<div dir="ltr"><div><div><div><div><div><div><div>Some references that ma/may-not be of help:<br><br><a href="https://en.wikipedia.org/wiki/Gaussian_grid" target="_blank">https://en.wikipedia.org/wiki/<wbr>Gaussian_grid</a><b><br></b><a href="http://journals.ametsoc.org/doi/pdf/10.1175/1520-0493%281999%29127%3C1872%3ASAMDF%3E2.0.CO%3B2" target="_blank">http://journals.ametsoc.org/<wbr>doi/pdf/10.1175/1520-0493%<wbr>281999%29127%3C1872%3ASAMDF%<wbr>3E2.0.CO%3B2</a><b><br><br>Question 1: </b><font face="times new roman">Is it appropriate to apply the gaussian weights method to my grid?<br><br></font></div><div><font size="2" face="times new roman">Yes. T42 (64 lat x 128 lon) is a gaussian grid where a spectral Triangular truncation has been applied.<br></font></div><div><font face="times new roman"><font size="2">The gaussian weights should be on the file [likely named: <b>gwt</b>].</font><br><br></font></div><div><font face="times new roman">In short, use the gaussian weights. <br>---<br></font></div><div><font face="times new roman"><br></font></div><div>If grid point weights (gaussian or, say, cos(lat)) are not provided you must calculate them:<br><br>(a) Gaussian Weights: <a href="https://www.ncl.ucar.edu/Document/Functions/Contributed/latGauWgt.shtml" target="_blank">https://www.ncl.ucar.edu/<wbr>Document/Functions/<wbr>Contributed/latGauWgt.shtml</a><br></div><div> This uses a fortran code that that yields gaussian weights such that global integrals will be exact.<br></div><div> The output matches what the models use.<br></div><div> <br></div><div>(b) Latitudinal weighting: <a href="https://www.ncl.ucar.edu/Document/Functions/Contributed/latRegWgt.shtml" target="_blank">https://www.ncl.ucar.edu/<wbr>Document/Functions/<wbr>Contributed/latRegWgt.shtml</a><br><br><br></div><div><b>Question 2: </b><font face="times new roman">What is not clear to me is why do we write dy(0) = abs(lat(2)-lat(1))*rr? </font><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman">Why do we not write dy(0) = abs(lat(1)-lat(0))*rr instead?<br></font><br>---<br></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)">Well if they are equally spaced it does not make any difference.<br>Likely, when I wrote this documentation I was mentally using fortran <br>subscripting/indexing (1-based) rather the C- which uses 0-based<br>subscripting.<br></pre></div></div></div></div></div></div></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Fri, Oct 27, 2017 at 7:44 AM, Amanda Frigola <span dir="ltr"><<a href="mailto:afrigola@marum.de" target="_blank">afrigola@marum.de</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><font face="times new roman">Dear all,</font><div><font face="times new roman"><br></font></div><div><font face="times new roman">I was trying to calculate a weighted average with a gaussian grid (CAM model, T42). </font></div><div><font face="times new roman"><br></font></div><div><font face="times new roman">I found this link:</font></div><div><font face="times new roman"><a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/wgt_areaave.shtml" target="_blank">http://www.ncl.ucar.edu/<wbr>Document/Functions/Built-in/<wbr>wgt_areaave.shtml</a></font></div><div><font face="times new roman"><br></font></div><div><font face="times new roman">The first example described in there suggests three possible different methods: </font></div><div><font face="times new roman">1. cell area method</font></div><div><font face="times new roman">2. gaussian weights method</font></div><div><font face="times new roman">3. cos(lat) method.</font></div><div><font face="times new roman"><br></font></div><div><font face="times new roman">I would like to use either the first or the second methods.</font></div><div><font face="times new roman">I would have two questions.</font></div><div><font face="times new roman"><br></font></div><div><font face="times new roman"><b>Question one</b>: Is it appropriate to apply the gaussian weights method to my grid? The appropriateness of this method is based on the assumption that the gaussian weights are proportional to the cell areas. What are the gaussian weights? How are they calculated? And why are they proportional to the cell areas?</font></div><div><font face="times new roman"><br></font></div><div><font face="times new roman"><b>Question two</b>: The code provided in the link above </font><span style="font-family:"times new roman"">to calculate the weighted average using the cell area method</span><span style="font-family:"times new roman""> is as follows:</span></div><div><font face="times new roman"><br></font></div><div><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman"> lat = f->lat
lon = f->lon
jlat = <a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/dimsizes.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">dimsizes</strong></a>( lat )
rad = 4.0*<a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/atan.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">atan</strong></a>(1.0)/180.0
re = 6371220.0
rr = re*rad
dlon = <a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/abs.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">abs</strong></a>(lon(2)-lon(1))*rr
dx = dlon*<a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/cos.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">cos</strong></a>(lat*rad)
dy = <a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/new.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">new</strong></a> ( jlat, <a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/typeof.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">typeof</strong></a>(dx))
dy(0) = <a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/abs.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">abs</strong></a>(lat(2)-lat(1))*rr
dy(1:jlat-2) = <a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/abs.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">abs</strong></a>(lat(2:jlat-1)-lat(0:jlat-<wbr>3))*rr*0.5
dy(jlat-1) = <a href="http://www.ncl.ucar.edu/Document/Functions/Built-in/abs.shtml" style="margin:0px;padding:0px;text-decoration-line:none;color:rgb(133,45,133)" target="_blank"><strong style="margin:0px;padding:0px">abs</strong></a>(lat(jlat-1)-lat(jlat-2))*<wbr>rr
area = dx*dy </font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman"> uAve_area = <strong style="font-size:13.3333px;margin:0px;padding:0px">wgt_areaave</strong><span style="font-size:13.3333px">(u, area, 1.0, 1)</span> </font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman"><br></font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman">My question regards the way dy is calculated.</font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman">I understand that dy(0) and dy(jlat-1) need to be calculated in a different way, because the general expression dy(j)= abs(lat(j+1)-lat(j-1))*rr*0.5, is not defined for j=0 and j=(jlat-1), since the subscript of the </font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman">function lat would go out of range. What is not clear to me is why do we write dy(0) = abs(lat(2)-lat(1))*rr? </font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman">Why do we not write dy(0) = abs(lat(1)-lat(0))*rr instead?</font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman">Hope you can help,</font></pre><pre style="font-size:13.3333px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;background-color:rgb(255,255,255)"><font face="times new roman">Amanda</font></pre></div></div>
<br>______________________________<wbr>_________________<br>
ncl-talk mailing list<br>
<a href="mailto:ncl-talk@ucar.edu">ncl-talk@ucar.edu</a><br>
List instructions, subscriber options, unsubscribe:<br>
<a href="http://mailman.ucar.edu/mailman/listinfo/ncl-talk" rel="noreferrer" target="_blank">http://mailman.ucar.edu/<wbr>mailman/listinfo/ncl-talk</a><br>
<br></blockquote></div><br></div>