Virtual Temperature Thickness Sea Level Pressure Potential Temperature Equivalent Potential Temperature
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Pressure Gradient Force Examples of Pressure Gradient Hurricane Andrew, 1992 Extratropical Cyclone
4/29/2011 Chapter 7: Forces and Force Balances Forces that Affect Atmospheric Motion Pressure gradient force Fundamental force - Gravitational force FitiFrictiona lfl force Centrifugal force Apparent force - Coriolis force • Newton’s second law of motion states that the rate of change of momentum (i.e., the acceleration) of an object , as measured relative relative to coordinates fixed in space, equals the sum of all the forces acting. • For atmospheric motions of meteorological interest, the forces that are of primary concern are the pressure gradient force, the gravitational force, and friction. These are the • Forces that Affect Atmospheric Motion fundamental forces. • Force Balance • For a coordinate system rotating with the earth, Newton’s second law may still be applied provided that certain apparent forces, the centrifugal force and the Coriolis force, are • Geostrophic Balance and Jetstream ESS124 included among the forces acting. ESS124 Prof. Jin-Jin-YiYi Yu Prof. Jin-Jin-YiYi Yu Pressure Gradient Force Examples of Pressure Gradient Hurricane Andrew, 1992 Extratropical Cyclone (from Meteorology Today) • PG = (pressure difference) / distance • Pressure gradient force goes from high pressure to low pressure. • Closely spaced isobars on a weather map indicate steep pressure gradient. ESS124 ESS124 Prof. Jin-Jin-YiYi Yu Prof. Jin-Jin-YiYi Yu 1 4/29/2011 Gravitational Force Pressure Gradients • • Pressure Gradients – The pressure gradient force initiates movement of atmospheric mass, widfind, from areas o fhihf higher to areas o flf -
Chapter 5. Meridional Structure of the Atmosphere 1
Chapter 5. Meridional structure of the atmosphere 1. Radiative imbalance 2. Temperature • See how the radiative imbalance shapes T 2. Temperature: potential temperature 2. Temperature: equivalent potential temperature 3. Humidity: specific humidity 3. Humidity: saturated specific humidity 3. Humidity: saturated specific humidity Last time • Saturated adiabatic lapse rate • Equivalent potential temperature • Convection • Meridional structure of temperature • Meridional structure of humidity Today’s topic • Geopotential height • Wind 4. Pressure / geopotential height • From a hydrostatic balance and perfect gas law, @z RT = @p − gp ps T dp z(p)=R g p Zp • z(p) is called geopotential height. • If we assume that T and g does not vary a lot with p, geopotential height is higher when T increases. 4. Pressure / geopotential height • If we assume that g and T do not vary a lot with p, RT z(p)= (ln p ln p) g s − • z increases as p decreases. • Higher T increases geopotential height. 4. Pressure / geopotential height • Geopotential height is lower at the low pressure system. • Or the high pressure system corresponds to the high geopotential height. • T tends to be low in the region of low geopotential height. 4. Pressure / geopotential height The mean height of the 500 mbar surface in January , 2003 4. Pressure / geopotential height • We can discuss about the slope of the geopotential height if we know the temperature. R z z = (T T )(lnp ln p) warm − cold g warm − cold s − • We can also discuss about the thickness of an atmospheric layer if we know the temperature. RT z z = (ln p ln p ) p1 − p2 g 2 − 1 4. -
Pressure Gradient Force
2/2/2015 Chapter 7: Forces and Force Balances Forces that Affect Atmospheric Motion Pressure gradient force Fundamental force - Gravitational force Frictional force Centrifugal force Apparent force - Coriolis force • Newton’s second law of motion states that the rate of change of momentum (i.e., the acceleration) of an object, as measured relative to coordinates fixed in space, equals the sum of all the forces acting. • For atmospheric motions of meteorological interest, the forces that are of primary concern are the pressure gradient force, the gravitational force, and friction. These are the • Forces that Affect Atmospheric Motion fundamental forces. • Force Balance • For a coordinate system rotating with the earth, Newton’s second law may still be applied provided that certain apparent forces, the centrifugal force and the Coriolis force, are • Geostrophic Balance and Jetstream ESS124 included among the forces acting. ESS124 Prof. Jin-Yi Yu Prof. Jin-Yi Yu Pressure Gradient Force Examples of Pressure Gradient Hurricane Andrew, 1992 Extratropical Cyclone (from Meteorology Today) • PG = (pressure difference) / distance • Pressure gradient force goes from high pressure to low pressure. • Closely spaced isobars on a weather map indicate steep pressure gradient. ESS124 ESS124 Prof. Jin-Yi Yu Prof. Jin-Yi Yu 1 2/2/2015 Balance of Force in the Vertical: Pressure Gradients Hydrostatic Balance • Pressure Gradients – The pressure gradient force initiates movement of atmospheric mass, wind, from areas of higher to areas of lower pressure Vertical -
Chapter 8 Atmospheric Statics and Stability
Chapter 8 Atmospheric Statics and Stability 1. The Hydrostatic Equation • HydroSTATIC – dw/dt = 0! • Represents the balance between the upward directed pressure gradient force and downward directed gravity. ρ = const within this slab dp A=1 dz Force balance p-dp ρ p g d z upward pressure gradient force = downward force by gravity • p=F/A. A=1 m2, so upward force on bottom of slab is p, downward force on top is p-dp, so net upward force is dp. • Weight due to gravity is F=mg=ρgdz • Force balance: dp/dz = -ρg 2. Geopotential • Like potential energy. It is the work done on a parcel of air (per unit mass, to raise that parcel from the ground to a height z. • dφ ≡ gdz, so • Geopotential height – used as vertical coordinate often in synoptic meteorology. ≡ φ( 2 • Z z)/go (where go is 9.81 m/s ). • Note: Since gravity decreases with height (only slightly in troposphere), geopotential height Z will be a little less than actual height z. 3. The Hypsometric Equation and Thickness • Combining the equation for geopotential height with the ρ hydrostatic equation and the equation of state p = Rd Tv, • Integrating and assuming a mean virtual temp (so it can be a constant and pulled outside the integral), we get the hypsometric equation: • For a given mean virtual temperature, this equation allows for calculation of the thickness of the layer between 2 given pressure levels. • For two given pressure levels, the thickness is lower when the virtual temperature is lower, (ie., denser air). • Since thickness is readily calculated from radiosonde measurements, it provides an excellent forecasting tool. -
Comparison Between Observed Convective Cloud-Base Heights and Lifting Condensation Level for Two Different Lifted Parcels
AUGUST 2002 NOTES AND CORRESPONDENCE 885 Comparison between Observed Convective Cloud-Base Heights and Lifting Condensation Level for Two Different Lifted Parcels JEFFREY P. C RAVEN AND RYAN E. JEWELL NOAA/NWS/Storm Prediction Center, Norman, Oklahoma HAROLD E. BROOKS NOAA/National Severe Storms Laboratory, Norman, Oklahoma 6 January 2002 and 16 April 2002 ABSTRACT Approximately 400 Automated Surface Observing System (ASOS) observations of convective cloud-base heights at 2300 UTC were collected from April through August of 2001. These observations were compared with lifting condensation level (LCL) heights above ground level determined by 0000 UTC rawinsonde soundings from collocated upper-air sites. The LCL heights were calculated using both surface-based parcels (SBLCL) and mean-layer parcels (MLLCLÐusing mean temperature and dewpoint in lowest 100 hPa). The results show that the mean error for the MLLCL heights was substantially less than for SBLCL heights, with SBLCL heights consistently lower than observed cloud bases. These ®ndings suggest that the mean-layer parcel is likely more representative of the actual parcel associated with convective cloud development, which has implications for calculations of thermodynamic parameters such as convective available potential energy (CAPE) and convective inhibition. In addition, the median value of surface-based CAPE (SBCAPE) was more than 2 times that of the mean-layer CAPE (MLCAPE). Thus, caution is advised when considering surface-based thermodynamic indices, despite the assumed presence of a well-mixed afternoon boundary layer. 1. Introduction dry-adiabatic temperature pro®le (constant potential The lifting condensation level (LCL) has long been temperature in the mixed layer) and a moisture pro®le used to estimate boundary layer cloud heights (e.g., described by a constant mixing ratio. -
MSE3 Ch14 Thunderstorms
Chapter 14 Copyright © 2011, 2015 by Roland Stull. Meteorology for Scientists and Engineers, 3rd Ed. thunderstorms Contents Thunderstorms are among the most violent and difficult-to-predict weath- Thunderstorm Characteristics 481 er elements. Yet, thunderstorms can be Appearance 482 14 studied. They can be probed with radar and air- Clouds Associated with Thunderstorms 482 craft, and simulated in a laboratory or by computer. Cells & Evolution 484 They form in the air, and must obey the laws of fluid Thunderstorm Types & Organization 486 mechanics and thermodynamics. Basic Storms 486 Thunderstorms are also beautiful and majestic. Mesoscale Convective Systems 488 Supercell Thunderstorms 492 In thunderstorms, aesthetics and science merge, making them fascinating to study and chase. Thunderstorm Formation 496 Convective Conditions 496 Thunderstorm characteristics, formation, and Key Altitudes 496 forecasting are covered in this chapter. The next chapter covers thunderstorm hazards including High Humidity in the ABL 499 hail, gust fronts, lightning, and tornadoes. Instability, CAPE & Updrafts 503 CAPE 503 Updraft Velocity 508 Wind Shear in the Environment 509 Hodograph Basics 510 thunderstorm CharaCteristiCs Using Hodographs 514 Shear Across a Single Layer 514 Thunderstorms are convective clouds Mean Wind Shear Vector 514 with large vertical extent, often with tops near the Total Shear Magnitude 515 tropopause and bases near the top of the boundary Mean Environmental Wind (Normal Storm Mo- layer. Their official name is cumulonimbus (see tion) 516 the Clouds Chapter), for which the abbreviation is Supercell Storm Motion 518 Bulk Richardson Number 521 Cb. On weather maps the symbol represents thunderstorms, with a dot •, asterisk , or triangle Triggering vs. Convective Inhibition 522 * ∆ drawn just above the top of the symbol to indicate Convective Inhibition (CIN) 523 Trigger Mechanisms 525 rain, snow, or hail, respectively. -
GEF2200 Spring 2018: Solutions Thermodynam- Ics 1
GEF2200 spring 2018: Solutions thermodynam- ics 1 A.1.T What is the difference between R and R∗? R∗ is the universal gas constant, with value 8.3143JK−1mol−1. R is the gas constant for a specific gas, given by R∗ R = (1) M where M is the molecular weight of the gas (usually given in g/mol). In other words, R takes into account the weight of the gas in question so that mass can be used in the equation of state. For the equation of state: m pV = nR∗T = R∗T = mRT (2) M It is important to note that we usually use mass m in units of [kg], which requires that the units of R is changed accordingly (if given in [J/gK], it must be multiplied by 1000 [g/kg]). A.2.T What is apparent molecular weight, and why do we use it? Apparent molecular weight is the average molecular weight for a mixture of gases. We introduce ∗ it to calculate a gas constant R = R =Md for the mixture , where Md is the apparent molecular weight of i different gases given by Equation (3.10): P m P m P n M M = i = i = i i d P mi n n Mi X ni = M (3) n i In meteorology the most common apparent molecular weight is the one of air. WH06 3.19 Determine the apparent molecular weight of the Venusian atmosphere, assuming that it consists of 95% CO2 and 5% N2 by volume. What is the gas constant for 1 kg of such an atmosphere? (Atomic weights of C, O and N are 12, 16 and 14 respectively.) Concentrations by volume (See exercise A.8.T): V v = N2 (4) N2 V V v = CO2 (5) CO2 V 1 Assuming ideal gas, we have total volume V = VN2 + VCO2 at a given temperature (T ) and pressure (p). -
Chapter 7 Isopycnal and Isentropic Coordinates
Chapter 7 Isopycnal and Isentropic Coordinates The two-dimensional shallow water model can carry us only so far in geophysical uid dynam- ics. In this chapter we begin to investigate fully three-dimensional phenomena in geophysical uids using a type of model which builds on the insights obtained using the shallow water model. This is done by treating a three-dimensional uid as a stack of layers, each of con- stant density (the ocean) or constant potential temperature (the atmosphere). Equations similar to the shallow water equations apply to each layer, and the layer variable (density or potential temperature) becomes the vertical coordinate of the model. This is feasible because the requirement of convective stability requires this variable to be monotonic with geometric height, decreasing with height in the case of water density in the ocean, and increasing with height with potential temperature in the atmosphere. As long as the slope of model layers remains small compared to unity, the coordinate axes remain close enough to orthogonal to ignore the complex correction terms which otherwise appear in non-orthogonal coordinate systems. 7.1 Isopycnal model for the ocean The word isopycnal means constant density. Recall that an assumption behind the shallow water equations is that the water have uniform density. For layered models of a three- dimensional, incompressible uid, we similarly assume that each layer is of uniform density. We now see how the momentum, continuity, and hydrostatic equations appear in the context of an isopycnal model. 7.1.1 Momentum equation Recall that the horizontal (in terms of z) pressure gradient must be calculated, since it appears in the horizontal momentum equations. -
1050 Clicker Questions Exam 1
Answers to Clicker Questions Chapter 1 What component of the atmosphere is most important to weather? A. Nitrogen B. Oxygen C. Carbon dioxide D. Ozone E. Water What location would have the lowest surface pressure? A. Chicago, Illinois B. Denver, Colorado C. Miami, Florida D. Dallas, Texas E. Los Angeles, California What is responsible for the distribution of surface pressure shown on the previous map? A. Temperature B. Elevation C. Weather D. Population If the relative humidity and the temperature at Denver, Colorado, compared to that at Miami, Florida, is as shown below, how much absolute water vapor is in the air between these two locations? A. Denver has more absolute water vapor B. Miami has more absolute water vapor C. Both have the same amount of water vapor Denver 10°C Air temperature 50% Relative humidity Miami 20°C Air temperature 50% Relative humidity Chapter 2 Convert our local time of 9:45am MST to UTC A. 0945 UTC B. 1545 UTC C. 1645 UTC D. 2345 UTC A weather observation made at 0400 UTC on January 10th, would correspond to what local time (MST)? A. 11:00am January10th B. 9:00pm January 10th C. 10:00pm January 9th D. 9:00pm January 9th A weather observation made at 0600 UTC on July 10th, would correspond to what local time (MDT)? A. 12:00am July 10th B. 12:00pm July 10th C. 1:00pm July 10th D. 11:00pm July 9th A rawinsonde measures all of the following variables except: Temperature Dew point temperature Precipitation Wind speed Wind direction What can a Doppler weather radar measure? Position of precipitation Intensity of precipitation Radial wind speed All of the above Only a and b In this sounding from Denver, the tropopause is located at a pressure of approximately: 700 mb 500 mb 300 mb 100 mb Which letter on this radar reflectivity image has the highest rainfall rate? A B C D C D B A Chapter 3 • Using this surface station model, what is the temperature? (Assume it’s in the US) 26 °F 26 °C 28 °F 28 °C 22.9 °F Using this surface station model, what is the current sea level pressure? A. -
Thunderstorm Predictors and Their Forecast Skill for the Netherlands
Atmospheric Research 67–68 (2003) 273–299 www.elsevier.com/locate/atmos Thunderstorm predictors and their forecast skill for the Netherlands Alwin J. Haklander, Aarnout Van Delden* Institute for Marine and Atmospheric Sciences, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands Accepted 28 March 2003 Abstract Thirty-two different thunderstorm predictors, derived from rawinsonde observations, have been evaluated specifically for the Netherlands. For each of the 32 thunderstorm predictors, forecast skill as a function of the chosen threshold was determined, based on at least 10280 six-hourly rawinsonde observations at De Bilt. Thunderstorm activity was monitored by the Arrival Time Difference (ATD) lightning detection and location system from the UK Met Office. Confidence was gained in the ATD data by comparing them with hourly surface observations (thunder heard) for 4015 six-hour time intervals and six different detection radii around De Bilt. As an aside, we found that a detection radius of 20 km (the distance up to which thunder can usually be heard) yielded an optimum in the correlation between the observation and the detection of lightning activity. The dichotomous predictand was chosen to be any detected lightning activity within 100 km from De Bilt during the 6 h following a rawinsonde observation. According to the comparison of ATD data with present weather data, 95.5% of the observed thunderstorms at De Bilt were also detected within 100 km. By using verification parameters such as the True Skill Statistic (TSS) and the Heidke Skill Score (Heidke), optimal thresholds and relative forecast skill for all thunderstorm predictors have been evaluated. -
1 Module 4 Water Vapour in the Atmosphere 4.1 Statement of The
Module 4 Water Vapour in the Atmosphere 4.1 Statement of the General Meteorological Problem D. Brunt (1941) in his book Physical and Dynamical Meteorology has stated, “The main problem to be discussed in connection to the thermodynamics of the moist air is the variation of temperature produced by changes of pressure, which in the atmosphere are associated with vertical motion. When damp air ascends, it must eventually attain saturation, and further ascent produces condensation, at first in the form of water drops, and as snow in the later stages”. This statement of the problem emphasizes the role of vertical ascends in producing condensation of water vapour. However, several text books and papers discuss this problem on the assumption that products of condensation are carried with the ascending air current and the process is strictly reversible; meaning that if the damp air and water drops or snow are again brought downwards, the evaporation of water drops or snow uses up the same amount of latent heat as it was liberated by condensation on the upward path of the air. Another assumption is that the drops fall out as the damp air ascends but then the process is not reversible, and Von Bezold (1883) termed it as a pseudo-adiabatic process. It must be pointed out that if the products of condensation are retained in the ascending current, the mathematical treatment is easier in comparison to the pseudo-adiabatic case. There are four stages that can be discussed in connection to the ascent of moist air. (a) The air is saturated; (b) The air is saturated and contains water drops at a temperature above the freezing-point; (c) All the water drops freeze into ice at 0°C; (d) Saturated air and ice at temperatures below 0°C. -
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.