Module 9 Weather Systems In this module the theory of atmospheric dynamics is applied to different weather phenomena. The first section deals with extratropical cyclones, low and high pressure areas of the temperate latitudes. Also the mesoscale (surface) fronts and associated weather changes are dealt with. After that the focus is on smaller scale systems, tropical cyclones, strong convective systems and tornadoes. The Rossby number is introduced for scaling purposes. Read the parts of Wallace and Hobbs indicated below: Chapter 8 Weather Systems 8.1 Extratropical Cyclones... 313 8.1.1 An Overview... 313 8.1.2 Fronts and Surface Weather (not: 8.1.2f and g)... 318 8.1.3 Vertical Structure (not: 8.1.3c)... 328 8.4 Tropical Cyclones... 366 8.4.1 Structure, Thermodynamics, and Dynamics... 366 8.4.2 Genesis and Life Cycle... 369 8.4.3 Storm Surges... 370 Key concepts of the reading material Ridge Trough Warm front Cold front Plotting synoptic charts Rossby number Convective Available Potential Energy Convective Inhibition Cyclostrophic wind speed Questions you should be able to answer after reading the material Explain the typical sequence of weather observations when a warm front passes Explain the typical sequence of weather observations when a cold front passes What is an occlusion front? Why can the Coriolis force be neglected in a cyclostrophic flow? Read the background material presented below: Rossby number Rotating systems in the atmosphere can be described with the gradient wind equation. This equation holds the balance between the centrifugal force, the horizontal pressure gradient force (P) and the Coriolis force (C). As a start we repeat equation 7.16 from Wallace and Hobbs (page 283): 2 V n = - Φ - f k V (9.1) R T which can also be written in component form using natural coordinates: 2 V - - fv (9.2) R n T To simplify these equations we need to find the relative importance of individual terms so one can apply scale analysis. Relatively small terms can then be neglected. Note that the pressure gradient force can never be neglected as it is Meteorology and Climate 57 of 93
the only force that can drive horizontal motions in the atmosphere. The other terms of Equation 9.1 can be neglected under certain conditions. In case the isohypses are straight and parallel (i.e. no centrifugal force) we are left with an equation that has been named geostrophic balance. In physical terms this would mean the radius of curvature is infinitely large ( R ± ), and thus the wind follows a straight line. Motions like this are described in Wallace and Hobbs equation 7.15 (page 281): 1 V g k (9.3) f This equation can be derived from Equation 9.1. It is easier if we put Equation 9.3 in component form and natural coordinates: V g - 1 (9.4) f n To describe the flow around a normal (anti)cyclone the full gradient wind equation is needed. The resulting wind speed is either subgeostrophic (for cyclones) or supergeostrophic (for anticyclones). Neglecting the Coriolis force is permitted in cases with small horizontal scale. The remaining equation is a cyclostrophic balance. In this case the direction of the flow is not determined by the Coriolis force and can be both cyclonic and anticyclonic around a low pressure area (Figure 9.1). Using Equation 9.2 this would lead to 2 V - R n T Equation 8.5 on page 352 of Wallace and Hobbs states the same result but for isobars instead of isohypses: 2 v 1 p (9.5) r r Note that Wallace and Hobbs have replaced the n -coordinate with the r - coordinate which is in the opposite direction, hence the minus sign has disappeared. Also note that the geopotential has been rearranged to pressure (using equation 3.20 of Wallace and Hobbs, page 68). To determine whether it is allowed to neglect the Coriolis force the Rossby number is often used. The Rossby number is a dimensionless [-] indicator of the relative importance of the Coriolis force to the centrifugal force. The formal definition is: 2 V Fcf RT V Ro (9.6) C f V f R T Small values ( Ro 0-0. 1) of the Rossby number indicate that the flow is nearly in geostrophic balance. Large values ( Ro > 100) of the Rossby number indicate that cyclostrophic balance is valid. T Meteorology and Climate 58 of 93
v L P Fcf C L P v Fcf (a) Figure 9.1 Force balance around an anti-clockwise turning Low pressure area (a) and a clockwise turning Low pressure area (b). Both in the Northern Hemisphere. The latter can only exist if the Coriolis force is small compared to the other forces (e.g. in dust devils). (b) Exercise 1 Extratropical Cyclones 1.1a What kind of weather do the symbols in figure 9.2 indicate? 1.1b Create a plot for the following weather situation: It has been a cloudy day with a moderate breeze (14 kts) from the north west. Surface pressure is 997.4 hpa and has risen slowly with 1.5 hpa. Temperature has been constant at 12 C (dew point 8 C). Continuous light rain led to a cumulative amount of 3 inches in the past 6 hours. Figure 9.2 Plot on a synoptic chart 1.2a What features indicate for an observer on Earth the passage of a: - cold front 1.2b - warm front Exercise 2* Simplifying Equations for Rotating Systems 2.1a In this exercise we will simplify the gradient wind equation, by neglecting small terms, depending on the magnitude of the terms. Which terms are important depends mainly on the size and the velocities of the system considered. Estimate typical velocities (V ) and length scales ( R T ) of: - a low-pressure system at 52 N 2.1b - a hurricane at 15 N 2.1c - a tornado at 52 N 2.1d - a dust devil at 52 N 2.1e - a bath-tube eddy at 52 N 2.2 For each of the systems now estimate the centrifugal force and the Coriolis force per unit mass. 2.3 Calculate the Rossby number, which is the ratio between the two forces. Meteorology and Climate 59 of 93
2.4 Now, for each of the systems rewrite Wallace and Hobbs Equation 7.17 and neglect (if possible) the smallest term. Give also the official name of the resulting simplified equations (gradient wind equation, geostrophic balance, cyclostrophic approximation) and motivate your answer. 2.5a Do Wallace and Hobbs exercise 8.8j (page 371) about the rotation of tornadoes. 2.5b Do Wallace and Hobbs exercise 8.8o (page 371) about the force balance in cyclones. * This is an exercise at exam level Exercise 3 Deep convection 3.1a Shade convective available potential energy in the thermodynamic diagram of figure 9.3. 3.1b Also indicate the energy needed to overcome the convective inhibition. 3.2a Find the wind speed for a tornado with radius 100 metres and a pressure deficit between core and surrounding environment of 4.0 kpa. 3.2b The Fujita (F) intensity scale is often used to classify the intensity of tornadoes. It is based on the damage caused by the tornado. The scale ranges from F0 for slight damage to F12 for damage caused by wind speeds of Mach 1. The lower wind speed bound for each F range (such as F2 and F3) is defined by: V = a ( 2F + 4) 1. 5 (9.6) -1 where a = 2.25ms. Tornadoes of F5 intensity and greater all cause nearly total destruction of most buildings and tress, so it is virtually impossible to identify tornadoes of F6 or greater based on damage surveys. In what category would the tornado of exercise 3.2a fall? Figure 9.3 Vertical profiles from a radio sounding from 24 June 1998 in Athens (Greece). Meteorology and Climate 60 of 93
Practical 9 Analysis of Weather Systems The typical characteristics of frontal systems and recognizing frontal systems on weather maps are connected to the weather elements measured at or near the surface. Especially for locating fronts on a surface chart it is important to know the differences between the various weather elements on both sides of a frontal system. Exercise 1. Characteristics of frontal systems - Read the separate file (in Blackboard or on W:\Projects\MAQ21806\unit9MC) Identification of fronts.pdf. It presents an overview of the way in which weather elements, such as wind, pressure and temperature, might change if a cold or warm front passes the observer. We have used the phrase might because not all elements will either: change at all, or change simultaneously, or change in the way described in the appendix. As these elements are measured near the earth s surface local circumstances such as the proximity to the coast, a lake, city or mountains or e.g. the fact that there is snow on the ground, may alter the behavior of these elements. What is in the tables must be rather viewed as a rule of thumb. 1. What usually happens with the pressure just after a cold front has passed the observer? 2. What is the reasons for this change in pressure? 3. What is the definition of the warm sector of a midlatitude cyclone? 4. Why is it sometimes difficult to locate fronts on the basis of gradients of surface temperature alone? 5. What usually happens with the cloud amount when a cold front passes the observer? 6. How can this be explained? 7. For a warm front, why is most of the precipitation located ahead of the front, i.e. before the front arrives? Exercise 2. Decoding meteorological data Meteorological data from observations is sent around the world in a specially coded and internationally accepted format, which makes it easy to read anywhere on earth. - To understand this format, open the file SYNOP_short.html (in Blackboard or on W:\Projects\MAQ21806\unit9MC) as you will need it to answer the following questions. We will decode some observational data in the following exercises. - For Nddff we have: 81226. 8. Give the wind direction (in degrees). 9. Give the wind speed (in kts). Note that the wind speed may be either in m s -1 or kts (=knots) depending on an index value not discussed at this moment. For now assume that the unit for wind speed is kts. - The group i Ri xhvv reads 41228. 10. Give the cloud base of the lowest clouds (average value in m). 11. Give the visibility (in km). - During the past hour a thunderstorm was observed, but at the moment of observation, say 15.00 hours UTC, the rain had stopped and the thunderstorm was no longer active and had moved away. 12. In the 7wwW 1W 2 group what numbers should be allocated to ww? 13. And for the same group, what number should be allocated to W 1? Meteorology and Climate 61 of 93
- Temperatures measured at a station are T = 3.7 C and Td = -1.2 C. 14. Give the value for the code 1s nttt. 15. Also give the value for the code 2s nt dt dt d. Exercise 3. Reading the plot model For use on a weather map all data, after decoding, should be represented in such a manner that it is easy to read. Therefore it should be printed both systematically and in an internationally agreed manner. Representing observation data is such a way is called plotting. Read Plotting symbols.pdf (in Blackboard or on W:\Projects\MAQ21806\unit9MC) carefully and then answer questions on the following observations: - Observation: total cloud cover = 4/8. 16. What is the corresponding codeletter of this observation? 17. What is the coded value of this observation? 18. What is the symbol of this observation? - Observation: low cloud type stratocumulus. 19. What is the corresponding code of this observation? 20. What is the coded value of this observation? 21. What is the symbol of this observation? - Observation: pressure decreasing, then increasing resultant pressure lower. 22. What is the corresponding code of this observation? 23. What is the coded value of this observation? 24. What is the symbol of this observation? - Weather type: continuous moderate rain. 25. What is the ww -value? 26. What is the symbol? - Weather type: fog, sky not visible, thinning. 27. What is the ww -value? 28. What is the symbol? - Weather type: light rain showers. 29. What is the ww -value? 30. What is the symbol? - Weather type: hail showers within the past hour, but not at observation time. 31. What is the ww -value? 32. What is the symbol? 33. What information is decoded correctly from the following plot: Exercise 4. Passage of two fronts In the course of 18 hours two fronts passed a certain station in the South of England. Figure 9.4 shows the observations of the most important meteorological variables versus time (UTC). 34. At what time (UTC) did the warm front pass over the station? 35. From the observations as presented in Figure 9.4, the warm front passage can be detected in the following elements. 36. At what time (UTC) did the cold front pass over the station? - The cold front passage can (or cannot!) be deduced from the following elements: 37. From the observations as presented in Figure 9.4, the cold front passage can be detected in the following elements. Meteorology and Climate 62 of 93
Exercise 5. Reading the weather map In the weather map (Figure 9.5) isobars (thin black lines and three cold fronts (thick black lines) have been drawn. Only one of the cold fronts is the real one, the other two are incorrect. 38. What is the estimated pressure (in hpa) of the cyclonic centre lying over the Irish Sea (i.e. between England/Wales and Ireland)? 39. Does the closed isobar over Southern Sweden indicate a high pressure (anticyclone) or a low pressure (cyclone) area? 40. What is the correct location of the cold front (A, B, or C)? Meteorology and Climate 63 of 93
Figure 9.4 Observations of meteorological data during the passage of two fronts in December in Southern England. Time is in UTC, p in hpa, T and Td in C, VV (horizontal visibility) in m, h* (height of the lowest cloud base) in m. Meteorology and Climate 64 of 93
Figure 9.5 Weather map with three possible cold front locations. A larger version (higher resolution) can be found on Blackboard. Meteorology and Climate 65 of 93