# Problem Sets

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```					Problem Sets for EEA
1. Calculation of flux from chamber measurements

(eq 1)

What are the units of NEE (net ecosystem exchange or net CO2 ﬂux)? Show the full
unit equation for both sides, and your workings.

ρ is molar air density (mol m–3),
V is the volume of the chamber plus base (m3),
C is CO2 concentration (µmol mol–1)
t is time (s)
A is the projected horizontal surface area of the chamber (m2).

2. Fick’s Law

What are the units of the flux of diffusing gas (F)? Show the full unit equation for

(  )
C C
F 1 2
r
s

Where C is gas concentration (kg m-3) in locations 1 and 2 (subscripts) and rs is the
diffusion resistance (s m-1).

3. Penman Monteith equation.

What are the units of E, evapotranspiration? Show the full unit equation for both

 sT ) H
(()ea
sRear
 sH//
E
c
p

a r r
r O
)H
(2 s a

Where cp is the volumetric heat capacity of air (J m-3 °C-1)
s is slope of saturation vapour pressure curve (kPa °C-1)
 is the psychometric constant (kPa °C-1)
es(Ta) is the saturated vapour pressure of air at air temperature (kPa), e is actual
vapour pressure (kPa).
H       H 2O
rs, ra and ra are stomatal and boundary layer resistances (s m-1) to heat (H) or water
(H2O).
is the latent heat of vapourisation (J g-1)
R is absorbed radiation (W m-2) [NB: 1 W = 1 J s-1]

4. Flux units conversion
A soil efflux of CO2 of 1.3 mol m-2 s-1 is measured on a field. How many tonnes of
C per hectare (tC ha-1) will be emitted over a year if this flux continued?

Atomic mass of C = 12 g mol-1.

5. Converting and adding conductance units

P
g     T
1 g  /g
t
/ s 1 a

What are the units of gt? Show the full unit equation for both sides, and your
workings.
Where P is pressure (kPa),  is the gas constant (J mol-1 K-1), T is temperature (K), gs
and ga are conductances (m s-1) of stomata (s) and boundary layer (a).

6. Water relations


l
E Rl
p s
d s gh 

R )
(                        
dt   (
Rs
CRp )
What are the units of ? Show the full unit equation for both sides, and your
workings.
Where R (MPa s m2 mmol-1) is hydraulic resistance, C (mmol MPa-1 m-2) is
capacitance,  is water potential (MPa) of leaves (l) and soil (s), h is height (m), g is

7. Boundary layer conductance

gb = Dwv/

What are the units of boundary layer conductance (gb), where D is diffusivity (m2 s-1)
and d is diffusion distance (m).

8. Hydraulics

h
Rp 
Gp   

What are the units of resistance (R) where h is height above ground (m) and Gp is
conductivity (mmol s-1 m-1 MPa-1).

dW
C=
d

What are the units of capacitance where dW is change in water content (mmol m-2)
and d is change in water potential (MPa)?

9. Sensible heat flux
H
p a T T
Q c g(a )
h                s

What are the units of sensible heat (Qh)? Show the full unit equation for both sides,
Where you are given specific heat of air (cp, J g-1 K-1), the density of air (, g m-3),
H
conductance of heat in air ( g a , m s-1) and temperature of air and soil (T, K)?


Q  T4
L

What are the units of emissivity ()? Show the full unit equation for both sides, and