Copyright © 2017 by Roland Stull. Practical Meteorology: An Algebra-based Survey of Atmospheric Science. v1.02 1 ATMOSPHERIC BASICS Contents Classical Newtonian physics can be used to de- scribe atmospheric behavior. Namely, air motions 1.1. Introduction 1 obey Newton’s laws of dynamics. Heat satisfies the 1.2. Meteorological Conventions 2 laws of thermodynamics. Air mass and moisture 1.3. Earth Frameworks Reviewed 3 are conserved. When applied to a fluid such as air, 1.3.1. Cartography 4 these physical processes describe fluid mechanics. 1.3.2. Azimuth, Zenith, & Elevation Angles 4 Meteorology is the study of the fluid mechanics, 1.3.3. Time Zones 5 physics, and chemistry of Earth’s atmosphere. 1.4. Thermodynamic State 6 The atmosphere is a complex fluid system — a 1.4.1. Temperature 6 system that generates the chaotic motions we call 1.4.2. Pressure 7 weather. This complexity is caused by myriad in- 1.4.3. Density 10 teractions between many physical processes acting 1.5. Atmospheric Structure 11 at different locations. For example, temperature 1.5.1. Standard Atmosphere 11 differences create pressure differences that drive 1.5.2. Layers of the Atmosphere 13 winds. Winds move water vapor about. Water va- 1.5.3. Atmospheric Boundary Layer 13 por condenses and releases heat, altering the tem- 1.6. Equation of State– Ideal Gas Law 14 perature differences. Such feedbacks are nonlinear, 1.7. Hydrostatic Equilibrium 15 and contribute to the complexity. 1.8. Hypsometric Equation 17 But the result of this chaos and complexity is a fascinating array of weather phenomena — phe- 1.9. Process Terminology 17 nomena that are as inspiring in their beauty and 1.10. Pressure Instruments 19 power as they are a challenge to describe. Thunder- 1.11. Review 19 storms, cyclones, snow flakes, jet streams, rainbows. 1.11.1. Tips for Using This Book 19 Such phenomena touch our lives by affecting how 1.11.2. Tips for the Homework 19 we dress, how we travel, what we can grow, where 1.12. Homework Exercises 21 we live, and sometimes how we feel. 1.12.1. Broaden Knowledge & Comprehension 21 In spite of the complexity, much is known about 1.12.2. Apply 22 atmospheric behavior. This book presents some of 1.12.3. Evaluate & Analyze 24 1.12.4. Synthesize 25 what we know about the atmosphere, for use by sci- entists and engineers. 1.1. INTRODUCTION In this book are five major components of me- teorology: (1) thermodynamics, (2) physical meteo- rology, (3) observation and analysis, (4) dynamics, and (5) weather systems (cyclones, fronts, thunder- storms). Also covered are air-pollution dispersion, numerical weather prediction, and natural climate processes. Starting into the thermodynamics topic now, the state of the air in the atmosphere is defined by “Practical Meteorology: An Algebra-based Survey of Atmospheric Science” by Roland Stull is licensed its pressure, density, and temperature. Changes of under a Creative Commons Attribution-NonCom- state associated with weather and climate are small mercial-ShareAlike 4.0 International License. View this license at http://creativecommons.org/licenses/by-nc-sa/4.0/ . This work is perturbations compared to the average (standard) available at https://www.eoas.ubc.ca/books/Practical_Meteorology/ 1 2 CHAPTER 1 • ATMOSPHERIC BASICS atmosphere. These changes are caused by well-de- A SCIENTIFIC PERSPECTIVE • fined processes. Descartes and the Scientific Method Equations and concepts in meteorology are simi- From René Descartes we get more than the name lar to those in physics or engineering, although the “Cartesian”. In 1637 he published a book Discours de jargon and conventions might look different when la Méthode, in which he defined the principles of the applied within an Earth framework. For a review of modern scientific method: basic science, see Appendix A. • Accept something as true only if you know it to be true. • Break difficult problems into small parts, and solve each part in order to solve the whole problem. • Start from the simple, and work towards the com- 1.2. METEOROLOGICAL CONVENTIONS plex. Seek relationships between the variables. • Do not allow personal biases or judgements to Although the Earth is approximately spherical, interfere, and be thorough. This method formed the basis of the scientific renais- you need not always use spherical coordinates. For sance, and marked an important break away from the weather at a point or in a small region such as a blind belief in philosophers such as Aristotle. town, state, or province, you can use local right-hand Cartesian (rectangular) coordinates, as sketched in Fig. 1.1. Usually, this coordinate system is aligned Up W with x pointing east, y pointing north, and z point- z ing up. Other orientations are sometimes used. Velocity components U, V, and W correspond to y North V motion in the x, y, and z directions. For example, a positive value of U is a velocity component from East U x west to east, while negative is from east to west. Figure 1.1 Similarly, V is positive northward, and W is positive Local Cartesian coordinates and velocity components. upward (Fig. 1.1). In polar coordinates, horizontal velocities can be expressed as a direction (α), and speed or magni- 0° 0° tude (M). Historically, horizontal wind directions 90° are based on the compass, with 0° to the north (the 180° 0° 270° 90° 270° 90° positive y direction), and with degrees increasing in a clockwise direction through 360°. Negative 270° 180° 180° angles are not usually used. Unfortunately, this dif- Azimuth Wind Direction fers from the usual mathematical convention of 0° Mathematical Meteorological in the x direction, increasing counter-clockwise through 360° (Fig. 1.2). Figure 1.2 Historically winds are named by the direction Comparison of meteorological and math angle conventions. from which they come, while in mathematics an- gles give the direction toward which things move. INFO • Weather-related Disasters Thus, a west wind is a wind from the west; namely, During 1970 to 2012 there were 8,835 disasters, from 270°. It corresponds to a positive value of U, 1.94 million deaths, and economic losses equivalent with air moving in the positive x direction. to US$ 2.4 trillion due to droughts, temperature ex- Because of these differences, the usual trigono- tremes, tropical cyclones, floods, and their related metric equations cannot be used to convert between health epidemics. Of these totals, storms caused 79% (U, V) and (α, M). Use the following equations in- of the disasters, 55% of lives lost, and 86% of economic stead, where α is the compass direction from which losses. Individual events included: 300,000 killed in winds come. 1970 cyclone Bhola in Bangladesh; 300,000 killed in 1983 drought in Ethiopia; 150,000 killed in drought in Sudan; and 138,866 killed in 1991 cyclone Gorky Conversion to Speed and Direction: in Bangladesh. Most of the deaths were in less-de- 12/ veloped countries, while most of the economic losses MU=+()22V •(1.1) were in the most-developed countries (e.g. US$ 147 billion and $50 billion from hurricanes Katrina and Sandy in the USA). Source: WMO, 2014: “The Atlas of 360° V αα=−90° ·arctan + o •(1.2a) Mortality and Economic Losses from Weather, Climate and C U Water Extremes, 1970-2012”. R. STULL • PRACTICAL METEOROLOGY 3 where αo = 180° if U > 0, but is zero otherwise. C is the angular rotation in a full circle (C = 360° = 2·π Sample Application radians). Find wind speed and direction, given eastward component 3 m s–1, and northward 4 m s–1. [NOTE: Bullets • identify key equations that are fundamental, or are needed for understanding later chap- Find the Answer ters.] (Problem-solving methods are given in Appendix A.) Given: U = 3 m s–1. eastward wind component. V = 4 m s–1. northward wind component. Some computer languages and spreadsheets al- Find: M = ? m s–1. wind speed low a two-argument arc tangent function (atan2): α = ? degrees. wind direction 360° Sketch: V M α= ·(atan2°VU,)+ 180 (1.2b) C Use eq. (1.1): M = [ U2 + V2 ] 1/2 –1 2 –1 2 0.5 [CAUTION: in the C and C++ programming languages, = [ (3 m s ) + (4 m s ) ] U 0.5 –1 2 0.5 you might need to switch the order of U & V.] = (9 + 16) ·[(m s ) ] α = (25)0.5 m s–1 = 5 m s–1. Some calculators, spreadsheets or computer Use eq. (1.2a): functions use angles in degrees, while others use α = 90° – (360°/C)·arctan(V/U) + 180° radians. If you don’t know which units are used, = 90° – (360/360)·arctan[(4 m s–1)/(3 m s–1)]+180° compute the arccos(–1) as a test. If the answer is 180, = 90° – tan–1(1.333) + 180° then your units are degrees; otherwise, an answer of = 90° – 53.13° + 180° = 216.87°. 3.14159 indicates radians. Use whichever value of C is appropriate for your units. Check: Units OK. Sketch OK. Values physical. Exposition: Thus, the wind is from the south-south- Conversion to U and V: west (SSW) at 5 m s–1. UM=− ·sin()α •(1.3) W VM=− ·cos()α •(1.4) N In three dimensions, cylindrical coordinates α (M, α, W) are sometimes used for velocity instead of M E Cartesian (U, V, W), where horizontal velocity com- ponents are specified by direction and speed, and Figure 1.3 the vertical component remains W (see Fig. 1.3). Notation used in cylindrical coordinates for velocity. Most meteorological graphs are like graphs in other sciences, with dependent variables on the ordinate (vertical axis) plotted against an inde- pendent variable on the abscissa (horizontal axis).