Fog Dissipation by artificial heating Table of contents 4 6 Summary…………………………………………………………………………………… Introduction………………………………………………………………………………... PART I GENERAL ASPECTS OF FOG DISSIPATION 8 1. Introduction to fog dissipation……………………………………………………….. 8 9 1.1. Historical review of weather modification…………………………………………….. 10 1.2. Historical review and methods of fog dissipation……………………………………... 11 1.2.1. Dissipation of supercooled fog…………………………………………………….. 1.2.2. Dissipation of warm fog.....………...………………………………...…………..... 13 2. Fog as a meteorological phenomenon……………………………………………….. 13 13 2.1. The fog liquid water content………………...……………………………………….... 14 2.2. Water-phase state and relative humidity of fogs.……....…………………………...… 14 2.3. Number of droplets and their distribution with respect to size………………………... 14 2.4. Vertical temperature profiles in fogs…………………...……………………………… 15 2.5. Role of the wind speed………………………………………………………………… 15 2.6. The upper boundary of fogs………………………………………………………….... 15 2.7. Impact of snow cover on fog formation………………………………………………. 16 2.8. Diurnal and annual fog variations…………………………………………………….. 2.9. Formation and evolution of a radiation fog…………………………………………… 18 3. Annotations of Austrian airport weather services to the profitability of fog dissipation……………………………………………………………………………... 18 18 3.1. Innsbruck Airport……………………………………………………………………... 19 3.2. Klagenfurt Airport…………………………………………………………………….. 19 3.3. Linz Airport…………………………………………………………………………… 20 3.4. Salzburg Airport………………………………………………………………………. 20 3.5. Graz Airport…………………………………………………………………………… 3.6. Vienna Airport………………………………………………………………………… 21 4. Fog dissipation by fuel combustion………………………………………………….. 21 22 4.1. What do we expect from artificial heating?………………………………………….... 4.2. What is the minimum temperature to dissipate fog?………………………………….. Table of contents 2 4.3. How does the minimum temperature increment necessary for fog dissipation depend on fog temperature?…………………………………………………………………… 23 4.4. What is the critical temperature for fog dissipation by means of real fuel?…………... 24 4.5. Heat diffusion in an isothermal atmosphere…………………………………………... 25 4.5.1. Analytical solution of the heat diffusion equation………………………………… 26 4.5.2. Results of the analytical solution………………………………………………….. 28 PART II CASE STUDIES 1. Case studies for a dry atmosphere…………………………………………………... 31 1.1. Does the numerical model work well?………………………………………………... 31 1.2. Which factors determine heat diffusion?……………………………………………… 32 1.2.1. Variable diffusion coefficient……………………………………………………... 33 1.2.2. Adiabatic mixing…………………………………………………………………... 33 1.2.3. Surface heating…………………………………………………………………….. 35 1.2.4. Initial stratification………………………………………………………………… 37 2. Case studies for a moist atmosphere………………………………………………… 39 2.1. How temperature, total water content, LWC and visibility profiles are found……….. 39 2.2. Total water content diffusion………………………………………………………….. 40 2.3. Ideal fuel heating and its consequences for a fog layer……………………………….. 42 2.4. Application of real fuel in a warm fog………………………………………………... 43 2.5. Approaching real atmospheric conditions…………………………………………….. 44 2.5.1. Artificial dissipation of a young radiation fog…………………………………….. 45 2.5.2. Artificial dissipation of a mature radiation fog……………………………………. 47 2.5.3. Implications of fog temperature and fuel type on fog dissipation………………… 49 APPENDICES Annex A: Model equations……………………………………………………………….. 54 1. The heat diffusion equation……………………………………………………………. 54 2. The total water content equation………………………………………………………. 56 3. The diffusion equation for total water content………………………………………… 56 4. Equation for the diffusion coefficient…………………………………………………. 57 5. Equation for the saturated water vapour pressure……………………………………... 57 6. Equation of state for the water vapour density………………………………………… 58 7. Visibility equation……………………………………………………………………... 58 Annex B: Initial and boundary conditions………………………………………………. 59 1. Initial conditions……………………………………………………………………….. 59 2. Lower boundary conditions……………………………………………………………. 59 Table of contents 3 3. Upper boundary conditions……………………………………………………………. 61 Annex C: Numerical method – finite differences……………………………………….. 62 1. Equation for the diffusion coefficient………………………………………………….. 62 2. Heat and TWC diffusion equation……………………………………………………... 63 3. Lower boundary conditions of the heat and TWC diffusion equations………………... 64 Annex D: Heat and moisture production ability of various fuel………………………. 65 Acknowledgements………………………………………………………………………... 66 References…………………………………………………………………………………. 67 Summary 4 Summary The present work essentially reports and summarizes work conducted at the Hydrometeorological University of St.Petersburg, Russia, based on ideas of the author’s supervisor Dr. V.I. Berkrjaev. The main focus of the diploma thesis is the development and application of a one-dimensional model to simulate fog dissipation by means of ground-operated artificial heating. In our case heating is realized by the combustion of fuel triggering an upward heat transport, which causes the fog layer to warm up and droplets to evaporate. As principal mechanism for the heat transport we consider turbulent diffusion, which in our simulation is adapted to the particular problem of artificial heating. Case studies have been performed in a dry and moist environment. The experiments in the dry atmosphere generally exhibit the relative importance of the diffusion coefficient, mixing processes, surface heating temperature and initial stratification for our results. We note that the atmosphere heats up more quickly, if we apply a non-constant diffusion coefficient, which depends on height and the temperature gradient. In this way we allow for a more realistic simulation of the large diffusion values near surface. Also the tendency of the atmosphere to become adiabatically stratified as a result of mixing becomes evident. The fuel type and the rate at which it is burned govern the surface heating temperature. We give quantitative results of their influence on the heating process, assuming that the fuel releases no water vapour (ideal fuel). When the general aspects of turbulent diffusion and artificial heating in a dry environment have been clarified the model is applied to a fog layer. In this context we visualize the process of fog dissipation and the improvement of visibility. For this purpose not only heat diffusion, but also diffusion of water vapour and liquid water content has to be considered, since their vertical distributions affect the dissipation process. Experiments with ideal fuel show that due to evaporation cooling fog air warms up less quickly than dry air. Given the initial vertical profile of temperature, liquid water content and relative humidity we can use the model to simulate the Summary 5 dissipation of a young and a mature radiation fog as they may really exist. The model shows not only how fog dissipates in lower layers due to artificial heating, but also changes in the upper fog boundary due to mixing processes. In our examples the fog upper boundary drops when it mixes with drier air aloft. If the fuel releases not only heat, but also water vapour (real fuel), the dissipation results are sensitive to the initial fog temperature and to the ratio between the fuel’s moisture and heat production ability. Whereas for initial fog temperatures close to 0°C results are comparable to ideal fuel heating, considerably less success in fog dissipation can be reported for colder fog. Furthermore the capacity of different fuel types to dissipate cold or warm fog is demonstrated. In cold fog conditions methane and propane, for instance, are similarly effective, whereas for warm fog methane is the better choice. Peat on the other hand could be used in warm fog, but, as experiments show, would be quite expensive for fog temperatures below -5°C. It could be estimated that for an area of 105 m2 fuel of the order of several hundred kilogram have to be provided, if the airport management aims to dissipate a radiation fog within one hour up to a height of 60m. 6 Introduction Fog is a widespread meteorological phenomenon that always has influenced and inspired mankind. It is not only a cloud touching the ground, but through its beauty and peaceful silence, motivation for innumerable poems, stories and images of rural and urban landscapes. But unfortunately fog is not always appreciated so much, mainly due the fact that it reduces visibility. It may be an expensive freak of nature, at the latest as civilisation began to drive cars, sail on ships or fly planes. Economical and partly maybe even scientific interests encouraged people to search for possibilities to dissipate inconvenient fog. Most efforts have been made on attempts to increase the runway visibility range on airports, since airline companies face millions of dollars loss every year due to fog appearance on the runway. In recent decades the development of radio navigation systems allowed aircraft to land nearly blindly, but until today the pilot has the last say. In the 20th century several methods have been proposed to dissipate fog. One of them – treated in the present work – is to burn fuel along the runway, heat the fog layer and evaporate droplets. It has been used in Great Britain during World War II to allow British bombers returning from Germany to land safely in fog conditions. In the remembrances of Terry Waddington (http://www.wartime-memories.fsnet.co.uk /northeast3.html) we read: 7 “Carnaby had a runway which was five times the width of normal