1 A SHORT COURSE ON MICROMETEOROL OGY (F. Castellví, Bahía Blanca, Oct. 2010) LECTURE 1. GENERAL CONCEPTS 1. The air The atmosphere has a mass of about 5 × 10 18 kg, three quar ters of which is within about 11 km ofthe surface. Dry air contains (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases (ozone, methane,..,wa ter vapour). Air also contai ns a variable amount ofwater vapor, on average around 1%. Recall that when 1 g ofwater vapour condense, the amount of energy delivered is capable to increase 2.5 C the temperature of about 1kg of air. 2. General properties A summary of concepts to recall are the following: 1.- Most of gas in an air parcel is N 2 and O 2 . Therefore, in practice, dry air is considered a diatomi c perfect gas. Fo r convenience, also air (dry air + water vapor + …) is as sumed a diatomic ideal gas. Therefore, (never seen in textbooks of meteorology or fluid dynamic s!) We do not measure Vof air parcels or n for each gas WhereMw is the molecular weight. Standard conditions (T=0 C, P=1 atm).Molecular Weight (g/mol) Density (kg m -3 ) Nitrogen28.01 1.250 Oxygen32.00 1.428 Argon38.98 1.782 Carbon dioxide44.01 1.977 Other 2.974 Dry air 29.00 1.292 nRT= PVTrm = TMw R m = PV
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When an air parcel rises adiabatically it expands because the
pressure of his surroundings decreases. Consequently, itstemperature also decreases (internal energy per unit mass only
depends on temperature). Therefore, as the parcel moves up, it
becomes closer to saturation and a cloud may be formed. If the
parcel is saturated and still moves up, the process is not
adiabatic [parcel is enriched of heat delivered in the change of
phase vapour-liquid and may loss some mass (droplets)]. It is called pseudo-adiabatic and it is not
a process at constant entropy.
The First Law of Thermodynamics in micrometeorology is often called the surface energy
balance and it is written as:
( Rn-G)= H+LE+other energy flux terms
Rn is the net radiation, G is the soil heat flux, H is the sensible heat flux, LE is the latent heat flux, and other energy terms refers to dissipation, to photosynthesis, storage ….Typical units;
Wm-2.
Note that the energy balance refers to a volume of air, so those terms are flux densities. However,
this terminology is not often used.
Exercices:
a.- During a calm night, the air temperature is T=0 C. A moist air parcel, which mass is 1kg, has1g of water that condenses and the parcel becomes dry. Determine the temperature rise of the
parcel.
b.- Consider a mass, m=1kg, for a given perfect gas. Derive the following expression valid for an
Where z0 is a reference height. Note that for a given height, z, the pressure is constant. Thus, by
virtue of the equation of state and definition of virtual temperature, the quantity, ( ρ T v), remains
constant at z. The right expression is obtained by assuming the initial condition that at z0 the
virtual temperature of the air parcel and its surrounding is the same. That is, in terms of T v it isnot possible to delimitate the boundary of the air parcel at z0. Therefore,
Tv = Tv(z) = Tv(zo) – αv( z- z0) where
∂
∂−=
z
T v
vα
Tvp = Tvp (z) = Tvp(zo) - γ( z- z0)
Exercise: Derive the following two expressions;
+
∂
∂=
∂
∂γ
θ θ
z
T
T z
v
v
vv
z
) z-(z g= z v
v
0
p∂
∂−
θ
θ &&
The latter expression derived in the exercise, which resembles the Hook’s law, indicates that
when
∂
∂
z
vθ = 0, the atmosphere is statically neutral. When it is negative, therefore, the
atmosphere is unstable and vice versa.
10.- Often the vertical profile of the humidity is not available. However, for many practical
purposes, within the first 10 m above the ground, it is not necessary to distinguish between T and
θ , and between θ and θ v. Therefore, for thin layers close to the surface the stability is mainly
explained by the sign of (γ−α), as shown in the next Figures. Such simplifications often are used
to remind that the troposphere is a thick stable layer (i.e., the mean value for α, is α=0.65 K/hm.)
which has a capping inversion (i.e., α<0 in the stratosphere).