tag:blogger.com,1999:blog-3829360315915666182017-06-06T22:20:11.284-07:00An Introduction to Dynamic MeteorologyDevoted to discussing the book and all things related to dynamic meteorology.Greg Hakimnoreply@blogger.comBlogger6125tag:blogger.com,1999:blog-382936031591566618.post-57492226190047610142013-02-25T10:48:00.001-08:002016-12-14T14:46:03.193-08:00ErrataThis post contains a list of known errors in the book. Equations are rendered using MathJax, which requires Javascript. Please send email to the Gmail account <span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">holton.hakim</span> if you know of errors not included below. Thank you --Greg Hakim<br /><hr color="black" size="4" width="95%" /><br /><ul><li>page 14, line 9: "measures" should be "measure"</li><li>page 15, line 3: "...increases the westerly momentum..." is confusing, and should read, "...increases the zonal momentum..." </li><li>section 2.1: all occurrences of "total derivative" should read "material derivative" since the former is used in contexts not related to rates of change following the motion. (Thanks Dale Durran) </li><li>page 57, line 5: (2.54) should be (2.53)</li><li>page 65, problem 2.10: this problem should be in the problem section for Chapter 3. </li><li>page 91, line 4 should read "... Southern Hemisphere (\(f<0 \)) case."</li><li>page 112, line 8: \(\frac{U \theta^*}{\rho H L} + \frac{f \theta^*}{H}\) should read \(\frac{U \theta^*}{\rho^* H L} + \frac{f \theta^*}{\rho^* H}\)</li><li>page 115, equation (4.31) is missing a minus sign. </li><li>page 115, sentence above equation (4.32) should read, "Integrating the hydrostatic equation from the top of the fluid, \(h(x,y,t)\), to level \(z\), gives..." </li><li>page 116, equation (4.35) and the logic leading to it, is wrong. Since pressure depends on (x,y,z,t), the total differential has contributions from those variables that give an identity for Dp/Dt. Instead, one may take \(\frac{D}{Dt}\) of (4.32), giving $$\frac{Dp}{Dt} = \rho_0 g\left(\frac{Dh}{Dt} - w \right) $$ which yields (4.36) at \( z = h\).</li><li>page 117, Figure 4.11: although technically correct, the labels for \(\theta\) on the right side of the figure should reflect \(z\).</li><li>page 118, the third line of section 4.5.1 should read "...density depends only on pressure." (thanks Leo Kroon).</li><li>page 118, Figure 4.12: in the upper panel of the figure, the rightmost vorticity value of \(\zeta < 0\) should read \(\zeta = 0 \). (Thanks Uma Bhatt)</li><li>page 142, last line: \(v' = -ikg/f\) should read \(v' = ikgh'/f\) (thanks Fang-Ching Chien)</li><li>page 143, 4th line: \(u' = c/\bar{h}\) should read \(u' = ch'/\bar{h}\) (thanks Fang-Ching Chien)</li><li>page 150, line before equation (5.73): should read "Using (5.71) and (5.72) to evaluate (5.70)..." (thanks Ewan Short)</li><li>page 151, three lines below equation (5.70): "...form of (5.49):" should read "...form of (5.69):" (thanks Leo Kroon)</li><li>page 152, Figure 5.11: \(\hat{M}_0\) should read \(M_0\) (thanks Fang-Ching Chien)</li><li>page 162, below equation (5.111) should read " which reduces to (5.107) when the..." (thanks Tom Guinn)</li><li>page 162, 6 lines from the bottom should read " ...(see Problem 5.15) ..." (thanks Tom Guinn)</li><li>page 181, line -8: "...we can make..." (extra "we") (Thanks Fang-Ching Chien)</li><li>page 190, line -10: "...and if the zonal wind increases..." should be "...and a zonal wind that increases..." </li><li>page 195, equation (6.37): a factor of \(f\) is missing from the right side. The full equation should read:$$ {\rm L} \frac{\partial p}{\partial t} \, = \, -{\bf V}_g {\bf \cdot} {\bf \nabla}_h (f \zeta_g) - {\bf V}_g {\bf \cdot \nabla}_h \left(f^2 \frac{\partial}{\partial z}\frac{d\bar{\theta}}{dz}^{-1} \theta \right)$$ (Thanks Joel Norris)</li><li>page 197, equation (6.40): \(\zeta\) should be \(\zeta_g\) (thanks Fang-Ching Chien</li><li>page 198, equation (6.42): \(\zeta\) should be \(\zeta_g\) (thanks Fang-Ching Chien</li><li>page 199, equation (6.47): the very last term should read $$ -v_j \frac{\partial}{\partial x_j}\frac{\partial\zeta}{\partial x_3}$$ (Thanks Joel Norris)</li><li>page 199, equation (6.49): the right hand side of the equation should have a minus sign.</li><li>page 201, line below equation (6.55): \(\partial v_i \partial x_3 \) should read \(\partial v_i/ \partial x_3 \). The three lines after (6.55) are mixed together, and should read "... is the deformation term. The deformation term is one of two terms in the divergence of the <b>Q</b>-vector. Noting that ..., in vector notation, " (thanks Fang-Ching Chien)</li><li>page 203, Fig. 6.17: the abscissa label should be \(y\) (thanks Fang-Ching Chien)</li><li>page 205, last sentence: "...we expect clouds to form, releasing latent heat." (thanks Fang-Ching Chien)</li><li>page 206, line 4, (see Figure 6.10a) should read: (see Figure 4.10a) (thanks Fang-Ching Chien) </li><li>page 240. The first sentence of constraint 1. should read, " If \(\partial\bar{u}/\partial z^* = 0 \) at \(z^* = 0\) ..." (Thanks Nora Leps)</li><li>page 262: There is an extraneous \(h\) in the definition of wind speed below the main equations. (Thanks Tom Guinn)</li><li>page 268: Footnote 3 should read "...eddy stress (see footnote 2)..." (Thanks Ben Green) </li><li>page 314, equation (9.58) should read: \(m \, = \, r v + \frac{1}{2} f r^2 \) </li><li>page 373, line 10: ..."water vapor increase..." should be "...water vapor increases..."</li><li>page 401: equations (11.27) and (11.28) should read \(-\partial\Phi^{'}/\partial x \) and \(-\partial\Phi^{'}/\partial y \), respectively. (Thanks Rob Korty)</li><li>page 499: in the statement of the divergence theorem \({\bf V \cdot B}\) should read \({\bf \nabla \cdot B}\) (Thanks Fred Carr)</li><li>page 499: in the statement of Stokes' theorem \({\bf V \times B}\) should read \({\bf \nabla \times B}\) (Thanks Fred Carr)</li></ul><br />Greg Hakimhttps://plus.google.com/106762170529442825085noreply@blogger.com6tag:blogger.com,1999:blog-382936031591566618.post-68168158911670204372012-10-31T11:34:00.002-07:002012-11-20T14:01:39.613-08:00Superstorm Sandy and the tropopauseAmong the many remarkable aspects of Superstorm Sandy is the evolution of the tropoause during the event. Lacking time for a full post on that right now, I will share the most recent view of potential temperature on the tropoause, which shows a plume of very warm air (>340K) over the North Atlantic ocean.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-NyumdTVHvKM/UJFtDmMSPvI/AAAAAAAAABM/ITsqIoOmoCQ/s1600/trop_theta_20121031.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-NyumdTVHvKM/UJFtDmMSPvI/AAAAAAAAABM/ITsqIoOmoCQ/s320/trop_theta_20121031.png" width="291" /></a></div>The plume has been stretched, with one blob over the central Atlantic and the other over eastern North America. These blobs are connected by a thin ribbon over the North Atlantic. An <a href="http://www.atmos.washington.edu/~hakim/loop.psp?url=~hakim/tropo/sandy/" target="_blank">animation</a> of over the past seven days shows the evolution of the tropical plume, and the thinning filament. One gets no hint of this detail from a 500 hPa map (NOAA/ESRL)<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-0FaAw4OLJHU/UJFuUZgyItI/AAAAAAAAABU/8TbmX8-42AM/s1600/500z_01.fnl_20121031.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="247" src="http://4.bp.blogspot.com/-0FaAw4OLJHU/UJFuUZgyItI/AAAAAAAAABU/8TbmX8-42AM/s320/500z_01.fnl_20121031.gif" width="320" /></a></div>which shows an omega-type blocking pattern (slightly different time, but that doesn't matter). There's no hint of the tropical air over eastern North America, or the filament.<br /><br />Greg Hakimhttps://plus.google.com/106762170529442825085noreply@blogger.com0tag:blogger.com,1999:blog-382936031591566618.post-11603290921191015012012-10-04T10:48:00.002-07:002012-10-04T10:48:35.072-07:00Eastern Pacific "modon" blockOver the northeastern Pacific Ocean right now there is a great example of a Rex block, which I prefer to refer to as a "modon" block, for reasons that I will mention shortly. These blocks consist of a high-over-low pattern, which is evident in the 500 hPa chart for today (lines are 500 hPa geopotential height every 30 m, and colors are absolute vorticity; <a href="http://credit/" target="_blank">credit</a>). <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-PoWKSWG9gMc/UG3GhcpxqcI/AAAAAAAAAA0/_Po5lbdlFEY/s1600/wrf_1004_modon.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="268" src="http://2.bp.blogspot.com/-PoWKSWG9gMc/UG3GhcpxqcI/AAAAAAAAAA0/_Po5lbdlFEY/s320/wrf_1004_modon.png" width="320" /></a></div><br />I call this a modon block because its structure is very close to analytical solutions known as modons. Here's an example from <a href="http://journals.ametsoc.org/doi/full/10.1175/JAS3958.1" target="_blank">Muraki and Snyder (2007)</a>, showing the streamfunction (like geopotential height): <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-BgYy8MQEc5w/UG3HMta9dbI/AAAAAAAAAA8/Nq2wzSBUa_8/s1600/Muraki_synder_modon.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="316" src="http://2.bp.blogspot.com/-BgYy8MQEc5w/UG3HMta9dbI/AAAAAAAAAA8/Nq2wzSBUa_8/s320/Muraki_synder_modon.jpg" width="320" /></a></div>Modon solutions are known for the barotropic and quasi-geostrophic equations, on the plane and on the sphere. What makes them truly remarkable is that they are <i><b>exact</b> solutions of the full nonlinear equations</i>, which is a rare. Perhaps more important is that they are useful for understanding the dynamics of weather systems! The low-over-high version is a good model of a jet streak, which is discussed in Chapter 6 of the book(see Figs. 6.12, 6.16 and 6.17).<br /><br />As can be seen from the figures above, the high-over-low version is a good model for blocking, and this subject is explored in Matlab problem M6.5, which uses the QG model and diagnostic package that come with the book. I will have more to say about those tools in future posts, because I think they provide a really cool way for students to explore dynamic meterology. <br /><br /><br />Greg Hakimhttps://plus.google.com/106762170529442825085noreply@blogger.com0tag:blogger.com,1999:blog-382936031591566618.post-83940911399473306742012-10-01T11:14:00.000-07:002012-10-01T11:14:47.011-07:00Companion web page for the bookThe companion website for the book is located <a href="http://booksite.elsevier.com/9780123848666/index.php" target="_blank">here</a>. This page provides all online support for the text, including all <a href="http://figures/" target="_blank">figures</a>, MATLAB <a href="http://booksite.elsevier.com/9780123848666/matlab_code.php" target="_blank">scripts</a>, and a solutions manual for instructors.<br /><br />These pages are under continual development, so you will see new features appear over time. In particular, we plan to add additional color figures to the image bank and links to other resources.<br /><br />Please note that equation references in the comments of Matlab scripts have not yet been updated to the 5th edition, but will soon.<br /><br /><br />Greg Hakimhttps://plus.google.com/106762170529442825085noreply@blogger.com2tag:blogger.com,1999:blog-382936031591566618.post-20302778598570967132012-09-27T12:11:00.000-07:002012-09-27T12:12:11.819-07:00Overview of changes from the 4th editionI finally have the book in my hands, which feels really good after working on this project for so long. I didn't get to do all that I planned, but most of the major changes in the book proposal are represented in the 5th edition.<br /><br />I view this book as having a "book within a book" involving the first six chapters. Those six chapters are essential for students studying dynamic meteorology, ranging from an introduction to the fundamental equations, to their simplification and application to understanding weather systems. I tried to restructure the book so that progression flows logically.<br /><br />You can read about the details of the changes in the preface to the 5th edition, but here's a brief summary of the highlights for the first six chapters.<br /><br /><ul><li>In Chapter 1, there's a new section on kinematics, the analysis of motion without reference to forces. This material introduces basic aspects of the structure of wind systems, and defines quantities used to measure those aspects throughout the book, such as vorticity and divergence.</li><li>Chapter 2 has new sections on the Boussinesq approximation and moist thermodynamics. These are used extensively later in the book, so I thought it made sense to elevate their status to the "basic conservation laws" chapter.</li><li>In Chapter 4, potential vorticity is given a richer treatment, including a simple derivation from the Kelvin circulation theorem, and an introduction to tropopause maps, which provide a modern perspective for extratropical dynamics. </li><li>Wave motions are vitally important in dynamic meteorology, so what was formerly Chapter 7 is now Chapter 5. Rossby waves, both stationary and propagating, are given expanded treatment, and the properties of these waves that distinguishes them from inertia-gravity waves are used to motivate the quasi-geostrophic equations that follow in Chapter 6.</li><li>Chapter 6 has been mostly re-written from the 4th edition. The goal was to provide a streamlined, accessible, introduction to quasi-geostrophic theory. The basic elements of the theory are relatively simple, but it is easy to make QG theory seem very complicated and abstract. Two perspectives are given: "PV Thinking" and "W Thinking." PV Thinking provides a concise and powerful view of extratropical dynamics, but lacks a connection to vertical motion. W Thinking promotes the importance of vertical motion and the role of ageostrophic circulations in changing momentum, vorticity, and potential temperature. These concepts are illustrated with idealized disturbances modeled on archetypal weather disturbances found in midlatitudes (short-wave troughs and jet streaks). Moreover, MATLAB codes, including a QG model and diagnostic package, are provided for students to explore these ideas on their own. Students that master both perspectives have a powerful arsenal for explaining the existence of large-scale cloud patterns, and understanding the interaction of extratropical weather systems and their components. </li></ul>So overall, the changes are meant to bring the book up to date, and to enrich the text with bits of synoptic meteorology that should help students make the leap from the text to the real atmosphere.Greg Hakimhttps://plus.google.com/106762170529442825085noreply@blogger.com2tag:blogger.com,1999:blog-382936031591566618.post-6885038462686165322012-06-19T15:19:00.000-07:002012-06-20T11:08:34.450-07:00Announcing the 5th edition of James R. Holton's classic textHello, World.<br /><br />This blog is devoted to the book entitled, <u><i>An Introduction to Dynamic Meteorology</i></u> by James R. Holton and Gregory J. Hakim. We'll use this space for a variety of purposes, including discussing the content and its use in the classroom, errata, plans for future editions, current weather, and anything else that makes sense in the world of atmospheric dynamics. <br /><br />The main announcement at the current time is that the 5th edition of the book is in the final stages of preparation, and <a href="http://store.elsevier.com/An-Introduction-to-Dynamic-Meteorology/James-Holton/isbn-9780123848666/">pre-orders are now accepted. </a><br /><br /><div class="separator" style="clear: both; text-align: center;"><img alt="" border="0" src="http://2.bp.blogspot.com/-S7Y5dJR_uR8/T-D47RJz8OI/AAAAAAAAAAY/H2_zHNoJ2r8/s1600/9780123848666.jpg" title="An Introduction to Dynamic Meteorology" /></div><br />Please add this page to your reader, or check back for future updates.Greg Hakimhttps://plus.google.com/106762170529442825085noreply@blogger.com1