Atmospheric Measurements and Observations EAS 535 Measuring characteristics of fronts Dr. J. Haase http://web.ics.purdue.edu/~jhaase/teaching/eas535/index.html
Vertical structure Contours of potential temperature (isentropes) are tightly packed at front in vertical cross-section. Parcel at 35 deg moving westward follows isentrope and moves upward. In 3D parcel follows topography of isentropic surface Strong temperature inversion at top of cold air
Definition of fronts
Typical fronts in central US
Geostrophic adjustment Pressure gradient force of cold air interface - balances - Coriolis force Therefore, steady geostrophic wind Ug blows from east to west.
Geostrophic adjustment External Rossby radius of deformation a =! R " g # H # $% / T v v f c $% v = difference in virtual potential temperature across front T v = average absolute virtual temperature ' U g = g # H # $% v / T v # exp y + a * ( ) a +, - ' h = H # 1 exp y + a * 0 / ( ) a +, 2. 1 h = height of the front
Geostrophic adjustment More realistic dynamic state after adjustment Low pressure above cold air, and high pressure above warm air creates opposite geostrophic winds Air is in equilibrium due to coriolis force, so cold air does not spread further Cyclones finish the process of redistribution of cold and warm air
Frontogenesis Potential temperature change per distance across the front is a measure of frontal strength Three types of frontogenetic physical processes increase the gradient: Kinematic Thermodynamic Dynamic Kinematics refers to advection Can t create temperature gradients Can strengthen or weaken existing gradients Examples of existing gradients: Global temp gradients from radiative heating Meanders in jet stream cause gradients along troughs and ridges Standard atmosphere vertical gradient Kinematics can indicate Confluence Shear Tilting
Kinematic frontogenesis Example: Initial field has uniform theta gradients in x,y,z directions Initially there is no front!" is positive!" is negative!y!"!z is positive FS #!" # frontal strength!fs % = $!" ( %!U ( %!t ' ) * + ' ) * $!" ( '!y ) * + %!V ( % ' ) * $!" ( %!W '!z ) * + ' ( ) * Strengthening confluence shear tilting
Confluence Suppose strong west wind U approaching from the west weaker west wind departing from the east Confluence tends to strengthen front!u is negative!" is positive!fs $ = #!" ' $!U '!t % ( ) * % ( ) confluence term is positive Front is strengthening
Shear Suppose wind from south stronger on the east side, than on west side Isentropes on east advect northward faster Potential temperature gradient is strengthened in between Creates a frontal zone Shear is positive!v = + North component of temperature gradient is negative!"!y = #!FS is positive => strengthening!t
Tilting Suppose updrafts are stronger on the cold side than on the warm side Vertical temperature gradient will be tilted Horizontal gradient of updraft velocity is negative!w = " Vertical potential temperature gradient is positive!#!z = +!FS is positive => strenghtening!t
Example!" = 0.01o C / km!"!y = 0.01o C / km!"!z = 3.3o C / km!u = #0.05(m / s) / km!v = 0.05(m / s) / km!w = 0.02(m / s) / km Draw horizontal potential temperature contours indicating gradient Draw horizontal wind vectors indicating wind gradients Draw vertical potential temperature contours and vertical wind vectors against x axis What is strengthening:!(fs)!t =
Example!" = 0.01o C / km!"!y = 0.01o C / km!"!z = 3.3o C / km!u = #0.05(m / s) / km!v = 0.05(m / s) / km!w = 0.02(m / s) / km!fs!t $ = "!# ' % ( ) * $ "!# ' $ %!z ( ) * % $ %!U ' $ ( ) "!# ' %!y ( ) * $!V %!W ' ( ) ( ) *("0.05(m / s) / km) ( ) *( 0.05(m / s) / km) ( ) * 0.02(cm / s) / km * 1m /100cm = " 0.01 o C / km " 0.01 o C / km " 3.3 o C / km = 0.0005 " 0.0005 " 0.00066 ' ( ) ( ) ( ) o C m / s / km 2 *( 1km /1000m) = "6.6 + 10 "7o C / s / km * 86400s / day = "0.057 o C / km / day In this example if the strength of the front was measured as a temperature change over 100 km, then the temperature change would have decreased by 5.7 degrees over one day leading to very rapid frontolysis.
Thermodynamics effects on Frontogenesis Earth and Atmospheric Sciences Three types of frontogenetic physical processes increase the gradient: Kinematic Confluence Shear Tilting Thermodynamic Dynamic Diabatic thermodynamic processes can heat or cool air at different rates on either side of the domain Diabatic warming rate = DW=!"!t!( FS)!t Radiative heating/cooling Conduction from the surface Turbulent mixing across front Latent heat release/absorption associated with phase changes of water in clouds =!DW
Differential diabatic warming Earth and Atmospheric Sciences Radiative heating/cooling Cooling from tops of stratus reduces temperature on warm side of front, can weaken front. Cooling from tops of post frontal stratocumulus can stengthen front by cooling already cold air. Conduction from the surface Behind a cold front, cold air blows over usually warmer surface, which heats cold air and reduces temperature contrast Behind warm front, warm air is usually advecting over warm surfaces Turbulent mixing across front Mixing air from warm and cold sides usually weakens front Latent heat release/absorption associated with phase changes of water in clouds Rising air causes condensation, warms already warm air, strengthens front
Full equation from Bluestein Earth and Atmospheric Sciences
Dynamics contribution to Earth and Atmospheric Sciences Frontogenesis Suppose geostrophic equilibrium, no P gradients at edges, only in middle Suppose a small amount of confluence Temperature gradient increases =>Pressure gradient increases (hypsometric eq.) Kinematics - factor of 3 strengthening Dynamics - factor of 15 strengthening
Ageostrophic flow Increased pressure gradient would give different, increased geostrophic wind Winds must adjust, increase to this new value In the process, they temporarily turn away from geostrophic direction because of coriolis force There is transient ageostrophic flow
Increased pressure gradient would give different, increased geostrophic wind Winds must adjust, increase to this new value In the process, they temporarily turn away from geostrophic direction because of coriolis force There is transient ageostrophic flow In the transient state, there is a component of wind in the x- direction. Because mass is conserved horizontal convergence of U causes temporary cross-frontal circulation Sawyer-Eliassen circulation Updraft can drive convection
During transient stage, ageostrophic cross frontal circulation caused extra confluence near the surface Dynamic confluence adds to kinematic confluence to strengthen the front Transverse circulation also tilts the front. Winds reach final equilibrium, with larger geostrophic wind. 1) large steady geostrophic wind blows parallel to front due to adjustment towards geostrophic equilibrium 2) weak transient cross frontal circulation can be superimposed that can strengthen front further
Summary Three types of frontogenetic physical processes increase the gradient: Kinematic Confluence Shear Tilting Thermodynamic Dynamic
Target due dates: 1 page powerpoint slide homework 4pts Sept 12, 2007 Group Planning minutes 4 pts end of lab 9/18 and 9/19, 2007 Planning document and powerpoint 10/8/2007 Preliminary demonstration dataset homework 10/22/07 Archived dataset and documentation 11/5/07 Experiment Final report 11/12/07 Experiment Final presentation 11/19/07