chapter 5 Copyright © 2011, 2015 by Roland Stull. Meteorology for Scientists and Engineers, 3rd Ed. Stability contentS A sounding is the vertical profile of tem- perature and other variables in the atmo- Building a Thermo-diagram 119 sphere over one geographic location. Sta- Components 119 5 bility refers to the ability of the atmosphere to be Pseudoadiabatic Assumption 121 turbulent. Stability is determined by temperature, Complete Thermo Diagrams 121 humidity, and wind profiles. Turbulence and stabil- Types Of Thermo Diagrams 122 ity vary with time and place because of the corre- Emagram 122 sponding variation of the soundings. Stüve & Pseudoadiabatic Diagrams 122 We notice the effects of stability by the: wind Skew-T Log-P Diagram 122 gustiness, dispersion of smoke, refraction of light Tephigram 122 Theta-Height (θ-z) Diagrams 122 and sound, strength of thermal updrafts, size of clouds, and intensity of thunderstorms. More on the Skew-T 124 Thermodynamic diagrams have been de- Guide for Quick Identification of Thermo Diagrams 126 vised to help us plot soundings and determine sta- Thermo-diagram Applications 127 bility. They look complicated at first, but with a bit Thermodynamic State 128 of practice they can make thermodynamic analysis Processes 129 much easier than solving sets of coupled equations. Parcels vs. Environment 134 In this chapter, we first discuss the different types Soundings 134 of thermodynamic diagrams, and then use them to Buoyancy 135 determine stability and turbulence. Brunt-Väisälä Frequency 136 Flow Stability 138 Static Stability 138 Dynamic Stability 141 Turbulence Determination 142 building a thermo-diagram Finding Tropopause Height & Mixed-layer Depth 143 Tropopause 143 components Mixed-Layer 144 In previous chapters, we learned how to compute Summary 145 isohumes (the Moisture chapter), dry adiabats Threads 145 (the Heat chapter), and moist adiabats (the Mois- Exercises 145 ture chapter). We plotted these isopleths on a back- Numerical Problems 145 ground graph having temperature along the abscis- Understanding & Critical Evaluation 148 Web-Enhanced Questions 149 sa and log of pressure along the ordinate. These are Synthesis Questions 150 reproduced here as Figs. 5.1a-d. When these isopleths are combined on a single Large-size Thermo Diagrams 151 Emagram 152 graph, the result is called a thermodynamic dia- Stüve Diagram 153 gram, or thermo diagram for short (Fig. 5.1e). At Skew-T Log-P Diagram 154 first glance, Fig. 5.1e looks like a confusing nest of Tephigram 155 lines; however, you can use the pattern-recognition Theta-Z Diagram 156 capability of your mind to focus on the components Skew-T Log-P Diagram (ABL) 157 as shown in Fig. 5.1a-d. Your efforts to master thermo Theta-Z Diagram (ABL) 158 diagrams now will save you time in the future. Several types of thermo diagrams are used in meteorology. They all can show the same informa- “Meteorology for Scientists and Engineers, 3rd Edi- tion, and are used the same way. The thermo dia- tion” by Roland Stull is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike gram we learned so far is called an Emagram. We 4.0 International License. To view a copy of the license, visit learned this one first because it was easy to create http://creativecommons.org/licenses/by-nc-sa/4.0/ . This work is available at http://www.eos.ubc.ca/books/Practical_Meteorology/ . using a computer spreadsheet. 119 120 chapter 5 STABILITy (a) (d) *TPUIFSNT .PJTU"EJBCBUT *TPCBST RX$ 1 L1B 1 L1B m m m m m m m m m 5 $ 5 $ (b) (e) STPSS HLH STPSS HLH *TPIVNFT &."(3". 1 L1B 1 L1B m m m m m m 5 $ 5 $ (c) R %SZ"EJBCBUT $ Figure 5.1 Components of an Emagram thermo diagram. (a) The background on all these charts are isotherms (vertical thin solid lines), and isobars (horizontal thin solid lines) plotted with logarithmic spacing. (b) Isohumes (from the Moisture chapter) are nearly vertical dotted lines. 1 L1B (c) Dry adiabats (from the Heat chapter) are diagonal solid lines; (d) Moist adiabats (from the Moisture chapter) are curved dashed lines. (e) Thermo diagram formed by combining parts m (a) through (d). P is pressure, T is temperature, r is mixing ra- m tio, rs is saturated mixing ratio, θ is potential temperature, and θw is wet-bulb potential temperature. m m m 5 $ r. STULL • METEOrOLOGy FOr SCIENTISTS AND ENGINEErS 121 On every thermo diagram, including the FOCUS • Why so many thermo dia- Emagram in Fig. 5.1e, are plotted at least five types grams? of lines: three give the state of the air (isobars, iso- therms, and isohumes) and two show how the state changes by a process of vertical movement of Meteorological thermo diagrams were originally air (dry and moist adiabats). Additional state lines created as optimized versions of the P vs. α diagrams for height contours are left out of this introductory of classical physics (thermodynamics), where α is the specific volume (i.e., α = volume per unit mass thermo diagram to avoid clutter, but are included in = 1/ρ, where ρ is air density). A desirable attribute full thermo diagrams at the end of this chapter. of the P vs. α diagram is that when a cyclic process is traced on this diagram, the area enclosed by the pseudoadiabatic assumption resulting curve is proportional to the specific work done by or to the atmosphere. The disadvantage of P In the Moisture chapter, we assumed an adia- vs. α diagram is that the angle between any isotherm batic process (no heat transfer or mixing to or from and adiabat is relatively small, making it difficult to the air parcel) when computing the moist adiabats. interpret atmospheric soundings. However, for any of the thermo diagrams, the moist Three meteorological thermo diagrams have been adiabats can be computed assuming either: devised that satisfy the “area = work” attribute, and • adiabatic processes (i.e., reversible, where all are optimized for meteorology to have greater angles liquid water is carried with the air parcels), or between the isotherms and adiabats: • pseudoadiabatic processes (i.e., irreversible, where all condensed water is assumed to • Emagram, fall out immediately). • Skew-T Log-P Diagram Air parcels in the real atmosphere behave between • Tephigram. these two extremes, because small droplets and ice Meteorologists rarely need to utilize the “area = work” crystals are carried with the air parcel while larger attribute, so they also can use any of three additional ones precipitate out. diagrams: When liquid or solid water falls out, it removes from the system some of the sensible heat associ- • Stüve Diagram, ated with the temperature of the droplets, and also • Pseudoadiabatic (Stüve) Diagram, changes the heat capacity of the remaining air be- • Theta-Height (θ-z) Diagram. cause of the change in relative amounts of the differ- ent constituents. The net result is that an air parcel Why are there so many diagrams that show the lifted pseudoadiabatically from 100 kPa to 20 kPa same things? Historically, different diagrams were will be about 3°C colder than one lifted adiabati- devised somewhat independently in different coun- cally. This small difference between adiabatic and tries. Nations would adopt one as the “official” di- agram for their national weather service, and teach pseudoadiabatic can usually be neglected compared only that one to their meteorologists. For example, to other errors in measuring soundings. the tephigram is used in British Commonwealth countries (UK, Canada, Australia, New Zealand). To complete thermo diagrams this day, many meteorologists feel most comfortable with the diagram they learned first. Color thermo diagrams printed on large-format For many readers, this myriad of diagrams might paper were traditionally used by weather services make an already-difficult subject seem even more for hand plotting of soundings, but have become ob- daunting. Luckily, all the diagrams show the same solete and expensive compared to modern plots by thermodynamic state (T, P, rs) and process lines (θ, computer. The simplified, small-format diagrams θw), but in different orientations. So once you have presented so far in this chapter are the opposite ex- learned how to read one diagram, it is fairly easy to treme – useful for education, but not for plotting real read the others. soundings. Also, some weather stations have sur- The skill to read diverse thermo diagrams will face pressure greater than 100 kPa, which is off the serve you well when acquiring weather data via the scale for the simple diagrams presented so far. internet, because they can come in any format. The As a useful compromise, full-page, black-and- internet is the main reason I cataloged the different white thermo diagrams in several formats are in- thermo diagrams in this book. Of all these diagrams, the Skew-T and Tephigram cluded at the end of this chapter. They are opti- have the greatest angle between isotherms and mized for you to reproduce on a copy machine. adiabats, and are therefore preferred when studying soundings and stability. These two diagrams look [Hint: Keep the original thermo diagrams in this book similar, but the Skew-T is growing in popularity be- clean and unmarked, to serve as master copies.] cause it is easier to create on a computer. 122 chapter 5 STABILITy into the dry adiabats at higher altitudes and colder typeS Of thermo diagramS temperatures. Isohumes are almost straight lines, tilting upward to the right. This diagram is designed so that the isotherms emagram and dry adiabats are nearly (but not perfectly) per- “Emagram” is a contraction for “Energy-per-unit- pendicular to each other. mass diagram.” This semi-log diagram (Fig. 5.3a) has temperature (T) along the abscissa, and pressure tephigram (P) decreasing logarithmically upward along the or- The name Tephigram is a contraction of Tee-Phi dinate.