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{mso-level-tab-stop:4.5in; mso-level-number-position:left; text-indent:-.25in;} --> </style> <!--[if gte mso 10]> <style> /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman";} </style> <![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="1050"/> </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 bgcolor=white lang=EN-US link=blue vlink=blue style='tab-interval:.5in'> <div class=WordSection1> <h2><span style='font-size:16.0pt;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'>Hypsometric Relation<o:p></o:p></span></h2> <p class=MsoNormal style='margin-left:27.0pt;text-indent:-27.0pt;tab-stops: .75in'><span style='font-size:16.0pt;mso-bidi-font-family:"Times New Roman"'>Heating the atmosphere causes it to expand (special application of the gas law, explained below) obtained by substitution of the hydrostatic equation (4) into the equation of state.(1).<span style="mso-spacerun:yes"> </span>This relation provides the basis of explaining many, many things that synoptic meteorologists see on weather maps and charts. <br> <br> <span style='color:#FF1537'>Thickness of layer between two pressure surfaces is directly related to the mean temperature of the layer.</span> <br> <br> Also, if we consider the thickness of a layer that is often of importance to synoptic meteorologists, the layer approximately between the ground (1000 <span class=SpellE>mb</span>) and about 6 km (500 <span class=SpellE>mb</span>), the Hypsometric Relation is <u1:p></u1:p><o:p></o:p></span></p> <p class=MsoNormal align=center style='margin-left:27.0pt;text-align:center; text-indent:-27.0pt;tab-stops:.75in'><span style='font-size:16.0pt;mso-bidi-font-family: "Times New Roman"'><u1:p></u1:p><u5:shape id="_x0000_i1027" type="#_x0000_t75" style="width:240pt;height:38pt"><u4:imagedata src="Primitive_Equations_files/image003.jpg" o:title="hypsometric.jpg"/><span style='position:relative;top:8.0pt;mso-text-raise:-8.0pt'><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id="_x0000_i1029" type="#_x0000_t75" style='width:348pt; height:87pt' o:ole=""> <v:imagedata src="Hypsometric_files/image001.emz" o:title=""/> </v:shape><![endif]--><![if !vml]><img width=350 height=89 src="Hypsometric_files/image002.png" v:shapes="_x0000_i1029"><![endif]></span><!--[if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1264062080"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></p> <p class=MsoNormal align=center style='margin-left:27.0pt;text-align:center; text-indent:-27.0pt;tab-stops:.75in'><i><u1:p></u1:p><span style='font-size: 16.0pt;mso-bidi-font-family:"Times New Roman"'>where k = R/g <span class=SpellE>ln</span> 2 and </span></i><span style='font-size:16.0pt; mso-bidi-font-family:"Times New Roman"'><u1:p></u1:p>"Z is the thickness of the layer between 1000 <span class=SpellE>mb</span> and 500 <span class=SpellE>mb</span> and <span class=SpellE>T<sub>v</sub></span> is the Virtual Temperature, which we will assume here is very close to the actual temperature.<o:p></o:p></span></p> <div align=center> <table class=MsoNormalTable border=1 cellpadding=0 width=799 style='width:799.0pt; mso-cellspacing:2.0pt;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='background:#F2FFC1;padding:0in 0in 0in 0in'> <p class=MsoNormal style='margin:0in;margin-bottom:.0001pt'><b><span style='font-size:16.0pt;mso-bidi-font-family:"Times New Roman"'>Applications: </span></b><span style='font-size:16.0pt;mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p> <p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo2; tab-stops:list .5in'><![if !supportLists]><span style='font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b><span style='font-size:16.0pt;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'><a href="Examples/trop_height1.gif"><span class=SpellE>Tropopause</span> is higher over the Equator than at the Poles </a>(generally, the <span class=SpellE>tropopause</span> corresponds in winter to the<a href="Examples/eta_300_000m.gif"> 300 <span class=SpellE>mb</span> surface</a>) </span></b><span style='font-size:16.0pt;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p> <p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo2; tab-stops:list .5in'><![if !supportLists]><span style='font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b><span style='font-size:16.0pt;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'>Since the surface pressure is nearly 1000 <span class=SpellE>mb</span>, deep cold air masses are associated with areas of low heights (troughs) in the<a href="Examples/upaCNTR_500.gif"> middle</a> and upper troposphere (and vice versa) </span></b><span style='font-size:16.0pt; mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p> <p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo2; tab-stops:list .5in'><![if !supportLists]><span style='font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b><span style='font-size:16.0pt;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'>Since the surface pressure is nearly 1000 <span class=SpellE>mb</span>, the 1000-500 <span class=SpellE>mb</span> thickness pattern can be used as <a href="Examples/Comparison.gif">a first guess approximation</a> of the 500 <span class=SpellE>mb</span> height pattern</span></b><span style='font-size:16.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'> <o:p></o:p></span></p> <p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo2; tab-stops:list .5in'><![if !supportLists]><span style='font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b><span style='font-size:16.0pt;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'>Since fronts are defined as the surface expressions of boundaries between deep air masses with significant temperature differences, as a first guess they can be found on the warm air side of the packing of, for example, <a href="Examples/500mb_InferredSFcFront.gif">500 <span class=SpellE>mb</span> height</a> (crudest), <a href="Examples/SfcFrontThickPackOnly.gif">1000-500 <span class=SpellE>mb</span> thickness</a> (crude) fields </span></b><span style='font-size:16.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><o:p></o:p></span></p> <p class=MsoNormal style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo2; tab-stops:list .5in'><![if !supportLists]><span style='font-family:Symbol; mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span style='mso-list:Ignore'><span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b><span style='font-size:16.0pt;mso-fareast-font-family: "Times New Roman";mso-bidi-font-family:"Times New Roman"'>The relation of surface winds to thickness contours allows one to assess temperature advection, and to make <a href="Examples/SfcFrontAdv.gif">a better estimate</a> of both the location and type of surface fronts (Note: In reality, finding surface fronts requires a careful analysis of actual temperature fields, instead of the layer mean temperatures inferred from thickness or height maps. Here is the <a href="Examples/namussfc18wbg.gif">NCEP analysis;</a> note that the general position of and type of fronts for the eastern two thirds of the US was well &quot;guessed&quot;, but the complications associated with the actual wind and temperatures in southwest TX made our &quot;first guess&quot; poor there) </span></b><span style='font-size:16.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family: "Times New Roman"'><o:p></o:p></span></p> </td> </tr> </table> </div> <div class=MsoNormal align=center style='margin:0in;margin-bottom:.0001pt; text-align:center'><span style='font-size:16.0pt;mso-fareast-font-family:"Times New Roman"; mso-bidi-font-family:"Times New Roman"'> <hr size=2 width="100%" align=center> </span></div> </div> </body> </html>