A climatology is represented by a frequency distribution divided in sectors and bins, which often is presented
graphically as a wind rose. In the below definition sketch a frequency distribution is presented as a rectangular
domain divided in 12 sectors of 30° intervals and 30 bins
with 1 m/s intervals. The frequencies are associated with the center points marked by black circles.
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Figure 1.
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Definition sketch of rectangular frequency distribution domain.
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Transferring a climatology to a new position implies that each frequency is adjusted
according to the changes in wind speed and direction between the original and transferred position.
In general these changes depend both on incoming wind speed and direction.
A specific frequency, with the given sector-bin interval represented by the orange area,
is transferred according to a speed-up and a directional shift into the blue area as outlined in figure 2.
Finally it is re-distributed among the closest frequencies.
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Figure 2.
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Definition sketch of the transfer and re-distribution of a given frequency, zoom from figure 1.
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The re-distribution imposes a smoothing of the frequency distribution. As a consequence,
any transferred climatology which is moved back to its original position will not be reproduced.
Let's look at a simple example to see what is happening.
Consider an artificial climatology with the occurrence of only one wind condition, defined as wind from north with
a wind speed of 7.5 m/s. Consider further that this artificial climatology is moved from position (1) to position (2)
and back again as outlined in figure 3. The response from the terrain in terms of speed-up and directional shifts are
given in table 1.
The changes in speed-up and directional shifts are reversible in the sense that adding directional shift for
one incoming wind direction when moving from position (1) to (2) and back again will give a shift of 0°,
likewise multiplication of speed-ups will give 1.0.
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Figure 3.
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Transfer of simplified climatology from position (1) to position (2) and back to position (1).
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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speed-up
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0.934
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0.789
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0.762
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0.776
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0.969
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0.985
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0.981
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0.799
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0.806
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0.935
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1.092
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1.158
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shift
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-9.894
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-7.071
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-0.535
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7.463
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9.462
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-1.777
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-8.588
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-3.998
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2.581
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8.148
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6.179
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-2.683
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speed-up
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1.071
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1.268
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1.312
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1.289
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1.032
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1.015
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1.019
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1.251
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1.241
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1.070
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0.916
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0.864
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shift
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9.894
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7.071
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0.535
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-7.463
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-9.462
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1.777
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8.588
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3.998
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-2.581
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-8.148
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-6.179
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2.683
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Table 1.
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Response from terrain versus sectors in terms of speed-up and relative directional shifts between position (1) and (2)
given in the first two lines and position (2) and (1) given in the last two lines.
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Clearly the climatology is not reproduced after the transfers.
The smoothing due to the re-distribution is given in details in table 2.
The original climatology with its only frequency occurring in sector 1 is shifted towards east
with a negative directional shift of -9.894° when moved from position (1) to position (2).
By transferring the climatology back to its original
position the climatology which now has non-zero frequencies in sector 12 and 1, is shifted back towards west
with an additional spreading into sector 2 and marginally into sector 3.
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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freq
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1.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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mean
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7.50
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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freq
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0.670
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.330
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mean
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7.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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7.00
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freq
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0.501
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0.244
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0.003
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.000
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0.251
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mean
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7.42
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7.49
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7.96
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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0.00
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6.52
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Table 2.
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Sector-wise frequency distribution for original climatology in position (1) given in first two lines, next the
distribution after transfer to position (2) and finally the distribution after moving the climatology back to
position (1).
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The above example serves as an illustration of the inaccuracies caused by the discretization of
the climatology. The situations could be improved by refinements in the discretization of the
climatology, using 16 or 24 sectors instead of 12 which is in common use.
Another way of increasing the accuracy would be to use sub-intervals in the re-distribution of
a transferred climatology. Sub-intervals for both bins and sectors as outlined in figure 4 have been
implemented in WindSim. However, the increased accuracy seems marginal and there are some extra
computational costs. For this reason, the implementation with sub-intervals is not set active in the
commercial version; contact VECTOR if you would like to test it.
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Figure 4.
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Definition sketch of sub intervals for the re-distribution of a transferred climatology,
zoom from figure 1.
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