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Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 28

The wind field in coastal areas

Niklas Sondell

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Abstract

The land-sea transition in coastal areas makes the meteorological conditions rather complex and the structure of the coastal boundary layer is important for many reasons. Two examples are air pollution dispersion and wind energy potential.

The wind field off the coast when offshore flow is present has been studied. At the coast there is a sudden change in surface properties that will affect the wind field in the area. When warm air is advected out over the much colder sea we get a stable stratification whose structure depends on wind speed and temperature difference. The roughness length over the sea is much less than over land, which gives less friction over the sea and usually increased winds. This is the general situation. But with a stable stratification the wind speed decreases near the surface partly due to the much denser air. However, there may be a wind speed decrease a certain distance from the coast, after an initial wind speed maximum. This is due to the growth of a stable internal boundary layer that develops over the sea. What is new in this investigation is that the more stable the stratification over the sea is, the farther offshore the decrease in wind speed occurs, probably more than 30 km. Thus with a very stable stratification the wind speed off the coast in coastal areas seems to be increased instead of decreased. This investigation also includes an explanation of why this behavior seldom is seen in measurements.

The wind field structure dependence of the IBL-height and the stability has been studied and an expression for the distance to the decrease in wind speed has been found. Also the prediction of a sea breeze circulation is studied as well as the affect a low-level jet has on the wind field near the coast. Measurements from three sites are used, the Baltic Sea near the Island of Gotland, around the strait of Öresund and outside the Atlantic coast near Duck in North Carolina, USA. These measurements are used in simulations with a 2-dimensional meso-γ-scale model as well as a lot of arbitrary simulations. All simulations correspond very well to the expression found and the simulated cases agree well with the measured ones.

In the lowest 100 m of the marine atmosphere over the Baltic Sea, the stratification is probably stable more than half of the year. Thus the behavior of decreased wind speeds a certain distance offshore, after an initial increase, would be a very common phenomenon. It must be of great importance in extracting wind energy, to avoid these areas and layers with decreasing wind speed, which in turn have lower wind energy potential. In an area with often very stable stratification over the sea there can be an energy loss of more than 50 % in the lowest 50 m of the boundary layer.

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Sammanfattning av ”Vindfältet i kustnära områden”

Övergången mellan land och hav gör de meteorologiska förhållandena i kustnära områden komplicerade. Vetskap om egenskaperna hos gränsskiktet vid kusten är viktigt av flera orsaker. Några exempel är spridning av luftföroreningar, vindenergipotential samt det faktum att man ska kunna ge rätt vindprognos till dem som av nytta eller nöje befinner sig utanför kusten.

Vindfältet utanför kusten vid frånlandsvind har studerats här. Vid kusten sker en plötslig ändring av ytans egenskaper. När varm luft strömmar ut över kallt hav fås en stabil skiktning som beror på vindhastighet och temperaturdifferensen mellan land och hav. Skrovlighetslängden är större över land än över hav. Det ger vanligtvis en ökning av vindhastigheten över havet då luften strömmar från land till hav. Men vid tillräckligt stabil skiktning över hav samt med instabil skiktning över land fås istället ett vindavtagande. Initialt ökar dock alltid vindhastigheten. Det beror på tillväxten av ett internt gränsskikt. Höjden på detta måste vara tillräcklig för att ett avtagande skall ske. Stabilare skiktning över hav ger längre sträcka till avtagandet i vindhastighet som kan ske mer än 30 km utanför kusten och det kan inte längre kallas för kustnära område. Varför detta beteende sällan upptäcks utreds också.

Vindfältets beroende av interna gränsskiktets höjd samt stabiliteten har studerats och ett uttryck för att beräkna avståndet till avtagandet i vindhastighet har också tagits fram. Även möjligheten att förutspå en sjöbris har studerats liksom den effekt en low-level jet har på vindfältet nära kusten. Mätningar från tre platser används, Östersjön nära Gotland, över Öresund samt vid Atlantkusten nära Duck i North Carolina, USA. Dessa tre fall simuleras i en 2-dimensionell modell liksom en mängd godtyckliga simuleringar av olika fall.

I de lägsta 100 metrarna av det marina gränsskiktet över Östersjön är skiktningen troligen stabil mer än halva året. Beteendet med initialt ökande vindhastighet följt av en dramatiskt avtagande en viss sträcka utanför kusten borde vara ett vanligt fenomen. Vid utvinning av vindenergi måste det vara av stort intresse att undvika dessa områden med lägre vindhastighet, som i sin tur har lägre vindenergipotential. I ett område där det ofta blir stabilt skiktat över havet kan energiförlusten bli på över 50 % i de lägsta 50 metrarna av gränsskiktet.

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Contents

1. Introduction...1

2. Theory ...2

2.1 Stability...2

2.1.1 Static stability...2

2.1.2 Dynamic stability...2

2.1.3 Gradient Richardson number ...2

2.2 Internal boundary layer, IBL...3

2.3 The sea breeze...5

2.4 Low Level Jet...8

2.5 The numerical model ...11

2.5.1 The closure problem ...11

2.5.2 The MIUU-model ...12

3. Baltic Sea...15

3.1 Advection and Stability...15

3.2 IBL-growth, Low-level jet and Sea breeze ...15

4. Simulations ...16

4.1 Parameters to change in the 2-dimensional MIUU-model ...16

5. Measurements ...17

5.1 The Baltic Sea case ...17

5.2 The Öresund case...19

5.3 The USA case ...20

6. Results ...21

6.1 The stability criterion...24

6.1.1 A case study...24

6.2 Importance of the IBL-height ...27

6.3 Verification of Lyon’s sea breeze index...29

6.4 Distance to decreasing wind speed...32

6.5 The effect of a low-level jet to the wind field near the coast ...35

6.6 Comparison with the USA case...35

6.6.1 Simulations of the USA case ...38

6.7 Comparison with the Öresund case ...40

7. Conclusions...43

7.1 Flowchart ...46

8. Acknowledgements ...48

9. References...48

Appendix 1, Characteristics of the air masses ...50

Appendix 2, Values of the IBL height for different cases ...51

Appendix 3, Data for the calculation of λ...52

Appendix 4, List of Symbols ...53

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1. Introduction

Many people live in coastal areas, and the land-sea transition makes the meteorological conditions rather complex. The meteorological conditions in coastal areas therefore receive much attention. The structure of the coastal boundary layer is important for many reasons. Two examples are air pollution dispersion and wind energy potential. It is also important to give accurate wind forecasts to the people living in coastal areas. In Sweden a lot of people spend their summers in the archipelago off the Swedish coast in the Baltic Sea. For them, it is of great importance to know if the wind speed is 6 or 11 m/s especially if they plan to go on a boat trip.

The purpose of this investigation is to study the wind field off the coast when offshore flow is present. At the coast there is a sudden change in surface properties that will affect the wind field in the area. Due to the much larger heat capacity of the water, the sea surface temperature is nearly constant during the day whilst the land surface is heated. This can give large temperature differences between land and water surfaces. When warm air is advected out over the much colder sea we get a stable stratification whose structure depends on wind speed and temperature differences.

Furthermore, the roughness length over the sea is much less than over land, which gives less friction over the sea and usually increased winds. This is the general situation, also stated by Mahrt and Vickers (2000). Doran and Gryning (1987) claim, however, that there may be a wind speed decrease a certain distance from the coast (near the surface), after an initial wind speed maximum. This is probably due to the growth of a stable internal boundary layer that develops over the sea. Garrat (1990) and Högström-Smedman (1984) among others also found the same feature. In the lowest 100 m of the marine atmosphere over the Baltic Sea, the stratification is probably stable more than half of the year. In spring, summer and early autumn the land is heated more than the sea during daytime, and when warm air is advected from either side of the Baltic Sea the stratification becomes stable. In such situations, the surrounding land areas may often affect the whole sea. As a summary, the main purpose with this investigation is to determine whether or not wind speed will decrease over the sea, and subsequently to find criteria and quantitative expressions for where and when the wind speed decrease occurs.

The land-sea temperature difference can also yield the well-known sea breeze circulation, which completely changes the wind field in coastal areas. For prediction of the sea breeze the so-called Lyon’s sea breeze index (Lyon, 1972) is used. This criterion will be tested against simulations with a meso-γ-scale model (the MIUU- model, Enger 1986).

Furthermore, a low-level jet can occur when warm air is advected over the relatively colder water, which can give super-geostrophic wind speeds with wind maxima just above the inversion-height. This can cause an increase in wind speed at the surface as well.

In the determination of the criteria and expressions for where and when the different wind regimes occur, schematic simulations with the MIUU-model are used.

Finally, the results are compared with measurements from the Baltic Sea, eastern USA and the Öresund strait situated between Sweden and Denmark.

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2. Theory

2.1 Stability

2.1.1 Static stability

Static stability is a measure of the capability for buoyant motion and is expressed as

z

∂ /θ , where θ is the potential temperature and z the height. Air is statically unstable when less dense air underlies more dense air. Thus if ∂θ /∂z<0 the stratification is statically unstable and when ∂θ/∂z>0 it is statically stable. The flow responds to this instability with convection. Air rises to the top of the unstable layer, and thereby stabilizing the fluid (Stull, 1988).

2.1.2 Dynamic stability

Even if the air is statically stable, wind shear may be able to generate turbulence dynamically. When ∂θ/∂z>0, and there is a velocity shear between the layers, the typical sequence of events is (Stull, 1988):

1. A shear exists across a density interface. Initially, the flow is laminar.

2. If a critical value of shear is reached (see below), then the flow becomes dynamically unstable, and gentle waves begin to form on the interface.

The crests of these waves are normal to the shear direction.

3. These waves continue to grow in amplitude, eventually reaching a point where each begins to ”roll up” or ”break”. This ”breaking” wave is called a Kelvin-Helmholtz (KH) wave, and is based on different physics than surface waves that ”break” on an ocean beach.

4. Within each wave, there exists some lighter fluid that has been rolled under denser fluid, resulting in patches of static instability. On radar, these features appear s braided ropelike patterns, ”cat’s eye” pattern or breaking wave patterns.

5. The static instability, combined with the continued dynamic instability, causes each wave to become turbulent.

6. The turbulence then spreads throughout the layer, causing diffusion or mixing of the different fluids. During this diffusion process, some momentum is transferred between the fluids, reducing the shear between the layers. What was formerly a sharp, well-defined, interface becomes a broader, more diffuse shear layer with weaker shear and static stability.

7. This mixing can reduce the shear below a critical value and eliminate the dynamic instability.

8. In the absence of continued forcing to restore the shears, turbulence decays in the interface region, and the flow becomes laminar again.

2.1.3 Gradient Richardson number

The Richardson number is a measure of the balance between mechanical production of turbulent kinetic energy (TKE) and the buoyant consumption/production of TKE.

Buoyancy may tend to suppress turbulence, while wind shear always tend to generate turbulence mechanically thus the relationship between the two tells us the possibility of the occurrence of turbulence. The gradient Richardson number is defined as

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







∂ + ∂





= 2 2

z V z

U z g Ri

θ

θ , (1)

where U and V is the mean wind speed in the zonal and meridional direction respectively. θ is the mean potential temperature and g the acceleration due to gravity.

Theoretical and laboratory research suggest that laminar flow becomes unstable to KH-wave formation and the onset of turbulence when Ri is smaller than a critical Richardson number, Ric. Another value, RiT indicates the termination of turbulence. The dynamic stability criteria can be stated as follows

• Laminar flow becomes turbulent when Ri < Ric.

• Turbulent flow becomes laminar when Ri > RiT.

It appears that Ric = 0.21 – 0.25 and RiT = 1.0 work fairly well. Thus, there appear to be a hysteresis effect because RiT is greater than Ric. (Stull, 1988)

2.2 Internal boundary layer, IBL

When air is advected over a discontinuity in surface properties, an internal boundary layer (IBL) is formed. It is called internal since it is a layer within the boundary layer and it grows with distance downstream from the property change (Garrat, 1990). The cause of this discontinuity can be a sudden change in surface roughness, temperature, humidity or in the surface flux of heat or moisture (Garrat, 1990). The IBL layer can be separated into two parts. Close to the ground there is a layer that is fully adjusted to the “new” surface. Within this layer, the turbulent flux of momentum is roughly equal to its surface value. Between the top of this layer and the top of the IBL layer the properties are different. This layer is only partly adjusted to the “new” surface, and there is a great variation in the momentum flux with height. The growth of the layer is slow, with distance from the coast in this case. The layer above is approximately ten times deeper than the equilibrium layer (McIlveen, 1997). According to Smedman and Högström (1984), the wind profile is often observed to have the characteristics typical of the “new” surface. Figure 1 shows a schematic picture of the transition in the IBL. When the discontinuity is a change related to surface temperature or heat flux, the IBL is called a thermal internal boundary layer (TIBL). The most common example of a TIBL is the one formed at the coast because of the so often large temperature differences between land and sea.

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Figure 1. Sketch of downwind growth of adjustment of a surface boundary layer to a change in surface roughness at C. The vertical is greatly enlarged, and the partly adjusted layer (transition layer) should be ≈ 10 times deeper than the fully adjusted layer. (McIlveen, 1997)

Studies of the TIBL at a coast are of importance especially because of the influence on pollution in coastal areas. According to Garrat (1990), less attention has been given to the stably stratified IBL than to the convective ones. It will be shown later that this stably stratified IBL over the sea has a great affect on the wind field outside the coast. When warm air from land is advected out over the relatively colder water this stable IBL starts to develop and grows when the air has passed the coastline. It would here be interesting to find an expression for the height of the IBL layer at a certain distance from the coast. The IBL top is readily identified with an elevated inversion in the convective case, and with the top of a surface-based inversion in the stable TIBL case, according to Garrat (1990). But the real IBL tops are hard to find in the stable case. Garrat (1990) used a mesoscale model to investigate growth and inner structure of a stable TIBL, formed by warm continental air flowing offshore. He used a model to find the following expression for the TIBL height

g x U

h  ⋅

 

 ⋅∆

=

−1 2

2

θ

α θ , (2)

where x which is the distance from the discontinuity, g the acceleration due to gravity, U is the large-scale wind, θ the mean potential temperature and ∆θ is the difference between the temperature over land and the sea surface temperature. The numerical coefficient α is defined as

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β α =2⋅A0f(z/h)⋅RfCD/cos3

where f(z/h) is a function of z/h (see Garrat 1990 for description), A0 is a parameter describing the shape of the temperature profile, β denotes the deviation angle from the normal to the coast and Rf is the flux Richardson number. CD is the geostrophic drag coefficient described as

2 2

* g

D V

C = u , (4)

where Vg is the geostrophic wind and u* is the friction velocity. Using least square regression, Garrat obtained the value

α = 0.014.

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The parameter α depends on the angle between the geostrophic wind and the coastline normal (β). By replacing x with the actual distance from the coast along the geostrophic wind axis, this problem can be avoided.

2.3 The sea breeze

Figure 2. The left figure shows a sharp fast-moving sea breeze front 45 km inland, with isopleths of specific humidity in g/kg. The right figure is a schematic picture of the sea breeze. (McIlveen, 1997).

When being in coastal areas one can often during the day observe both onshore and offshore winds. In the morning the sun starts to heat up the land surface near and at the coast. The sea surface however, has a nearly constant temperature during the day and land can quickly become considerably warmer than the nearby sea. When onshore winds are present the temperature difference between land and sea get somewhat lower because of the advection of colder air from the sea. Thus offshore winds tend to be more favorable for getting a large temperature difference. The sharp temperature contrast between land and sea is what drives the sea breeze circulation. In addition to the normal convection over land, there is in such conditions a tendency for the air to rise relative to the nearby cooler and denser air over the sea (McIlveen, 1997). The warm air over land rises and expands faster than the cooler air over the water surface.

Due to hydrostatic conditions the vertical gradient of pressure is larger over sea than over land. This is easily seen from the hydrostatic equation

dz g

dp =−ρ⋅ , (5)

and the fact that ρ, which is the density, for cold air is larger than ρ for warm air. The pressure is p, and g is the acceleration due to gravity. Assuming the same pressure at ground level over both sea and land, the pressure at any constant height above land and sea must be higher over land than over sea because the pressure decreases more rapidly with height over sea than over land. The atmosphere strives for equilibrium.

As seen to the right in figure 2, there is a flow of air towards the coast near the surface and a return flow aloft. The flow at the surface is seldom more than a few hundred meters deep but the return current aloft is more than twice the depth of the flow near the surface and thus the wind speed of the return current is much lower. In figure 2, convergence near (C) will cause an increase of pressure and a resulting departure from hydrostatic equilibrium. In the equation above one can see that the density must increase and this more dense air subsides from (C) to (D). Subsidence at (D) but convergence at (A) due to heating of the land causes a pressure gradient between (D) and (A), producing a flow of air from (D) to (A). A flow of air from (A) to (B)

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neutralizes the divergence at (B) caused by air flowing from (B) to (C), which in turn started the circulation because of the pressure gradient aloft. The sea breeze circulation is now completed. The rising air at (A) is replaced by the cool, moist air, which flows inland from (D) to (A). As the air flows inland, the boundary between the sea and land air can be very sharp, with marked contrast in temperature, humidity and haziness being ascribed to the presence of a sea breeze (McIlveen, 1997). The first few hours the sea breeze is more or less perpendicular to the coast but later on there is usually a rotation of the breeze vector in a clockwise direction to be expected from the operation of the Coriolis force in the Northern Hemisphere.

The sea breeze can be described with the thermal wind and the vorticity equation. The basic theory is taken from Holton (1992). If there is a temperature contrast in the horizontal as in this case, the warm air over land rises and expands faster than the cooler air over water surface as mentioned earlier. This is similar to the thermal wind in a cold or warm front except for the fact that in the sea breeze case, the horizontal temperature gradient persists only near the surface because it is the same air mass. It can be described as the initial force creating the flow aloft towards the sea, which gives convergence over the sea and subsequently subsidence. The thermal wind can be described as



 

 



− ∂

=

1

ln 0

p p y

T f u R

p

T , 

 

 



= ∂

1

ln 0

p p x

T f R

p

vT , (6)

where <T> is the mean temperature in the layer between p0 and p1. If <T> = 2.5, ∂x

= 25 000 m, p0 = 1000 hPa and p1 = 980 hPa, the thermal wind becomes 5.45 m/s.

This is the wind speed without taking into account the frictional forces and the overall geostrophic wind.

The circulation can also be described using the vorticity equation. Circulations may be generated by the pressure-density solenoid term when the fluid is in a baroclinic atmosphere. The situation is shown in figure 3.

Figure 3. Application of the circulation theorem to the sea breeze problem. The closed heavy solid line is the loop about which the circulation is to be evaluated. Dashed lines indicate surfaces of constant density (Holton, 1992).

At ground level the pressure is the same. Land is warmer than the sea and according to the hydrostatic equation above, the isobaric surfaces above the ground will slope

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downward toward the ocean while the isopycnal (constant density) surfaces will slope downward toward the land. The vorticity equation in Cartesian coordinates is

( ) ( )



 

−∂

∂ + ∂



 

−∂

− ∂



 

∂ +∂

∂ + ∂

=

+ x

p y y p x z

u y w z v x w y

v x f u Dt f

D ρ ρ

ζ ρ

ζ 12 ,

where the solenoid term is the last term on the right side, x, y and z is the horizontal and vertical directions respectively and u, v and w is the corresponding wind speeds.

The relative vorticity is ζ, g is the acceleration due to gravity, p is the pressure and ρ is the density. It is obvious that vorticity will be created caused by the horizontal gradients in pressure and density. When the circulation is started and there is subsidence over the sea and convection over land the tilting term also contributes to the vorticity. This is shown in the right picture in figure 4. Thus, if ∂v/z>0 and

w/x<0, there will be a generation of positive vertical vorticity. As a conclusion, the thermal wind and solenoid term starts the circulation and the tilting term enhances it.

The picture to the left in figure 4 shows the secondary circulation in a baroclinic atmosphere caused by the convergence that is created by the positive vertical vorticity.

Figure 4. The right figure shows streamlines of the secondary circulation forced by frictional convergence in the planetary boundary layer for a cyclonic vortex in a stably stratified baroclinic atmosphere. The circulation decays with height in the interior. The left figure shows the vorticity generation by the tilting of a horizontal vorticity vector (double arrow). (Holton, 1992)

In the meso-scale low-pressure created by the sea breeze circulation, the cyclonal circulation at the ground gives a greater convection because of the greater friction at the surface. That is because in the balance between the Coriolis force, the pressure gradient force and the friction force. It is the latter that make the wind veer towards the center of the low pressure. A sea breeze is often developed when offshore flow is present because that favors the offshore flow in the above circulation. Near the ground the larger roughness length over land makes the wind speed relatively low and easy to overcome for the onshore sea breeze circulation flow, which in turn is twice as strong as the above airflow.

Because of the larger number of observations over land, the penetration inland of the sea breeze is the better-documented part of this circulation. In mid-latitudes, sea

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breezes tend to reach 20-50 km inland but in the tropics they can in extreme cases reach up to and over 300-km inland (Källstrand, 1997). According to Källstrand (1997), the extent of the sea breeze decreases rapidly with latitude in spring, with a limit at 70° latitude. Above this limit there are no detected sea breezes in spring.

Whereas during summer the sea breeze extent and strength only slightly decreases with latitude due to the increased insolation and longer days. The sea/land breeze occur more frequently in the tropics than in the middle latitudes since the solar radiation, which is the main force, driving the circulation is much stronger close to the equator than in higher latitudes. In the mid-latitudes the sea breeze often occurs only in spring and summer when the land is heated while the water still is relatively cool.

The sea breeze affects the climate at the coast. The flow of air from the sea is lowering the temperature. The subsidence is reducing clouds and showery rainfall at the coast, compared with more than a few kilometers inland. (McIlveen, 1997)

In forecasting sea breezes Lyon (1972) suggests the following dimensionless index

T c SBIndex V

p⋅∆

= 2 . (7)

Here V is the wind speed, cp is the specific heat of air at constant pressure and T is the land-sea temperature difference near the surface. The index is essentially the ratio of internal to buoyancy forces. The index has been verified by Lyon (1972). He uses the geostrophic wind speed (Vg) in the index as,

T c

V

p g

= ⋅

2

σ , (8)

and gets σ < 10 as a limit for the sea breeze. This works well except for the cases when there is a wind nearly parallel to the coast. Lyon is aware of this and states that using the wind normal to the coast (Vg sin α)2, will improve the result. Here α is the angle between the coast and the wind speed direction. But as θ becomes parallel to the coast, σ then drops to zero.

The accuracy of this index will be verified and reconfirmed in section 6.3, with the aid of simulations made with the MIUU-model (described in section 2.5).

2.4 Low Level Jet

The low-level jet is a phenomenon with a well-pronounced wind speed maximum below 1500 m, which often is super-geostrophic. That means wind speeds stronger than the geostrophic wind speed at relatively low levels. Stull (1988) for example, tried to define the jet as wind speeds of a certain magnitude to the wind speeds above it. Many different mechanisms cause this low-level jet phenomenon, including synoptic-scale baroclinicity, fronts, advective accelerations, confluence in connection with mountain barriers splitting the flow, land-sea breezes, mountain and valley winds and inertial oscillation (Stull, 1988). Low-level jets over the Baltic Sea are mostly advective phenomena. When warmer air from the heated landmasses surrounding the Sea is advected out over the relatively colder sea, the stratification in the layer near the surface suddenly gets very stable. Above the inversion the turbulence dies out according to Blackadar (1957). Furthermore he states that both heat and momentum are removed from the upper portion of the inversion and subsequently carried

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downward to the surface by turbulent mixing. At the surface the turbulence is then dissipated very effectively. Because of this continuous downward transport of turbulent energy, the turbulent shearing stress becomes almost zero at the top of the inversion layer. The wind does not ”feel” the surface, the friction ”disappears” and an inertial oscillation can develop. This process is called ”quasi-frictional decoupling”, because the friction does not disappear after the flow has passed the coastline but is reduced substantially (Smedman et al., 1996).

A simple theoretical explanation can look like this (Blackadar, 1957): If the motion is completely horizontal, and the horizontal pressure gradient is assumed to be constant in time and in each horizontal plane, the equations of motion can be written as

(

u ug

) (

f v vg

t − = −

)

, and

(

v vg

) (

f u ug

)

t − = −

∂ . (9)

The components u, v, ug, vg are the mean wind and the geostrophic wind respectively, and f is the Coriolis parameter. A complex number can be written as

(

u ug

) (

iv vg

)

W = − + − , (10)

and introduce it in the equations above. Then there is only one complex differential equation

t ifW W =−

∂ . (11)

Here, W is a vector in the complex plane and represents the deviation of the wind from the geostrophic wind. The complex differential equation has the solution

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e ift

W W = 0

there W0 is the deviation of the actual wind vector from the geostrophic wind vector at the initial time t = 0, i.e. at the time when the ”quasi-frictional decoupling” occurs.

This inertial oscillation occurs with a period equal to the inertial period at given latitude. That is a period of 2π/f. At mid-latitudes this is a period of 14 to 17 hours. The maximum wind speed occurs then tmax = 5-7 hours. In this advective case it represents a distance from the coast of L = tmaxVadv, there Vadv is the speed of the advection.

The larger the surface friction is before the oscillation starts, the larger is the deviation vector as can be seen in the theoretical description above. Thus the magnitude of the low-level jet is largest when a convective boundary layer exists (over land in this advective case), and when there are large roughness lengths, both resulting in high surface friction. A large friction-force due to a surface of large roughness length makes the wind speed less than over a surface with lesser roughness length. Hence, the low-level jet oscillation starts when the friction force more or less suddenly disappears when the stratification suddenly gets stable (advection over sea or in the evening). Thus the larger this friction-force vector is, the larger becomes the maximum wind speed during the low-level jet oscillation.

Figure 5 shows a simulation with Blackadar’s theory. For this, ug = 5.3 m/s and vg = 6.3 m/s are used. In figure 5a the veering of the deviation vector and the following changes in wind speed and wind direction are shown. Figure 5b shows the variation of the total wind speed during 9 hours.

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−100 −5 0 5 10 15 2

4 6 8 10 12 14 16

Wind speed in the x−direction, km.

Wind speed in the y−direction, km.

The variation of the wind speed during 9 hours with constant geostrophic wind speed

Vg t = 3 h

t = 8 h

Figure 5a. The variation of the deviation vector together with the geostrophic wind vector and the total wind speed at t = 3 h, and t = 8 h.

1 2 3 4 5 6 7 8 9 10

4 6 8 10 12 14 16 18

Time in hours

Total wind speed

The variation of the total wind speed during 9 hours

Figure 5b. The variation of the total wind speed for 9 hours during the LLJ oscillation.

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2.5 The numerical model 2.5.1 The closure problem

The number of unknowns in the set of equations for turbulent flow is larger than the number of equations. A variable is considered to be unknown if one does not have a prognostic or diagnostic equation defining it.

A quantity can be expressed as a mean value and its deviation from that mean value, called Reynolds averaging. For the horizontal velocities it becomes U =u+u' and V =v+v'. The vertical velocity is W =w+w', the pressure p= p0 + p' and the density 'ρ = ρ0 +ρ . The first equation of motion DU/Dt is

x V p

z f W U y V U x U U t U

⋅∂

=

∂ −

⋅∂

∂ +

⋅∂

∂ +

⋅∂

∂ +

ρ

1 , (13)

where f is the Coriolis term. If the mean value and its deviation are used in the equation it becomes

x p p

v v z f

u w u

y w u v u

x v u u u

t u u u

∂ +

⋅∂

− +

= +

∂ − +

⋅∂ +

∂ + +

⋅∂ +

∂ + +

⋅∂ +

∂ + +

' '

1

) ' ' (

) ' ' (

) ' ' (

) ' ' (

0

0 ρ

ρ

Taking the mean value of each term above and using the fact that the mean of the deviation is zero yields

x v p

f w zu z w u v yu y v u u xu x u u t u

⋅∂

=

∂ − + ∂

⋅∂

∂ + + ∂

⋅∂

∂ + + ∂

⋅∂

∂ +

0

0

' 1 ' '

' '

' ρ

which includes terms of second order moment as u'v', describing the nonlinear interactions between variables that are associated with turbulence. There are six equations describing the atmosphere, the equations of motion, the continuity equation, the thermodynamic equation, the hydrostatic equation and the ideal gas law. But these second order moments give us more than six unknowns. In the expression for these second order moment terms, there are triple order moments as u'v'2 . Thus to express the first unknowns we get even more unknowns. To make the mathematical/statistical description of turbulence easier to handle, one approach is to use only a finite number of equations, and then approximate the remaining unknowns in terms of known quantities. Such closure assumptions are named by the highest order prognostic equations that are retained (Stull, 1988). When some of the third order moments are expressed with prognostic equations and others with diagnostic equations the model is called a 2.5-order closure model. In the equation above for example, u' w' can be parameterized as

z K u w

u M

− ∂

= '

' , (14)

where KM is the turbulent exchange coefficient and is expressed empirically. Now the second order moment has been expressed in terms of the vertical gradient of the mean

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horizontal wind speed. Thus it is a first order closure, and the rest of the second order moments can be expressed the same way.

2.5.2 The MIUU-model

The MIUU model that is used for the simulations is a meso-γ-scale model. It was developed by Leif Enger (1983-) and is used at the Department of Meteorology at the Uppsala University in Sweden. It is a nonlinear, 3-dimensional, hydrostatic and incompressible numerical model where a higher-order turbulence closure scheme is employed. The model has a terrain-following coordinate system and the turbulence is parameterized with a 2.5-level scheme. In the literature it has been well documented, tested against measurements and analytical solutions (Enger and Grisogono, 1997). In particular, the model has been employed for studies of orographic and coastal flows.

It solves the prognostic equations for the horizontal wind components (U and V), potential temperature (θ), specific humidity and turbulent kinetic energy. The other meteorological parameters involved are solved diagnostically every time-step. The best characteristics of the model are nonlinearity and the treatment of turbulence (the 2.5-level scheme).

The topography is introduced in the model by application of a terrain- following coordinate system. The new vertical coordinate η is defined as

g g

z s

z s z

⋅ −

η= , (15)

where s is the height to the top of the model, zg the terrain height and z is the height above the surface. All heights are above sea level. With this coordinate the height over the ground at lower levels is nearly the same as just z-zg but higher up it approaches z. That corresponds to the atmosphere, which is more affected by the terrain near the ground. This is shown in figure 6.

Figure 6. The left figure shows the height in usual height coordinates, and the left figure shows a schematic height over the ground in η-coordinates. (Euromet Homepage)

The equations of motion, the continuity equation, the thermodynamic equation and the hydrostatic equation have to be changed to correspond to the new coordinate.

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The basic equations of the model, transformed to this η co-ordinate system are presented below. For the mean horizontal wind components they become

fV x fV

z s g s x K U

z s

s dt

dU

g g M

g

+

∂ −

− ∂

∂ + Π

− ∂

 ∂



= − θ η

η η

2

, (16) and

fU y fU

z s g s y K V

z s

s dt

dV

g g M

g

∂ +

− ∂

∂ + Π

− ∂

 ∂



= − θ η

η η

2

, (17) where

η

∂ + ∂

∂ + ∂

∂ + ∂

= ∂ W*

V y U x t dt

d . (18)

U and V are the new quasi-horizontal wind components, f is the Coriolis parameter, Ug and Vg are the geostrophic wind components, g is the acceleration due to gravity, KM is the turbulent exchange coefficient for momentum, W* is the vertical wind in the terrain-following coordinate system, and Π is the scaled pressure (Exner function), defined as

p d c R

p p

c p

/

00

 

= 

Π . (19)

Here, p is the pressure, p00 is a reference pressure, cp is the specific heat at constant pressure, and Rd is the gas constant for dry air.

The potential temperature θ is obtained from

r H

g

z K s

s dt

d σ

η θ η

θ +

 ∂



= −

2

, (20)

where KH is the turbulent exchange coefficient for heat, and σR includes the radiative heating/cooling rate as well as enthalpy sources/losses coming from phase changes of the water vapor.

Since the new set of wind components differs from the ordinary Cartesian ones, the equation of continuity is different and becomes



 

∂ + ∂

= −

∂ +∂

∂ +∂

y V z x U z z s W y V x

U g g

g

1

η (21)

in the terrain-following system. With the hydrostatic approximation to the third equation of motion for the vertical velocity W* is written as

v g

s z g s

θ η

⋅ 1

⋅ −

∂ = Π

∂ . (22)

In contrast to the original third equation of motion several small terms have been omitted in carrying out the coordinate transformation (Pielke and Martin, 1981). Thus this equation is only valid if the terrain slope in the model always is much below 45°.

For moisture, the equation of the mixing ratio R becomes

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η

∂ η

 ∂



= − R

z K s

s dt

dR

R 2

g

. (23)

The equation for twice the turbulent kinetic energy Q2 is given by







 

∂ + ∂



 

 ∂



 + −



 

 ∂



= −

2 2 2

2 1

2 2

3 2 5

η η

λ η η α

V K U

z s

s Q Q

z s

s dt

dQ

M g g

λ η

θ

θ 1

3 0

2

2 B

K Q g z s

s

H g

∂ −

− − , (24)

where the last term gives the dissipation. The principal difficulty with second-order closure modeling is to determine the length-scale λ together with six empirical closure constants, including α1 and B1.

For more information see e.g. Enger (1986) and Andrén (1990).

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3. Baltic Sea

3.1 Advection and stability

The Baltic Sea is a semi-enclosed sea situated at relatively high latitudes between the Swedish east coast and the Baltic States. Air is advected from land over the sea for almost every wind direction since it is almost surrounded by land. Especially in late autumn when the water temperature still is relatively warm while the temperature over land can fall well below zero, the stratification can get unstable in the lowest parts of the boundary layer when cold air is advected out over the warmer water. This occurs even in early autumn and winter, but the water surface gets colder and the temperature difference decreases in winter except for some specific wind directions. The temperature over land can in winter be as low as 20 degrees below zero but in that case the advection often is very weak, otherwise the temperature would not have been that low (cooling due to radiation). But in the case of air coming down from the Arctic Sea and northern Russia the temperature contrast can be huge, and subsequently there will be strong convection and a lot of snow will fall along the Swedish east coast. Turning to spring and summer the land is heated by the sun and can quickly get much warmer than the sea surface. The great heat capacity of the sea and the mixing of warmer surface water with colder underlying water make the heating of the sea slow. It takes several months to heat up the sea, thus in spring and early summer the temperature difference can be huge. And in summer the land is effectively heated during the day while the temperature over the sea is nearly constant. In these parts of the year the warm air that is advected out over the colder sea is greatly stabilized in the lowest parts. This is probably the fact for more than half of the year.

3.2 IBL-growth, low-level jet and sea breeze circulation

In the stable stratification over the sea mentioned above, a “quasi-frictional decoupling” (section 2.4) often occur. This leads to super-geostrophic wind speeds.

Depending on wind direction and wind speed (section 2.4), the maximum wind speed occurs at different places.

A sea breeze develops often at the coast in spring and summer, but most probably strongest in the beginning of the summer. Because then the insolation is strong and the temperature difference large, warming the land and creating convection.

The stable stratification over the Baltic Sea during more than half of the year is caused by a stable thermal internal boundary layer, slowly growing with distance from the coast. The highly stable stratification in the IBL makes the wind speed to decrease in the lowest parts when offshore flow is present. Källstrand (1997) also noticed this. The wind speed will increase initially followed by a decrease when the IBL-height is enough high so that the wind field can be affected by the stability.

Doran and Gryning suggest that the wind field will respond like this and they have also noticed it in measurements from the Öresund strait between Sweden and Denmark. This phenomenon will be investigated later in section 5.2 and 6.7.

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4. Simulations

The purposes with this investigation can be summarized as follows:

1. To find the different parameters which play an important role in determining whether the wind speed will decrease or increase after the passage of the coastline in offshore flow.

2. If the criterion for decreasing wind speeds is fulfilled it is of interest to find an expression for the distance to where the wind speed will decrease, provided that an initial increase was present.

3. An investigation of Lyon’s index for sea breezes (described earlier) will be done using data from the model simulations.

4. Conclusions about the effect the creation of a low-level jet has on the wind field near the coast will be made.

Here the first two points in the list above are the most important and the main purpose is to find these parameters and expressions.

For simulations the 2-dimensional meso-γ-scale MIUU-model is used. An expanding grid is used and the runs are schematic and made to isolate important parameters. The model domain is 211 km in the horizontal with the coast situated at 58 km, thus there is 153 km of water surface and 58 km of land. In the vertical the domain is 10 000 m with the finest resolution at the surface, approximately 1 m between the grid points. At the 10 000 m level the spacing is 250 m. The number of grid points is 129 × 39. Around the coast the spacing between the grid points is 1 km, whereas further inland and after a distance of 25 km outside the coast, the spacing between the grid points expands to 2 km. In the Öresund case described later, the grid is changed in the horizontal. 75 grid points with spacing of 1 km are used. The sea is 25 km wide with 25 km of land on each side.

4.1 Parameters to change in the 2-dimensional MIUU-model

In the simulations a lot of parameters are changed to see which of them that plays the most important role in describing the wind field. The following parameters were used in the model runs:

• The surface temperature over land – sea surface temperature:

Using different temperatures and differences between the two.

• Roughness length over land:

The roughness lengths 0.02, 0.1 and 0.5 m were used.

• Roughness length over sea:

Put to 0.00025 m by the model.

• Topography:

Different topographies near the coast but no high mountains, which can affect the wind field with for example catabatic winds.

• Cloudiness:

Clear, cloudy and overcast are used.

• The characteristics of the air mass, temperature/humidity:

Different types of air masses are used, meaning different combinations of temperature and humidity throughout the atmosphere.

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• Geostrophic wind speed and direction:

Different geostrophic wind speeds and directions, and some runs with a veering of the wind vector due to a thermal wind.

• Time-step

The time-step 12 s was chosen, because shorter time-steps gave a much longer simulation time, whereas longer time-steps gave an oscillation in the model results.

• Day of the year

Winter, spring and summer days were used.

• Number of grid points

As mentioned above a 2-dimensional version of the model with 129 × 39 grid points is used. The finest resolution is around the coast. One exception is the Öresund case with constant spacing and 75 × 39 grid points.

• Latitude and longitude

These parameters are changed to represent the different areas in comparison with the simulations.

The most important parameters have been the following:

Mean wind speed.

Wind direction.

Potential temperature.

The height of the boundary layer inversion.

Stratification.

The values of temperature and humidity for different air masses are calculated with the aid of statistical mean profiles for the specific month, see Appendix 2 for values used in the simulations. Mechanisms not included are complex wave states, for example young wind driven waves and incoming swell. But this seems to be most important for very weak winds according to Mahrt and Vickers (2000).

5. Measurements 5.1 The Baltic Sea case

During 3-4 may (1997) a lot of aircraft measurements were made over the Baltic Sea along the Swedish coast and around the Island of Gotland. The Baltic Sea is almost surrounded by land, with a typical distance from coast to coast of 200 – 300 km. The island Gotland is situated about 100 km from the Swedish mainland. The main difference between the two measurement days is the strength of the geostrophic wind.

For the sea breeze day (4 May), the geostrophic wind speed is weak, and there is a sea breeze with winds nearly opposite to the geostrophic wind direction near the surface at the coast. For the other day, according to Källstrand (1997), the slow growth of an internal boundary layer over the sea gives a wind speed decrease with distance from the coast. During both days, the wind field modifications over most Baltic Sea are primarily caused by land-sea transition. (Källstrand, 1997)

For measurements over the sea an aircraft is used. The measurements are performed by the UK Met Office, within the framework of the EU project STAARTE, with the MET Research flight C-130 aircraft. Position of the aircraft is measured with GPS. The area and the flight legs are shown in figure 7. The speed of the aircraft was

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about 100 m/s. Measurements include wind speed and temperature. Other measurements are made at Östergarnsholm (an island outside the east coast of Gotland) where a 30 m tower is situated. Measurements are made with slow response sensors for temperature, wind speed and direction at the heights above the tower base of 7, 12, 14, 20 and 29 m. Also pilot balloons (its movements followed by a theodolite), tethered balloons and radio soundings are used giving profiles of wind speed and direction. (Källstrand, 1997)

Figure 7. The Swedish east coast is to the left and Gotland to the right. The drawn lines represent flight-legs. (Källstrand, 1997)

On 3 May the geostrophic wind speed was about 15-17 m/s and the wind direction 300 - 320° as an average during the day. The wind speed at Östergarnsholm increases from 2 m/s at 0000 LST to 12 m/s at 1200 LST the same day. The maximum temperature at 2 m height over the Swedish mainland was 285° K and the sea surface temperature was 277° K. On 4 May the geostrophic wind speed decreases to 4 m/s around noon with a direction of 290°. The temperature over the Swedish mainland is 286° K, and the sea surface temperature the same as earlier, 277° K. During the two days only a few cumulus clouds grew up. The roughly estimated characteristics of the air mass are taken from plots and information in Källstrand (1997), which I refer to for more information. The values are shown in Appendix 2.

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5.2 The Öresund case

Öresund is a strait situated between the Malmö region of Sweden and the Copenhagen region of Denmark, near 56° N and 13° E. The coastlines on the opposite sides of the strait are roughly parallel. Measurements are made over an 80-km extent, ranging from Borlunda in Sweden to Risö, Denmark. The area is shown in figure 8.

Figure 8. Map over the area around Öresund with Copenhagen to the west of the strait. The figure shows different measurement sites, 1) is Risö, 2) Köpenhamn, 3) Gladsaxe, 4) Charlotenlund, 5) Middelgrunden, 6) Barsebäck, 7) Furulund and 8) Borlunda. The letters show where offshore measurements have been made with the ship Aranda.

Over the water, measurements were made from the ship Aranda, determining the wind velocity, wind direction, temperature, humidity and the sea surface temperature.

Over land, tall masts (over 100 m) are used to measure wind and temperature profiles.

Pilot balloons, Doppler sodars and radiosondes were also used for this purpose.

Furthermore an airplane measured temperature between 50 and 300 m.

Figure 9 shows the measurements of the wind speed and the expected behavior drawn with a curve between the measurement points. Figure 10 is a plot from Andrén (1989), showing vertical profiles of measured values for wind speed, wind direction and potential temperature at Borlunda, site 8 in figure 8. This plot has been used to create an initial profile for the simulation. Doran and Gryning (1986) use 13° C as the temperature for the sea surface and it is supposed to be nearly constant except perhaps for the shallow water areas very near the coasts.

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Figure 9. Measured values of the wind speed at 10 and 100 meters height in the area shown in figure 8.

The shaded area represents land. The drawn lines should be seen as an assumption based on simulations. (Doran and Gryning 1986).

Figure 10. Measured profiles of wind speed, wind direction and potential temperature at Borlunda, site (8) in figure 8. After Andrén (1989).

5.3 The USA case

The data is collected over the Atlantic coastal water off the Outer Banks near Duck, North Carolina. Low-level aircraft data from 37 flights on 35 days, at an average height of 15 m above the sea surface were performed. A sonic anemometer was also used, which operated approximately 18 m above the water on a tower at the end of a 570 m pier. Thirteen flights measured horizontal and vertical structure in the lowest few hundred meters above the sea surface in the first 10 – 20 km offshore. Other types of flight patterns include a series of flight tracks parallel to the coast and 100 km transects perpendicular to the coast. Measurements are made for every 25 m in the

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vertical starting at 10 m, and for every 500 m offshore in the horizontal starting at the coast. Figure 11 shows the area where the measurements were made.

Figure 11. The area around Outer Banks where the measurements were made. The mean flow is from southwest in all the experiments used in this investigation.

6. Results

The most important parameters describing the wind regime in coastal areas turned out to be the stratification and the geostrophic wind speed. Thus the surface temperature over land, the sea surface temperature and the temperature difference between land and sea are all very important because they affect the stability. Also the cloudiness, day of year, and to some extent the air mass properties, are factors affecting the stability. The roughness length over land plays a large role in the formation of a low- level jet or a sea breeze. The wind speed gradient becomes larger with larger roughness lengths, giving higher friction against the surface and larger deviation vector in the low-level jet case (described in section 2.4). In some cases it can affect the stability so that the wind field behavior changes. The influence of topography is not studied here. Wind directions in the simulations are between 240 and 290°, corresponding more or less to offshore flow perpendicular to the coast.

From the simulations it appears that it is only when there is stably stratified air over the water and unstably stratified air over land that there is a decrease in wind speed off the coast. Thus, this phenomenon should only occur during daytime in offshore flow. The height of the unstable layer seems to be of minor importance. In near neutral stratification a decrease in wind speed is rarely observed. Furthermore the stratification of the stable layer that forms over the sea must have a value above Ri = 0.1. This will be shown in section 6.1. In mid-latitudes, this criterion is fulfilled many days during the spring and summer when warm continental air flows out over the relatively colder sea and there also exists a convective boundary layer over land. In the tropics one would expect this to be a very common phenomenon during daytime since the insolation is large year round, and thus the land surface is heated much more

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than the water surface (described in section 3.1). The stability can also be compared to the height of the IBL-layer since a large stability gives a low IBL-height and vice versa. This is shown in section 6.2. Furthermore, if the wind speed is low to moderate the Lyon’s index for sea breezes must be above the value of 10. Otherwise there might be a sea breeze circulation. This index will be verified in section 6.3.

When the above criterion is fulfilled the wind regime behavior can be split into three general parts. In figure 12, Ri > 0.1 and the IBL-height is h 55 m. Here the wind speed starts to increase for at least 1 km, thus X1 > 1 km. Then the wind speed decreases over a distance of X2 ≈ 5-50 km. At the distance of X3 the wind speed again increases. This is because of the decrease in stability further off the coast (described later). As a summary U0<U1, U1>U2, U2<U3.

Figure 12. The first case with Ri>0.1 and h≈55 m. U0<U1, U1>U2, U2<U3.

In figure 13, Ri >> 0.1 and h ≈ 30 m. Here the stable internal boundary layer is too shallow to affect the wind speed. Thus the distance offshore where increased wind speed (X1) would be observed can be 20-30 km or more. That is too far offshore to be called a coastal area. The more stable the stratification, the larger the distance of increased wind speed. In coastal areas this appears as increased wind speeds all down to the lowest meter of the wind field when there is a very stable boundary layer. At last the wind speed decreases when the IBL-layer becomes deep enough. The distance X2 is now larger than in the former case and it commonly exceeds 100 km. Then the wind speed again increases over a distance X3 far offshore and this higher wind speed is constant.

Figure 13. The second case with Ri >>0.1 and h≈30 m.

The third case in figure 14 is somewhat uncertain. It is near the limiting values that determine whether or not there will be an increase in wind speed. Here Ri is near the critical value of 0.1 and h ≈ 60 m. When the stability decreases to just 0.095 there will not be a decrease in wind speed, but if the value is near but still above 0.1 the following can be expected. The distance X with increasing wind speed is short, less

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than 1 km. Similarly, for the distance of decreasing wind speed X2, just a short distance of 1-5 km. The stability quickly decreases to below Ri = 0.1 and the wind speed again increases over a distance X3.

With Ri < 0.1 and h >> 60 m there can be a fourth case. Here the wind speed, as mentioned earlier, increases immediately after the passage of the coastline and is kept constant without any decrease.

Fig 14. The third case with Ri≈0.1 and h≈60 m.

I refer to the flowchart in section 7.1 for instructions in determining the wind field.

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6.1 The stability criterion

0 1 2 3 4 5 6 7 8 9 10 11

0 0.05 0.1 0.15 0.2 0.25

Comparison between different Richardsson number for decreasing and increasing wind outside the coast

Richardsson number

Different cases

The gradient Richardson number is calculated using values from the simulations. The gradients are calculated at the height of 10 m. In figure 15, the results from ten runs with no decrease at all in wind speed and ten runs with a decrease in wind speed somewhere off the coast are plotted. The two cases seem to have a limit at approximately Ri = 0.1. All cases with a decrease in wind speed somewhere off the coast are above that value, and all cases with no decrease at all are below.

Figure 15. The distribution of simulated cases with different Richardson values. 10 cases each for no decrease at all (x) and a decrease (*) in wind speed somewhere outside the coast. The Öresund case is marked with an ‘o’. There is no value for the Baltic Sea case since there are no ground-based profiles available over the sea far from the coast.

6.1.1 A case study

The figures 16 and 17 show two almost identical simulated cases. The only difference is the cloudiness that shifts from partly cloudy in the first case to overcast in the second. This difference gives a slightly lower temperature over land in the second case, which reduces the stability over the sea (and instability over land). In the first case there is a decrease in wind speed and Ri=0.106, whereas in the second case with there is no decrease and Ri=0.094.

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40 50 60 70 80 90 100 110 0

10 20 30 40 50 60 70

1 1

2 2

3 4

4 5

5

6

6

7 MIUU model: MEAN WIND SPEED (m/s), Directory:test4

height z (m)

Date: 960626 Time: 14LST Y: 0km vg: 8.0m/s Max: 7.56 m/s Min: 0.00 m/s 0 1 2 3 4 5 6 7 8

Figure 16a. The wind field at the coast when Ri = 0.106 over the sea; distance (35-115 km) versus height (0-70 m) with the coast situated at 58 km where the sharp black color ends.

16 16.2 16.4 16.6 16.8 17 17.2 17.4 17.6 17.8 18

0 10 20 30 40 50 60 70 80

MIUU model: POTENTIAL TEMPERATURE IN C, Directory:test4

Time: 14LST

Date: 960626 X: 79km Y: 0km vg: 8.0m/s Max: 17.68 Min: 16.01

height z (m)

.

Figure 16b. The potential temperature profile over the sea for the wind field in figure 16a; temperature (16°-18°) versus height (0-80 m) at the distance of 79 km (21 km outside the coast).

References

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