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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<span class=GramE>.(</span>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="HypsometricShort_files/image001.emz" o:title=""/> </v:shape><![endif]--><![if !vml]><img width=350 height=89 src="HypsometricShort_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="_1264062098"> </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'><span class=GramE><i><u1:p></u1:p><span style='font-size:16.0pt;mso-bidi-font-family:"Times New Roman"'>where</span></i></span><i><span style='font-size:16.0pt;mso-bidi-font-family:"Times New Roman"'> 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 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>