Atmosferik sınır tabakanın yüksek mertebe kapama yöntemi ile bir boyutlu modellenmesi /
Yazar: ŞÜKRAN SİBEL MENTEŞ
Danışman: PROF. DR. SÜREYYA ÖNEY
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Doktora, 1996
Konu: Meteoroloji = Meteorology
Dizin: Atmosfer sınır tabakası = Atmospheric boundary layer

Özet:
Bu çalışmada ölçüm bölgesi olarak seçilen Göztepe Meteoroloji İstasyonu'nda, atmosferik sınır tabakanın düşey yapısını belirlemek üzere bir boyutlu Mellor- Yamada seviye 2.5 türbülans kapama modeli uygulanmıştır. Bu model yardımıyla, sıcaklık, nem ve hız alanlarının saatlik tahmini için düşey türbülans katsayısı hesaplanmıştır. Atmosferik Sınır Tabaka'nın (AST) sayısal olarak modellenebilmesi için, tüm sınır tabaka boyunca başlangıç değeri olarak bir çok parametreye ihtiyaç vardır. Başlangıç düşey profil değerleri (sıcaklık, nem, rüzgar, basınç değerleri) radyosonde gözlemleri ile elde edilmiştir. Buna ilave olarak, toprak yüzey sıcaklığı, nem tutma kapasitesi, toprak altı sıcaklıkları gibi toprağın termik özellikleri, toprağın cinsi, geçirgenliği gibi fiziksel özellikleri ve yüzey pürüzlülüğü gibi yüzey karakteristiklerin girdi parametreleri olarak bilinmesi gerekir, ölçümlerin yapıldığı bölgede modelde kullanılan bu parametrelerin çeşitli yöntemlerle belirlenmesine çalışılmıştır. Bu nedenle çalışma, ölçüm safhası ve sayısal modelleme safhası olarak iki aşamadan oluşmaktadır. Yüzey tabaka yapısının belirlenmesi için yüzey akılarının hesaplanmasında iki farklı metod kullanılmıştır. Yüzey enerji bütçesi eşitlikleri kullanılarak bir model oluşturulmuştur. İkinci olarak, Monin-Obukhov Benzeşim Teorisi esas alınarak Mellor- Yamada tarafından oluşturulan model kullanılmış ve her iki sonuç mukayese edilmiştir. AST' da türbülans katsayılarının (Km, Kt,, Kq) fonksiyonu olarak, rüzgar, sıcaklık, nem parametrelerinin 24 saatlik periyot boyunca değişimini hesaplamak için mevcut prognostik denklem sistemlerinin çözümünde önemli parametrelerden biri de jeostrofik rüzgardır. Bu çalışmada jeostrofik rüzgarın hesaplanması amacıyla bir model oluşturulmuştur. Bu modelle, her bir seviyedeki basınç gradyanı, Coriolis ve sürtünme kuvvetleri arasındaki denge durumu yardımıyla jeostrofik rüzgarın sayısal olarak hesaplanması sağlanmıştır. AST içindeki seviyelerde sıcaklık, hız ve nemin zamana bağlı olarak değişimi problemi sonlu farklar yöntemiyle çözülmüştür. Denklem sistemlerinin çözümünde G koordinat sistemi kullanılmıştır. Model sonuçlan ve gözlem değerleri arasında yapılan istatistiksel değerlendirmede, modelin sıcaklık ve nem değişimi için hıza göre daha uyumlu olduğu görülmüştür.

Abstract:
Atmospheric Boundary Layer (ABL) is the lowest part of the atmosphere through which directly interacts with the Earth's surface. Most of the heat, moisture and momentum exchange between the atmosphere and Earth's surface occurs in this layer. Therefore, in order to understand the dynamics and thermodynamics of the whole atmosphere, ABL is very important. In addition, the control of the air pollution, which gains great importance in recent years, depends very much upon the structure of the ABL. Diffusion and dispersion of the pollutants are highly related to the ABL' s structure. The factors that control the structure of the ABL are the distribution of water vapour, and the heating and cooling rates of the layer. The heating of the Earth's surface due to solar radiation results in convective motions, and consequently turbulence. If the air is stable, turbulence reaches its minimum, and it becomes maximum when the air is unstable. During the day, due to the heating of the surface, the rising motions start from the surface to the atmosphere thus causing the ABL parameters to mix uniformly. Because the surface loses heat due to radiation, it cools, and the ABL becomes stable. The mixing in this case is very small, and it is very likely that the concentration of pollution will increase as one gets closer to the Earth's surface. The structure of the ABL is very complicated. The reason for that is the turbulence which usually occurs in this layer. Turbulence phenomena is itself a complex problem. There are several approaches to solve the turbulence related problems. Almost all of these approaches are semi-emprical. Some of the meteorological parameters have to be given as input. The oldest approach, and still the mostly used one, is to model the turbulence based on an anology to the behavior of the molecules in the gas kinetic theory. According to this model, the transfer of the momentum and other properties of the molecules are the result of the eddies. In this model, the corresponding concepts, to the molecular viscosity are "viscosity of eddy" and "diflusivity of eddy". Another approach, which is widely used in the similarity theory, that is based on the dimensional analysis. For the surface layer which is the lowest part of the ABL, this theory is found to be succesful. xixIn the last two decades, there has been many studies which apply high order turbulence closure methods to the ABL. These theories require a complete understanding of the turbulence phenomenon and necessitate a high computational power. They are especially advantages when used for studying short term fluctuations. However, it is more appropriate and economical to use a "mixed layer approach" in the case of longer term variations, especially in climate studies. In this study, we used "one-dimensional Mellor- Yamada level 2.5 turbulence closure model" to study the vertical structure of the ABL by using observations obtained at the Göztepe Meteorological Station in Istanbul. The vertical eddy diffusion is computed to predict the temperature, mixing ratio of moisture and velocity fields for a 24 hour period. The main feature of this model in comparison to the other turbulence closure methods is that it computes the time variation of turbulence kinetic energy by numerically solving a set of differential equations. To construct the model, we need several initial parameters at different levels of ABL. These vertical distribution of values (temperature, mixing ratio, wind and pressure) are initially obtained from radiosonde measurements. Also, it is neccessary to input the time change of the geostrophic wind. Other parameters, which need to be known before the model is run, are the thermal and physical characteristics of the soil, such as surface temperature right below the surface, type of the soil, emissivity and surface porosity of the soil. These parameters are determined by using the measurements taken around the region of Göztepe. Therefore, this study is organized in two stages: namely the measurement and numerical modeling. In meteorological stations, due to a high financial cost, the radiosonde measurements can only be taken twice a day. To compare observations with model simulations it is necessary to make the measurements more than twice a day but at shorter vertical distances in ABL at each time. Therefore, as a first step in this study, we set up a system which will provide us with such measurements. The system is composed of a barrel of windlass and a resistance cable which connects the radiosonde baloon to barrel of windlass. It is a static system in the sense that it will not reflect the changes in the wind, especially in the wind direction. In fact, this is the most basic problem and also the difference from the real radiosonde system. Therefore, it is expected naturally that there will be differences between the wind measurements taken using this method and those from the real radiosondes. However, this difference is reduced by assuming the position of the cambel connecting the radiosonde baloon to the barrel of windlass has a parabolic or linear change at a certain time; then this will allow us to make some simplifications for computing the wind strength in the balance equations. Hence the final wind from the model with this assumption will approximate the true wind. As a boundary value, the soil surface temperature is also needed for the ABL parameterization. Using energy budget, it is possible to calculate the surface temperature change during the day. The effects of vegetation in the computation are ignored. xxLocal change of the soil surface temperature is predicted by using the energy budget equation. The energy budget equation in given by oT. 1 - L = - (RN-GH-SH-LH) öt cg where cg is the heat capacity for a unit volume, Rn is the net radiation flux, GH is the heat flux just below the earth's surface, SH is the sensible heat flux, and LH is the latent heat flux. To calculate surface fluxes in determening the surface layer structure, two different models are used. The first model uses the surface energy butget equation. The second one is the Mellor- Yamada model based on the Monin Obukhov similarity theory. These two model results are compared in this study. Mellor- Yamada 2.5 level closure model uses momentum conservation, continuity, thermodynamic energy equations to obtain time dependent expressions of temperature, humidity, wind parameters and turbulence kinetic energy in the ABL as a function of turbulence coefficients. The following equations are used for the conservation of momentum. Here, the advection term is neglected. dü 1 öfpü'v/) / \ dt p dz dv 1 c(pv'w') dt p dz + fMJ Here, u and v are mean horizontal velocity components; u'w' and v'w' are Reynolds stresses for ü and v; ug and vg are components of geostrophic velocity, and p is the air density. In terms of mean velocity fields at different levels these stresses are determined by, S(u,v) (u'v')w' = -K m dz where Km is the turbulent coefficient for momentum. Conservation of mass is given by XXI|+V.(p.V) = 0 For an incompressible fluid this equation becomes, V-V = 0 Thermodynamic energy equation is defined as, ae 1 a(o9'w') dt p dz where 0 is potential temperature and 9'w' is the eddy flux for potential temperature. For a moist air, eddy flux (pq^w) is given in dqv _ _ 1 jm>') dt p dz where qv is mixing ratio. Heat and moisture fluxes in terms of mean potential temperature and moisture are given by, 9'w' = -K, q>' = -K, ae dz dq~v ' dz where, Kh is turbulence coefficient for heat and moisture. The model is completed by including the turbulent kinetic energy equation. Turbulent kinetic energy equation is given by f^2\ a V^ J dz f~2\ K 4 dzV 2 J P. + Pn-e Here the first term on the left hand side of the equation gives the local change of turbulent kinetic energy and the second is the eddy diffusion term in which Kq is XXlldiffusion coefficient. On the right hand side of turbulent kinetic energy equation, Ps and Pb give the shear generation of eddy kinetic energy and the buoyancy generation of eddy kinetic energy respectively, and the last term 8 gives the diffusion of the turbulent kinetic energy. Km and Kh, the turbulence coefficients are obtained from Kh=^.q.SH Here, t is the mixing length for turbulence, q is the turbulent kinetic energy and is defined as, q = Vu'2+v'2 where u',v' are turbulence components of velocity. Sm and Sh are stability parameters for momentum and heat. Geostrophic wind is one of the most important parameter in the solutions of prognostic equations. It is defined for a flow which is horizontal and has no friction and acceleration. It is not possible to express the geostrophic wind in terms of horizontal pressure gradient because of the difficulties in determining the horizontal variation of the pressure for each ABL level in microscale. In this study, a sub-model is performed to compute the geostrophic wind. This sub-model numerically calculates the geostrophic wind by using the balance between pressure gradient, coriolis and friction forces at each level of ABL. The main model uses the finite difference methods to solve prognostic equations for temperature, velocity and humidity in ABL. a-coordinate system is used to solve the differential equation sets. The model used in this study gives the profiles of different parameters computed from both the Monin Obukhov similarity theory and energy butget method. Model first computes the surface fluxes and use it to obtain the temperature and moisture profiles. These profiles of temperature and moisture are then compared with the observations taken at each 6 hours during the course of a day. In this study, it is shown that the model results are consistent with these observations. For example, on the average, there is a 2°C of difference in temperature, 3 gr/kg of difference in mixing ratio in the model when compared to the observed values. However, model wind profile results are found to be less consistent with observations. The difference between the two is on the order of 5 m/sec at the greatest. Distributions of turbulence coefficients and fluxes are consistent with those of model. xxniTo study the model performance, some statistical tests are carried out over the model simulated data. The simulated and observed temperature profiles correlate each other considerably well with a correlation coefficent of 0.91, which is above 95% significance level, and root mean square (RMS) errors are found to be around 2°C. The observed and simulated mixing ratio profiles give a correlation of approximately 0.83, and RMS errors of approximately 1.7 g/kg. On the other hand, model performance for the wind profiles is not as good as temperature and moisture profiles. Correlation coefficient obtained between observed and simulated wind profiles are around 0.44 and RMS erros are 2. 149 m/sn. As a conclusion, much of the variability for temperature and moisture is simulated quite successfully. This indicates that this type of model suffices to study the thermodynamics variables such as temperature and moisture fields in the ABL.