We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byHannah Campbell
Modified about 1 year ago
Copyright © 2010 R.R. Dickerson & Z.Q. Li 1 The Slice Method Chapt 4 page 51. A conceptual model accounting for compensating motion by ambient air as a parcel or column rises. Introduced by Bjerknes, J. 1938: Saturated ascent of air through a dry adiabatically descending environment. Quart. J. Royal Meteorological Society, 65
Copyright © 2010 R.R. Dickerson & Z.Q. Li 2 Conditions to which the method applies: Initially horizontal layer of saturated air. There may be several regions in which the air is ascending and cooling moist adiabatically. Within the remainder of the layer there must be regions of descent with warming at the dry adiabatic rate.
Copyright © 2010 R.R. Dickerson & Z.Q. Li 3 Let * Ascending air have total horizontal area A and upward speed w. * Descending air have area A ’ and vertical speed w ’. Assume Rate at which mass descends through a fixed reference level in the slice of originally saturated air is equal to the rate at which mass ascends through the reference level.
Copyright © 2010 R.R. Dickerson & Z.Q. Li 4 In time dt, the mass dm transported upward and the mass dm` transported downwards may be written as: dm = Awdt = Adz = - AdP/g dm` = `A`w`dt = ` `dz` = - A`dP`/g dz/dz` = vertical distance traveled by ascending/descending air.
Copyright © 2010 R.R. Dickerson & Z.Q. Li 5 At the initial moment, the slice is horizontally homogenous: `. Since dm = dm`, we can divide the ascending equation by the descending: Assume also that advection is negligible.
Copyright © 2010 R.R. Dickerson & Z.Q. Li 6 Consider the layer as conditionally unstable: Let z o – reference level in the layer T – initial temperature of ascending air T ’ – initial temperature of descending air T f, T f ’ – final temperatures of a/de-scending air – lapse rate of ambient air When ascending air reaches z o : T f = T – s dz When descending air reaches z o : T f ’ = T ’ + d dz
Copyright © 2010 R.R. Dickerson & Z.Q. Li 7 popo zozo p o -dp ’ p o +dp z o -dz z o +dz ’ T ToTo T’T’ T f ’ = T ’ + d dz ’ T f = T- s dz So for the unstable case T f > T f ’ or T - s dz > T ’ + d dz ’ But for the initial conditions T = T o + dz T ’ = T o - dz ’
Copyright © 2010 R.R. Dickerson & Z.Q. Li 8 The two preceding expressions can be combined: ( – s )dz > ( d – dz ’ for instability to occur. ( – s )A ’ > ( d – A : unstable ( – s )A ’ = ( d – A : neutral ( – s )A ’ < ( d – A : stable
Copyright © 2010 R.R. Dickerson & Z.Q. Li 9 Define the lapse rate for neutral equilibrium Then the stability criteria reduce to n - unstable n - neutral n - stable Note: n is a weighted average of d and s with the weighting factors the areas of ascent and descent.
Copyright © 2010 R.R. Dickerson & Z.Q. Li 10 Thus, for the conditionally unstable case we are considering, accounting for compensating vertical motions by the ambient air requires the lapse rate to be steeper for instability to occur. The slice method is not easy to apply in practice Because it requires knowledge of the relative areas Of ascent (A) and descent (A ’ ). The stability criteria indicate that the chances for development of slice instability are greatest when A ’ is large and A is small for then n is small and more easily exceeded. Severe storms tend to have small updrafts and large are areas of subsidence.
4.2 Moist air thermodynamics (Reading Text , p79-101) Reading: Trenberth et al Climate dynamics, S for water vapor increase with temperature.
AIR POLLUTION AND METEOROLOGY Dr.K. Subramaniam, Senior Lecturer (Environmental Health and Safety )
Stable Equilibrium Unstable. Neutral Equilibrium.
Meteorology ENV 2A23 Stability and Moisture Lectures.
The Analysis of Convective Storms. Thermodynamic Diagrams There are three desirable characteristics of atmospheric thermodynamic diagrams: The area enclosed.
Richard (Rick) Jones SWFDP Training Workshop on Severe Weather Forecasting Bujumbura, Burundi, Nov 11-16, 2013.
15 Chapter 15 Moisture, Clouds, and Precipitation.
Time to failure Probability, Survival, the Hazard rate, and the Conditional Failure Probability.
1 Weather Essentials Concept Map MoistureTemperature Density / pressure Highs, lows, and fronts Wind/air motion (horizontal & vertical) Clouds Daily weather.
If θ/z = 0, the atmosphere is said to be neutral,or neutrally stratified, and the lapse rate is equal to the dry adiabatic lapse rate (DALR) Γ d ~= 10.
How do the clouds form?. Water Vapor Basics (names of different phase changes, latent heat) Humidity indices (there are 6 total). Saturation vapor pressure.
AP C UNIT 3 WORK & ENERGY. SCALAR PRODUCT or DOT PRODUCT Dot Product is defined as the magnitude of 1 st ( ) times scalar component of 2nd vector ( )
If the number of air molecules above a surface increases, there are more molecules to exert a force on that surface and consequently, the pressure increases.
Authored By Lt Colonel Garrett L. Sager 30-Jan-2006 Modified by Lt Colonel Fred Blundell TX-129 Fort Worth Senior Squadron For Local Training Rev Jan-2014.
Guided Notes on Thunderstorms Chapter 13, Section 1.
The Environment of Warm- Season Elevated Thunderstorms Associated with Heavy Rainfall over the Central United States Authors: James T. Moore Fred H. Glass.
Lecture 7 Grand Canonical Ensemble and Criteria for Equilibrium Problem 7.2 Grand Canonical Ensemble Entropy and equilibrium.
1 Numerical Weather Prediction Parameterization of diabatic processes Convection III The ECMWF convection scheme Peter Bechtold and Christian Jakob.
Copyright © by Holt, Rinehart and Winston. All rights reserved. ResourcesChapter menu Chapter 2 Table of Contents Section 1 Displacement and Velocity Section.
1 Peter Bechtold and Christian Jakob Numerical Weather Prediction Parametrization of diabatic processes Convection I An overview.
Severe Weather Part II: The Synoptic Scale Sets the Table Lab 11 Anthony R. Lupo Atms 4310 / 7310.
Warm-up 1/24/08. PS-2.2 Illustrate the fact that the atoms of elements exist as stable or unstable isotopes.
1 SKYAERO I shot an arrow toward the sky It hit a white cloud passing by The cloud fell dying to the shore I dont shoot arrows anymore - Shel Silverstein.
© Crown copyright Met Office Regional climate model formulation PRECIS Workshop, Reading University, 23 rd – 27 th April 2012.
PTT 204/3 APPLIED FLUID MECHANICS SEM 2 (2012/2013)
Numerical Weather Prediction Moist Thermodynamics Peter Bechtold and Adrian Tompkins.
Topic 2: Motion and Force Dynamics By: Mrs. Fagan.
Time averages and ensemble averages Values such as pressure or heat capacity generally depend upon the positions and momenta of the N particles that comprise.
Chapter 13 Middle Latitude Cyclones This chapter discusses: 1.The location, vertical structure, and developmental stages of middle latitude cyclones 2.How.
© P K Bharti, IIT Kharagpur. Please revise these topics before studying this chapter: TOPICS Kinematics (Displacement, velocity & acceleration)
© 2016 SlidePlayer.com Inc. All rights reserved.