displays stationarity. If the difference is between 30 and 50%, then the data set is
considered of acceptable quality. According to these authors, the stationary test is a
prerequisite for data quality.
Monin–Obukhov’s theory of dynamic similarity is a key empirical tool for
studying meteorological parameters and flow in the atmospheric surface layer. This
similarity theory deals with all scalar quantities, variances, and linear correlations
between variables.
Experiments conducted on flat terrain made it possible to confirm Monin–
Obukhov hypothesis (e.g., The Kansas Field Program 1968). According to this
theory, the structure of turbulence in the constant flux layer or surface layer can be
described or parameterized by key variables such as height h, buoyancy g/T,
kinematic tangential tension s/q, and surface temperature flux H/qc p (Kaimal and
Finnigan 1994). According to Monin–Obukhov theory, universal functions for the
stability parameter n (equal to (z-d)/L) can be obtained from various atmospheric
parameters and statistics (gradient, variance, and covariance) when normalized by
the appropriate powers, u à ; T à ,and q à in which q is the absolute air humidity.
The relationship among the ratios r W =u à ; r T =T à and r q =q à can be expressed as
(Lee and Black 2003a):
r W =u à ¼ a W ½Àn
1=3
ð3:210Þ
r T =T à ¼ a T ½Àn
À1=3
ð3:211Þ
r q =q à ¼ a q ½Àn
À1=3
ð3:212Þ
where r w , r u, and r T are the standard deviations of the vertical, longitudinal, and
temperature components, respectively, and n is the stability parameter.
The values for a w , a T, and a q are of the order of 1.9, 0.9, and 1.1, respectively.
Flows can be calculated from the definitions of u à , T à and q à .
A relationship proposed for the dependency of r W =u à , with respect to (z−d)/L,
(Panofsky and Dutton 1984), valid under conditions of instability, is as follows:
r W =u à ¼ 1:25½1 À 3n
1=3
ð3:213Þ
Compliance with the dynamic similarity relationships can be checked using the
flow-variance expressions, or integral characteristics (Foken and Wichura 1996;
Foken 2017):
r w
u Ã
¼ a 1 n
½
b1
ð3:214Þ
r u
u Ã
¼ a 1 n
½
b1
ð3:215Þ
94
3 Characterization of Turbulent Flow in the Surface Boundary Layer
considered of acceptable quality. According to these authors, the stationary test is a
prerequisite for data quality.
Monin–Obukhov’s theory of dynamic similarity is a key empirical tool for
studying meteorological parameters and flow in the atmospheric surface layer. This
similarity theory deals with all scalar quantities, variances, and linear correlations
between variables.
Experiments conducted on flat terrain made it possible to confirm Monin–
Obukhov hypothesis (e.g., The Kansas Field Program 1968). According to this
theory, the structure of turbulence in the constant flux layer or surface layer can be
described or parameterized by key variables such as height h, buoyancy g/T,
kinematic tangential tension s/q, and surface temperature flux H/qc p (Kaimal and
Finnigan 1994). According to Monin–Obukhov theory, universal functions for the
stability parameter n (equal to (z-d)/L) can be obtained from various atmospheric
parameters and statistics (gradient, variance, and covariance) when normalized by
the appropriate powers, u à ; T à ,and q à in which q is the absolute air humidity.
The relationship among the ratios r W =u à ; r T =T à and r q =q à can be expressed as
(Lee and Black 2003a):
r W =u à ¼ a W ½Àn
1=3
ð3:210Þ
r T =T à ¼ a T ½Àn
À1=3
ð3:211Þ
r q =q à ¼ a q ½Àn
À1=3
ð3:212Þ
where r w , r u, and r T are the standard deviations of the vertical, longitudinal, and
temperature components, respectively, and n is the stability parameter.
The values for a w , a T, and a q are of the order of 1.9, 0.9, and 1.1, respectively.
Flows can be calculated from the definitions of u à , T à and q à .
A relationship proposed for the dependency of r W =u à , with respect to (z−d)/L,
(Panofsky and Dutton 1984), valid under conditions of instability, is as follows:
r W =u à ¼ 1:25½1 À 3n
1=3
ð3:213Þ
Compliance with the dynamic similarity relationships can be checked using the
flow-variance expressions, or integral characteristics (Foken and Wichura 1996;
Foken 2017):
r w
u Ã
¼ a 1 n
½
b1
ð3:214Þ
r u
u Ã
¼ a 1 n
½
b1
ð3:215Þ
94
3 Characterization of Turbulent Flow in the Surface Boundary Layer