Preparatory Exercise #5
ATMS 111 – Understanding the Atmosphere (Lab)
Wind
Due: 26 Oct 2015
In order to receive full credit for each correct response, you must show the steps taken to arrive at
the result.
𝑇(𝑧) = 𝑇(𝑧𝐵 ) − Γ ∗ [𝑧 − 𝑧𝐵 ] (5.1)
𝐻=
𝑅𝑇̅
𝑔
(5.2)
𝑝(𝑧) = 𝑝(𝑧𝐵 )exp {−
𝑉=
𝑅𝑇̅ Δ𝑝
𝑝̅ 𝑓 Δ𝑛
=
(𝑧−𝑧𝐵 )
𝐻
𝑅𝑇̅ |pS − pN |
𝑝̅ 𝑓
Δ𝑛
} (5.3)
(5.4)
where the terms in Eq. (5.1) are air temperature at some altitude [oC], air temperature at some
lower level [oC], environmental lapse rate (= 6.5 oC/ km), altitude [m], and altitude at some lower
level [km]. The terms in Eq. (5.2) are scale height [m], dry air gas constant [= 287 J kg-1 K-1], layer
average air temperature [K], and the acceleration due to gravity [= 9.81 m s-2]. The terms in Eq.
(5.3) are such that p(z) is the air pressure [hPa] at altitude z [meters], p(zB) is the air pressure
[hPa] at some lower altitude zB [meters], H is scale height [meters], and exp{} is the exponential
function equal to (2.71…) raised to the {} power. The terms in Eq. (5.4) are the wind speed [m s-1],
dry air gas constant [= 287 J kg-1 K-1], layer average air temperature [K], average air pressure
[Pascals] between a north and south location, Coriolis parameter [=8.0x10-5 s-1], air pressure
difference [Pascals] between a north and south location, and horizontal distance between the
north and south locations [meters].
(1) We travel from Station A (elevation=2000 feet) where we measure a surface temperature of
20oC and a surface air pressure of 960 hPa. We travel 90 km to the southwest (compass
heading 190o) and measure a surface air pressure of 997 hPa at Station B (elevation = 1000
feet). As a final result, compute the surface wind speed [m s -1] between Station A and Station
B using Eq. (5.4). Before estimating the surface wind speed, there are intermediate steps that
must be taken.
A. Determine the air temperature “below ground” at Station A corresponding to the
same altitude as Station B using Eq. (5.1), where the altitudes must be in units of km.
[15 points]
B. Determine the layer average air temperature at Station A between 1000 and 2000
feet using the air temperature calculated in Part A and the surface temperature
measured in Problem (1). [10 points]
C. Calculate the scale height (H) using Eq. (5.2) remembering to convert the layer
average air temperature found in Part B to Kelvin. [15 points]
D. Reduce the surface air pressure measured at Station A to 1000 feet elevation using
Eq. (5.3), recognizing that the altitudes must be in units of meters. [15 points]
E. Determine the average air pressure at 1000 feet elevation using the reduced surface
air pressure calculated in Part D and the surface air pressure measured at Station B,
converting the final result to Pascals rather than hPa. [10 points]
F. Calculate the surface wind speed estimate speed [m s-1] between Station A and
Station B using Eq. (5.4), recalling that all pressure values must be in units of
Pascals and horizontal distance between Stations A and B must be in meters. [15
points]
Preparatory Exercise #5
ATMS 111 – Understanding the Atmosphere (Lab)
(continued)
Wind
Due: 26 Oct 2015
(2) Let us assume that the air pressure changes most rapidly from Station A to Station B in the
horizontal on a direct line between Station A and Station B (see figure below). Determine the
most likely wind direction between Station A and Station B given the calculated and measured
air pressures at 1000 feet, assuming that the winds are geostrophic and that air flow is without
the influence of friction. How would the wind direction change from your estimate if the
influence of friction suddenly became important (explain how the numerical estimate of
geostrophic wind direction would increase or decrease based on the influence of friction)?
[20 points]