<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<!--[if !mso]><style>v\:* {behavior:url(#default#VML);}
o\:* {behavior:url(#default#VML);}
w\:* {behavior:url(#default#VML);}
.shape {behavior:url(#default#VML);}
</style><![endif]--><style><!--
/* Font Definitions */
@font-face
        {font-family:"Cambria Math";
        panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
        {font-family:Calibri;
        panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
        {font-family:Consolas;
        panose-1:2 11 6 9 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
        {margin:0in;
        margin-bottom:.0001pt;
        font-size:11.0pt;
        font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
        {mso-style-priority:99;
        color:blue;
        text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
        {mso-style-priority:99;
        color:purple;
        text-decoration:underline;}
code
        {mso-style-priority:99;
        font-family:"Courier New";}
pre
        {mso-style-priority:99;
        mso-style-link:"HTML Preformatted Char";
        margin:0in;
        margin-bottom:.0001pt;
        font-size:10.0pt;
        font-family:"Courier New";}
span.EmailStyle17
        {mso-style-type:personal-compose;
        font-family:"Calibri",sans-serif;
        color:windowtext;}
span.apple-converted-space
        {mso-style-name:apple-converted-space;}
span.HTMLPreformattedChar
        {mso-style-name:"HTML Preformatted Char";
        mso-style-priority:99;
        mso-style-link:"HTML Preformatted";
        font-family:"Courier New";}
span.pln
        {mso-style-name:pln;}
span.pun
        {mso-style-name:pun;}
span.str
        {mso-style-name:str;}
span.com
        {mso-style-name:com;}
span.lit
        {mso-style-name:lit;}
span.kwd
        {mso-style-name:kwd;}
.MsoChpDefault
        {mso-style-type:export-only;
        font-family:"Calibri",sans-serif;}
@page WordSection1
        {size:8.5in 11.0in;
        margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
        {page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="EN-CA" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">Hi,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">I have a<span class="apple-converted-space"> </span></span><a href="https://www.dropbox.com/s/9x951b2qwjwfktf/qu.nc?dl=0"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#005999;border:none windowtext 1.0pt;padding:0in;background:white">.nc</span></a><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">file
 with 2 variables<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">q</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">an<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">u</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">and
 4 dimensions namely<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">lat</span></code><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">,<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">lon</span></code><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">,<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">pressure
 level </span></code><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">and<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">time</span></code><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">.
 This is a sample data of specific humidity and wind direction from ERA_interim.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">How can i calculate the integration of product of variables<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">q</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">and<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">u</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">at
 each grid cell ( ie the vapour flux)  for all time steps i e how to solve following equation in<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">R</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">to
 get<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">int</span></code><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">.<span class="apple-converted-space"> <o:p></o:p></span></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><img border="0" width="181" height="87" style="width:1.8854in;height:.9062in" id="Picture_x0020_1" src="cid:image002.jpg@01D2B44F.1A97D5A0"><o:p></o:p></p>
<p class="MsoNormal">I <span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">
have tried to make stacks of<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">q</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">and<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">u</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">for
 3 levels as<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">qs</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">and<span class="apple-converted-space"> </span></span><code><span style="font-size:10.0pt;font-family:Consolas;color:#242729;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">us</span></code><span class="apple-converted-space"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white"> </span></span><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">using
 raster package but got lost on calculating the integration value.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.5pt;font-family:"Arial",sans-serif;color:#242729;background:white">The sample data file
<b>qu.nc</b> (529 KB) is <a href="https://www.dropbox.com/s/9x951b2qwjwfktf/qu.nc?dl=0">
here</a>.</span> <o:p></o:p></p>
<p class="MsoNormal"> Any help to write a function to solve this integration would be greatly appreciated.<o:p></o:p></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">required (raster)<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">    ncfl<-</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">"qu.nc"</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">
</span><span style="font-size:10.0pt;font-family:Consolas;color:#858C93;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">#.nc datafile
</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1"><o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">    ncf<-stack(ncfl)<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">    print(ncf)<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">n <-
</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">3</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">
</span><span style="font-size:10.0pt;font-family:Consolas;color:#858C93;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1"># Pressure levels 1000,950,900</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1"><o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#101094;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">for</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">
 (i </span><span style="font-size:10.0pt;font-family:Consolas;color:#101094;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">in</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">
</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">1</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">:n)
 {<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">  names <- paste(</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">"u"</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">,
 i, sep=</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">"."</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">)<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">  assign(names, brick(ncfl, varname =</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">"u"</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">,
 lvar = </span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">3</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">,
 level <o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">                      = i) )<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">}<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#101094;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">for</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">
 (i </span><span style="font-size:10.0pt;font-family:Consolas;color:#101094;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">in</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">
</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">1</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">:n)
 {<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">  names <- paste(</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">"q"</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">,
 i, sep=</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">"."</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">)<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">  assign(names, brick(ncfl, varname =</span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">"q"</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">,
 lvar = </span><span style="font-size:10.0pt;font-family:Consolas;color:#7D2727;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">3</span><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">,
 level <o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">                      = i) )<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">}<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1"><o:p> </o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">qs<-stack(q.1,q.2,q.3)<o:p></o:p></span></p>
<p class="MsoNormal" style="background:#EFF0F1"><span style="font-size:10.0pt;font-family:Consolas;color:#303336;border:none windowtext 1.0pt;padding:0in;background:#EFF0F1">us<-stack(u.1,u.2,u.3)<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thank you,<o:p></o:p></p>
<p class="MsoNormal">as<span lang="EN-US" style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</body>
</html>