*************************************************************************** * * * These algorithms were collected, edited, commented, and tested * * by Thomas W. Schlatter and Donald V. Baker from August to * * October 1981 in the PROFS Program Office, NOAA Environmental * * Research Laboratories, Boulder, Colorado. Where possible, * * credit has been given to the original author of the algorithm * * and a reference provided. * * * *************************************************************************** =========================================================================== General information: -------------------- This is an index of the thermodynamic subprograms located in THERMO.OLB. They are listed according to the general type of calculation that is desired, divided into the following categories: (a) moisture parameters (b) latent heat (c) pressure (d) temperature (e) thickness These algorithms were collected, edited, commented, and tested by Thomas W. Schlatter and Donald V. Baker from August to October 1981 in the PROFS Program Office, NOAA Environmental Research Laboratories, Boulder, Colorado. Where possible, credit has been given to the original author of the algorithm and a reference provided. The input/output units are as follows: Temperature Celsius Pressure millibars Relative humidity percent Saturation specific humidity g vapor/kg moist air Mixing ratio g vapor/kg dry air Thickness meters Precipitable water centimeters Latent heat joules/kg The following symbols are used in subprogram calls: EW water vapor pressure EQPT equivalent potential temperature P pressure PC pressure at the convective condensation level PS surface pressure RH relative humidity T temperature TC temperature at the lifting condensation level TD dew point TH potential temperature (a dry adiabat) THW wet bulb potential temperature (a moist adiabat) W mixing ratio WBAR mean mixing ratio from surface to pressure pm Note: all routines are function subprograms except for "PTLCL", which is a subroutine. Index: routines available for various calculations --------------------------------------------------- (A) Moisture Parameters To Calculate: Available Routine(s): 1. Saturation mixing ratio 1. a) WMR(P,T) b) W(T,P) 2. Precipitable water 2. PRECPW(TD,P,N) (Td and P are dimensioned by N) 3. Relative humidity 3. HUM(T,TD) 4. Saturation specific humidity 4. SSH(P,T) (B) Latent Heat To Calculate Latent Heat Of: Available Routines: 1. Evaporization/Condensation 1. HEATL(1,T) 2. Melting/Freezing 2. HEATL(2,T) 3. Sublimation/Deposition 3. HEATL(3,T) (C) Pressure To Calculate: Available Routine(s): 1. Pressure at Lifting 1. a) ALCL(T,TD,P) Condensation Level b) PCON(P,T,TC) c) (subroutine) PTLCL(P,T,TD,PC,TC) 2. Saturation vapor pressure 2. a) ESW(T) over liquid water b) ES(T) c) ESAT(T) d) ESGG(T) e) ESRW(T) f) ESLO(T) 3. Saturation vapor pressure 3. a) ESICE(T) over ice b) ESILO(T) 4. Pressure at Convective 4. PCCL(PM,P,T,TD,WBAR,N) Condensation Level (P, T, and Td are dimensioned by N) (D) Temperature To Calculate: Available Routine(s): 1. Difference in Wet Bulb Poten- 1. WOBF(T) tial Temperatures for two parcels of air at the same temperature - one saturated and the other completely dry 2. Equivalent temperature 2. TE(T,TD,P) 3. Equivalent potential 3. a) OE(T,TD,P) temperature b) EPT(T,TD,P) c) OS(T,P) 4. Dew point 4. a) DPT(EW) b) DEWPT(EW) c) DWPT(T,RH) 5. Wet bulb potential 5. a) POWT(T,P,TD) temperature b) OW(T,TD,P) c) THM(W,P) 6. Potential temperature 6. O(T,P) 7. Convective temperature 7. CT(WBAR,PC,PS) 8. Virtual temperature 8. TV(T,TD,P) 9. Wet bulb temperature 9. TW(T,TD,P) 10. Temperature at Lifting 10. a) TCON(T,TD) Condensation Level b) TLCL(T,TD) c) (subroutine) PTLCL(P,T,TD,PC,TC) d) TLCL1(T,TD) 11. Temperature along moist 11. SATLFT(THW,P) adiabat at given pressure 12. Temperature on a dry adiabat 12. TDA(TH,P) at given pressure 13. Temperature on a moist adiabat 13. a) TSA(EQPT,P) corresponding to an Equivalent b) TMLAPS(EQPT,P) Potential Temperature "EQPT", at given pressure 14. Temperature on a mixing ratio 14. TMR(W,P) line at given pressure (E) Thickness To Calculate: Available Routine: 1. Thickness between the surface 1. Z(PT,P,T,TD,N) and any other pressure level PT in the sounding. (P,T, and Td are dimensioned by N.) Notes prepared by D. Baker, 24 Dec 86. ############################################################################### General information: -------------------- The following tables give results of the tests performed on routines in [BAKER.THERMO]THERM.FOR. These routines calculate thermo- dynamic parameters that are of interest when analyzing sound- ings. the "Smithsonian Meterological Tables" were utilized to test the accuracy of each routine where possible...otherwise, a Skew T-Log p chart was used. In cases where more than one routine calculates a given parameter, an efficiency test is also included. For the efficiency tests, a specified number of calcula- tions was done by each routine using identical input. After 10 trials, the average time needed by each routine was determined and is listed, thereby indicating which routine is most efficient. for further information involving any of the routines to follow, refer to documentation in [BAKER.THERMO]THERM.FOR. Computer used: VAX 11/780 @ NOAA/ERL/PROFS...Boulder, Colorado. Input/output units: Temperature............celsius Pressure...............millibars Mixing ratio...........gm vapor/kg dry air Relative humidity......percent Sat specific humidity..gm vapor/kg moist air Note: Smith = Smithsonian table value. Where these values do not appear, the routines have been verified using a Skew T- Log p chart due to lack of an applicable table. The number in parentheses next to "Smith" indicates the page number (6th revised edition) of the table used for the test. ############################################################################### TEST OF FUNCTIONS ESW,ES,ESAT,ESGG,ESRW,ESLO PURPOSE: CALCULATE SATURATION VAPOR PRESSURE OVER LIQUID WATER GIVEN TEMPERATURE. TEMP ESW ES ESAT ESGG ESRW ESLO SMITH.(340) ---- ----- ----- ------ ------ ------ ------ ------ -50 .06356 .06357 .06356 .06356 .06362 .06337 .06356 -30 .50878 .51036 .50878 .50880 .50843 .50877 .5088 -10 2.8627 2.8677 2.8626 2.8627 2.8625 2.8635 2.8627 0 6.1080 6.1121 6.1076 6.1078 6.1084 6.1078 6.1078 10 12.272 12.272 12.272 12.272 12.274 12.271 12.272 20 23.372 23.370 23.372 23.373 23.375 23.371 23.373 30 42.430 42.457 42.429 42.430 42.431 42.429 42.430 EFFICIENCY TEST: 5000 CALCULATIONS AT T=20C. FUNC. T(SEC) ---- ------ ESW 1.12 ES 0.88 ESAT 4.50 ESGG 4.63 ESRW 1.08 ESLO 0.64 ############################################################################### TEST OF FUNCTIONS WMR,W PURPOSE: CALCULATE MIXING RATIO GIVEN PRESSURE AND TEMPERATURE. PRES TEMP WMR W SMITH.(302) ---- ---- ------ ------ ------ 1000 30 27.699 27.560 27.69 1000 0 3.840 3.822 3.839 850 10 9.147 9.112 9.146 700 10 11.135 11.099 11.13 500 -20 1.568 1.564 1.568 400 -30 0.794 0.792 0.794 EFFICIENCY TEST: 2000 CALCULATIONS AT T=-10C, P=850MB. FUNC. T(SEC) ----- ------ WMR 0.82 W 1.86 ############################################################################### TEST OF FUNCTIONS TCON,TLCL,TLCL1 PURPOSE: CALCULATE TEMPERATURE AT THE LCL GIVEN TEMPERATURE AND DEW POINT. TEMP DWPT TCON TLCL TLCL1 SMITH.(329) ---- ---- ------ ------ ------ ------ 40 20 15.473 15.449 15.450 15.48 -20 -45 -48.703 -48.768 -48.689 -48.79 10 -20 -25.237 -25.295 -29.401 -25.29 0 -25 -29.277 -29.331 -29.401 -29.31 30 10 5.708 5.682 5.679 5.72 40 35 33.710 33.727 33.636 33.74 EFFICIENCY TEST: 5000 CALCULATIONS AT T=20C, TD= 10C. FUNC. T(SEC) ----- ------ TCON 0.65 TLCL 0.96 TLCL1 1.70 ############################################################################### TEST OF FUNCTION PCON PURPOSE: CALCULATE LCL PRESSURE GIVEN INITIAL TEMPERATURE, DEW POINT, AND LCL TEMPERATURE (TEML). PRES TEMP TEML PCON ---- ---- ---- ------ 1000 35 20 839.59 975 30 20 866.89 950 15 -10 691.24 900 10 -25 566.87 500 -20 -20 500.00 500 -20 -50 321.40 ############################################################################### TEST OF SUBROUTINE PTLCL, AND FUNCTION ALCL PURPOSE: GIVEN TEMPERATURE, DEW POINT, AND PRESSURE... PLTLCL ESTIMATES LCL TEMPERATURE AND PRESSURE; ALCL CALC- ULATES LCL PRESSURE ONLY. PRES TEMP DWPT PTLCL:P PTLCL:T ALCL ---- ---- ---- ------- ------- ------ 1000 35 20 811.46 16.63 806.71 900 25 20 837.04 18.83 840.12 1000 30 28 971.57 27.51 973.34 850 0 -30 544.92 -34.66 528.01 900 16 16 900.00 16.00 900.00 700 -10 -60 333.50 -65.69 300.97 ############################################################################### TEST OF FUNCTION WOBF PURPOSE: CALCULATE THE DIFFERENCE WBPTS-WBPTD (SEE NOTES IN [SCHLATTER]THERMO.FOR FOR EXPLANATION) GIVEN THE TEMPER- ATURE. IN THIS CASE, EQUIVALENT POTENTIAL TEMPERATURE WAS INPUT SO RESULTS COULD BE CHECKED USING THE SMITHSONIAN TABLES. EQPT WOBF(=EQPT-WBPT) SMITH.(319) ---- --------------- ------ 205.24 165.2104 165.24 161.04 125.0629 125.04 113.04 83.1266 83.04 70.34 48.8294 48.34 54.84 37.4419 36.84 42.14 28.6543 28.14 6.74 8.8176 8.74 ############################################################################### TEST OF FUNCTIONS POWT,OW PURPOSE: CALCULATE THE WET-BULB POTENTIAL TEMPERATURE GIVEN THE TEMPERATURE, DEW POINT, AND PRESSURE. TEMP DWPT PRES POWT OW ---- ---- ---- ----- ----- 35 25 1000 27.55 27.61 10 -15 1000 2.13 1.83 -10 -60 850 -4.64 -4.68 15 10 900 16.29 16.42 37 30 1050 29.98 30.13 -5 -5 500 22.05 22.22 EFFICIENCY TEST: 500 CALCULATIONS AT T=10C, TD=-10C, P=850MB. FUNC. T(SEC) ----- ------ POWT 0.53 OW 17.31 ############################################################################### TEST OF FUNCTIONS DPT,DEWPT PURPOSE: CALCULATE DEW POINT GIVEN SATURATION VAPOR PRESSURE. SAT.VP. DPT DEWPT SMITH.(351) ------- ------ ------ ------ 0.1891 -40.002 -40.025 -40 1.2540 -20.000 -20.032 -20 2.8627 -10.000 -10.022 -10 6.1078 0.000 -0.010 0 12.272 10.000 10.000 10 23.373 20.000 20.003 20 EFFICIENCY TEST: 3000 CALCULATIONS AT SVP=.1891MB. FUNC. T(SEC) ----- ------ DPT 1.92 DEWPT 0.59 ############################################################################### TEST OF FUNCTION SATLFT PURPOSE: CALCULATE TEMPERATURE WHERE A MOIST ADIABAT CROSSES A GIVEN PRESSURE GIVEN THE VALUE OF THE MOIST ADIABAT AND THE PRESSURE. PRES THETAW SATLFT SMITH. ----- ------ ------- ------ 204.3 34 -19.791 -20 200 20 -60.356 -62 1071.4 38 40.151 40 501 32 9.941 10 422.7 0 -51.876 -52 ############################################################################### TEST OF FUNCTION HUM PURPOSE: CALCULATE RELATIVE HUMIDITY GIVEN TEMPERATURE AND DEW POINT. TEMP DWPT HUM ---- ---- ----- 35 30 75.46 25 10 38.77 0 -15 31.18 20 -10 12.22 30 28 89.09 TEST OF FUNCTION TW PURPOSE: CALCULATE WET-BULB TEMPERATURE GIVEN TEMPERATURE, DEW POINT, AND PRESSURE. TEMP DWPT PRES TW ---- ---- ---- ----- 30 15 1000 19.99 0 -20 700 -6.05 10 0 850 5.11 -15 -25 500 -17.39 25 20 900 21.57 ############################################################################### TEST OF FUNCTIONS OE,EPT PURPOSE: CALCULATE EQUIVALENT POTENTIAL TEMPERATURE GIVEN TEMP- ERATURE, DEW POINT, AND PRESSURE. TEMP DWPT PRES OE EPT ---- ---- ---- ----- ----- 30 15 1000 62.24 62.49 0 -20 700 33.10 33.01 10 0 850 36.97 37.01 -15 -25 500 45.04 45.02 25 20 900 85.02 84.60 EFFICIENCY TEST: 1000 CALCULATIONS AT T=20C, TD=10C, P=1000MB. FUNC. T(SEC) ----- ------ OE 18.50 EPT 0.80 ############################################################################### TEST OF FUNCTION TE PURPOSE: CALCULATE EQUIVALENT TEMPERATURE GIVEN TEMPERATURE, DEW POINT, AND PRESSURE. TEMP DWPT PRES TE ---- ---- ---- ----- 30 15 1000 62.24 0 -20 700 3.31 10 0 850 22.88 -15 -25 500 -12.18 25 20 900 74.38 ############################################################################### TEST OF FUNCTION TDA PURPOSE: CALCULATE THE TEMPERATURE ON A DRY ADIABAT GIVEN THE VALUE OF THE DRY ADIABAT AND THE PRESSURE. THETA PRES TDA SMITH.(308) ----- ---- ------ ------ 132.74 250 -0.12 0 35.44 500 -20.05 -20 -14.66 1050 -11.03 -11 28.64 850 14.93 -15 18.24 700 -10.02 -10 ############################################################################### TEST OF FUNCTIONS TSA,TMLAPS PURPOSE: CALCULATE TEMPERATURE ON A MOIST ADIABAT GIVEN EQUIVALENT POTENTIAL TEMPERATURE AND PRESSURE. EQPT PRES TSA TMLAPS SMITH.(319) ------ ------ ------ ------- ------ 181.64 870.9 34.170 33.940 34 113.04 577.0 12.139 12.080 12 70.34 896.0 18.057 17.950 18 10.24 496.0 -41.766 -41.669 -42 54.84 309.5 -39.658 -39.600 -40 EFFICIENCY TEST: 500 CALCULATIONS AT EQPT=113.04, P=577MB FUNC. T(SEC) ----- ------ TSA 7.16 TMLAPS 6.81 ############################################################################### TEST OF FUNCTION O PURPOSE: CALCULATE POTENTIAL TEMPERATURE GIVEN TEMPERATURE AND PRESSURE. TEMP PRES O SMITH.(309) ---- ---- ----- ------ -35 850 -23.66 -23.66 -10 500 47.74 47.74 -20 950 -16.26 -16.26 10 1000 10.04 10.00 ############################################################################### TEST OF FUNCTION OS PURPOSE: CALCULATE EQUIVALENT POTENTIAL TEMPERATURE FOR AIR SAT- URATED AT GIVEN TEMPERATURE AND PRESSURE. TEMP PRES OS SMITH.(319) ---- ----- ------ ------- 0 275.3 179.88 181.64 -10 321.4 112.03 113.04 10 501.0 126.27 127.34 10 816.0 54.89 54.84 -50 282.7 47.63 48.14 ############################################################################### TEST OF FUNCTION TMR PURPOSE: CALCULATE THE TEMPERATURE ALONG A GIVEN MIXING RATIO LINE AT A GIVEN PRESSURE. W PRES TMR SMITH.(302) ----- ---- ----- ------ 9.146 850 10.07 10 1.120 700 -19.96 -20 7.710 500 0.03 0 1.960 400 -19.97 -20 14.95 1000 20.10 20 ############################################################################### TEST OF FUNCTION THM PURPOSE: CALCULATE WET-BULB POTENTIAL TEMPERATURE OF A PARCEL SATURATED AT A GIVEN TEMPERATURE AND PRESSURE. TEMP PRES THM SMITH.(319) ---- ------ ------ ------ 12 369.6 46.277 40 -32 188.2 41.376 32 38 1069.8 35.751 36 10 908. 14.205 14 -14 648. 7.841 8 -50 301.7 13.961 14 ############################################################################### TEST OF FUNCTION DWPT PURPOSE: CALCULATE DEW POINT GIVEN TEMPERATURE AND RELATIVE HUM- IDITY. TEMP REL.HUM. TD TD* ---- -------- ------ ----- 35 75.46 30.14 30 25 38.77 9.93 10 0 31.18 -15.19 -15 20 12.22 -10.16 -10 30 89.09 28.01 28 * INPUT RELATIVE HUMIDITY FROM OUTPUT OF FUNCTION HUM. EXPECT DEW POINT OUTPUT TO BE APPROX. DEW POINT INPUT USED IN "HUM". SEE TEST OF FUNCTION HUM FOR COMPARISON. ############################################################################### TEST OF FUNCTION SSH PURPOSE: CALCULATE SATURATION SPECIFIC HUMIDITY GIVEN THE PRESSURE AND TEMPERATURE. PRES TEMP SSH !CHECKED ON HAND CALCULATOR. ---- ---- ----- 1000 10 7.70 1000 0 3.82 850 -10 2.11 700 0 5.46 500 -20 1.57 300 -30 1.06 ############################################################################### TEST OF FUNCTION TV PURPOSE: CALCULATE VIRTUAL TEMPERATURE GIVEN TEMPERATURE, DEW POINT, AND PRESSURE. TEMP DWPT PRES TV !CHECKED ON HAND CALCULATOR. ---- ---- ---- ----- 30 25 1000 33.69 20 0 1000 20.68 10 -10 850 10.36 0 -10 700 0.42 -20 -30 500 -19.90 -40 -60 300 -39.99 ############################################################################### TEST OF FUNCTIONS ESICE,ESILO PURPOSE: CALCULATE SATURATION VAPOR PRESSURE OVER ICE GIVEN TEMP- ERATURE. TEMP ESICE ESILO SMITH.(360) ---- ------- ------- ------ -50 .03935 .03963 .03935 -40 .1283 .1283 .1283 -30 .3798 .3796 .3798 -20 1.032 1.032 1.032 -10 2.597 2.596 2.597 EFFICIENCY TEST: 2000 CALCULATIONS AT T=-10C. FUNC. T(SEC) ----- ------ ESICE 1.10 ESILO 0.39 ############################################################################### TEST OF FUNCTION HEATL PURPOSE: GIVEN TEMPERATURE, TO CALCULATE..... 1) LATENT HEAT OF EVAPORATION/CONDENSATION (KEY=1) 2) LATENT HEAT OF FREEZING/MELTING (KEY=2) 3) LATENT HEAT OF SUBLIMATION/DEPOSITION (KEY=3) (RESULTS VERIFIED USING P.343, SMITH.) TEMP KEY=1 SMITH. KEY=2 SMITH. KEY=3 SMITH. ---- -------- ------- -------- ------ --------- ------ -100 674.2192 674.4 -80 676.1257 676.3 -60 677.3396 677.5 -50 628.1667 629.3 48.7133 48.6 -40 56.1209 56.3 677.8610 678.0 -30 615.5021 615.0 62.9107 63.0 -20 69.0828 69.0 677.6898 677.9 -10 603.2438 603.0 74.6372 74.5 677.3444 677.5 0 597.2670 597.3 79.5740 79.7 676.8259 677.0 10 591.3918 591.7 20 585.6181 586.0 40 574.3755 574.7 50 568.9066 569.0 NOTE: HEATL IS DESIGNED TO RETURN THE LATENT HEATS IN UNITS OF JOULES/KG. TO MAKE RESULTS COMPATIBLE WITH VALUES IN THE SMITHSONIAN TABLES (IT-CAL/GRAM), ANSWERS WERE MULTIPLIED BY THE CORRECTION FACTOR 2.3884E-04 TO OBTAIN THOSE SHOWN ABOVE. ###############################################################################