http://atomix.app.uib.no/index.php?action=history&feed=atom&title=Processing_your_ADCP_data_using_structure_function_techniquesProcessing your ADCP data using structure function techniques - Revision history2026-05-18T03:47:12ZRevision history for this page on the wikiMediaWiki 1.44.2http://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4060&oldid=prevYuengdjern at 15:51, 30 May 20222022-05-30T15:51:51Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, t_s)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file). Note <math> t_s </math> is the timeseries index within a segment. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, t_s)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file). Note <math> t_s </math> is the timeseries index within a segment. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn, spectral range corresponding to <math> k^{-5/3} <<del style="font-weight: bold; text-decoration: none;">\</del>math>). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn, spectral range corresponding to <math> k^{-5/3} <<ins style="font-weight: bold; text-decoration: none;">/</ins>math>). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4059&oldid=prevYuengdjern at 15:51, 30 May 20222022-05-30T15:51:12Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, t_s)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file). Note <math> t_s </math> is the timeseries index within a segment. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, t_s)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file). Note <math> t_s </math> is the timeseries index within a segment. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn<ins style="font-weight: bold; text-decoration: none;">, spectral range corresponding to <math> k^{-5/3} <\math></ins>). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4058&oldid=prevYuengdjern at 15:13, 30 May 20222022-05-30T15:13:06Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:13, 30 May 2022</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<del style="font-weight: bold; text-decoration: none;"><sub>0</del></sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: or as </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: or as </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}+a_3((\delta r)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}+a_3((\delta r)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4057&oldid=prevYuengdjern at 15:12, 30 May 20222022-05-30T15:12:26Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:12, 30 May 2022</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta <del style="font-weight: bold; text-decoration: none;">r_0</del>)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta <ins style="font-weight: bold; text-decoration: none;">r</ins>)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}</math>; </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: or as </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: or as </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}+a_3((\delta r)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: <math>D_{ll} = a_0 + a_1 (\delta r)^{2/3}+a_3((\delta r)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4056&oldid=prevYuengdjern at 15:11, 30 May 20222022-05-30T15:11:55Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:11, 30 May 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7">Line 7:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta <del style="font-weight: bold; text-decoration: none;">r_0</del>)^{2/3}</math>; </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta <ins style="font-weight: bold; text-decoration: none;">r</ins>)^{2/3}</math>; </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: or as </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:: or as </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>:: <math>D_{ll} = a_0 + a_1 (\delta <del style="font-weight: bold; text-decoration: none;">r_0</del>)^{2/3}+a_3((\delta <del style="font-weight: bold; text-decoration: none;">r_0</del>)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>:: <math>D_{ll} = a_0 + a_1 (\delta <ins style="font-weight: bold; text-decoration: none;">r</ins>)^{2/3}+a_3((\delta <ins style="font-weight: bold; text-decoration: none;">r</ins>)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ol type="1" start=6></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><ol type="1" start=6></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><li> Use the coefficient <math>a_1</math> to calculate <math>\varepsilon</math> as <br /><br /> <math>\varepsilon = \left(\frac{a_1}{C_2}\right)^{2/3}</math> <br /><br /> where <math>C_2</math> is an [[ Structure function empirical constant | empirical constant]], typically taken as 2.0 or 2.1. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><li> Use the coefficient <math>a_1</math> to calculate <math>\varepsilon</math> as <br /><br /> <math>\varepsilon = \left(\frac{a_1}{C_2}\right)^{2/3}</math> <br /><br /> where <math>C_2</math> is an [[ Structure function empirical constant | empirical constant]], typically taken as 2.0 or 2.1. </div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4052&oldid=prevYuengdjern at 12:32, 30 May 20222022-05-30T12:32:04Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:32, 30 May 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7">Line 7:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}</math>; or as <del style="font-weight: bold; text-decoration: none;"><br /> </del><math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}+a_3((\delta r_0)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}</math>; </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"># </del>Use the coefficient <math>a_1</math> to calculate <math>\varepsilon</math> as <br /><br /> <math>\varepsilon = \left(\frac{a_1}{C_2}\right)^{2/3}</math> <br /><br /> where <math>C_2</math> is an [[ Structure function empirical constant | empirical constant]], typically taken as 2.0 or 2.1. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:: </ins>or as </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:: </ins><math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}+a_3((\delta r_0)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><ol type="1" start=6></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><li> </ins>Use the coefficient <math>a_1</math> to calculate <math>\varepsilon</math> as <br /><br /> <math>\varepsilon = \left(\frac{a_1}{C_2}\right)^{2/3}</math> <br /><br /> where <math>C_2</math> is an [[ Structure function empirical constant | empirical constant]], typically taken as 2.0 or 2.1. </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ol></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4049&oldid=prevYuengdjern at 15:10, 27 May 20222022-05-27T15:10:48Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:10, 27 May 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4">Line 4:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, <del style="font-weight: bold; text-decoration: none;">t</del>)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, <ins style="font-weight: bold; text-decoration: none;">t_s</ins>)</math>] <ins style="font-weight: bold; text-decoration: none;"> </ins>from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file)<ins style="font-weight: bold; text-decoration: none;">. Note <math> t_s </math> is the timeseries index within a segment. </ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / \delta r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=4048&oldid=prevYuengdjern at 14:37, 27 May 20222022-05-27T14:37:08Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:37, 27 May 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, t)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math>b’(n, t)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file)</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / r_0</math>]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / <ins style="font-weight: bold; text-decoration: none;">\delta </ins>r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}</math>; or as <br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}+a_3((\delta r_0)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of [[Regressing structure function against bin separation | special considerations for forward-difference, center-difference schemes]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}</math>; or as <br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}+a_3((\delta r_0)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring).</div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=3900&oldid=prevYuengdjern at 09:49, 23 May 20222022-05-23T09:49:31Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 09:49, 23 May 2022</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4">Line 4:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Extract or compute the [[along-beam bin center separation]] [<math>\delta r_0</math>] based on the instrument geometry</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math><del style="font-weight: bold; text-decoration: none;">v’</del>(n, t)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Calculate the [[along-beam velocity fluctuation]] time-series in each bin <math>n</math>, where [<math><ins style="font-weight: bold; text-decoration: none;">b’</ins>(n, t)</math>] from the along-beam velocity data that has met the QC criteria (i.e. the data in Level 2 of the netcdf file)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / r_0</math>]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
</table>Yuengdjernhttp://atomix.app.uib.no/index.php?title=Processing_your_ADCP_data_using_structure_function_techniques&diff=2995&oldid=prevYuengdjern at 10:46, 10 December 20212021-12-10T10:46:19Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:46, 10 December 2021</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7">Line 7:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / r_0</math>]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Select the maximum distance (<math>r_{max}</math>) over which to compute the structure function based on conditions of the flow (e.g., expected max overturn). The corresponding number of bins is [<math>n_{\text{rmax}} = r_{max} / r_0</math>]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Calculate the structure function <math>D_{ll}</math> for all possible bin separations <math>\delta</math> within <math>r_{max}</math> using either a [[bin-centred difference scheme]] or a [[forward-difference]] scheme. </div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div># Perform a <del style="font-weight: bold; text-decoration: none;">[[Regressing structure function against bin separation | </del>regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math><del style="font-weight: bold; text-decoration: none;">]] </del>for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of special considerations for forward-difference, center-difference schemes. <del style="font-weight: bold; text-decoration: none;"> </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div># Perform a regression of <math>D_{ll}(n,\delta)</math> against <math>(\delta r_0)^{2/3}</math> for the appropriate range of bins and <math>\delta</math>r<sub>0</sub> separation distances. Be aware of <ins style="font-weight: bold; text-decoration: none;">[[Regressing structure function against bin separation | </ins>special considerations for forward-difference, center-difference schemes<ins style="font-weight: bold; text-decoration: none;">]] in setting up the regression calculation. The regression is typically done as a least-squares fit, either as: <br /><br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}</math>; or as <br /> <math>D_{ll} = a_0 + a_1 (\delta r_0)^{2/3}+a_3((\delta r_0)^{2/3})^3 </math> <br /><br /> the former being the [[canonical structure function method | canonical method]] that excludes non-turbulent velocity differences between bins, whereas the latter is a [[modified structure function method | modified method]] that includes non-turbulent velocity differences between bins due to any oscillatory signal (e.g. surface waves, motion of the ADCP on a mooring)</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Use the coefficient <math>a_1</math> to calculate <math>\varepsilon</math> as <br /><br /> <math>\varepsilon = \left(\frac{a_1}{C_2}\right)^{2/3}</math> <br /><br /> where <math>C_2</math> is an [[ Structure function empirical constant | empirical constant]], typically taken as 2.0 or 2.1. </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div># Use the coefficient <math>a_1</math> to calculate <math>\varepsilon</math> as <br /><br /> <math>\varepsilon = \left(\frac{a_1}{C_2}\right)^{2/3}</math> <br /><br /> where <math>C_2</math> is an [[ Structure function empirical constant | empirical constant]], typically taken as 2.0 or 2.1. </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>Yuengdjern