ASRAdvances in Science and ResearchASRAdv. Sci. Res.1992-0636Copernicus PublicationsGöttingen, Germany10.5194/asr-13-57-2016On the correlation of spatial wind speed and solar irradiance variability above the North SeaMehrensAnna Riekeanna.mehrens@forwind.devon BremenLuederForWind, Center for Wind Energy Research, Department of Physics, Carl von Ossietzky University Oldenburg, Oldenburg, GermanyAnna Rieke Mehrens (anna.mehrens@forwind.de)12April201613576115January20161April20164April2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://asr.copernicus.org/articles/13/57/2016/asr-13-57-2016.htmlThe full text article is available as a PDF file from https://asr.copernicus.org/articles/13/57/2016/asr-13-57-2016.pdf
Mesoscale wind fluctuations on a time scale of tens of minutes to several
hours lead to high wind power fluctuations. Enhanced mesoscale wind
variability emerges during cold air outbreaks and resulting cellular
convection. The study investigates spatial wind and solar variability and
their correlation during cellular convection. Cellular convection leads to
simultaneous high solar and wind variability, but the highest solar or wind
variability occurs due to other meteorological phenomena.
Introduction
Mesoscale wind fields on a time scale of tens of minutes to several hours can
be very variable above the North Sea. An example how mesoscale wind
fluctuations are transformed into wind power fluctuations is shown in
Fig. . Around the 8 February 2009, the wind speed shows
recurring wind speed changes. These wind fluctuations are in a wind speed
range, where the power curve is steep. Consequently the wind fluctuations are
transformed to very large power fluctuations.
, and others showed that a typical weather
situation, which enhances mesoscale wind variability, are cold air outbreaks
on the rear of low pressure systems. When the cold air is advected over warm
water, cellular clouds develop. It is also possible to simulate these
fluctuations in mesoscale models ().
The fluctuations in the example time series in Fig. occur
during such a cold air outbreak with cellular convection, which is visible in
the satellite image in Fig. .
If mesoscale fluctuation occurs during cellular convection, the question
arises if it is possible to estimate the variability of the wind by the
variability of the solar irradiance field? The solar field can be derived
from satellite measurements.
Under the assumption that temporal mesoscale wind fluctuations occur because
of a spatial inhomogeneous wind field which is advected to a measurement
point, the relation between the spatial variability of the wind field and the
spatial variability of the solar field is analysed in this study, in
particular during cellular convection cases.
Wind data
Due to the lack of mesoscale spatial measurements of the chosen site,
simulated wind speed data of the Weather Research & Forecasting Model (WRF)
are used. The WRF dataset has a spatial resolution of 1.75 km and a time
resolution of 10 min. The simulation uses MERRA as initial and boundary
conditions () and the NCEP OISST dataset () for
the daily update of the Sea surface Temperature. For the planetary Boundary
Layer subgrid parametrisation the YSU scheme and for the Cumulus
parametrisation the Kain-Fritsch (new Eta) scheme was used. The model runs
without any reinitialisations and is driven by the lateral boundary
conditions to obtain a continuous time series. The analysed area is a part of
the third domain with a size of 105 km × 105 km
(Fig. ) and data in a height of 54 m are used.
Figure compares the power spectral density of the WRF wind
speed with the offshore measurements at Fino1 to test if the model set up is
capable to simulate mesoscale wind fluctuations. Although the measurement and
the simulated time series are not at the exact same position, it can be seen
that the model underestimates the power spectral density, especially at the
mesoscale.
Example wind speed time series of the offshore met mast
Fino 1 (a) and resulting wind power time series by using a power
curve of an offshore turbine (b). The power is normalized with the
maximum power.
Satellite image of the 8 February 2009 12:00 UTC by Meteosat. The
red dot marks the study domain above the North Sea
(Fig. ).
Solar data
To calculate the spatial solar variability, global horizontal irradiance
(ghi) data, which are derived by the Heliosat method, are used
(). The data have a spatial resolution of 2.2 km
and a time resolution of 15 min. For the comparison with the WRF wind field,
the same 1.75 km grid is used. Consequently the nearest solar grid point
value is chosen. This may lead to a reduced spatial variability of the solar
field than the wind field, because 685 points out of 3600 points have the
same value due to the lower resolution of the satellite data than the wind
simulation. Both datasets cover the same study domain and the whole year of
2009.
Analysed study domain to calculate the spatial variability of the
wind and solar field.
Methodology
To obtain mesoscale fluctuations only, the time series are filtered with a
Fast Fourier Transformation filter. This filter removes the energy of all
frequencies with a cycle duration of 6 h and longer.
Figure shows the power spectral density of the original and the
filtered time series of one solar irradiance and one wind speed grid point in
the study domain. The comparison of the original and the filtered power
spectral density demonstrates that the filtered time series have the same
spectral power density like the original time series, but all scales, with
greater cycle durations than the mesoscale, are removed.
This procedure provides a fluctuation time series for wind and solar. The
result for the wind speed is shown in Fig. .
Figure a shows the original time series of the wind speed at
one grid point of the WRF simulation and a wind speed measurement at the
nacelle of one wind turbine, which is located in a wind park in the study
domain. The fluctuation time series for the simulation and the measurement
after the filtering procedure are shown in Fig. b. Because of
the filter, the larger time scales are removed and the wind speed fluctuates
around zero. The mesoscale fluctuations at the 8 February, are clearly
visible. It is also visible that the fluctuations are shifted in the WRF
simulation data towards the next days. A likely reason is the model set up
without reinitialisation. Thus, the simulation and the measurements have a
phase shift. This filter is applied on all grid point time series in the wind
and solar field. The result is a spatial wind and solar field which contains
mesoscale fluctuations only.
Power spectral density of the WRF wind speed and the solar
irradiance for the original time series in black and in red for a time series
where all cycle durations higher than 6 h are removed with a Fast Fourier
Transform filter. The dashed black line shows the Power spectral density for
the wind speed measurements for the same year in 50 m height at
Fino 1.
To measure the variability of the solar and wind fields, the longitudinal and
lateral increments between the grid points are added (spatial increment sum).
Because of the phase shift in the measurements and the WRF simulation a daily
mean is calculated. The daily mean increment sum is then normalized by the
average of the year to get dimensionless results.
To compare the spatial variability of wind and solar for days with cellular
convection, a measure is needed to select these days. Currently no general
method exists to detect cellular convection above the North Sea. It was found
that stability measures like the Richardson number are not sufficient. Thus,
days in 2009 are chosen based on satellite images of Meteosat, which clearly
show cellular convection (Fig. ). It is cross checked if these
fluctuations are resolved in the WRF simulation. Based on this procedure
three days in 2009 are found.
Figure illustrates the fluctuation time series and the
spatial field during a cold air outbreak. The filtered wind speed and solar
time series (Fig. a) show strong fluctuations. The spatial
field of the filtered wind time series shows structures which move with the
wind direction through the chosen area (Fig. b). The solar
radiation fluctuation field is also very heterogeneous due to clouds
(Fig. c).
Results and discussion
The comparison of the mesoscale spatial fluctuation of wind and solar shows
that the solar variability has a stronger pronounced yearly cycle
(Fig. ). Although the yearly cycle was filtered, the monthly
mean value of the spatial fluctuation measure reaches a maximum in the summer
months of 2009 and is minimal in the winter months. In contrast to this, the
spatial wind fluctuation measure has a smaller maximum in winter and a higher
minimum in summer. Thus, the monthly mean of the spatial mesoscale
variability of wind and solar are opposed.
Original wind speed time series of one grid point of the WRF
simulation (a) and fluctuation time series after
filtering (b).
Fluctuation time series and spatial field for a cellular convection
case. Panel (a) shows a filtered measurement at a wind turbine whose
position is marked in (b) and the filtered solar time series for the
measurement point, marked in (c). Panel (b) shows the WRF
fluctuation wind field and (c) the solar fluctuation field. Because
of the phase shift between the measurements and the WRF simulation,
(b) shows a later time step.
Monthly mean of the 10 min spatial mesoscale wind and solar
variability. The errorbars show the standard error.
Daily spatial wind and solar variability for all days in the year
2009. The days with cellular convection are marked in green.
Figure shows the relation between the daily fluctuation
measures for wind and solar. The three days with investigated cellular
convection are marked in green. These days do not yield to maximal spatial
solar and wind variability. Thus, there have to be other meteorological
phenomena which yield either to higher spatial solar or wind fluctuations.
All of the days with the highest mean values for the solar variability are in
summer. The days with the highest values for the wind variability are in
winter. The figure also demonstrates that there is no linear relation which
would allow to expect mesoscale wind fluctuations, when there is a very
heterogeneous solar field.
However, Fig. demonstrates that the example days with
prevailing open cellular convection have comparable variability measure
values for solar and wind.
Beside of the investigation of the influence of
open cellular convection on the relation between the solar and wind
variability, the Richardson number, a classification of the daily circulation
(), and the wind direction are examined. Days that were
selected based on this indicators did not show a relation between wind and
solar variability.
The resolution of the original solar data grid is lower than the resolution
of the wind grid, but the results show that the daily solar variability is
not lower than the wind variability.
Conclusions
This study demonstrates that cellular convection leads to simultaneous high
spatial solar and wind fluctuations, but the highest fluctuations occur due
to other weather phenomena.
Due to the fact that the WRF simulation does not resolve all mesoscale
fluctuation cases and the unavailability of a method to detect cellular
convection, the sample size was reduced to only three test cases.
The spatial analysis of mesoscale wind fields is strongly hampered by the
unavailability of measurements with a good spatial and temporal resolution.
Mesoscale models may close this gap, as they are capable to resolve mesoscale
fluctuations. However, depending on the simulation set up and initialisation,
a phase shift between measurement and simulation may occur. In future studies
we want to use Lidar scans, to investigate the spatial variability of wind
fields. But these measurements have a smaller study domain than the
simulation.
Acknowledgements
The work presented in this study is funded by the ministry of science and
culture of Lower Saxony within the PhD Program System Integration of
Renewable Energies and the project ventus efficiens (ZN3024, MWK Hannover).
We thank Axel Kemper (University of Oldenburg, EnMetSol) for providing the
solar data, Francisco Javier Santos Alamillos (University of Reading) for
providing the WRF wind data and the Federal Maritime and Hydrographic Agency
(BSH) for providing the Fino 1 measurements. We thank the reviewers for their
constructive reviews. Edited by: S.-E.
Gryning Reviewed by: two anonymous referees
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