# Re: Question of theta-e

```Paul:

> Does anyone know if it is possible to determine the value of a wet adiabat
> on a thermodynamic diagram given the pressure and temperature. I would lke
> to interrogate a sounding, determine the value of the wet adiabat that
> passes through each point, thereby determining what theta-e ought to
> approach in order to break the observed cap.

Many years ago, we started doing this by an iterative process that produces
excellent results.  Below are a bunch of static methods taken from a Java class
that deals with sounding and some thermodynamic computations.  The last method
will show you the technique.  Hope this helps.

tom

/** Virtual Temperature
*
*/
public static double virtualTemperature(double t, double td, double p) {
return ( t * (1.0 + .000609*mixingRatio(td, p)) );
}

/** saturation vapor pressure over water.  t in kelvin.
*
*/
public static double satVapPres(double t) {
double coef[]={6.1104546,0.4442351,1.4302099e-2, 2.6454708e-4,
3.0357098e-6, 2.0972268e-8, 6.0487594e-11,-1.469687e-13};

// sat vap pressures every 5C from -50 to -200
double escold[] = {
0.648554685769663908E-01, 0.378319512256073479E-01,
0.222444934288790197E-01, 0.131828928424683120E-01,
0.787402077141244848E-02, 0.473973049488473318E-02,
0.287512035504357928E-02, 0.175743037675810294E-02,
0.108241739518850975E-02, 0.671708939185605941E-03,
0.419964702632039404E-03, 0.264524363863469876E-03,
0.167847963736813220E-03, 0.107285397631620379E-03,
0.690742634496135612E-04, 0.447940489768084267E-04,
0.292570419563937303E-04, 0.192452912634994161E-04,
0.127491372410747951E-04, 0.850507010275505138E-05,
0.571340025334971129E-05, 0.386465029673876238E-05,
0.263210971965005286E-05, 0.180491072930570428E-05,
0.124607850555816049E-05, 0.866070571346870824E-06,
0.605982217668895538E-06, 0.426821197943242768E-06,
0.302616508514379476E-06, 0.215963854234913987E-06,
0.155128954578336869E-06};

double temp = t - 273.16;
double retval;

if (temp > -50.) {

retval = ( coef + temp*(coef + temp*(coef + temp*(coef +
temp*(coef + temp*(coef + temp*(coef + temp*coef)))))) );

} else {
double tt = (-temp - 50.)/5.;
int inx = (int) tt;
if (inx < escold.length) {
retval = escold[inx] + (tt % 1.)*(escold[inx+1]-escold[inx]);
} else {
retval = 1e-7;
}

}

return retval;
}

/** mixing ratio
*
*/
public static double mixingRatio(double t, double p) {
double e = satVapPres(t);
return ( 621.97*e/(p - e) );
}

/** temperature at LCL (old SELS method)
*
*/
public static double tempAtLCL(double t, double td) {
return (td - (.001296*td - .15772)*(t-td) );
}

/** define the parcel's theta-E.  Pressure should be Station Pressure!
*
*/
public static double parcelThetaE(double t, double td, double p) {
double theta = t * Math.pow ( 1000.0/p, .286);
return (theta * Math.exp(2481.9e-3*mixingRatio(td,p)/tempAtLCL(t, td)) );
}

/** pressure at the LCL
*
*/
public static double pressureAtLCL(double t, double td, double p) {
double theta = t * Math.pow( 1000.0/p, .286);
return (1000./ Math.pow( theta/tempAtLCL(t, td), 3.5) );
}

/** compute temperature along Pseudo Adiabats.  This iterates
* until it converges....
*
*/
public static double tempAlongSatAdiabat(double thetaE, double p) {
double s, th;

double pcon = Math.pow( 1000.0/p, .286);
double t = 273.0;
double delta = 20.;
do {
s = mixingRatio(t, p);
th = t * pcon * Math.exp(2.5*s/t);
if ( (th-thetaE)*delta > 0.0) delta = -.5 * delta;
t = t + delta;

} while (Math.abs(delta) > .1);

return (t);
}

}

--
Tom Whittaker (tomw@xxxxxxxxxxxxx)
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