Environmental Engineering Reference
In-Depth Information
lower end of this range applies to a horizon of 10 years, while the upper end applies
to a horizon as long as 25 years.
Combining the two components leads to an uncertainty of 1.4% for a 10-year
project horizon and 2.2% for a 25-year project horizon. The climate-change component
is negligible in the first instance—leaving it out would reduce the uncertainty by just
0.1%. It becomes increasingly important as the horizon increases.
It should be noted that these uncertainty estimates ignore the time value of money.
In a present-value analysis supporting a plant investment decision, plant production,
and hence revenues, in the distant future would be discounted more heavily than
plant production in the near future. Taking this into account would tend to moderate
the perceived financial risk associated with climate change, but would increase that
associated with normal climate fluctuations.
15.4 WIND SHEAR
The wind shear uncertainty can likewise be divided into two components: the uncer-
tainty in the observed wind shear due to possible measurement errors and the uncer-
tainty in the change in wind shear above mast height. The two components are
independent of one another, so the sum-of-the-squares rule applies.
The first component can be estimated using the following equation, which we first
saw in a slightly different form in Chapter 10:
3
log
+
σ
r
,
v
)
log
h
2
/
(
1
=
h
1
α
obs,
v
(15.4)
The numerator contains the uncertainty in the speed ratio,
σ
r
,
v
. Under most circum-
stances, this is approximately the uncertainty in the measured speed at each height
multiplied by the square root of two.
4
For a speed ratio uncertainty ranging from 1.4%
to 3.5% (corresponding to an uncertainty for a single anemometer ranging from 1.0%
to 2.5%), and for upper and lower heights (
h
2
and
h
1
) of 60 and 40 m, respectively,
the uncertainty in the shear exponent
works out to be 0.034-0.085.
Note that any differences in the influence of the tower or other equipment on the
speeds measured by the two anemometers could increase this uncertainty (assuming
no correction can be made). Examples include when the uppermost sensors are placed
too close to the top of the tower, when the sensor booms are not pointing in the same
direction, and when the ratio of boom length to tower width varies.
α
3
Unlike other uncertainties quoted in this chapter, the wind shear uncertainty is expressed as a deviation
in the magnitude rather than as a proportion of the mean value. We use the delta prefix (
) to remind
the reader of this distinction. One reason for this convention is that shear exponents can take on small or
even negative values, making a percentage uncertainty difficult to interpret. In addition, a deviation in shear
exponent translates directly into a percentage deviation in the hub-height speed (Eq 15.6).
4
This follows because errors in the speed measurements at each height are assumed to be uncorrelated.
Thus, the uncertainty in their ratio equals the square root of the sum of the squares of the uncertainties in
each speed. Assuming the two speed uncertainties are the same, the result is the square root of two times
the speed uncertainty.
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