Chapter 2: Literature review
2.6 Scintillometry method
3 1/ 2
2 1
exp ( ) exp ( )
T T
p
T a
kgz C A B S
H c
C T A B S
ρ ⎧⎪⎛σ ⎞ ⎛ ⎞ + ⎫⎪
= ⎨⎜ ⎟ ⎜ ⎟ ⎬
⎝ ⎠ ⎝ ⎠
⎪ ⎪
⎩ ⎭
(2.47)
High frequency air temperature data is only needed as input in Eq. (2.47), which makes the FV method attractive, however friction velocity is required in Eq.
(2.43) to calculate the stability parameter z Lo. Tillman (1972) proposed the following relationship for estimating friction velocity (u*):
1/ 3 1/ 2 2
*
1
( )
, 3.0 0.03
( )
T o
o a o
kgz C z L
u z L
C z L
T
⎡⎛ ⎞⎛σ ⎞ − ⎤
=⎢⎢⎣⎜⎝ ⎟⎜⎠⎝ ⎟⎠ − ⎥⎥⎦ − < ≤ − (2.48)
Substituting Eq. (2.46) for z Lo in Eq. (2.48) gives u* as:
[
2]
1/ 3 1/ 2*
1
exp ( ) exp ( )
T T a T
C A B S
u kgz
C T A B S
⎧⎛σ ⎞⎛ ⎞ + ⎫
⎪ ⎪
= ⎨⎜ ⎟⎜ ⎟ ⎬
⎝ ⎠⎝ ⎠
⎪ ⎪
⎩ ⎭
(2.49)
The FV method is attractive for long-term surface flux measurements since it does not require distortion corrections, favourable wind directions, careful sensor positioning and alignment necessary for eddy covariance (Lloyd et al., 1991; Katul et al., 1996). The disadvantage of the FV method is that it is based on MOST, which refers to a surface layer over an extensive flat and homogeneous surface and the absence of flux divergence (Wesson et al., 2001).
refractive index of the air. The fluctuations of the refractive index are caused by turbulent fluctuations of temperature and humidity (Thiermann and Grassl, 1992). At the receiver end the fluctuation of the beam intensity is analyzed to give the variance of the natural logarithm of intensity related to a property called the refractive index structure parameter Cn2 (m-2/3) defined by Hill (1992) as:
2 2
2 1 2
2 / 3 12
( ) ( )
n
n s n s
C s
= − (2.50)
where n s( ) is the refractive index at location s and the distance s12 lies in between the so-called inner scale of turbulence (which is of the order of 5 to 10 mm) and the outer scale, which is of the order of the height of the beam above the surface (de Bruin et al., 1995).
The optically most active eddies have sizes of the order of the Fresnel zone radius ZF defined as
ZF = λR (2.51)
where λ is the optical wave length and R is the beam path length. The distance between the transmitter and the receiver can range from tens to thousands of meters depending on the type of scintillometer (Thiermann and Grassl, 1992). Depending on the aperture size compared to the Fresnel zone, scintillometers are classified into two major types. If the aperture size is less than the Fresnel zone, the scintillometer is classified as a small aperture scintillometer and the ones with large aperture sizes than the Fresnel zone are referred to as large aperture scintillometers. Different types of radiation source can be used with different beam wavelength. The beam wavelength for the different scintillometer types is also different, with large aperture scintillometer types having beam wavelength of 930 nm ± 5 nm.
In this study, a displaced-beam surface layer scintillometer (SLS40-A) is used.
The transmitter emits a beam of one source which splits into two parallel displaced beams with orthogonal polarizations (Thiermann and Grassl, 1992). The SLS40-A
uses a class 3a type laser at a wavelength of 670 nm, a beam displacement distance of 2.7 mm and a detector diameter of 2.5 mm (Thiermann and Grassl, 1992). From the variance of the logarithm of the amplitude of the signals from the two beams, and the covariance of the two beams, inner scale length lo (mm) which is the smallest diameter of the occurring eddies and Cn2 can be determined (Hartogensis et al., 2002).
The path length of the SLS40-A (that is the separation distance between the transmitter and receiver units) is 50 to 250 meters (Scintec, 2006).
The refractive index structure parameter Cn2 (m-2/3) depends mainly on air temperature fluctuations in the atmosphere and slightly on humidity (Thiermann, 1992). Using the Kolomogrov (1941) cascade process of turbulent flow in the atmosphere, and neglecting the contribution by water vapour, the structure constant of temperature CT2 (K2 m-2/3)can be calculated from Cn2 (Green et al., 1994) as:
2 2
2 2
7.89 10 4 a
T n
C C T
− P
⎛ ⎞
= ⎜⎝ × ⎟⎠ (2.52)
where Ta is the absolute air temperature (K), and P is the atmospheric pressure (kPa), where the dependence on water vapour pressure has been ignored. The inner scale length lo is related to the dissipation rate of the kinetic energy of turbulence ε (m2 s-3) (Hill and Clifford, 1978) as:
3 1/ 4 o 7.4
l ν
ε
⎛ ⎞
= ⎜ ⎟
⎝ ⎠ (2.53)
where ν is the kinematic viscosity of air (1.46 × 10-5 m2 s-1 at standard temperature and atmospheric pressure).
The scintillometry method is dependent on algorithms based on MOST, for determining atmospheric surface-layer fluxes. The inner scale length lo, structure constant of temperature CT2, and empirical algorithms based on MOST functions are used to determine the friction velocity u* and the turbulent temperature scale T*
(Hartogensis et al., 2002). A detailed theory of these algorithms is described in Thiermann and Grassl (1992) and Hill (1997). Sensible heat flux H and momentum flux τo are then obtained from u* and T* as (Thiermann and Grassl, 1992):
* *
H =ρc u Tp (2.54)
and
2
*
o u
τ =ρ (2.55)
Several studies (Hill, 1992; Hill et al., 1992; Thiermann and Grassl, 1992;
Green et al., 1994; de Bruin et al., 1995; McAneney et al., 1995; Andreas, 2000;
Green et al., 2001; de Bruin and Meijninger, 2002; Savage et al., 2004; Savage et al., 2005) have indicated that scintillometer measurements can be used for reliable and routine measurements of momentum and sensible heat flux. Green et al. (2000) and Meijninger and de Bruin (2000) used a large aperture scintillometer to determine sensible heat flux over irrigated areas. Meijninger et al. (2002) showed that the large aperture scintillometer can be applied over heterogeneous terrain provided the beam of the scintillometer is in the surface layer. Kohsiek et al. (2002) used an extra large aperture scintillometer with a 9.8 km path length. Large aperture scintillometer has also been used to validate satellite-derived estimates of the surface fluxes (Watts et al., 2000).
The advantage of the displaced-beam surface layer scintillometer (SLS) used in this study over large aperture scintillometers is that it does not need the additional wind speed measurement to estimate friction velocity. Other advantages of SLS over the eddy covariance and other conventional point measurement methods is that flow distortion effects are minimized due to intensity fluctuations being path averaged in a parabolic manner with maximum at mid-way and decreasing to zero at either ends of the optical path be used (Thiermann and Grassl, 1992).
The disadvantage of scintillometers is that they cannot distinguish between the upward and downward direction of the sensible heat flux density (Savage et al., 2004)
and the methods suffers from a saturation problem because the method is based on the theory of weak scattering which may not always apply (Wang et al., 1978;
Thiermann, 1992). In addition, the cost of a scintillometer is high compared to the cost of the conventional point measurement sensors such as eddy covariance and the temperature based methods.