14 Thunderstorm Fundamentals
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Laboratory Studies of Turbulent Mixing J.A
Laboratory Studies of Turbulent Mixing J.A. Whitehead Woods Hole Oceanographic Institution, Woods Hole, MA, USA Laboratory measurements are required to determine the rates of turbulent mixing and dissipation within flows of stratified fluid. Rates based on other methods (theory, numerical approaches, and direct ocean measurements) require models based on assumptions that are suggested, but not thoroughly verified in the laboratory. An exception to all this is recently provided by direct numerical simulations (DNS) mentioned near the end of this article. Experiments have been conducted with many different devices. Results span a wide range of gradient or bulk Richardson number and more limited ranges of Reynolds number and Schmidt number, which are the three most relevant dimensionless numbers. Both layered and continuously stratified flows have been investigated, and velocity profiles include smooth ones, jets, and clusters of eddies from stirrers or grids. The dependence of dissipation through almost all ranges of Richardson number is extensively documented. The buoyancy flux ratio is the turbulent kinetic energy loss from raising the potential energy of the strata to loss of kinetic energy by viscous dissipation. It rises from zero at small Richardson number to values of about 0.1 at Richardson number equal to 1, and then falls off for greater values. At Richardson number greater than 1, a wide range of power laws spanning the range from −0.5 to −1.5 are found to fit data for different experiments. Considerable layering is found at larger values, which causes flux clustering and may explain both the relatively large scatter in the data as well as the wide range of proposed power laws. -
Boundary Layer Verification
Boundary Layer Verification ECMWF training course April 2015 Maike Ahlgrimm Aim of this lecture • To give an overview over strategies for boundary layer evaluation • By the end of this session you should be able to: – Identify data sources and products suitable for BL verification – Recognize the strengths and limitations of the verification strategies discussed – Choose a suitable verification method to investigate model errors in boundary layer height, transport and cloudiness. smog over NYC Overview • General strategy for process-oriented model evaluation • What does the BL parameterization do? • Broad categories of BL parameterizations • Which aspects of the BL can we evaluate? – What does each aspect tell us about the BL? • What observations are available – What are the observations’ advantages and limitations? • Examples – Clear convective BL – Cloud topped convective BL – Stable BL Basic strategy for model evaluation and improvement: Observations Identify discrepancy Model Output Figure out source of model error Improve parameterization When and where does error occur? Which parameterization(s) is/are involved? What does the BL parameterization do? Attempts to integrate Turbulence transports effects of small scale temperature, moisture and turbulent motion on momentum (+tracers). prognostic variables at grid resolution. Stull 1988 Ultimate goal: good model forecast and realistic BL Broad categories of BL parameterizations Unified BL schemes Specialized BL scheme •Attempt to integrate BL (and •One parameterization for each shallow cloud) effects in one discrete BL type scheme to allow seamless transition •Simplifies parameterization for •Often statistical schemes (i.e. each type, parameterization for making explicit assumptions about each type ideally suited PDFs of modelled variables) using •Limitation: must identify BL type moist-conserved variables reliably, is noisy (lots of if •Limitation: May not work well for statements) mixed-phase or ice •Example: Met-Office (Lock et al. -
Meteorology – Lecture 19
Meteorology – Lecture 19 Robert Fovell [email protected] 1 Important notes • These slides show some figures and videos prepared by Robert G. Fovell (RGF) for his “Meteorology” course, published by The Great Courses (TGC). Unless otherwise identified, they were created by RGF. • In some cases, the figures employed in the course video are different from what I present here, but these were the figures I provided to TGC at the time the course was taped. • These figures are intended to supplement the videos, in order to facilitate understanding of the concepts discussed in the course. These slide shows cannot, and are not intended to, replace the course itself and are not expected to be understandable in isolation. • Accordingly, these presentations do not represent a summary of each lecture, and neither do they contain each lecture’s full content. 2 Animations linked in the PowerPoint version of these slides may also be found here: http://people.atmos.ucla.edu/fovell/meteo/ 3 Mesoscale convective systems (MCSs) and drylines 4 This map shows a dryline that formed in Texas during April 2000. The dryline is indicated by unfilled half-circles in orange, pointing at the more moist air. We see little T contrast but very large TD change. Dew points drop from 68F to 29F -- huge decrease in humidity 5 Animation 6 Supercell thunderstorms 7 The secret ingredient for supercells is large amounts of vertical wind shear. CAPE is necessary but sufficient shear is essential. It is shear that makes the difference between an ordinary multicellular thunderstorm and the rotating supercell. The shear implies rotation. -
On the Computation of Planetary Boundary-Layer Height Using the Bulk Richardson Number Method
Geosci. Model Dev., 7, 2599–2611, 2014 www.geosci-model-dev.net/7/2599/2014/ doi:10.5194/gmd-7-2599-2014 © Author(s) 2014. CC Attribution 3.0 License. On the computation of planetary boundary-layer height using the bulk Richardson number method Y. Zhang1, Z. Gao2, D. Li3, Y. Li1, N. Zhang4, X. Zhao1, and J. Chen1,5 1International Center for Ecology, Meteorology & Environment, Jiangsu Key Laboratory of Agricultural Meteorology, College of Applied Meteorology, Nanjing University of Information Science and Technology, Nanjing 210044, China 2State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry (LAPC), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China 3Program of Atmospheric and Oceanic Sciences, Princeton University, Princeton, NJ 08540, USA 4School of Atmospheric Sciences, Nanjing University, Nanjing, 210093, China 5Department of Geography, Michigan State University, East Lansing, MI 48824, USA Correspondence to: Z. Gao ([email protected]) Received: 15 March 2014 – Published in Geosci. Model Dev. Discuss.: 24 June 2014 Revised: 12 September 2014 – Accepted: 22 September 2014 – Published: 10 November 2014 Abstract. Experimental data from four field campaigns are 1 Introduction used to explore the variability of the bulk Richardson num- ber of the entire planetary boundary layer (PBL), Ribc, which The planetary boundary layer (PBL), or the atmospheric is a key parameter for calculating the PBL height (PBLH) boundary layer, is the lowest part of the atmosphere that is in numerical weather and climate models with the bulk directly influenced by earth’s surface and has significant im- Richardson number method. First, the PBLHs of three differ- pacts on weather, climate, and the hydrologic cycle (Stull, ent thermally stratified boundary layers (i.e., strongly stable 1988; Garratt, 1992; Seidel et al., 2010). -
Chapter 5 Frictional Boundary Layers
Chapter 5 Frictional boundary layers 5.1 The Ekman layer problem over a solid surface In this chapter we will take up the important question of the role of friction, especially in the case when the friction is relatively small (and we will have to find an objective measure of what we mean by small). As we noted in the last chapter, the no-slip boundary condition has to be satisfied no matter how small friction is but ignoring friction lowers the spatial order of the Navier Stokes equations and makes the satisfaction of the boundary condition impossible. What is the resolution of this fundamental perplexity? At the same time, the examination of this basic fluid mechanical question allows us to investigate a physical phenomenon of great importance to both meteorology and oceanography, the frictional boundary layer in a rotating fluid, called the Ekman Layer. The historical background of this development is very interesting, partly because of the fascinating people involved. Ekman (1874-1954) was a student of the great Norwegian meteorologist, Vilhelm Bjerknes, (himself the father of Jacques Bjerknes who did so much to understand the nature of the Southern Oscillation). Vilhelm Bjerknes, who was the first to seriously attempt to formulate meteorology as a problem in fluid mechanics, was a student of his own father Christian Bjerknes, the physicist who in turn worked with Hertz who was the first to demonstrate the correctness of Maxwell’s formulation of electrodynamics. So, we are part of a joined sequence of scientists going back to the great days of classical physics. -
Basic Features on a Skew-T Chart
Skew-T Analysis and Stability Indices to Diagnose Severe Thunderstorm Potential Mteor 417 – Iowa State University – Week 6 Bill Gallus Basic features on a skew-T chart Moist adiabat isotherm Mixing ratio line isobar Dry adiabat Parameters that can be determined on a skew-T chart • Mixing ratio (w)– read from dew point curve • Saturation mixing ratio (ws) – read from Temp curve • Rel. Humidity = w/ws More parameters • Vapor pressure (e) – go from dew point up an isotherm to 622mb and read off the mixing ratio (but treat it as mb instead of g/kg) • Saturation vapor pressure (es)– same as above but start at temperature instead of dew point • Wet Bulb Temperature (Tw)– lift air to saturation (take temperature up dry adiabat and dew point up mixing ratio line until they meet). Then go down a moist adiabat to the starting level • Wet Bulb Potential Temperature (θw) – same as Wet Bulb Temperature but keep descending moist adiabat to 1000 mb More parameters • Potential Temperature (θ) – go down dry adiabat from temperature to 1000 mb • Equivalent Temperature (TE) – lift air to saturation and keep lifting to upper troposphere where dry adiabats and moist adiabats become parallel. Then descend a dry adiabat to the starting level. • Equivalent Potential Temperature (θE) – same as above but descend to 1000 mb. Meaning of some parameters • Wet bulb temperature is the temperature air would be cooled to if if water was evaporated into it. Can be useful for forecasting rain/snow changeover if air is dry when precipitation starts as rain. Can also give -
HODOGRAPHS and SEVERE WEATHE B E. W. Mccaul. Jr.. Steve
HODOGRAPHS AND SEVERE WEATHE B E. W. McCaul. Jr.. Steve Lazarus. Fred Carr One ingredient which is believed to be important in governing the morphology of thunderstorms is the profile of vertical shear in the environment which supports the storms. Numerous observational and theoretical studies have shown that storms which form in weakly-sheared environments tend to have non-steady circulations (multicells), while those that form in strongly-sheared environments can develop steady, persistent circulations (supereells). Although intuition suggests that strong shear can only inhibit the formation of organized updrafts, this tendency is partly offset by the ability of shear flows to generate a variety of hydrodynamical instabilities which allow for the possibility of updraft growth. Forecasters who work in areas of the country prone to outbreaks of severe weather should be prepared to recognize not only the thermodynamic conditions but also the vertical shear conditions favorable for various types of severe storms. Inspection of temperature and moisture soundings can reveal the presence of the necessary thermodynamic instability, while inspection of wind profiles (hodographs) can help diagnose whether conditions are right for the development of tornadoes. Hodographs can be drawn either as plots of u (z) vs. v (z) in Cartesian coordinates or V (z) vs. 8 (z) in cylindrical coordinates. In either case, the actual shape of the hodograph will be the same for any given wind profile. On the OU Meteorology weather computer, hodographs from any raob station may be plotted using "mchodo" in GEMPAK. Each plotted hodograph represents nothing more than the curve which connects, in order of ascending altitude, the tips of all the observed wind vectors from a sounding, with the bases of the vectors attached to a common origin. -
NOAA Technical Memorandum NWS WR-221 UTILIZATION of the BULK RICHARDSON NUMBER, HELICITY and SOUNDING MODIFICATION in the ASSESS
NOAA Technical Memorandum NWS WR-221 UTILIZATION OF THE BULK RICHARDSON NUMBER, HELICITY AND SOUNDING MODIFICATION IN THE ASSESSMENT OF THE SEVERE CONVECTIVE STORMS OF 3 AUGUST 1992 ~ \ Eric C. Evenson Weather Service Forecast Office Great Falls, Montana November 1993 u.s. DEPARTMENT OF I National Oceanic and National Weather COMMERCE Atmospheric Administration I Service 75 A Study of the Low Level Jet Stream of the San Joaqnin Valley. Ronald A Wlllis and NOAA TECHNICAL MEMORANDA Philip Williams, Jr., May 1972. (COM 72 10707) National Weather Service, Western Region Subseries 76 Monthly Climatological Charta of the Behavior of Fog and Low Stratus at Los Angeles International Airport. Donald M. Gales, July 1972. (COM 72 11140) The National Weather Service (NWS) Western Region (WR) Subseries provi~es an informal 77 A Study of Radar Echo Distribution in Arizona During July and August. John E. Hales, Jr.. medium for the documentation and quick dissemination of results not. appropnate, or not ~et July 1972. (COM 72 11136) ready, for formal publication. The series is used to report. o'! work '-? progreas, to des~ 78 Forecasting Precipitation at Bakersfield, California, Using Preasure Gradient Vectors. Earl technical procedures and practices, or. to relate progre_as ~ a limited. audience. These Techrucal T. Riddiough, July 1972. (COM 72 11146) Memoranda will report on investigations devoted primarily to regtonal and local problems of 79 Climate of Stockton, California. Robert C. Nelson, July 1972. (COM 72 10920) interest mainly to penionnel, and hence will not be widely distributed. 60 Estimation of Number of Days Above or Below Selected Temperatures. Clarence M. -
The Effect of Stable Thermal Stratification on Turbulent Boundary
The effect of stable thermal stratifcation on turbulent boundary layer statistics O.Williams, T. Hohman, T. Van Buren, E. Bou-Zeid and A. J. Smits May 22, 2019 Abstract The effects of stable thermal stratifcation on turbulent boundary layers are ex- perimentally investigated for smooth and rough walls. Turbulent stresses for weak to moderate stability are seen to scale with the wall-shear stress compensated for changes in fuid density in the same manner as done for compressible fows, sug- gesting little change in turbulent structure within this regime. At higher levels of stratifcation turbulence no longer scales with the wall shear stress and turbu- lent production by mean shear collapses, but without the preferential damping of near-wall motions observed in previous studies. We suggest that the weakly sta- ble and strongly stable (collapsed) regimes are delineated by the point where the turbulence no longer scales with the local wall shear stress, a signifcant departure from previous defnitions. The critical stratifcation separating these two regimes closely follows the linear stability analysis of Schlichting (1935) [Schlichting, Hauptaufs¨atze. Turbulenz bei W¨armeschichtung, ZAMM-J. of App. Math. and Mech., vol 15, 1935 ] for both smooth and rough surfaces, indicating that a good predictor of critical stratifcation is the gradient Richardson number evaluated at the wall. Wall-normal and shear stresses follow atmospheric trends in the local gradient Richardson number scaling of Sorbjan (2010) [Sorbjan, Gradient-based scales and similarity laws in the stable boundary layer, Q.J.R. Meteorological Soc., vol 136, 2010], suggesting that much can be learned about stratifed atmo- spheric fows from the study of laboratory scale boundary layers at relatively low Reynolds numbers. -
Thickness and Thermal Wind
ESCI 241 – Meteorology Lesson 12 – Geopotential, Thickness, and Thermal Wind Dr. DeCaria GEOPOTENTIAL l The acceleration due to gravity is not constant. It varies from place to place, with the largest variation due to latitude. o What we call gravity is actually the combination of the gravitational acceleration and the centrifugal acceleration due to the rotation of the Earth. o Gravity at the North Pole is approximately 9.83 m/s2, while at the Equator it is about 9.78 m/s2. l Though small, the variation in gravity must be accounted for. We do this via the concept of geopotential. l A surface of constant geopotential represents a surface along which all objects of the same mass have the same potential energy (the potential energy is just mF). l If gravity were constant, a geopotential surface would also have the same altitude everywhere. Since gravity is not constant, a geopotential surface will have varying altitude. l Geopotential is defined as z F º ò gdz, (1) 0 or in differential form as dF = gdz. (2) l Geopotential height is defined as F 1 z Z º = ò gdz (3) g0 g0 0 2 where g0 is a constant called standard gravity, and has a value of 9.80665 m/s . l If the change in gravity with height is ignored, geopotential height and geometric height are related via g Z = z. (4) g 0 o If the local gravity is stronger than standard gravity, then Z > z. o If the local gravity is weaker than standard gravity, then Z < z. -
Stable Boundary Layer Issues
Stable Boundary Layer Issues G.J. Steeneveld Meteorology and Air Quality Section, Wageningen University Wageningen, The Netherlands [email protected] Abstract Understanding and prediction of the stable atmospheric boundary layer is a challenging task. Many physical processes are relevant in the stable boundary layer, i.e. turbulence, radiation, land surface coupling, orographic turbulent and gravity wave drag, and land surface heterogeneity. The development of robust stable boundary layer parameterizations for use in NWP and climate models is hampered by the multiplicity of processes and their unknown interactions. As a result, these models suffer from typical biases in key variables, such as 2m temperature, boundary layer depth, boundary layer wind speed. This paper summarizes the physical processes active in the stable boundary layer, their particular role, their interconnections and relevance for different stable boundary layer regimes (if understood). Also, the major model deficiencies are reported. 1. Introduction The planetary boundary layer (PBL) over land experiences a clear diurnal cycle due to the diurnal cycle of incoming radiation. From the evening transition, the Earth’s surface cools due to net longwave radiative loss. Consequently, the potential temperature increases with height, and a stable boundary layer (SBL) develops. As an illustration, Figure 1 depicts a histogram of near surface stability expressed in the bulk Richardson number (Ri) for one year (2008) of observations at the Wageningen observatory (Netherlands). For this mid-latitude station, the atmosphere is stably stratified for 51% of the time. Considering only stable conditions, the Ri distribution is heavily skewed with a median Ri of 0.01, and mean of 0.22. -
Analysis of Stability Parameters in Relation to Precipitation Associated with Pre-Monsoon Thunderstorms Over Kolkata, India
Analysis of stability parameters in relation to precipitation associated with pre-monsoon thunderstorms over Kolkata, India H P Nayak and M Mandal∗ Centre for Oceans, Rivers, Atmosphere and Land Sciences, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India ∗Corresponding author. e-mail: [email protected] The upper air RS/RW (Radio Sonde/Radio Wind) observations at Kolkata (22.65N, 88.45E) during pre- monsoon season March–May, 2005–2012 is used to compute some important dynamic/thermodynamic parameters and are analysed in relation to the precipitation associated with the thunderstorms over Kolkata, India. For this purpose, the pre-monsoon thunderstorms are classified as light precipitation (LP), moderate precipitation (MP) and heavy precipitation (HP) thunderstorms based on the magnitude of associated precipitation. Richardson number in non-uniformly saturated (Ri*) and saturated atmosphere (Ri); vertical shear of horizontal wind in 0–3, 0–6 and 3–7 km atmospheric layers; energy-helicity index (EHI) and vorticity generation parameter (VGP) are considered for the analysis. The instability measured ∗ in terms of Richardson number in non-uniformly saturated atmosphere (Ri ) well indicate the occurrence of thunderstorms about 2 hours in advance. Moderate vertical wind shear in lower troposphere (0–3 km) and weak shear in middle troposphere (3–7 km) leads to heavy precipitation thunderstorms. The wind shear in 3–7 km atmospheric layers, EHI and VGP are good predictors of precipitation associated with thunderstorm. Lower tropospheric wind shear and Richardson number is a poor discriminator of the three classified thunderstorms. 1. Introduction high socio-economic impact, thunderstorms are of serious concern to researchers and meteorologists.