Example Questions and Answers - Terrestrial Hydrometeorology - page 405

(b) A hydrometeorologist is making measurements at 7080 ft at the nearby Kitt
Peak Observatory. Neglecting any small changes in specific humidity
between the desert floor and the top of Kitt Peak (and hence in the gas
constant for moist air) and assuming the lapse rate in the lower atmosphere
is that of the US Standard Atmosphere, estimate what she measures for the
air temperature in K and the air pressure in kPa.
(c) She decides to boil water to make coffee. Water boils when its saturated
vapor pressure equals air pressure. Calculate the temperature in °C at which
she finds her water boils. (Hint: compare with the calculation of dew point.)

Assume parcels of air that are warmed by the surface are 5°C warmer than the
surrounding ambient air but have the same vapor pressure.

(d) At what temperature will these parcels saturate? Assuming the air parcels
rise and cool at the adiabatic lapse rate, at what height above the desert floor
will they saturate? At approximately what height do the warmed parcels
lose relative buoyancy? Was there convective cloud on this day? Why?

(Assume 0°C = 273.15 K; 1 inch = 2.54 cm; 1013.3 mb = 30.006 inches of mercury;
c p = 1010 J kg −1 K −1 ; and the gas constant for moist air R a = 286.5(1+0.61 q ) J kg −1 K −1 ).

Question 2 (Uses understanding and equations

from Chapters 2 and 5.)

Assume that at the top of the atmosphere the instantaneous incoming flux of solar
radiation, S top , can be computed in W m −2 from:

( )

top

S = S d . .cos( q ) = S d . . sin f sin d + cos f cos d cos w (26.1)

or or

where S o is the solar constant ( = 1367 W m −2 ) ; d r is eccentricity factor of the
Earth's orbit (no units); f is the latitude of the site in radians; d is the solar
declination in radians; and w is the hour angle in radians. This equation is implicit
in Equations (5.14) and (5.15). When Equation (26.1) computes a negative value
for S top the Sun is below the horizon and the true value is zero. The variables d r and
d are functions of the day of the year, and w is a function of the hour, t , within the
day in local time. (Definitions of d r , d and w are given in Chapter 5). Equation
(5.16), which is called the Brunt Equation, is normally used to estimate the all-day
average solar radiation reaching the ground from the all-day average value at the
top of the atmosphere. However, for the purpose of this question the Brunt
Equation is also assumed to apply when calculating S grnd , the instantaneous flux of
solar radiation reaching the ground, hence S grnd is given by:

S grnd =[ a s +(1- c ). b s ]S top (26.2)