Model Studies of Surface Waves and Sediment Resuspension in the Baltic Sea

(1)

Model Studies of Surface

Waves and Sediment

Resuspension in the Baltic Sea

Anette Jönsson

(2)

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

(3)

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.

(4)

(5)

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.,

(8)

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.

(9)

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

(10)

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

(11)

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

(12)

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.

(13)

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.

(14)

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.

(15)

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 <0.01

3 Aleurite peltic mud <0.01

2 Fine aleuritic mud 0.05-0.01

1 Coarse silt 0.06-0.02

18 Coarse aleurite 0.10-0.05

14 Fine sand 0.20-0.06

15 Fine sand 0.25-0.10

7 Glacial deposits (till)

-11 Medium sand 0.50-0.25

8 Mixed sediments

-12 Sand 1.0-0.1

13 Coarse and medium sand 2.0-0.2

10 Coarse sand 1.0-0.5 4 Gravel 10-1 6 Pebble 100-10 9 Sedimentary bedrocks -17 Crystalline bedrock -2.2 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.

(16)

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).

13 15 17 19 21 23 25 27 29 55 57 59 61 63 65 Finland Erosion Transport Accumulation Sweden Estonia Lithuania

(17)

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}

z w y v x u ¶ ¶ º ¶ ¶ º ¶ ¶ º f f f , (1)

where u, v and w are the velocities in the x, y and z-directions, z being

(18)

0 = ¶ ¶ + ¶ ¶ + ¶ ¶ z w y v x u (2) shows that the velocity potential has to satisfy the Laplace equation

0 2 2 2 2 2 2 = ¶ ¶ + ¶ ¶ + ¶ ¶ z y x f f f

_.

₍₃₎

For surface gravity waves this equation can be solved with the boundary conditions 0 = ¶ ¶ z f _at_z₌₀ ₍₄₎ t z ¶ ¶ = ¶ ¶f h _at_z₌_D ₍₅₎ h f _g t = -¶ ¶ _at_z₌_D ₍₆₎

where D is the water depth, _{h the surface displacement around the}

undisturbed surface at z= , g is the acceleration due to gravity, and t isD 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

( )

x t a

(

kx wt

)

h , = cos - , (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 T k _w p l p 2 and 2 = = , (8)

where T is the period of the wave and the wavelength _{l is defined}

(19)

Figure 5. Illustration of the hyperbolic functions. ÷ ø ö ç è æ =T g D l p p l tanh 2 2 2 . (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

( )

( ) (

kD kx t

)

z k k a w w f = sin -sinh cosh , (10)

which implies for the two velocity components,

( )

( ) (

kD kx t

)

z k a u= w cos -w sinh cosh (11) and

( )

( ) (

kD kx t

)

z k a w= w sin -w sinh sinh . (12)

(20)

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

(21)

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

( )

kD T H U sinh 0= p (13)

where H =2a is the wave height. The maximum amplitude of the

horizontal motion at the bottom is then given by w

0

U

A_b = . (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

( )

kD k

g tanh =

w (15)

or in terms of the phase speed

( )

kD k

g k

c= w = tanh . (16)

The phase speed is dependent on depth and wave number. For deep water Eq. 16 reduces to

k g

c» (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

(22)

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

k c_g

d dw

= , (19)

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

k c d dw = g . (20) 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_a2_{, 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

(23)

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

0 4 m H_s ₌ , (21) where

( )

ò

= E f df m₀ (22)

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) S y E c x E c t E gy gx = ¶ ¶ + ¶ ¶ + ¶ ¶ ₍₂₃₎

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,

(24)

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

( )

_{( )}

_÷÷ ø ö ç ç è æ ÷÷ø ö ççè æ -= -4 5 4 2 PM exp 0.74 π 2 fm f f g f E a , (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

2 . 0 2 10 0662 . 0 -÷ ÷ ø ö ç ç è æ = u g X a , (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

( )

( ) ÷÷_ø ö ç ç è æ_- -= 2 2 2 2 exp PM J m m f f f f E f E g s , (26)

where the form parameters _{g =E}Jmax/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

(25)

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).

( )

f E

( ) (

f f D

)

E_TMA = _J f , . (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, f}m, 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 wave-wave 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

(26)

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).

(27)

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 0 2 1 _f _U w w r t = , (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

n

b

A U₀

Re= or the relative roughness A_b k_N of the bed. Here

6 10 3 . 1 × -=

n m2_{/s is the kinematic viscosity and}_k _d

N =2.5 is the Nikuradse

(28)

be smooth (Ab kN ®¥), the friction factor is only dependent on flow regimes (laminar, turbulent or transitional). For this type of bottoms

Re Re Re Re Re Re f_w £ × × < < × × £ ï ï î ï ï í ì × + × = -6 6 5 5 123 . 0 9 3 10 1 10 1 10 3 10 3 024 . 0 10 05 . 1 10 34 . 3 2 (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

÷ ÷ ø ö ç ç è æ -÷÷ø ö ççè æ = -3 . 6 5 . 5 exp 2 . 0 N b w k A f (30)

Figure 8. Relation between wave friction factor and (a) Reynolds number and (b) the relative roughness of the bed.

(29)

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 fw=0.3 for very rough bottoms

(Ab kN <1.57) in the latter paper.

The bed shear-stress is often expressed in other forms than t for_w

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

r tw

u* = . (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 shear-stress,

(

)

d g _s w r r t q -= . (32)

Here ρs is the density of the sediment grains, in our studies taken as

2650 =

s

r 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

(

)

(

*

)

* 020 . 0 exp 1 055 . 0 2 . 1 1 30 . 0 D D cr = ₊ + - -q (33)

(30)

( )

_÷ ø ö ç è æ -= ₂ * 1 n s g d D (34)

and s=rs 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):

( )

R _l cr u ws z C z C ÷ £ £ < ø ö ç è æ-= 0 exp q q 0.8and * (35) 3 0R 0.005 r C = q . (36)

(31)

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 D , maximum orbital wave velocity at the_r

bottom U0 and grain settling velocity ws,

ïî ï í ì _< = otherwise. 4 . 1 18 075 . 0 0 0 r s r s w U w U l D D ₍₃₇₎

The decay length scale is always positive. The parameter q is a_r

modification of the ordinary Shields number to compensate for the flow enhancement that occurs near the ripple crest,

(

₁

)

2 r r r l D p q q -= (38)

where l is the ripple length._r

(32)

( )

s b S _z w z C z C > > ÷÷ø ö ççè æ = -* 0 0 q 0.8andu (39)

(

)

(

)

1.75 75 . 1 0 045 . 0 46 . 0 331 . 0 1 045 . 0 331 . 0 -+ -= q q S C . (40)

Here z₀ =2.0d is the virtual bed level and the exponent b=w_s ku_*, 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.

(33)

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).

(34)

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.).

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 ja n -9 9 feb-99 ma r-99 ap r-9 9 ma j-99 ju n-99 ju l-9 9 au g-99 se p-99 ok t-99 no v-9 9 de c-9 9 ja n-00 feb -00 ma r-00 ap r-0 0 ma j-00 ju n-00 ju l-0 0 au g-00 se p -0 0 ok t-00 no v-0 0 de c-0 0 ja n -0 1 feb -01 ma r-0 1 Month P e rc en t of to ta l w in d >20 m/s 15-20 m/s 10-15 m/s

(35)

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

NW W SW S SE E NE N 30 25 20 15 10 5 0 * _* _* * * * * * o _o o o o _o o o

(36)

before but the maximum waves showed higher values in Skagerrak and the Gulf of Bothnia in 2000, see Fig. 12c and d.

10 12 14 16 18 20 22 24 26 28 30 Lon. E 55 56 57 58 59 60 61 62 63 64 65 Lat . N 1999 10 12 14 16 18 20 22 24 26 28 30 Lon. E 55 56 57 58 59 60 61 62 63 64 65 0 m 1 m 2 m 3 m 4 m 5 m 6 m 7 m 2000 a. b. 9 11 13 15 17 19 21 23 25 27 29 Lon. E 55 56 57 58 59 60 61 62 63 64 65 L at. N -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Hsmax 2000-1999 [m] 9 11 13 15 17 19 21 23 25 27 29 Lon. E 55 56 57 58 59 60 61 62 63 64 65 La t. N -0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 Hsmean 2000-1999 [m] c. 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

(37)

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.

Figure 13. Maximum peak period during December 1999.

10 12 14 16 18 20 22 24 26 28 30 Long. E 55 56 57 58 59 60 61 62 63 64 65 L at. N 4 6 8 10 12 Tp [s]

(38)

12 14 16 18 20 22 24 26 28 30 Lon. E 55 56 57 58 59 60 61 62 63 64 65 Lat . N 1.2 2.7 5.0 Max u* [cm/s]

Figure 14. Maximum u_* during 1999. The 80-m bathyline is included.

5.3 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,

(39)

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,

(40)

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).

200009 200004 199911 199906 199901 Re su sp en de d a rea [ % ] 100 80 60 40 20 0 Silt (4.0) F. sand (1.0) M. Sand (1.4) C. sand (2.3) Gravel (4.0)

(41)

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

(42)

be somewhat damped. However, also during the productive period resuspension events occur, and in some shallow areas these are frequent.

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 w ind [m /s ]; Hs [m ]; Tp [ s] w ind ; 55 .5N 2 0 .7 E H s Tp w ind ; 55 .9N 2 0 .7 E H s Tp 0 0,2 0,4 0,6 0,8 1 1,2 1999 -11-2₈ 1999-11-2₉ 1999-11-3₀ 1999-12-0₁ 1999-12-0₂ 1999-12-0₃ 1999-12-0₄ 1999-12-0₅ 1999-12-0₆ C [kg /m 3] 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

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

(43)

calculated the net internal load of nitrogen to ₃₀_-₂₆₀_×₁₀3_{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

(44)

(45)

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

(46)

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 two-dimensional 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.

(47)

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).

0 20 40 60 80 100 120 140 160 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1 1,2 u [m/s] H ei ght abo ve bott o m [m m] 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

(48)

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.

(49)

7 Acknowledgement

First of all I would like to thank my supervisor Lars Rahm and my co-supervisor 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

(50)

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.

(51)

8 References

Alexandersson, H., Schmith, T., Iden, K. and H. Tuomenvirta, 1998. Long-term Variations of the Storm Climate over NW Europe. The Global Atmosphere and Ocean System 6, 97-120.

Alexandersson, H., Tuomenvirta, H., Schmith, T. and K. Iden, 2000. Trends of storms in NW Europe derived from an updated pressure data set. Climate Research 14, 71-73. Allan, J. and P. Komar, 2000. Are Ocean Wave Heights Increasing in the Eastern North

Pacific? EOS 81(47), 561-567.

Bacon, S. and D. Carter, 1991. Wave climate changes in the North Atlantic and North Sea. International Journal of Climatology 11, 545-558.

Bianchi, T.S., Engelhaupt, E., Westman, P., Andrén, T., Rolff, C. and R. Elmgren, 2000. Cyanobacteria blooms in the Baltic Sea: Natural or human-induced? Limnology and Oceanography 45(3), 716-726.

Blomgren, S., Larsson, M. and H. Hanson, 2001. Numerical Modeling of the Wave Climate in the Southern Baltic Sea. Journal of Coastal Research 17(2), 342-352.

Bouws, E., Günther, H., Rosenthal, W. and C.L. Vincent, 1985. Similarity of the Wind Wave Spectrum in Finite Depth Water: Part 1. Spectral Form. Journal of Geophysical Research 90(C1), 975-986.

Brydsten, L., 1993. Characterization of transport bottoms in the Gulf of Bothnia - A model approach. Aqua Fennica 23(2), 153-164.

Buch, E. and H. Dahlin (Editors), 2000. The BOOS Plan: Baltic Operational Oceanographic System, 1999-2003. EuroGOOS Publication No. 14, Southampton Oceanographic Centre, Southampton.

Carman, R. and H. Cederwall, 2001. Sediments and Macrofauna in the Baltic Sea -Characteristics, Nutrient Content and Distribution. In: F. Wulff, L. Rahm and P. Larsson (Editors), A Systems Analysis of the Baltic Sea. Ecological Studies. Springer, Berlin, pp. 289-327.

Carter, D.J.T. and L. Draper, 1988. Has the north-east Atlantic become rougher?, Nature, pp. 494.

Danielsson, Å., Carman, R., Rahm, L. and J. Aigars, 1998. Spatial estimation of nutrient distributions in the Gulf of Riga sediments using cokriging. Estuarine, Coastal and Shelf Science 46(5), 713-722.

(52)

Emeis, K., Christiansen, C., Edelvang, K., Jähmlich, S., Kozuch, J., Laima, M., Leipe, T., Löffler, A., Lund-Hansen, L.C., Miltner, A., Pazdro, K., Pempkowiak, J., Pollehne, F., Shimmield, T., Voss, M. and G. Witt, 2002. Material transport from the nearshore to the basinal environment in the southern Baltic Sea. II. Synthesis of data and on origin and properties of material. Journal of Marine Systems 35, 151-168.

FredsÝe, J. and R. Deigaard, 1992. Mechanics of Coastal Sediment Transport. Advanced

Series on Ocean Engineering, 3. World Scientific, Singapore, 369 pp.

Friedrich, C.T., Wright, L.D., Hepworth, D.A. and S.C. Kim, 2000. Bottom-boundary-layer processes associated with fine sediment accumulation in coastal seas and bays. Continental Shelf Research 20, 807-841.

Granéli, E., Wallström, K., Larsson, U., Granéli, W. and R. Elmgren, 1990. Nutrient limitation of primary production in the Baltic Sea. Ambio 19, 142-151.

Grimvall, A. and P. Stålnacke, 2001. Riverine Inputs of Nutrients to the Baltic Sea. In: F. Wulff, L. Rahm and P. Larsson (Editors), A Systems Analysis of the Baltic Sea. Ecological Studies. Springer, Berlin, pp. 113-131.

Gulev, S.K. and L. Hasse, 1999. Changes of wind waves in the North Atlantic over the last 30 years. International Journal of Climatology 19, 1091-1117.

Günther, H. and W. Rosenthal, 1995. Model Documentation of HYPAS, Institut für Gewässerphysik - Abteilung GMS - GKSS-Forschungszentrum Geesthacht GmbH, Geesthacht, 20 pp.

Günther, H., Rosenthal, W., Weare, T.J., Worthington, B.A., Hasselmann, K. and J.A. Ewing, 1979. A Hybrid Parametrical Wave Prediction Model. Journal of Geophysical Research 84(C9), 5727-5738.

Hagatun, K. and K.J. Eidsvik, 1986. Oscillating Turbulent Boundary Layer With Suspended Sediments. Journal of Geophysical Research 91(C11), 13045-13055.

Harris, P.T. and R. Coleman, 1998. Estimating global shelf sediment mobility due to swell waves. Marine Geology 150, 171-177.

Hasselmann, K., 1962. On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. Journal of Fluid Mechanics 12, 481-500.

Hasselmann, K., Barnett, T.P., Bouws, E., Carlson, H., Cartwright, D.E., Enke, K., Ewing, J.A., Gienapp, H., Hasselmann, D.E., Kruseman, P., Meerburg, A., Müller, P., Olbers, D.J., Richter, K., Sell, W. and H. Walden, 1973. Measurements of Wind-Wave Growth and Swell Decay during the Joint North Sea Wave Project (JONSWAP). Deutschen Hydrographischen Zeitschrift/Ergänzungsheftz. Reihe A 8(12), 95. Holmedal, L.E., Myrhaug, D. and K.J. Eidsvik, 2004. Sediment suspension under sheet flow

conditions beneath random waves plus current. Continental Shelf Research 24(17), 2065-2091.

Håkanson, L. and M. Jansson, 1983. Principles of Lake Sedimentology. Springer-Verlag, Berlin Heidelberg, 316 pp.

Häggmark, L., Ivarsson, K.-I., Gollvik, S. and P.-O. Olofsson, 2000. Mesan, an operational mesoscale analysis system. Tellus 52A, 2-20.

(53)

Jensen, B., Sumer, B. and J. FredsÝe, 1989. Turbulent oscillatory boundary layers at high Reynolds numbers. Journal of Fluid Mechanics 206, 265-297.

Karlström, C.E. and H. Vedin, 2001. Årets väder 2000 - Regn, regn och åter regn, Väder och Vatten. SMHI, pp. 15. (in Swedish)

Khandekar, M.L., 1989. Operational Analysis and Prediction of Ocean Waves. Coastal and Estuarine Studies, 33. Springer-Verlag, New York, 214 pp.

Kuhrts, C., Fennel, W. and T. Seifert, 2004. Model studies of transport of sedimentary material in the western Baltic. Journal of Marine Systems 52(1-4), 167-190.

Kundu, P.K., 1990. Fluid Mechanics. Academic Press, Inc., San Diego, 638 pp.

Källén, E., 1996. Hirlam Documentation Manual, System 2.5, SMHI, Norrköping, 243 pp. Leipe, T., Loeffler, A., Emeis, K.-C., Jaehmlich, S., Bahlo, R. and K. Ziervogel, 2000.

Vertical Patterns of Suspended Matter Characteristics Along a Coastal-basin Transect in the Western Baltic Sea. Estuarine, Coastal and Shelf Sciences 51, 789-804. Meier, H.E.M., Broman, B., Kallio, H. and E. Kjellström, 2005. Projections of future surface

winds, sea levels, and wind waves in the late 21st century and their application for impact studies of flood prone areas in the Baltic Sea region. Submitted to Geological Survey of Finland, Special Paper.

Myklebust, E., 2005. Utvärdering av WAM, SMHI, Uppsala, 45 pp.

Myrhaug, D., Holmedal, L.E., Simons, R.R. and R.D. MacIver, 2001. Bottom friction in random waves plus current flow. Coastal Engineering 43, 75-92.

Nielsen, P., 1992. Coastal bottom boundary layers and sediment transport. Advanced Series on Ocean Engineering, 4. World Scientific, Singapore, 324 pp.

PapliÕska, B., 1999. Wave analysis at Lubiatowo and in the Pomeranian Bay based on

measurements from 1997/1998 -- comparison with modelled data (WAM4 model). Oceanologia 41(2), 241-254.

Pierson, W.J. and L. Moskowitz, 1964. A Proposed Spectral Form for Fully Developed Wind Seas Based on the Similarity Theory of S. A. Kitaigorodskii. Journal of Geophysical Research 69(24), 5181-5190.

Precht, E. and M. Huettel, 2003. Advective pore-water exchange driven by surface gravity waves and its ecological implications. Limnology & Oceanography 48(4), 1674-1684. Rahm, L. and Å. Danielsson, 2005. The spatial heterogeneity of nutrients in the Baltic Proper,

Baltic Sea. Submitted.

Repecka, M. and I. Cato (Editors), 1998. Bottom sediment map of the Central Baltic Sea, scale 1:500 000, Vilnius - Uppsala.

Rugbjerg, M. and D. Mühlestein, 1997. Wave Atlas for the Inner Danish Water - Pilot Project, Phase 0, Danish Hydraulic Institute, Hörsholm, 18 pp.

Seibold, E. and W.H. Berger, 1982. The Sea Floor - An Introduction to Marine Geology. Springer - Verlag, Berlin, 288 pp.

Sellner, K.G., 1997. Physiology, ecology and toxic properties of marine cyanobacteria blooms. Limnology and Oceanography 42, 1089-1104.

Model Studies of Surface Waves and Sediment Resuspension in the Baltic Sea