Review: Week of 31 August

• Decode station model on surface weather maps • Ideal gas law • Vapor pressure and virtual temperature • Hydrostatic equation and vertical distribution of pressure • Geopotential and geopotential height • Thickness and hypsometric equations Surface Observations 19Z Thr Sep 03 2020 Surface Weather Maps

• Decode DEN station model - Temperature - Dew point temperature - Wind speed and direction - Sea level pressure - Cloud cover - Significant weather - Valid time of map WW2010 (http://ww2010.atmos.uiuc.edu/) Atmospheric Sciences, University of Illinois at Urbana-Champaign Surface Weather Maps

• More details about surface station models can be found at: • https://www.weather.gov/jetstream/wxmaps_max • https://www.weather.gov/media/jetstream/synoptic/surface_plot_key.pdf ( ) ) ) ( ( )

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Ideal Gas Law

• In ATOC 5050 we will use the ideal gas law to relate pressure, temperature and density

• We will use the gas constant for dry air (Rd) and virtual temperature (Tv) • Remember: Pressure must be in Pa and temperature must be in K

� "# "# � = �! = 287 J �� !�$ Vapor Pressure and Virtual Temperature

• Vapor pressure (e): This is the partial pressure exerted by the water vapor in moist air and is an absolute measure of the amount of water vapor in the atmosphere

p = pd + e

• Virtual temperature (Tv) is the temperature dry air (no water vapor) would need to have if it were to have the same density as moist air at the same pressure � �$ = � 1 − 1 − � � � = 0.622 Calculate Density from ATOC weather obs

• Weather observation: T = 77.3 F; Td = 45.9 F; p = 842.2 mb

• Convert temperature from F to K and pressure to Pa • T = 77.3 F = 298.3 K • Td = 45.9 F = 287.1 K • p = 842.2 mb = 84220 Pa • Calculate vapor pressure from Td (WH Ch3-3) • Calculate Tv from T, p and e • Use ideal gas law to calculate density Calculate vapor pressure from dew point temperature

• Td = 287.1 K gives e = 15.9 mb

�" �# − �" � = �!�� # − �$

�! = 6.112 mb �" = 17.67 �" = 273.15 K �$ = 29.65 K Calculate the virtual temperature

• T = 298.3 K; p = 842.2 mb; e = 15.9 mb � �$ = � 1 − 1 − � � 298.3 � = = 300.4 � 15.9 �� 1 − 1 − 0.622 842.2 �� • Tv is 0.7% larger than T (Remember: Tv is always greater than or equal to T) Calculate the density with the ideal gas law

• T = 298.3 K; Tv = 300.4 K; p = 842.2 mb; e = 15.9 mb � � � = � = �!� �!�$

84220 �� 84220 �� = � = 287 � ��"#�"# 298.3 � 287 � ��"#�"# 300.4 � � = 0.984 �� "% � = 0.977 �� "%

• Density calculated with Tv is 0.7% less than when calculated with T Check units � � = �!�$

�� Pa = kg m-1 s-2 � = "# "# � �� J = kg m2 s-2 �� "#�"& � = �� & �"& ��"#�"# �

�� = �% Hydrostatic Equation

• Hydrostatic balance is a balance between the upward directed vertical pressure gradient force and the downward directed force of gravity �� = −�� • This equation shows that the vertical rate of change of pressure is proportional to density %& • What is the value of in the lower atmosphere? %' Hydrostatic Equation

• The vertical integral of the hydrostatic equation shows that pressure at a given height is equal to the weight per unit area of the air above that height ( � � = −�� ' • This means that pressure will always decrease with height if the atmosphere is in hydrostatic balance Geopotential and Geopotential Height

• Geopotential and geopotential height indicate the work done against gravity to raise a unit mass to a given height.

• These quantities are related to potential energy

' Φ(�) 1 ' �Φ = �� Φ(�) = �� = = �� ) �) �) ) Thickness Equation

• The thickness equation allows us to calculate the thickness or distance (in geopotential height) between two pressure levels • For a given pressure interval thickness is proportional to temperature • Forecast weather maps often show 1000-500 mb thickness and this is used as a proxy for average temperature in the lower half of the troposphere

�!�$ �# �& − �# = �� ) �& Thickness

• Forecast map of: - SLP (black) - 1000-500 mb thickness (red and blue dashed lines) - Accumulated precipitation (green shading) Hypsometric Equation

• The hypsometric equation allows us to calculate the pressure at some height in the atmosphere given the pressure and height at another height in the atmosphere • The calculated pressure depends on the height difference and the layer averaged temperature between the heights • This equation is often used to calculate SLP from surface pressure

�) �& − �# �& = �#�� − �!�$ Sea Level Pressure

• How will the calculated sea level pressure change as the layer averaged temperature decreases? • Why does the calculated SLP change in this way? • We need to be careful when we use the observed temperature to calculate SLP • How would the diurnal cycle in temperature impact the calculated SLP?

�) �& − �# �& = �#�� − �!�$ p2 = SLP; Z2 = 0 m; p1 = surface pressure