Copyright © 2017 by Roland Stull. Practical Meteorology: An Algebra-based Survey of Atmospheric Science. v1.02 17 REGIONAL WINDS Contents Each locale has a unique landscape that creates or modifies the wind. These local winds affect where 17.1. Wind Frequency 645 we choose to live, how we build our buildings, what 17.1.1. Wind-speed Frequency 645 we can grow, and how we are able to travel. 17.1.2. Wind-direction Frequency 646 During synoptic high pressure (i.e., fair weather), 17.2. Wind-Turbine Power Generation 647 some winds are generated locally by temperature 17.3. Thermally Driven Circulations 648 differences. These gentle circulations include ther- 17.3.1. Thermals 648 mals, anabatic/katabatic winds, and sea breezes. 17.3.2. Cross-valley Circulations 649 During synoptically windy conditions, moun- 17.3.3. Along-valley Winds 653 tains can modify the winds. Examples are gap 17.3.4. Sea breeze 654 winds, boras, hydraulic jumps, foehns/chinooks, 17.4. Open-Channel Hydraulics 657 and mountain waves. 17.4.1. Wave Speed 658 17.4.2. Froude Number - Part 1 659 17.4.3. Conservation of Air Mass 660 17.4.4. Hydraulic Jump 660 17.5. Gap Winds 661 17.1. WIND FREQUENCY 17.5.1. Basics 661 17.5.2. Short-gap Winds 661 17.1.1. Wind-speed Frequency 17.5.3. Long-gap Winds 662 Wind speeds are rarely constant. At any one 17.6. Coastally Trapped Low-level (Barrier) Jets 664 location, wind speeds might be strong only rare- 17.7. Mountain Waves 666 ly during a year, moderate many hours, light even 17.7.1. Natural Wavelength 666 more hours, and calm less frequently (Fig. 17.1). The 17.7.2. Lenticular Clouds 666 number of times that a range ∆M of wind speeds 17.7.3. Froude Number - Part 2 667 occurred in the past is the frequency of occurrence. 17.7.4. Mountain-wave Drag 668 Dividing the frequency by the total number of wind 17.8. Streamlines, Streaklines, and Trajectories 668 measurements gives a relative frequency. The ex- 17.9. Bernoulli’s Equation 669 pectation that this same relative frequency will oc- 17.9.1. Principles 669 cur in the future is the probability (Pr). 17.9.2. Some Applications 672 The probability distribution of mean wind speeds 17.10. Downslope Winds 675 M at any location is described by the Weibull dis- 17.10.1. Bora 675 tribution: 17.10.2. Foehns and Chinooks 676 α α ··∆MMα−1 M 17.11. Canopy Flows 677 Pr (17.1) = α ·exp − 17.11.1. Forests and Crops 677 Mo Mo 17.11.2. Cities 678 17.12. Review 679 17.13. Homework Exercises 680 0.2 17.13.1. Broaden Knowledge & Comprehension 680 17.13.2. Apply 681 0.15 17.13.3. Evaluate & Analyze 684 0.1 17.13.4. Synthesize 686 Probability 0.05 0 “Practical Meteorology: An Algebra-based Survey of Atmospheric Science” by Roland Stull is licensed 0 1 2 3 4 5 6 7 8 9 10 11 12 under a Creative Commons Attribution-NonCom- M (m/s) mercial-ShareAlike 4.0 International License. View this license at Figure 17.1 http://creativecommons.org/licenses/by-nc-sa/4.0/ . This work is Wind-speed M probability (relative frequency) for a Weibull dis- available at https://www.eoas.ubc.ca/books/Practical_Meteorology/ –1 tribution with parameters α = 2 and Mo = 5 m s . 645 646 CHAPTER 17 • REGIONAL WINDS where Pr is the probability (or relative frequency) Sample Application –1 of wind speed M± 0.5·∆M. Such wind-speed vari- Given Mo = 5 m s and α = 2, find the probability that the wind speed will be between 5.5 & 6.5 m s–1? ations are caused by synoptic, mesoscale, local and boundary-layer processes. Find the Answer Location parameter Mo is proportional to the –1 –1 Given: Mo = 5 m s , α = 2, M= 6 m s mean wind speed. For spread parameter α, small- ∆M = 6.5 – 5.5 m s–1 = 1 m s–1, er α causes wider spread of winds about the mean. Find: Pr = ? (dimensionless) Values of the parameters and the corresponding dis- tribution shape vary from place to place. Use eq. (17.1): The bin size or resolution is ∆M. For exam- 21− 2 21·( m/sm)·()6 /s 6m/s ple, the column plotted in Fig. 17.1 for M = 3 m s–1 Pr =−·exp 2 is the probability that the wind is between 2.5 and ()5m/s 5m/s 3.5 m s–1. The width of each column in the histo- = 0.114 = 11.4% gram is ∆M = 1 m s–1. The sum of probabilities for all wind speeds should equal 1, meaning there is a Check: Units OK. Physics OK. 100% chance that the wind speed is between zero Exposition: This agrees with Fig. 17.1 at M = 6 m s–1, which had the same parameters as this example. To and infinity. Use this to check for errors. Eq. (17.1) is get a sum of probabilities that is very close to 100%, use only approximate, so the sum of probabilities almost a smaller bin size ∆M and be sure not to cut off the tail equals 1. of the distribution at high wind speeds. Wind-speed distributions are useful to estimate electrical power generation by wind turbines, and when designing buildings and bridges to withstand N extreme winds. NNW 30% NNE You can express extreme-wind likelihood as a re- turn period (RP), which is equal to the total period NW NE 20% of measurement divided by the number of times the wind exceeded a threshold. For example, if winds exceeding 30 m s–1 occurred twice during the last WNW ENE 10% century, then the return period for 30 m s–1 winds is RP = (100 yr)/2 = 50 years. Faster winds occur less frequently, and have greater return periods. W E near calm 5.3% 17.1.2. Wind-direction Frequency By counting the frequency of occurrence that 10% WSW ESE winds came from each compass direction (N, NNE, NE, etc.) over a period such as 10 years, and then plotting that frequency on a polar graph, the result 20% SW SE is called a wind rose. For example, Fig. 17.2 shows the wind rose for Vancouver Airport (CYVR). SSW SSE The total length of each wind line gives the total S 30% Speed legend frequency of any wind speed from that direction, >5.5 m/s while the width (or color) of the line subdivides that 3.4 - 5.5 Figure 17.2 frequency into the portions associated with various 1.9 - 3.4 wind speeds. (Not all wind roses are subdivided by 0.5 - 1.9 Wind rose for Vancouver Airport (CYVR), Canada. Circles indicate frequency. wind speed.) The frequency of calm winds is usu- ally written in the center of the circle if it fits, or is indicated off to the side. The sum of all the frequen- cies (including calm) should total 100%. At a glance, Sample Application How frequent are east winds at Vancouver airport? the longest lines indicate the predominant wind di- rections for any location. Find the Answer For example, at Vancouver Airport, East (E) winds Use Fig. 17.2. Frequency ≈ 26% . (winds from the east) are most frequent, followed by winds from the WNW and then from the ESE. Air- Exposition: This is the sum of 2% for 0.5 < M ≤ 1.9, craft take-offs and landings are safer — and require plus 9% for 1.9 < M ≤ 3.4, plus 10% for 3.4 < M ≤ 5.5, plus shorter distances — if they are done into the wind. 5% for M > 5.5 m s–1. Hence, airports are built with their runways aligned R. STULL • PRACTICAL METEOROLOGY 647 parallel to the predominant wind directions (within 08L CYVR reason, as dictated by property boundaries and ob- stacles). Fig. 17.3 shows that the runways at Vancouver 12 Terminal 26R Airport are appropriate for the wind climatology of Building N the previous figure. The end of each runway is la- true N beled with the magnetic compass direction (in tens magnetic of degrees; e.g., 12 means 120° magnetic) towards which the aircraft is flying when approaching that 08R Magnetic Variation = 19°E end of the runway from outside the airport. Thus, aircraft will use runway 30 for winds from 300°. Parallel runways are labeled as left (L) or right (R). 30 26L Figure 17.3 Plan view of runways at Vancouver International Airport (CYVR), Canada. 17.2. WIND-TURBINE POWER GENERATION Power is defined as the rate of energy production. Sample Application Kinetic energy of the wind is proportional to air A wind turbine at sea level uses a 30 m radius blade to convert a 10 m s–1 wind into electrical power at 40% mass times wind-speed squared. The rate at which efficiency. What is the theoretical power output? this energy is blown through a wind turbine is the wind speed. Thus, the theoretical power available Find the Answer from the wind is proportional to wind speed cubed: –3 –1 Given: ρ =1.225 kg·m , R=30 m, Min = 10 m s , E = 0.4 Find: Power = ? kW (Appendix A defines Watt, W) 23 PowerE=π(/2)·ρ··RM· in (17.2) Use eq. (17.2): –3 2 –1 3 where R is the turbine-blade radius, Min is incoming Power = (π/2)·(1.225 kg·m )·(0.4)·(30m) ·(10m s ) wind speed, and ρ is air density.