Environmental Engineering Reference
In-Depth Information
the area of the case study three sites were identified where extensive vertical profile
measurements are performed. Specific runs with the same boundary conditions
and set-up were performed with several models and profile data were stored. In
this type of evaluation, the representativeness of the measurements of the vertical
profile becomes an important issue.
2. Representativeness
The natural variability in the measurements - also called representativeness -
depends on the state of the atmosphere and the averaging time of the measurements.
Here we evaluate a model by assuming that the model prediction of a given
parameter represents the average (representative) value. Then the uncertainty due.
to the natural variability of the measurements is added as error bars on the results
from the model simulation. The actual measurement represents one realization
only; if the measurement is inside the error bar then it is within the expected
natural variability of the model prediction.
Thus, the model evaluation method is used to associate the uncertainty that
arises from the natural variability in the atmosphere for the parameter in question -
in this paper we take wind speed as example - but the method is applicable for
other parameters as well. The standard deviation in the measurements of the wind
speed
u
,
σ depends on the averaging time
T
of the measurements. Under
stationary conditions and for an the integration time scale
T
much longer than the
integral time scale τ, Tennekes (1973) suggests:
T
σ
≈
2
σ
τ
Τ
u
,
T
u
where σ is the standard deviation of the fluctuating wind speed.
An applied method proposed by Sreenivasan et al. (1978) to determine the
standard deviation of the wind speed for a given averaging time is used here:
z
σ
=
12
u
u
,
T
T
u
It can be seen that the standard deviation σ increases with height and decreases
with averaging time. The method can also be applied to other parameters, for
example, the sensible heat flux. It is interesting to note that the higher the moments
the larger the standard deviation. Thus, a longer averaging time is required for a
higher order moment if the same standard deviation is aimed as for mean value or
lower order moment.
The assumption of stationarity is typically not fulfilled in the atmosphere due to
the daily variation of the insolation, but can be fulfilled in wind tunnel modeling.
However, this deficit is a principal problem as stationarity is also a basic assumption
in the Reynolds decomposition of fluxes, which is fundamental for all RANS
