Influence of fog on stratification and turbulent fluxes over the ocean

Transkript

1 Examensarbete vid Institutionen för geovetenskaper ISSN Nr 8 Influence of fog on stratification and turbulent fluxes over the ocean Linda Lennartsson

2 Abstract In this thesis a case of advection fog over the Baltic Sea is studied. The period examined is from June 5 th to 7 th Data is taken from the instrumented mast, situated on the island Östergarnsholm, a small and flat island without trees outside of Gotland. From the measurements among others the heat flux, relative humidity and temperature are analyzed. In the evening June 5 th 1995 the fog is advected in over Östergarnsholm. This can both be seen from the increasing relative humidity and the decreasing temperature. Before the fog arrived the boundary layer was stably stratified. This stratification quickly changed to neutral as the fog reaches Östergarnsholm. After careful evaluation the neutral stratification is shown not to be neutral at all. The stratification closest to the ground up to 15 meters is unstable and above the stratification is stable. From this the conclusion is made that the fog is low only 15 meters high during this period. At noon June 6 th the air temperature decreases dramatically below the sea surface temperature at the same time as the relative humidity increases up to 1%. The fog is now thick enough to have most of the outgoing radiation coming from the top, which decreases the temperature a few degrees. As the stability is investigated it shows unstable stratification up to the highest level (28 meters). The assumption is made that the fog is at least 3 meters deep. Also the normalized standard deviations for temperature and vertical velocity are examined to find out if they behave as the variation in the undisturbed boundary layer. 2

3 Sammanfattning av Påverkan av dimma på skiktningen och turbulenta flöden över hav I detta arbete studeras ett fall av advektions dimma över Östersjön. Perioden undersökt är från den 5 till den 7 juni Mätmasten står på ön Östergarnsholm, en liten och låg ö utan träd utanför Gotland. Ur mätningarna fås bl.a. värmeflödet, relativa fuktigheten och temperaturen. På kvällen den 5 juni 1995 advekteras dimman in över Östergarnsholm. Detta ses både från att relativa fuktigheten stiger och att temperaturen sjunker. Innan dimman anlände var gränsskiktet stabilt skiktat. Denna skiktning ändrades snabbt till neutral då dimman når fram. Denna till synes neutrala skiktning visade sig efter noggrannare undersökning att inte alls vara neutral. Skiktet närmast marken upp till 15 meters höjd visade sig vara instabilt och däröver var det stabilt. Utifrån detta dras slutsatsen att dimman är låg endast 15 meter hög under denna period. Vid 12 tiden på dagen den 6 juni sjunker lufttemperaturen dramatiskt under ytvatten temperaturen samtidigt som relativa fuktigheten stiger upp till 1 %. Dimman är nu så pass tjock att den största delen av utstrålningen sker ifrån toppen vilket sänker luft temperaturen flera grader. Då stabiliteten undersöks visar den sig vara instabil skiktad ända upp till högsta mät nivån (28 meter). Antagandet görs att dimman är minst 3 meter djup. Även normaliserad standard avvikelse för temperaturen och den vertikala hastigheten undersöks för att ta reda på om de uppvisar samma variation som i det ostörda gränsskiktet. 3

4 Table of contents 1 Introduction Theory List of symbols Turbulence Monin-Obukhov similarity theory Standard deviation for vertical velocity and temperature Effect of fog on the turbulence structure Spectrum Measuring site and measurements Measuring site Measurements Results Overview The period before fog, (period I) The unstable period, (period III) The neutral period, (period II) Discussion and Conclusion Acknowledgements References

5 1 Introduction The purpose of this thesis is to investigate a case of advection fog and its effect on the turbulence structure as it reaches Östergarnsholm. This case will illustrate how fog may influence the stability and the turbulent fluxes over the ocean. The period investigated is June 5 th to 7 th Data used to analyze these days are taken from the measuring site Östergarnsholm. The site used is situated on the island of Östergarnsholm, which is a small and flat island east of the bigger island Gotland. The measuring mast stands on the tip on the south side of the island, equipped with profile measurements for wind and temperature, turbulence measurements and humidity measurements. A buoy measures the surface temperature 4 km from the site out in the ocean. From the measurements 3 minutes mean are calculated. The fog analysed in this study is probably developed over the ocean and is a so-called advection fog, i.e. a fog developed from warm and humid air cooled of by the colder ocean. In this case the fog is developed over the Baltic Sea and reaches Östergarnsholm in the evening on June 5 th. Before the fog reaches Östergarnsholm the stratification is stable. The stability parameter changes sign and become near neutral or slightly unstable as the fog arrives. At the same time the heat flux decreases. The neutral time period is studied more in detail and some complications are discovered. After the neutral time period the stratification turns unstable as the fog develops more and grows vertically. Up to the highest measuring level (28 meters) the stratification becomes unstable, which indicates that the fog reaches that height. During the night of June 6 th the surface layer turns stable again and the fog is dissolved. 5

6 2 Theory 2.1 List of symbols w ' θ ' u ' deviation from vertical velocity deviation from temperature deviation from horizontal velocity w 'θ kinematic heat flux u 'w' kinematic momentum flux 1 u ( ) 2 * θ * σ w σ θ u'w' that is the friction velocity, characteristic velocity w' θ that is the temperature scale, characteristic temperature u * standard deviation for vertical velocity standard deviation for temperature σ w u * σ θ θ * normalized standard deviation for vertical velocity normalized standard deviation for temperature 2 u ' variance of horizontal velocity ρ c p T o g density for air, value kg/m³ specific heat capacity for air, value J/kg K surface temperature gravitation, value 9.82 m/s² k von Karmans constant, value.4 z height L Monin-Obukhov length z L stability parameter H o τ c p ρ w' θ, sensible heat flux 2 ρ u *, stress g T buoyancy parameter 6

7 2.2 Turbulence The turbulent motion consists of eddies in different sizes. They are three-dimensional and interact somewhat with each other. The so called cascade process is very characteristic for turbulence. Larger eddies breaks down into smaller once and these smaller eddies breaks down to even smaller etc, down to viscosity and heat. Another characteristic of turbulence is the stochastic movement, which are irregular and random movements. The motion is also diffusive; an example of this is that turbulence transports momentum, heat and moisture. There are two different sources of turbulence. One source is when cold air flows above a warmer surface and create convection at the ground or the air is heated during the day. Mechanical turbulence is created when the mean wind speed is decreased by the presence of the ground and a wind gradient is formed. The turbulent flux examined here is the kinematic heat flux, is ρ c p w' θ calculated from the measured value w ' and θ '. w ' θ. The sensible heat flux 2.3 Monin-Obukhov similarity theory Monin-Obukhov similarity theory, also sometimes called surface layer similarity is valid in the surface layer. It describes the properties of turbulence within the surface layer. The surface layer is a constant flux layer and with this knowledge the fluxes can be described by measurements from one level. The parameters that influence the surface layer according to Monin-Obukhov similarity theory are the buoyancy parameter g T, the surface heat flux H, the stress τ and the height z. From dimensional analysis following expression is received. z g k H ρ c p u 3 * T = z g k u T 3 * ( w' θ ) (2.1) Where 3 u* T L = (2.2) g k ( w'θ ) From this it is concluded that equation (2.1) is equal to z L, the stability parameter. Equation (2.2) shows the expression for Monin-Obukhov length that does not vary vertically within the surface layer because the characteristic velocity and temperature are 7

8 constants. The similarity is valid down to approximately the value of -1 for the stability parameter, with a larger negative value the buoyancy is to great. The stability parameter z L is a function of height, z in meters and Monin-Obukhov length, L also in meters. Monin-Obukhov length is dependent on the kinematic heat flux w ' θ. When w ' θ >, L is negative unstable, w ' θ <, L is positive stable stratification. As w ' θ = ±, L is ± neutral stratification. Monin-Obukhov similarity for normalized standard deviation is an expanded theory developed Following equations were produced. σ w u * = F ( z 1 ) L (2.3) ( z ) σ θ = F θ 2 L (2.4) * Equations (2.3) and (2.4) are evidently unambiguous functions of the stability parameter Standard deviation for vertical velocity and temperature The expressions for standard deviations are taken from (Johansson et al 21). These values are compared with the measured ones in the Results section. During stable conditions the surface layer is shallow, often only a few meters. To analyze the turbulence structure in terms of Monin-Obukhov similarity measurements have to be done close to the surface. For the convective surface layer an empirical expression is used and for the stable boundary layer a constant value is used both for the standard deviations of θ and w. For the Stable Boundary layer a constant value is used. σ w u * = 1.2 (2.5) Where u* is the friction velocity and σ w is the standard deviation for vertical velocity. 8

9 σ θ θ * = 3. (2.6) Where θ * is the temperature scale and σ θ is the standard deviation for temperature. During unstable stratification following expressions are valid. σ w u * z = 1.2 * 1 3 L 1/ 3 (2.7) σ θ θ * z =.95 * L 1/ 3 (2.8) 2.4 Effect of fog on the turbulence structure Figure 2.1a-b. The general development of fog. Figure (a) shows the stable stratification before the fog develops. Figure (b) shows the period when fog is developed and cooling at the surface by outgoing radiation starts, which create the mixing within the fog. The stable boundary layer theory can be used to describe fogs development. The stratification before fog is shown in figure 2.1 (a) where the potential temperature increases with height, i.e. stable stratification. 9

10 The mist is starting to form within the stable boundary layer. Mist sometimes has greater relative humidity in the lower regions than in the higher, so the top is diffuse with no sharp edge. Still at the beginning the heat loss is coming from the surface. The mist becomes thicker and denser. As it thickens the net radiative heat loss will be generated more from the dense part of the fog and less from the ground. When the fog becomes optically thick enough the radiative heat flux is greater at the top of the fog than at the bottom. Now the cooling is at the top of the fog and cold thermals are created. These cold thermals sink from the top to the bottom and create a mixing of the fog as shown in figure 2.1(b). The fog becomes more and more uniform vertically and the top is more defined with a sharp edge. With a more defined top more outgoing radiation is concentrated from that area, which increases the mixing of the fog. A lot of the solar radiation is now reflected at the top of the fog and the radiative cooling continues. At this moment the fog starts to behave like a stratocumulus cloud and follows Mixed Layer scaling. The thermals mix the fog and make it uniform, which create a neutral stratification or even slightly unstable. The fog examined in this study is an advection fog and once it is formed it behaves like the fog explained above. 2.5 Spectrum Spectral analysis is used to illustrate turbulence energy as a function of frequency. Energy spectra are usually calculated for u', v ', w ' and θ '. Momentum, heat and moisture are different vertical fluxes that are of great interest in meteorology, which can be represented by co-spectra. Co-spectrum is used to show how two simultaneous time series behaves, that is for example w ' and θ ' heat flux or w ' and u' momentum flux. Figure 2.2 Co-spectrum for heat flux where n is the frequency. During unstable stratification co-spectra is positive and during stable stratification co-spectra is negative. 1

11 By knowing frequency and fluctuations co-spectra can be calculated. The frequency, n is measured in Hz. u' 2 ρ () t 2 Φ ( ω) cos( ω t) dω = (2.9) Equation (2.9) shows the Fourier integral theorem (Högström, Smedman 1989), where Φ ( ω) is the energy spectra and ω = 2 π n. With time, t = the auto-correlation function ρ t will be equal to one. () ( ω) dω 2 u' = Φ (2.1) For two variables ( w' and θ ') a co-spectra can be calculated, which contain a real and an imaginary part, representing the co-spectrum and the quadrature-spectrum. Integrations over all frequencies of co-spectra give the total fluxes. The energy for different eddies is plotted in the figure (2.2) for respective frequency. The figure shows a schematic picture of co-spectrum for heat flux. The area below the curve is the total flux, in this case the total heat flux. If the integrated area is positive the stratification is unstable, if it is negative the stratification is stable and if it is zero the stratification is neutral. 11

12 3 Measuring site and measurements 3.1 Measuring site Figure 3.1 Shows the measuring site the island Östergarnsholm in the Baltic Sea outside of Gotland. The measuring site is on Östergarnsholm, an island situated 4 kilometers east of the bigger island Gotland in the Baltic Sea, see figure 3.1. It is a low island with no treas. The measuring mast is a 3-meter high tower located on the south side of the island. The base is located 1 meter above the mean sea level. Outside the peninsula the slope of the seafloor is approximately 1:7, an optimal slope when considering disturbances from incoming surface waves. The area with undisturbed fetch is over 15 km in the sector The measuring mast is on Östergarnsholm but because of the dispersion of fluxes, the source region of the turbulent flux is some distance outside the island and has been calculated. The wind is blowing from the sector 8-22 during the measurements used in this investigation, this means that the turbulent fluxes are from over the ocean. 12

13 3.2 Measurements There are two different categories of instruments, slow response instruments also called profile instruments and fast response instruments, called turbulence instruments. For the turbulence instruments the typical accuracies of the horizontal and vertical wind speeds are ±.1 m/s, for temperature ±.1 C and moisture ±.1g/kg. For the slow response instruments following accuracies are obtained, mean wind speed ±.2 m/s, mean temperature ±.2 C and mean moisture ±.2 g/kg. To measure profiles for temperature, wind speed and wind direction the tower is equipped with slow response sensors at the heights 7, 11.5, 14, 2 and 28 meters above the base. With modified cup-anemometers the wind speed and direction are measured. The anemometer used is a Casella-anemometer with modification done by MIUU (institute of meteorology at Uppsala University). The instrument consists of a light weighted cup and a small and light wind vane. Temperature is measured with a platinum sensor with 5 ohm at 2 C. At the height 8 m above tower base the humidity is measured. Turbulence measurements are performed with instruments developed by MIUU. The instrument is based on the hot wire principle and is located at 9 meters height. Another type of turbulence instruments are the Sonic-anemometer, which are placed at the heights 16 and 24 meters. The surface water temperature is measured with a waverider buoy, 4 km south-southeast of the mast above an ocean depth of 4m. The buoy is owned by the Finish Marine Research Center. The average time for measurements at Östergarnsholm is 3 minutes. 13

14 4 Results 4.1 Overview In this section an overview over the three days is shown to receive a general view over the case. Figures of ( w 'θ ), z L, relative humidity and temperature are shown for these days. Also the normalized standard deviation is given both for the vertical wind speed ( w' ) and temperature ( θ ). The measuring period of 3 days is divided into 3 parts according to stability. 2 Heat flux [ W m 2 ] I II III June 5 th June 6 th June 7 th Time Figure 4.1 The variation of the heat flux is shown at the height 9 meters during the period June 5 th to 7 th The stratification during the 3 periods is: stable, near neutral and unstable respectively as can be seen in figure 4.1. The figure shows the heat flux as a function of time. 14

15 2 1 z/l Time Figure 4.2 The stability parameter z/l at the height 9 meters for the period June 5 th to 7 th When calculating u * imaginary parts appeared that have been eliminated, see the missing measurements. The stratification is stable at the beginning of the measurements, on June 5 th from 1 p.m. until 9 p.m. (period I). In figure 4.1 it is seen that the heat flux is negative during this time period, which indicate stable stratification. The stability parameter z L in figure 4.2 shows positive values from 1 p.m. until 9 p.m., which again indicates stable stratification. 1 Relative humidity [ % ] Time Figure 4.3 The relative humidity during the period of June 5 th to 7 th

16 18 Temperature [ C ] air temperature at 5 different heights sea surface temperature Time Figure 4.4 Air and sea surface temperature from June 5 th to 7 th The relative humidity is shown in figure 4.3, it is around 7 % in the beginning but at 8 p.m. the humidity starts to increase. At the same time the temperature begins to decrease almost down to the same temperature as the ocean surface temperature, see figure 4.4. From these observations it is concluded that around 8 p.m. on the 5 th of June the cold and humid fog is advected in over Östergarnsholm. The fog is an advection fog, developed by warm moist air transported over colder ocean. The ocean cools the air and the relative humidity increases. Soon the fog is developed. Not long after the cold and humid air reaches Östergarnsholm a time period of near neutral stratification is observed. The near neutral period (period II) begins right before 11 p.m. on the 5 th and ends at 11 a.m. on the 6 th of June. This is observed in figures 4.1 and 4.2 where both the heat flux and stability parameter are close to zero. Under the section neutral period (period II) some complications are presented and discussed for this time period. At 11 a.m. on the 6 th of June the stratification turns unstable, i.e. z L becomes negative (see figure 4.2). The relative humidity starts to increase at the same time up to 1% (figure 4.3) and the vertical extent of the fog increases. After the unstable period (period III) with fog the stratification turns back to stable. The stability parameter at midnight is again positive (figure 4.2). The relative humidity decreases (figure 4.3) and the temperature increases (figure 4.4) at 3 a.m. on June 7 th and the fog is dissolved. 16

17 1 8 measured values theoretical values σ θ / θ * z/l Figure 4.5 The normalized standard deviation of temperature a function of the stability parameter at the height 9 meters. During the unstable period for both measured and theoretical calculated values absolute values are shown. The solid curve is taken from Johansson et al (21). Figure 4.5 shows the theoretical and measured values for standard deviation of temperature normalized with θ * (the temperature scale) as a function of stability ( z L ). The solid curve in the figure is the curve given by Johansson et al (21). For the unstable side absolute values are shown. The values shown as dots in the figure are the measured normalized standard deviation values. The equations used are described in theory section For the stable boundary layer, when the stability parameter is larger then zero the often used value is taken from equation 2.6 with the constant value of 3.. When the stability parameter is less then zero, i.e. the convective boundary layer values calculated by equation 2.8 are used. 17

18 3 2.8 measured values theoretical values with constant 1.2 theoretical values with constant σ w / u * z/l Figure 4.6 The normalized standard deviation of vertical velocity as a function of stability parameter at 9 meters height. The broken curve is a theoretical calculated curve with the constant 1.5 and not 1.2 (solid curve) as taken from Johansson el al (21). Figure 4.6 shows the standard deviation for the vertical wind normalized with the friction velocity ( u * ) as a function of the stability. The solid curve represents as before the curve given by Johansson et al (21) and the dots represents the measured values. The theoretical values are calculated by expressions shown in theory section For the stable values equation 2.5 is used with the constant 1.2 and for the unstable part equation 2.7 is used. 18

19 4.2 The period before fog, (period I) The air temperature over the Baltic states and Gotland was up to 3 ºC but the water temperature was only around ºC the month before June 5 th, which create a very stable boundary layer over the Baltic Sea and Östergarnsholm (Smedman et al. 1997). The stratification is stable at the beginning of the measurements on the 5 th of June as it also was the case during the whole month before meters 11.5 meters 14 meters 2 meters 28 meters water temperature 15 Temperature [ C] Time Figure 4.7 The air temperature at 5 different levels and sea surface temperature during stable conditions on the 5 th of June. 19

20 Up to around 9 p.m. on the 5 th of June the stratification is stable, z L is larger then zero as is seen in figure 4.2. From figure 4.7 the stable stratification is also observed. The air temperature is warmer then the sea surface temperature and also the temperature increases with height, this indicating a stable stratification. The figure shows that the temperature starts to decrease at 8 p.m. the same time as humidity increases. The influence of the fog on the air is first seen at the lowest level where the temperature decrease begins. The temperature levels above will soon after follow the decrease. The water temperature is at a constant value around 12 C during this period. As the air temperature decreases it almost reaches the same temperature as the sea surface. During the stable period the heat flux is negative, see figure 4.1. This continues until 11 p.m. June 5 th as it then increases up to zero. When the heat flux is negative the heat is transported downwards by turbulence. Relativa humidity [%] Time Figure 4.8 Relative humidity for the stable period and the beginning of the period when fog arrives on June 5 th. The relative humidity is shown in per cent. Between 1 p.m. and 8 p.m. on June 5 th the relative humidity is below 8%. At 8 p.m. the relative humidity starts to increase rapidly and within two hours it is already above 9%, which is an indication of the fog reaching Östergarnsholm. 2

21 2 x nc wθ (n) frequency, log n [s 1 ] Figure 4.9 Co-spectra for the sensible heat flux during stable stratification on June 5 th at 9 meters height. Figure 4.9 shows a co-spectrum on the 5 th of June as the stratification is stable. This figure will represent the appearance of all the other heat fluxes at different moments during the stable period. They all have negative heat fluxes. The circles indicate measured sensible heat flux. The figure shows that both for high and low frequencies the heat flux is on the negative side. When integrating the curve total heat flux is achieved, that is in this case negative. In figure 4.5 the standard deviation for temperature normalized with θ * is shown as a function of stability. On the stable side as the stability parameter is close to zero (around.2) more scattered values occur with values from 2 to 6. The theoretical values are somewhat higher than the measured values but not that much. Otherwise measurements are scattered around a constant value. Figure 4.6 shows the standard deviation for vertical velocity normalized with u * as a function of stability. On the stable side the measured values should behave like a constant but are a bit scattered. The scattered values should behave like the constant value of 1.2 shown in the figure as a solid line. But when analyzing the measurements the values appear to be close to the constant 1.5 instead (broken line). 21

22 4.3 The unstable period, (period III) meters 11.5 meters 14 meters 2 meters 28 meters water temperature 12.5 Temperature [ C] Time Figure 4.1 The air temperature for the 5 levels of the measuring mast and the ocean surface temperature on June 6 th to 7 th. The unstable period starts around 12 p.m. on the 6 th of June and continues until midnight, as the stability parameter negative, see figure 4.2. At 11.3 a.m. June 6 th the temperature suddenly decreases, see figure 4.1. This occurs because now the fog is thick enough to have the radiative heat flux greater at the top then at the bottom of the fog. Heat loss from the top of the fog will create temperature decrease within the fog (see section 2.4, Effect of fog on the turbulence structure). The temperature decrease is very fast, in a time period of 2 hours the temperature has reduced by over 2 C, from 13 C to less then 11 C. The air temperature is now below the ocean surface temperature with a few degrees. 22

23 In the same time as the temperature decreases the relative humidity increases, see figure 4.3. At 19.3 p.m. the relative humidity is 1 % and now the fog is up to the highest level of the measuring mast, 28 meters. Maybe the fog is even higher than 28 meters. 1 % relative humidity continues until 4 o clock in the morning on June 7 th. 3 2 p.m p.m. Height [ m ] 2 1 Height [ m ] Temperature [ C ] Temperature [ C ] Figure 4.11 The temperature profile at 2 p.m. and 4.3 p.m. June 6 th. Figure 4.11 shows the stratification during the period of thick fog. These 2 figures represent the stratification during the whole period III. The figures show potential temperature decrease with height, which indicate unstable stratification. The temperature decrease is not very pronounced but the shape of the temperature profiles is more or less constant throughout the period. During this period the heat flux in figure 4.1 is positive. At the same time as the sudden temperature decrease occurs the heat flux increases from close to zero up to 2 W/m². Figure 4.1 only shows heat flux measured at the 9 meters level, but the other levels have the same appearance. The high value of 2 W/m² does not last for long, soon it decreases. At 12.3 a.m. the heat flux turns negative again, which indicates stable stratification. Around 1 p.m. the temperature starts to increase again and at 7 a.m. the air temperature is back to being warmer then the sea surface temperature. At midnight the stability changes from unstable to stable conditions when looking at the stability parameter in figure 4.2. The relative humidity shown in figure 4.3 shows that the humidity starts to decrease not before 3 a.m. some time after the stability changed. 23

24 3 x nc wθ (n) frequency, log n [s 1 ] Figure 4.12 Co-spectra for the sensible heat flux during the unstable period. Figure 4.12 is an example of how the appearance of co-spectrum is during the unstable period. The circles show the sensible heat flux. Here it is seen that the sensible heat flux is positive for all the different sizes of eddies except one dip below zero. When integrating the curve the total heat flux is achieved and the result is positive. This shows that the stratification is unstable. In figure 4.5 the normalized standard deviation for temperature as a function of stability is shown. During the unstable conditions the equation is not a constant but an expression. The tendency for the convective side is increasing values seen from larger negative values to smaller. As the stability parameter comes closer to zero the theoretical standard deviation goes to infinity. The measured values are somewhat higher than the theoretical calculated values. But the overall picture shows the same tendency between them. The measured values have the same tendency as the theoretical values and they agree reasonably. In figure 4.6 the normalized standard deviation for vertical velocity as a function of stability is shown. For the convective part the theoretical values are a function of the stability parameter shown as the solid curve. The measured values are a bit higher than the theoretical calculated ones but with the same tendency. The same expression is used with the constant 1.5 instead, shown as the broken line in the figure. These values agree more with the measured values. 24

25 4.4 The neutral period, (period II) This period appears to be a near neutral period that is a transition period from the stable to the unstable period. In figure 4.1 and 4.2 it is shown that heat flux and stability parameter z L are close to zero. This period starts around 11. in the evening June 5 th and continues until 11. in the morning on the 6 th. In this section this period is examined more in detail. 3 (a) 3 (b) Height [ m ] 2 15 Height [ m ] Temperature [ C ] Temperature [ C ] 3 (c) 25 Height [ m ] Temperature [ C ] Figure 4.13 Temperature profile up to 3 meters height during quasi-neutral stratification. Figure (a) is the mean for the time , (b) is the mean for and (c) is for Figure 4.13 shows the temperature profile for the time period when z L and w ' θ are close to zero. The mean values over a time period of one and a half hour are calculated 25

26 during the quasi-neutral case and plotted in the figure. The profiles here show that there is unstable stratification up to the height 15-2 meters and stable above, up to 28 meters. Even though the temperature differences are small only a few tenths of a degree they show a clear pattern of unstable stratification at the bottom and stable stratification at the higher levels. These temperature profiles show that the stratification is slightly unstable at the measuring height of 1 meters. The air temperature is about the same as the sea surface temperature. This can be seen in figure 4.4. The relative humidity is shown in figure 4.3. At 4 a.m. on the 6 th of June the relative humidity decreases after a time period of constant value of 95 %. The decrease is almost down to 6 % at the end of this period without any change in stability. Why the relative humidity decreases is unknown. This issue will be discussed in the section Discussions and Conclusions. 5 x nc wθ (n) ferquency, log n [s 1 ] Figure 4.14 Co-spectra for the sensible heat flux where the stability parameter is zero. Figure 4.14 shows co-spectrum for the quasi-neutral case. The circles represent the measured sensible heat flux. In the co-spectrum the heat flux is shown to be both positive and negative. For the higher frequencies the circles are on the positive side, for the lower they are on the negative side and for the lowest frequencies they are close to zero. When 26

27 integrating the sensible heat flux over the spectral curve the result is close to zero. The total resulting value for the heat flux during period II is the same shown in figure 4.1. Cospectrum and the temperature profiles in figure 4.13 are both showing a surface layer that is somehow divided into two different stabilities. The upper region is stable and the lower is unstable. When looking at the spectral curve it is seen that for the smaller eddies, that is the high frequency part, the sensible heat flux is positive. This implies that the smaller eddies only feel the unstable stratification at the lower part of the surface layer. For the larger eddies the sensible heat flux is negative, this imply that they feel the unstable stratification in the upper part of the surface layer. The larger eddies behave like there are stable stratification and the smaller behave like there are unstable stratification. As seen in figure 4.13 there are unstable stratification at the lower heights and stable above. The large eddies reach the stable stratification above, thus the negative heat flux and the small eddies are within the unstable stratification, thus the positive heat flux. 27

28 5 Discussion and Conclusion At first it can be concluded that the stratification is stable before the fog is advected in over Östergarnsholm. This is shown in figure 4.1 and 4.2 where w ' θ is negative and the stability parameter is positive. The fog reaches Östergarnsholm at 8 p.m. June 5 th seen in figures 4.7 and 4.8 where the relative humidity increases rapidly and the temperature decreases at this time. Soon after 11 a.m. June 6 th the temperatures decrease rapidly a few degrees Celsius. At the same time the stability parameter turns negative and the heat flux increases up to positive values. This indicates unstable stratification which also can be seen in figure 4.11 where the temperature profile is shown. The relative humidity rapidly increases to 1 %. The unstable stratification implies that the fog is developed up to the highest level of measurements. Figure 4.1 shows that the temperature differences are small but consistent, the temperature decreases with height during the period with thick fog. Also the sea surface temperature is warmer than the air. The reason for this rapid decrease is described in the theory section, Effect of fog on the turbulence structure. The theory states that when the fog is optically thick enough the outgoing radiative heat flux becomes greater at the top than at the bottom. From this the conclusion is made that the fog has now become optically thick enough. By the cooling of the top cold thermals are created and a circulation within the fog has begun. This creates almost the same temperature throughout the humid air. At this point the fog begins to grow vertically because of the outgoing radiation at the top that cools the air. At the ground the temperature decreases, the humidity increases and the vertical extent of fog increases. Figure 5.1 A sketch of the hypothesis for the period with the stability parameter and w ' θ close to zero. The fog is 15 meters high with unstable stratification and above there is stable stratification. 28

29 In the measurements it is shown that the stratification is slightly unstable and not strictly neutral during period II. Soon after the fog reached Östergarnsholm at 11 p.m. June 5 th both the stability parameter and the sensible heat flux turn close to zero, this indicates that the stratification is neutral, although the potential temperature gradient indicates unstable stratification. The following interpretation is made. The stratification can be divided into 2 different stabilities during this period in the layer close to the ground. The lower layer, from the surface up to 15 meters is unstable and the layer above is stable. The hypothesis for this event is that the fog reaches to the level of 15 meters, see figure 5.1. The fog creates the unstable stratification and the stable condition from earlier continues above. The reason why the heat flux and the stability parameter are close to zero even though there is no neutral stratification is because of the frequency distribution of heat flux. The smaller eddies feel the unstable stratification and transport the heat flux upwards. The larger eddies only feel the stable stratification and transport the heat flux downwards. These transports of turbulent heat flux upward and downward eliminate each other and the resulting value is close to zero..2.2 u w [ m 2 s 2 ] Time Figure 5.2 The momentum flux during the 3 day period from June 5 th to 7 th on the 16 meters level. 29

30 During the quasi-neutral period the fog reach up to about 15 meters. An increase of the fog-top depends on a balance of production, dissipation and consumption of turbulent kinetic energy. Welch and Ravichandran (1986), show that increase of turbulence is necessary for a fog to grow. Figure 5.2 shows u 'w' as a function of time and it can be seen an increase of momentum flux around 11 a.m. on June 6 th, which caused the top of the fog to increase vertically. From previous discussions and results the conclusion is made that fog does influence the stratification over ocean. It may create unstable stratification depending on the turbulent fluxes. The standard deviations are also examined in this paper to investigate if they behave in a normal way. Figures 4.5 and 4.6 show normalized standard deviations for temperature and vertical wind speed as a function of stability for both measured and theoretical values. The measured normalized standard deviation for temperature is similar to the theoretical calculated values. But the deviation is larger for the normalized standard deviation for vertical velocity, where the measured values are somewhat higher than the theoretical calculated ones. When recalculating the theoretical values with a new constant of 1.5 the measured values agree more. The higher values may be a result of the influence of long waves (Smedman et al., 1999). Long waves and swell decrease the momentum flux and thus u *, giving higher normalized values. Still the conclusion is made that the temperature structure is close to normal but σ w u * show large scatter around neutral, which may be an indication of a disturbed surface layer. The relative humidity is up above 9 % as the fog reaches Östergarnsholm. A complication with this case of fog is that after a while at 4 a.m. June 6 th the relative humidity decreases rapidly down to almost 6%. The reason is still unknown. Why does it decrease unless the fog is for a while dissolved? The complication is that the other parameters investigated do not show any of this. The stability does neither change nor the temperature. Some theories are now presented. One explanation is that the relative humidity instrument is not responding correctly during this period and the humidity is not really decreasing. Another theory is that the sun rises at this time of day. The relative humidity starts to decrease at 4 a.m. in the morning June 6 th, which also is the time for sunrise in the beginning of June. As the sun rises the radiation will evaporate the droplets. This decreases the height of the fog. 3

31 Acknowledgements First and foremost I would like to thank my supervisor professor Ann-Sofi Smedman for all the help and guidance whom without this study would not have been possible. Also I want to show my appreciation to the staff at MIUU for the help they have given me. At last thank you fellow students for all the rewarding discussions, uplifting moments and laughter. 31

32 References Högström, U., Smedman, A-S.: 199, Kompendium i atmosfärens gränsskikt, del1. Turbulensteori och skikten närmast marken, Department of Meteorology, Uppsala University, 134 pp Högström, U., Smedman, A-S.: 199, Kompendium i atmosfärens gränsskikt, del 2. Övergångsskiktet, Numerisk modellering samt spridning, Department of Meteorology, Uppsala University, 149 pp Johansson, C.: 21, Similarity theory of the art of scaling benefits and drawbacks, Department of Earth and Science, Meteorology, Uppsala University, 29 pp Johansson, C., Smedman, A-S., Högström, U., Brasseur, J.G., Khanna, S.: 21, Critical Test of the Validity of Monin-Obukhov Similarity during Convective Conditions, Journal of Atmospheric Science, 58, p Panofsky, H., Dutton, J.: 1984, Atmospheric Turbulence, Models and Methods for Engineering Applications, John Wiley & sons, 397 pp Smedman, A-S., Högström, U., Bergström, H.: 1997, The turbulence regime of a very stable marine airflow with quasi-frictional decoupling, Journal of Geophysical Research, vol. 12, No. C9, , September 15 Smedman, A-S., Högström, U., Bergström, H., Rutgersson, A.:1999, A case study of airsea interaction during swell conditions, Journal of Geophysical Research, vol. 14, No. C11. p. 25,833-25,851, September 15 Stull, R.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, 666 pp Welch, R. M., Ravichandran, M.G.: 1986, Prediction of Quasi-Periodic Oscillations in Radiation Fogs. Part I: Comparison of Simple Similarity Approaches, Journal of the Atmospheric Science, vol. 43, No. 7, p The picture on the front-page is taken from