Environmental Engineering Reference
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one particular forecast horizon will verify at four different times each day. The forecast
error was accumulated in 6 hour bins with centre at 3, 9, ..., 45 hour prediction horizon for
additional smoothing. This hides the disturbing diurnal cycle arising from verification once
per day. Thereby a linear error growth with prediction horizon is achieved. Figure 2 shows
such an error decomposition for a 1-year verification over the forecast length 3-45 hours
with data from the western part of Denmark. By generating a decomposition of the fore-
casting error it can be illustrated, which parts of the error can actually be due to the weather
forecast process. In Figure 2, we have split the error into a background error and a pre-
diction system error with a linear error growth. We illustrated the potential improvements
from the weather part with “good forecast”, “average forecast” and “poor forecast”, which
differ to a certain degree. However, when looking at the background error, then the differ-
ences between a “good forecast” and a “poor forecast” is less significant. The background
error is not directly “felt” by end users, because this initial error is in the daily operation
either recovered by short-term forecasts with use of online measurements or if this is not
available, by extrapolating the online measurements a few hours ahead. In the day-ahead
trading, which takes place in most countries approximately 12 hours before the time period
at which the bids have to be given on the market, the first few hours of the forecast are also
irrelevant. The light gray line represents a typical pattern of an online forecast. This forecast
has a steeper error growth, but starts from zero. A short-term forecast 1-2 hours ahead is
typically close to the persistence level except in time periods, where the wind power ramps
significantly.
The linear error growth indicates that the weather forecast is responsible for about 1/3 of
the error in the forecast for the next day and the remainder is a background error originating
from different sources. These additional error sources were found to be due to: (i) the ini-
tial weather conditions; (ii) sub grid scale weather activity; (iii) coordinate transformations;
(iv) the algorithm used to compute the wind power; (v) imperfection of turbines and mea-
surement errors. The question remains, which fraction of the background error is caused by
imperfect initial conditions of the weather forecast and which fraction is due to erroneous
wind power parameterisations. By extrapolating the linear forecast error growth from 9-45
hours down to the 0 hour forecast, the background mean absolute error (MAE) could be
estimated to be just under 4% of installed capacity. Therefore, we added an additional fixed
uncertainty band of +/- 4% of the installed capacity to the native MSEPS ensemble uncer-
tainty to account for the background error that exists in addition to the weather forecast
generated error. With this band, we achieved that 8120 hours out of 9050 hours or 89.7%
of the hours are covered by the predicted uncertainty interval. The remaining 10% have
numerically large errors that are only partially covered by the MSEPS uncertainty predic-
tion. Figure 3 shows a scatter plot of this test. The x-axis shows the measured wind power
[MWh] and the y-axis the mean absolute error (MAE) in % installed capacity. The black
crosses are those forecasts that deviate less than +/- 4% from the measurements. Here 8120
hours are equivalent to 89.7% of the time. The gray crosses towards the top show those
errors that are greater than +4% and are measured for 576 hours, equivalent to 6.4%. The
gray crosses towards the lower boundary are 354 hours and equivalent to 3.9% of the time.
A 4% constant background error is a poor approximation and probably the explana-
tion why 10% of the error events are unpredicted. Part of the background error is due to
the computation of the wind power.
The inherent error from the conversion of wind to
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