.
All this indicates that there might be an ongoing change in wind climate,
and if this continues new areas will be resuspended, releasing more nutrients
(and pollutants) to the water mass. Especially the Bothnian Sea might be
affected by these changes, as well as the already today very exposed eastern
side of the Baltic Proper.
6.2
Benthic boundary layer models
To further study the physical behaviour of water and sand just above the
sediment surface, a benthic boundary layer model can be applied. So far we
have only modelled the hydrodynamics coupled to surface wave motion, a
steady current or both, but this model can be extended to include also
sediment concentrations. In these studies the equation solver Probe,
classified as an ‘equation solver for one-dimensional transient, or twodimensional steady, boundary layers’ have been used (Svensson, 1986). In
our set-up a k-e model was used to calculate the mixing coefficients. In
Fig. 18 modelled values are compared to observations made in an
oscillatory-flow water tunnel experiment by Jensen et al. (1989), and the
correspondence is good between modelled values and observations.
If suspended sediment concentration is included in the model, this will
show the temporal changes of the vertical concentration profile on a longer
time scale as well as within a wave period. To model the sediment
concentration it is important to use a very high resolution in the model, both
in the vertical and in time. Similar model studies have been made, e.g., by
Holmedal et al. (2004); Myrhaug et al. (2001) as well as by Hagatun and
Eidsvik (1986). This is a very interesting field and further studies will
increase our knowledge of the interactions between sediment and water,
including the nutrient dynamics coupled to this.
40
160
Height above bottom [mm]
140
120
M 0 deg
M 45 deg
M 90 deg
M 135 deg
M 180 deg
D 0 deg
D 45 deg
D 90 deg
D 135 deg
D 180 deg
100
80
60
40
20
0
-0,4
-0,2
0
0,2
0,4
0,6
0,8
1
1,2
u [m/s]
Figure 18. Vertical profiles from different phases during a wave cycle. The lines denoted M in
the legend show data modelled with Probe and the lines denoted D show measurements made
by Jensen et al. (1989). Horizontal velocity from their Test 12 with U0=1.02 m/s and
Tp=9.72 s have been used.
6.3
Sediment-water exchanges
The high-energy areas found on the eastern side of the Baltic Sea might have
a large influence on the biogeochemistry. This may primarily be achieved by
increasing the total system mineralization and productivity through increased
ventilation and reworking of the surficial sediments. Reintroducing DIN to
the water mass becomes an additional internal nitrogen source beside the
nitrogen fixation studied in Paper V. A related field not studied in this thesis
is wave-pumping through permeable beds (see, e.g., Precht and Huettel,
2003; Shum and Sundby, 1996). The pressure difference along a sediment
ripple will cause the water to flow through the porous sediment, ventilating it
and increasing the degradation rate compared to more compact bottoms.
Also this is a very interesting research field since large areas in the Baltic
Sea are covered with permeable sediments and get rippled beds from time to
time (Paper IV).
41
The Baltic Sea is eutrophicated and different remedy actions are tried to
overcome this. However, to see the full complexity of the problem, it is
needed to understand and include also the bottom dynamics in these
estimates. Wulff et al. (1986) estimated that 47% of the organic nitrogen
sedimenting from the primary production will recirculate as inorganic
compounds. This has management implications, external loads from land
may be decreased, but the sediment dynamics cannot be controlled in a
feasible way.
42
7 Acknowledgement
First of all I would like to thank my supervisor Lars Rahm and my cosupervisor Åsa Danielsson for their help and support. You have always taken
your time when I have needed it, and you have steered me in the right
direction in times when I have taken a too devious path.
I have done much of my wave modelling at SMHI in Norrköping, and I
am grateful for the help and support that I have got from different people
there. Especially Lennart Funkquist is acknowledged for his help to get me
started with the wave model Hypas. Barry Broman made a lot of filing of
model result and patiently answered all my early wave questions. When I
started to use Probe, Jörgen Sahlberg’s experience of that model was
invaluable.
During the same period, when trying to model suspended sediments, I
contacted Lars Erik Holmedal at UNIK in Norway. His knowledge and
advices regarding benthic boundary layer models have been extremely
valuable. Thank you for all the time you took answering my e-mails, and for
letting my supervisor and me visit you at UNIK.
Göran Broström at MISU is acknowledged for reading, commenting and
discussing an earlier draft of this thesis at my ‘slutseminarium’. Thank you
for taking your time and I hope you think the text improved according to
your suggestions. All other friends and colleagues, who commented the
same text, thanks also to you. You all helped me improve the text.
At the University there are many people that have made work easier;
Susanne, Marie, Kerstin, Ian, Christina and Rosmari, thank you for this. All
present and former PhD-students at the Department of Water and
Environmental Studies are acknowledged for making the place a nice and
interesting interdisciplinary research department. The D97’s are especially
remembered as well as Lotta P., Teresia, Emma, Mimmi and Carina. And of
43
course, my happy friends Annika, Tessan and Anna, thanks for all nice talks
and laughs. I am really glad I got to know you!
At the end of 1999 I started to work as an operational oceanographer at
SMHI. It was a great escape from the ‘selfish’ PhD-work to manage the
ocean forecasts and distribute them to the users. However, my mental
presence at SMHI has not always been the best due to the PhD-work, and I
appreciate very much the patience Lars Häggmark has had with me every
time I have asked for more leave of absence to finish the thesis.
Finally, mamma, pappa, Karin och mormor tack för allt stöd och “tjat”
om att jag borde bli klar någon gång. Nu, äntligen, är jag klar! And dear
Claes, thank you for valuable mathematical and aesthetic discussions as well
as for being patient and understanding. I will not postpone anything anymore
now due to the fact that ‘I have to work with my thesis’.
This work was financially supported within the MAST/EU program
BASYS (Baltic Sea System Study), the MISTRA project MARE (Marine
Research on Eutrophication), as well as by VR, NFR and INTAS projects.
44
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