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Geophysical Research Letters
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Supporting Information for
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HIGH-RESOLUTION WIND SPEED MEASUREMENTS USING ACTIVELY HEATED
FIBER OPTICS
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Chadi Sayde1, Christoph K. Thomas2,3, James Wagner1, John Selker1
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1Dept.
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of Biological & Ecological Engineering, Oregon State University, Corvallis, OR, USA
of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR, USA
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at: Micrometeorology Group, University of Bayreuth, Bayreuth, Germany
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Contents of this file
Text S1 to S2
Figures S1 to S4
Table S1
Additional Supporting Information (Files uploaded separately)
Captions for Movie S1
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Text S1. Calculating the shortwave radiation fluxes intercepted by the FO cable
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The incoming short wave radiation (St.h) and outgoing (reflected) short wave solar
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radiation ( ρSt.h ) fluxes were measured by a pyranometer (normal to horizontal plane )
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installed at the site. St.h is the sum of the horizontal direct solar radiation (Sb,h) and the
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horizontal diffuse solar radiation (Sd,h). Sb,h and Sd,h were calculated from St.h using the
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Clear Sky Model [Bird and Hulstrom, 1981].
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Assuming that the diffuse and the reflected solar radiation fluxes are independent
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on fiber orientation, the method described by Monteith and Unsworth [2007] for a
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cylinder intercepting diffuse and reflected solar radiation yields:
𝑆𝑑̅ =
𝑆𝑑,ℎ
2
(1)
𝜌𝑆𝑡̅ =
𝜌𝑆𝑡.ℎ
2
(2)
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and
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Cylindrical interception of direct short wave radiation, ̅𝑆𝑏 can be calculated from
Sb,h as follows [Monteith and Unsworth, 2007]:
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̅𝑆𝑏 =
cosec 𝛽 (1 − cos2 𝛽 cos2 𝜃)0.5
𝑆𝑏,ℎ
𝜋
(3)
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where θ is the angle between the axes of the cylinder and the solar azimuth [ ° ] (Figure
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S3). β is the angle of incident direct sunshine relative to the cylinder surface [ ° ].
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In the case of a horizontal cylinder:
β = ω = 90°- ζ
(4)
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where ω is the sun elevation [ ° ] and ζ is the solar zenith angle [ ° ].
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Accounting for the cable inclination
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In some cases the fiber optic cable can be inclined relative to the horizon at an
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angle α [ ° ] (Figure S3). In this case of an inclined surface, a corrected angle of incidence
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can be calculated as follows [Stine and Geyer, 2001]:
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𝑐𝑜𝑠 𝛿 = 𝑠𝑖𝑛 𝜔 𝑐𝑜𝑠 𝛼 + cos 𝜔 sin α cos θ
(5)
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Where 𝛿 is the angle of incidence of direct sunshine relative to the normal of the
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inclined surface [ ° ].
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Then δ can be used to calculate β as follows:
β = 90°- δ
(6)
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Text S2. Calculating the longwave radiation fluxes intercepted by the FO cable
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radiation are assumed to be isotropic and independent of fiber orientation, and thus,
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according to Monteith and Unsworth [2007], the cylinder interception of long wave
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radiation may be expressed as:
The incoming longwave radiation fluxes from downward and upward longwave
𝐿̅↓ =
𝐿ℎ↓
2
(7)
𝐿̅↑ =
𝐿ℎ↑
2
(8)
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and
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where 𝐿ℎ↓ and 𝐿ℎ↑ [J s-1 m-2] are the upward and downward longwave radiation
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measured on a horizontal surface. In our case, 𝐿ℎ↓ and 𝐿ℎ↑ were assumed uniform across
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the FO cable transect and equal to the values measured by a pyrgeometer installed at the
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site.
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References for Text S1and S2
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Bird, R. E., and R. L. Hulstrom, Simplified Clear Sky Model for Direct and Diffuse
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Insolation on Horizontal Surfaces, Technical Report No. SERI/TR-642-761,
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Golden, CO: Solar Energy Research Institute, 1981
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Monteith, J., and M. Unsworth (2007), Principles of environmental physics, Edward
Arnold, London, UK.
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Stine, W.B., M. Geyer (2001), Power from the sun, Power from the sun.net.
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Thomas, C., & Foken, T. (2005). Detection of Long-term Coherent Exchange over
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Spruce Forest Using Wavelet Analysis. Theor. Appl. Climatol., 80, 91–104.
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doi:10.1007/s00704-004-0093-0
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Figure S1. The AHFO system experimental setup in the field.
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Figure S2. Incoming (red) and outgoing (blue) energy fluxes that a segment of the FO
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cable is subject to.
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Figure S3. Schematic representation of the different angles mentioned in Eq.(3) through
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(6) of Text S1. The shaded area represents the inclined plane relative to the horizon. N is
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the vector normal to the cable main axis. S is a vector oriented toward the Sun.
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Figure S4. Time series of UN (red dots), UNS (blue line), φ (green line), and scatter plots
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of UN vs. UNS (blue circles) at the 0.5 m sonic location during the night time period
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(upper plots) and the day time period (bottom plots). The dashed lines in the scatter plots
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marks unity.
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Re
C
m
1-40
0.75
0.4
40 – 1000
0.51
0.5
103 - 2 x 105
0.26
0.6
2 x 105 - 106
0.076
0.7
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Table S1. Constant of Equation 9 for a circular cylinder in cross flow (Zhukauskas,
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1972).
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Movie S1. AHFO wind speed measured at 2 m elevation (red line) and 0.5 m elevation
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(blue line) along the 230 m transect from 3 am CST to 7 am CST. The clock format at
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the top right corner is HH:MM:SS. A biorthogonal wavelet filter BIOR5.5 (Thomas &
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Foken, 2005) was applied to the temperature data pre-processing to reduce the noise in
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calculated wind speed.
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