Humidity，Pressure，Temperature humidity是什么意思

Humidity ratio can be expressed by mass of water or by the vaporpartial pressure in the moist air.

Humidity Ratio by Mass

Humidity ratio can be expressed as the ratio between the actualmass of water vapor present in moist air - to the mass of the dryair. Humidity ratio is normally expressed in kilogram or pounds ofwater vapor per kilogram or pounds of dry air.

Humidity ratio expressed by mass:

x = m_w /m_a(1)

where

x = humidity ratio (kg_water/kg_air,lb_water/lb_{dry_air})

m_w = mass of water vapor (kg, lb)

m_a = mass of dry air (kg, lb)

Humidity Ratio by Vapor Partial Pressure

Humidity ratio can also be expressed with the partial pressureof water vapor:

x = 0.62198 p_w / (p_a -p_w)(2)

where

p_w = partial pressure of water vapor in moist air(Pa, psi)

p_a = atmospheric pressure of moist air (Pa, psi)

The maximum amount of water vapor in the air is achieved whenp_w = p_ws the saturation pressure of watervapor at the actual temperature. (2) can be modifiedto:

x_s = 0.62198 p_ws / (p_a -p_ws)(3)

where

x_s = specifichumidity at saturation (kg_water/kg_air,lb_water/lb_{dry_air})

p_ws = saturation pressure of watervapor

Since the water vapor pressure is small regarding to theatmospheric pressure, the relation between the humidity ratio andthe saturation pressure is almost linear.

Maximum specifichumidity at some common temperatures:

Note that the saturation pressure of watervapor, - and the maximum humidity ratio, increases dramaticallywith the air temperature. This important for the capacity of dryingprocesses.

Example - Humidity Ratio of Moist Air

The specifichumidity for saturated humid air at 20^oCwith water vapor partialpressure 2333 Pa at atmospheric pressure of101325 Pa (1013 mbar, 760 mmHg) can be calculatedas:

x = 0.62198 (2333 Pa) / ((101325 Pa) - (2333Pa))

= 0.0147 (kg/kg)

= 14.7 (g/kg

1.饱和比湿：先求饱和水汽压(E)：（玛格努斯经验公式）E=E_0×10^(at⁄((b+t)))(其中E_0=6.11hPa,t为实际温度（摄氏度），a=7.5,b=237) 带入t=15℃ E=17.08hPa饱和比湿=0.622×E/p=0.0105克/克2.水汽压（e）： 混合比s=0.622e/（p-e）e=s*p/(0.622+s)=16.06hPa3.饱和差（d）: d=E-e=1.02hPa4.相对湿度(f):f=e/E*100%=94.03%参考资料：《自然地理学》杨达源，南京大学出版社Andrew Revering's List of Meteorological Formulas

New formulas will be added providing you submit any formulasyou know of that are not listed here.

1� Latitude=	69.125 miles
Temp(F)=	Tf= (1.8*Tc)+32
Temp(C)=	Tc= (Tf-32)/1.8
Kelvin(Tk)=	Tk= 273.15 + Tc
Temp (Reamur)=	(25/36)(癋-32)
Temp (Rankine)=	癋 + 459.67
Knots=	Knots= Wind Speed MPH *0.868976241091
MPH=	MPH= Knots *1.15077944802
Miles=	MI= Kilometers *0.6214
Kilometers=	KM= Miles * 1.61
Kilometers=	KM= Meters / 1000
Meters=	Meters= Kilometers *1000
Meters=	M= Feet * 0.305
Meters PerSecond=	M/S= Knots *0.5148
Feet=	Ft= Meters*3.2808
Inches=	IN= CM / 2.54
Centimeters=	CM = IN * 2.54
Pascals(Pa)=	Pa= (Mb*100)
Kilopascal(Kp)=	Kp= InHg *3.38638815789
Millibars(Mb)(Hectopascal)=	Mb=(In*33.86388158)
Inches ofMercury(InHg)=	InHg=(Mb/33.86388158)
Dew Point(F) KnowingTc=	X= 1-(0.01*RH) K= Tc-(14.55+0.114*Tc)*X-((2.5+0.007*Tc)*X)^3-(15.9+0.117*Tc)*X^14 Tdf= (K*1.8)+32
Dew Point(F) KnowingTf=	Tdf=((((Tf-32)/1.8)-(14.55+0.114*((Tf-32)/1.8))* (1-(0.01*RH))-((2.5+0.007*((Tf-32)/1.8))*(1-(0.01*RH))) ^3-(15.9+0.117*((Tf-32)/1.8))*(1-(0.01*RH))^14)*1.8)+32
Before Winter2001/2002 Wind Chill(F)=	Wc=0.0817*(3.71*SQRT(WIND SPEED MPH)+ 5.81-0.25*WIND SPEED MPH)*(Tf-91.4)+91.4
Starting Winter2001/2002 Wind Chill 癋 = T = Air Temperature 癋 V = Wind Speed MPH	35.74 + 0.6215 * T -35.75(V ^ 0.16) + 0.4275 * T (V ^ 0.16)
HeatIndex(HI)=	HI= -42.379 +2.04901523(Tf) + 10.14333127 (RH) - 0.22475541(Tf)(RH) - 6.83783x10^(-3)*(Tf^(2))- 5.481717x10**(-2)*(RH^(2)) + 1.22874x10^(-3)* (Tf^(2))*(RH) + 8.5282x10^(-4)*(Tf)*(RH^(2)) - 1.99x10^(-6)*(Tf^(2))*(RH^(2))

Wind Speed &Direction Estimation Calculation

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Summer SimmerIndex(SSI)=	SSI= 1.98(Tf - (0.55 -0.0055(RH))(Tf-58)) - 56.83
Saturation VaporPressure(Mb)=	Es=(6.11*10^(7.5*Tc/(237.7+Tc))
VaporPressure(Mb)= From Dew Point	E=(6.11*10^(7.5*Tdc/(237.7+Tdc)))
VaporPressure(Mb)= From Temp and Humidity	E = (6.11*10^(7.5*((Tc -(14.55 + 0.114 * Tc) * (1 - (0.01 * RH)) - ((2.5 + 0.007 * Tc) * (1- (0.01 * RH))) ^ 3 - (15.9 + 0.117 * Tc) * (1 - (0.01 * RH)) ^14))/(237.7+((Tc - (14.55 + 0.114 * Tc) * (1 - (0.01 * RH)) - ((2.5+ 0.007 * Tc) * (1 - (0.01 * RH))) ^ 3 - (15.9 + 0.117 * Tc) * (1 -(0.01 * RH)) ^ 14)))))
SpecificHumidity(kg/kg)=	SH=(0.622*E)/(Mb-(0.378*E))
RelativeHumidity(%)=	RH= (E/Es)*100
Relative Humidity(%)Knowing Tdf and Tf=	RH =(((6.11*10^(7.5*((Tdf-32)/1.8)/(237.7+((Tdf-32)/1.8))))/((6.11*10^(7.5*((Tf-32)/1.8)/ (237.7+((Tf-32)/1.8)))))*100))
Relative Humidity andDew Point knowing Wet & Dry Bulb Temps	Relative Humidity& Dew Point using Wet & Dry BulbTemps 'Saturation VaporPressure Wet Ew = 6.1078 * exp([(9.5939 * Tw) - 307.004]/[(0.556 * Tw) +219.522]) 'Saturation Vapor Pressure Dry Es = 6.1078 * exp([(9.5939 * Td) - 307.004]/[(0.556 * Td) +219.522]) E = Ew - 0.35 * (Td - Tw) 'Actual Vapor Pressure Relative Humidity RH = (E / Es) * 100 Dew Point Tp = -1 * {[ln(E/6.1078) * 219.522] + 307.004} / {[ln(E/6.1078) *0.556] - 9.59539}
Dew Point from just Tand RH:	Tdc = (Tc - (14.55 +0.114 * Tc) * (1 - (0.01 * RH)) - ((2.5 + 0.007 * Tc) * (1 - (0.01* RH))) ^ 3 - (15.9 + 0.117 * Tc) * (1 - (0.01 * RH)) ^ 14)
LCL Height (EstimatedFT)=	H= 222(Tf-Tdf)
LCL Height (EstimatedMeters)=	H= 67(Tf-Tdf)
LCL Height in Millibars=	SP = (Surface Millibars)* 1000 ST = (Surface Temperature in � C) + 273.16 SDP = (Surface Dew Point in � C) + 273.16 'Find the LCL Level andParcel Temp at LCL Height PT = ((1 / (1 / (SDP - 56) + Log(ST / SDP) / 800)) + 56) -273.16 LCLMB = (SP * (((PT + 273.16) / ST) ^ (3.5))) / 1000
RankineTemperature(R)=	R= Tf+460
Saturation MixingRatio(g/kg)=	Ms= ((Val(Humidity) /100) / Val(MixingRatio)) * 100 OR MORE ACCURATELY 0.622 * Es/(P - Es)
MixingRatio(g/kg)=	M= RH*Ms/100 & M= ((0.622*E)/(Mb-E))*1000
VirtualTemperature(C)=	Tv= ((TemperatureC +273.16) / (1 - 0.378 * (VaporPressure / StationPressure))) -273.16
LiftedIndex=	LI= Tc(500mb) -Tp(500mb)
ShowalterIndex=	SI= 1) From the 850mbtemp, raise a parcel dry adiabatically to the mixing ratio linethat passes through the Tdc(850mb) 2) From that point, raise the parcel moist adiabatically to500mb. 3) SI= Tc(500mb) - Tp(500mb)
Vertical Totals=	VT= T(850mb) -T(500mb)
Cross Totals=	CT= Td(850mb) -T(500mb)
TotalTotals=	TT= Tc(850mb) +Tdc(850mb) - 2*Tc(500mb)
(30 or greater strongthunderstorms) Deep Convection Index =	DCI= T(850 mb) + Td(850mb) - LI(sfc-500 mb)
K Index=	KI= (T850 - T500 ) +Td850 - T dd700 Basically double theKI value to calculate the chance of thunderstorms.
Energy Helicity Index=	EHI= (CAPE * Helicity) /160000
Significant TornadoParameter = F2+ damage associated with STP values >1	STP= (mean layer CAPE /1000) * ((2000 - mean layer LCL meters) / 1500) * (0-1 km Helicity/ 100) * (0-6 km Shear meters per second / 20)
ThetaE (any level)= [Saturated Potential Temperature]	ThetaE = (Tc + 273.15) *( 1000 / Mb ) ^ 0.286 + (3 * M) OR ThetaE = (273.15 + Tc) * ( 1000 / Mb ) ^ 0.286 + (3 * (RH *(3.884266 * 10 ^ [( 7.5 * Tc ) / ( 237.7 + Tc )] ) /100 ))
Theta (any level)= [Dry Potential Temperature]	Theta= (T + 273.15) *(1000 / P) ^ 0.2854
WMAX (Maximum PotentialSpeed of an Updraft) =	WMAX = (( SQRT(2 * CAPE)) / 2 ) / 0.5148
Vertical Velocities canovercome the cap if:	VV >SQRT(2 * CINH)
ConvectiveTemperature=	CT = CCL Tc *(1000.0/CCLMb)0.286 * (SFC Mb/1000.0)*0.286
Maximum HailSize=	Hail =2*((3*0.55*1.0033*(MVV*MVV))/(8*9.8*900))*100 MVV = Max Vertical Velocities in M/S
NormalizedCAPE=	NCAPE = CAPE / (ELm -LFCm) <= 0.1 Weak Updrafts 0.1 - 0.3 Moderate Updrafts >= 0.3 Strong Updrafts
How tocalculateCAPE
TQ Index (low topconvection potential)=	(T850 + Td850 ) - 1.7(T700) > 12 Storms Possible > 17 Low-Top Storms Possible
Delta Theta-E= (Wet Microburst Potential)	(SFCThetaE -LowestMidLevel ThetaE) >= 20 Wet Microbursts Likely <= 13 Wet Microbursts Unlikely
U and V Components ofHorizontal Wind= SPD is in Knots DIR is in Degrees	U = -(SPD * 0.5148) *Sin(DIR * (PI / 180)) V = -(SPD * 0.5148) * Cos(DIR * (PI / 180))
Speed (Knots) andDirection (Degrees) from U and V Components=	Speed = Sqr(U ^ 2 + V ^2) / 0.5148 If V > 0Then ANG = 180 If U < 0 And V < 0 Then ANG = 0 If U > 0 And V < 0 Then ANG =360 Direction = (180 / PI) * Atn(U / V) + ANG
BRN Shear =	0.5 (( 6km AVG UComponent) ^ 2)
Bulk Richardson Number=	BRN= (CAPE / BRNShear)
Air Density (km/m3)=	D=(mb*100)/((Tc+273.16)*287)
Absolute Humidity=	Ah=((6.11*10.0**(7.5*Tdc/(237.7+Tdc)))*100)/((Tc+273.16)*461.5)
Station Pressure=	Ps = Altimeter in Inches* ((288 - 0.0065 * Elevation in Meters)/288)^5.2561
Altimeter Setting=	As = (Station Pressurein MB - 0.3) * (1 + (((1013.25^0.190284 * 0.0065)/288) * (Elevationin Meters/(Station Pressure in MB-0.3)^0.190284)))^(1/0.190287)
Sea Level Pressure=	SLP = Station Pressure&R-Factor You most likely will have Altimeter Setting information that needsto first be converted to Station Pressure using the equationabove. You can get historical temperature and dew point informationfromhere. Click'History Data' --> Enter your location--> Click Custom.
Pressure Altitude (Ft)=	Ap = (1-(StationPressure in MB/1013.25)^0.190284)*145366.45

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The Wind Index (WINDEX) is defined as a parameter, developed byMcCann (1994), that indicates the maximum possible convective windgusts that could occur in thunderstorms. The WINDEX is representedby the following equation:

WI = 5[HM*RQ(G^2 - 30 + QL - 2QM)]^0.5

where HM is the height of the melting level in km above theground; G is the temperature lapse rate in degrees C km-1 from thesurface to the melting level; QL is the mixing ratio in the lowest1 km above the surface; QM is the mixing ratio at the meltinglevel; and RQ = QL/12 but not > 1

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Cap Strength (Lid Strength Index)= Saturated wet bulb potentialtemperature (Theta-E) between the surface and 500 mb MINUS themaximum saturated wet bulb potential temperature (Theta-E) in thelowest 100 mb of the atmosphere. Note in the formulas below M =Mixing Ratio & WBc = Wet Bulb Temperature in 癈.

MB = Surface Level Pressure Do until MB <= 500               Q = (WBc + 273.15) * ( 1000 / Mb ) ^ 0.286 + (3 * M)            If Q > Qsw then                  Qsw = Q         End If  MB = MB - 25    LoopSFC100 = Surface Level Pressure - 100MB = Surface Level Pressure    Do until MB <= SFC100            Q = (WBc + 273.15) * ( 1000 / Mb ) ^ 0.286 + (3 * M)            If Q > Qwmax then                        Qwmax = Q               End If  MB = MB - 25    LoopLSI = Qsw - Qwmax

A cap of 2 degrees Celsius or greater is a good inhibitor ofconvection. A strong cap is can hold energy down too much and thuscause thunderstorms not to break. A weak cap can cause developmentto occur before enough energy builds up for the cells to becomesevere. A median of a strong cap and a weak cap (a cap strengthfrom 1-2癈) is generally ideal to allow enough time for energy tobuild and then break the cap, allowing storms to go severe andpossibly tornadic.

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SWEAT = 12 [Td(850 mb)] + 20 (TT - 49) + 2 (850mb wind speed) + 500mb wind speed + 125 (sin(500mb wind dir - 850mb wind dir) + 0.2)where D = Td850 (癈); if D < 0, change it to D = 0    TT = total totals index; if TT < 49 then drop term               v8 = 850 mb wind speed (kts)            v5 = 500 mb wind speed (kts)                            S = sin [wind direction at 500 mb (degrees) - wind direction at 850 mb]                 the term 125(S + 0.2) should be dropped in any of the following cases:                  when the wind direction at 850 mb is between 130� and 250�                      when the wind direction at 500 mb is between 210� and 310�                      when (wind direction at 500 mb - wind direction at 850 mb) > 0                   when v8 < 15 kts and v5 < 15 kts 

SWEAT is only used to predict severe thunderstorms. Valuesover 300 are considereda severe producing atmosphere.

Meaux Saturation Pressure Curve Formuladryr = (dry bulb temperature deg.F) + 459.67  <--conversion to RankinePsat = 29.9213 / (EXP((671.67 - dryr) * 35.913 * (dryr ^ -1.152437)))Note on this formula from the author:14 years ago I purchased a SF901 computer automotive engine dynometer.The dyno came with a psychrometric lookup chart to lookup vapor pressure.Part of engine dyno testing , is the "ability" to have repeatable "standardized"testing...this means that along with trying to control / isolate every componetvariable...weather influences / conditions have to accounted for!(Note=> the racing industry uses 60 deg F instead of 59 degF as part ofSTP ) The raw, uncorrected Horsepower and Torque output is corrected(standardized) to 29.92 inches Hg. / 60 deg. F / 0.00 % Relative Humiditythrough a "correction factor" in part computed by = Barometric press. Hg - Vapor press Hg.The more accurate the weather data ..the more accurate / repeatable testing.The included dyno vapor pressure chart was hard to read and hard todetermine vapor pressure accuracy to better than a 1/10th inch Hg.,so I began research 14 years ago at local college libraries on variousweather formulas ..... I came across Smithsonian Meteorological Tables from -60 F to+212F with saturation data to .00001 accuracy, just what I was looking for,but the formulas listed in Smithsonian Tables did not always match theirdata especially being able to use only 1 formula to cover -60F to +212F range,so I researched through all the saturation - vapor pressure formulas I couldfind ......couldn't find one single formula that would "mirror" theSmithsonian data,..so I began to develop my own formula....in 1995 Ifinally finished my formula that does "mirror" Smithsonian data from -60F to212 F with as much accuracy as their published data!(c)1995 by Larry Meaux/MaxRace Software, All Rights Reserved.Larry Meaux ( MaxRace Software & Meaux Racing Heads/Engines)9827 LA Hwy. 343Abbeville, LA 70510337-893-1541This formula "mirrors" Smithsonian Meteorlogical Tables from -65 F to 212 F degWet Bulb TemperatureHere is a process requiring only Tc, RH and P (mb) as input: ** Note that if you want to estimate Wet Bulb and not have to enter Pressure, replace all 'P' variables ** with a realistic average pressure for the level you are calculating. Example: Surface might be best  ** represented with an average P of about 985. Error should be no more than 0.2� by using this constant.Variables:Tc = Temperature in Degrees CRH = Relative Humidity in form 88 not 0.88Optional Variable (for more accuracy):P = Pressure     orConstant (with up to 0.2� inaccuracy):P = 985Tdc = ((Tc - (14.55 + 0.114 * Tc) * (1 - (0.01 * RH)) - ((2.5 + 0.007 * Tc) * (1 - (0.01 * RH))) ^ 3 - (15.9 + 0.117 * Tc) * (1 - (0.01 * RH)) ^ 14))E = (6.11 * 10 ^ (7.5 * Tdc / (237.7 + Tdc)))WBc = (((0.00066 * P) * Tc) + ((4098 * E) / ((Tdc + 237.7) ^ 2) * Tdc)) / ((0.00066 * P) + (4098 * E) / ((Tdc + 237.7) ^ 2))

From: BEK@MMF.ruc.dk (Bernd Kuemmel)Newsgroups: sci.geo.meteorologySubject: Temp, Humidity & Dew Point ONADate: 12 Jun 1997 15:45:34 GMTMessage-ID: <5np5iu$ivj$1@news.uni-c.dk>Reply-To: Bernd Kuemmel <BEK@mmf.ruc.dk>Archive-name: meteorology/temp-dewpointPosting-Frequency: About monthly.Version: 008Date: May 27, 1997Updated: When necessaryLines: about 680  The _Temp, Humidity & Dew Point_  ONA (Often Needed Answers)Table-of-contents:1)  Introduction.2)  Formulae.3)  Examples.4)  Literature.5)  Committment.6)  Outlook.7)  Signature.A plain text version of this text can also be found on:http://mmf.ruc.dk/~bek/relhum.htm1)Introduction:From the discussions on the newsgroup sci.geo.meteorology this is acollection of some formulae and texts that reflect on connectionsof temperature, humidity and dew point temperature (BeK):Air will normally contain a certain amount of water vapour. Themaximum amount of water vapour, that air can contain, depends onthe temperature and, for certain temperature ranges, also on whetherthe air is near to a water or ice surface. If you have a closed con-tainer with water and air (like a beaker) then there an equilibriumwill develop, where the air will contain as much vapour as it can.The air will then be saturated with respect to water vapour.The real world outside is not closed, so that the air normally willcontain less vapour as it could. Sources of vapour are evaporationprocesses from water and ice surfaces and transpiration from plantsand respiration from animals. The expression "evapotranspiration"takes into consideration plants' large share of evaporation overland areas.Sinks of water vapour are clouds or condensation on surfaces.Dew is created when a surface temperature has such a low temperaturethat the air chills to the dew point and the water vapour condenses.Physically at the dew point temperature the vapour loses the energythat it gained at evaporation, the latent energy, again.The precipitable water (total column water vapor) is stronglycorrelated (r > 0.9) with the surface dew point on most days.Exceptions to the rule include days when a cold front has passedand during other transient events. (Kerry Andersen)NET readings :http://covis2.atmos.uiuc.edu/guide/wmaps/general/rhdef.htmlhttp://njnie.dl.stevens-tech.edu/curriculum/oceans/rel.htmlhttp://www.mtc.com.my/fpub/lib/drying/ch11.htm2)Formulae:Enough for dry physical theories; here comes the practice.For some people skipping this and going directly to the exampleswould be the most rewarding. Especially as they treat the conversionof relative humidity and psychrometer temperatures. (BeK)Vapor pressure (e) is the fraction of the ambient pressure that isdue to the fraction of water vapor in the air.Saturation vapor pressure (es) is the maximum vapor pressure that theair can support (non supersaturated) at a given temperature.e  can vary from 0 (verrry dry) to the maximum, es.es is a function of temperature es(T).Relative humidity (RH) is 100% times the ratio of the environmentalvapour pressure, e(T), to the saturation vapour pressure es(T).        RH = 100% * e(T)/es(T)The environmental vapour pressure is the saturation vapour pressureat the dew point or        e(T) = es(Td)so RH becomes        RH = 100% * es(Td)/es(T)In other words: if you have a parcel of air and cool it until thewater vapor in it condenses then you have reached the saturation point.At this point you will measure the same vapour pressure as in youroriginal air probe.Some more elaborate expressions follow here:es0 = reference saturation vapor pressure (es at a certain temp,                                           usually 0 deg C)    = 6.11 hPaT0  = reference temperature (273.15 Kelvin,  Kelvin = degree C +                                                      273.15)Td  = dew point temperature (Kelvin)T   = temperature (Kelvin)lv  = latent heat of vaporization of water (2.5 * 10^6 joules                                                       per kilogram)Rv  = gas constant for water vapor (461.5 joules* Kelvin / kilogram)e  = es0 * exp( lv/Rv * (1/T0 - 1/Td))es = es0 * exp( lv/Rv * (1/T0 - 1/T))RH= e/es * (100%) = relative humidity !!!!So just above is the answer to many questions in the direction ofhow to calculate the relative humidity if you have the dew pointand air temperature.There are some simple and more complicated formulas for thesaturation vapour pressure at a given temperature.A simple first guess (assuming the latent heat of vaporization isconstant with temperature) would be:        log10(es) = 9.4041 - 2354/Tor           ln(es) = 21.564 - 5420/Twhere T is in Kelvin (i.e., 273.15+T(C)). {After inverting thelogarithms es in given in hPa.}Another approximation (Magnus' formula) would be        log10(es) = -2937.4/T - 4.9283*log10(T) + 23.5470In the following the input gets a little more complicated. Here wealso shall distinguish between the saturation vapour pressure overice or water. Both are different, as the molecular forces bind muchmore in an ice crystal than in a water bobble. So the saturationpressure esW will be larger than esI (W for water, I for ice). 1.  Vapor pressure (e):                             dew point temperature in degrees C.                            /     e  = 6.1078 * 10 ** ((TD * A)/(TD + B)) in hPa 2.  Saturated vapor pressure (es):     es = 6.1078 * 10 ** ((T * A)/(T + B))                                                         temperature in C                   A =   7.5 } for use in vapor pressure                   B = 237.3 } with respect to WATER                 * A =   9.5 } for use in vapor pressure                   B = 265.5 } with respect to ICE 3.  Absolute virtual temperature (TV):                                 vapor pressure                                /     TV = (T + 273.15)/(1-0.379*e/Press)                                                                         total pressure     TV does take into consideration that you could try to condense     all the water vapour in your air parcel and use the condensation     heat to warm up the air. This is a first way to distinguish     different air parcels that may have the same temperature but     have different relative humidity. 4.  Mixing ratio (W):                                 vapor pressure                                /                        .62197 e                      grams water                    W = --------                      -------------                           P - e                      grams dry air                                                          |                             total pressure                |                                                   Thus 12 g/Kg comesout                                                   as .012 5.  Wet Bulb     Vapor Pressure     Dew Point               (P365, Smithsonian for first part)     Ew - e     ------      = .000660 (1 + .00115 T )     Press (T-Tw)                       w Therefore:            e = Ew - Press (T-T ) (.000660) (1 + .00115 T )                               w                        w           Tw = Wet bulb temperature (degrees C.)           Ew = Saturated vapor pressure at temperature Tw            e = Vapor pressure in air        Press = Total barometric pressure (units same as Ew, e)            T = Air temperature (degrees C.) e is the vapor pressure in the air, which is the vapor pressure at the dew point temperature.  To solve for the dew point temperature, use the formula:            e = 6.1078 * 10 ** ((Td * A)/(Td + B)) in hPa                 let C = log   (e/6.1078)                            10 Then:            C T  + C B = A T               d            d                    B*C               T =  ---     Dew point in degrees C                d   A-C                                           where A =   7.5                                                 B = 237.3All the above saturation pressure temperature relationships arerelatively uncomplicated. Here one that is more mindboggling:A saturation-pressure-curve which is valid for a total pressure of1000 hPa. "This curve was computed by approximating the standardsteam table for pure water using the least square method by aBulgarian colleague. I experienced it to be quite exact, but I'dbe glad to be corrected." (Dr Haessler)Psat  = 610.710701 + 44.4293573*t + 1.41696846*t^2 +        0.0274759545*t^3 + 2.61145937E-4*t^4 + 2.85993708E-6*t^5The pressure is in Pa, the temperature in degrees Celsius (C).Relative Humidity then is:Phi = Psteam/Psat = (Ptot/Psat)*x / ((Rair/Rsteam)+x),where x is the absolute humidity in kilogramm water per kilogrammof dry air,Rair and Rsteam are the specific gas constants for air and steam,whereRair/Rsteam has a value of 0.622.For the handling:1. Calculate the saturation pressure at Your dew point, giving Your   steam pressure.2. Calculate the saturation pressure at Your temperature.3. Divide'em (see above) to get Your relative humidity.4. Calculate Your absolute humidity, if desired.5. Mail me for further informations, if necessary.6. The reverse way is possible.For the pressure dependence of relative humidity:If air and steam behave as ideal gases, there is no pressuredependence.This is so around 1000 hPa (+-100hPa, approx.).NET reading :http://www.mindspring.com/~pjm/pmtherm.html (free psychrometer program)http://nwselp.epcc.edu/elp/wxcalcsc.html (Perl-scripts)CAUTIONS:Good psychrometersa) Air velocityk (and A) don't really become (sorta) independent of the air velocitypast your wet bulb until velocities above 3 meters/ second.Velocities greater than 1 m/s are sufficient at temperatures of 60 Cor more.The worse your arrangement, (less adiabatic, i.e. the more extraneousenergy radiates/conducts into the water) the steeper k over velocitybecomes for lower velocities. So you can compensate poor design tosome extent by cranking up that fan.k and A are really device-dependent. This k (and A, of course)strictly refers to the "Assmann psychrometer" only - two radiationshields, thermal insulation, fan downstream from the thermometers. kshould be similar for any well-made psychrometer.b) Adiabatic wet bulbShield it from radiative & conductive errors, i.e. all energy tovaporize the water must come from the air and thus be reflected inthetaf.In wetting the wet bulb, use distilled water. Salty scale on your"sock" can change the vapor pressure, and will really messmeasurements near zero. Use enough water to hit steady-stateconditions well before you start to dry out.If you use a wick for continuous wetting, make it long enough so thatconductive errors are minimized, and it is cooled to the wet bulbtemperature by the time it gets near the thermometer. Make sure enoughwater can reach the wet bulb, so don't overdo the "long enough" part.Don't get anything but the wet bulb wet. Getting the radiation shieldor the thermal insulation wet will introduce errors.Keep direct sunlight off. A great way to pump heat into your"adiabatic" system. Don't ever paint the outside black. Manycommercial humidity meters are a pretty black finish. They will besensitive to indirect sunlight (and other radiative sources). Humiditymeasurements are VERY sensitive to temperature!c) Supercooled water and ice below freezingYour measurement will become screwy below freezing, as you cannotreally distinguish between supercooled water (evaporation) and ice(sublimation) in your wet bulb, and the vapor pressures differ. AndLueck says supercooled water can be present as low as -12 C. Itsuggests manually scraping the wet bulb to ensure that supercooledwater turns to ice.And note that humidity measurements never are terribly accurate, 2%error in absolute hum. are pretty good, depending on where you are interms of temp and water content. Anything that reads "relativehumidity=52.783 %" is guessing (if you paid less than 100k$...:-)Thomas PruferWet bulb temperature is really defined by the psychrometer and is notan atmospheric water vapor property (compared with Td which has a firmdefinition)!!!!   The above computations assume the standardpsychrometer equation, but the psychrometer constant (0.00066*P inkPa/C) is a theoretical value that is not always matched even by verygood psycrchrometers.  PLEASE note this psychrometer constant dependsdirectly on atmospheric pressure so it's value is not a "universal"constant!Terry HowellNET readings:http://www.uswcl.ars.ag.gov/exper/relhumeq.htmhttp://nwselp.epcc.edu/elp/rhsc.htmlhttp://storm.atmos.uiuc.edu/covis2/visualizer/help/general/rh.dwp.html3)Examples1. EXAMPLE      X M P L    X M P L    X M P L    X M P L    X M P L>My problem is the following. I want to calculate wetbulb temperature>(Tw) where my input is drybulb temperature (T) and relative humidity>(rH). (Pieter Haasbroek)Pieter:Your problem can be solved explicitly using the methods from Jensen etal. (1990) ASCE Manual No. 70 (see pages 176 & 177) using thefollowing steps and equations:1)  compute e as [es(T)*rH/100]    where es(T) = 0.611*EXP(17.27*T/(T+237.3)) in kPa    T is drybulb temp in C    e = (rH/100)* 0.611*EXP(17.27*T/(T+237.3))    where e is ambient vapor pressure in kPa2)  compute dewpoint temperature (Td)    Td = [116.9+237.3ln(e)]/[16.78-ln(e)] in C3)  compute wet bulb temperature (Tw)    Tw = [(GAMMA*T)+(DELTA*Td)]/(GAMMA+DELTA)    GAMMA = 0.00066*P where P is ambient barometric pressure in kPa    DELTA = 4098*e/(Td+237.3)^2This method should be close, especially when Tw is close to Td (DELTAshould be evaluated at (Tw+Td)/2.For example: T = 25CrH = 50%assume elev is sea level and P = 100 kPa.1)  es(25) = 0.611*EXP(17.27*25/(25+237.3)) = 3.17 kPa    e = (50/100)* es(25) = 1.58 kPa2)  Td = [116.9+237.3*ln(1.30)]/[16.78-ln(1.30)] = 13.85 C3)  GAMMA = 0.00066*100 = 0.066 kPa/C    DELTA = 4098*(1.58)/(13.85+237.3)^2 = 0.103 kPa/C    Tw = [(0.066*25)+(0.103*13.85)]/(0.066+0.103) = 18.21 CCHECK ANSWER:    EW(Tw) = 0.611*EXP(17.27*18.21/(18.21+237.3)) = 2.09 kPa    e  = EW(Tw) - GAMMA*(T-Tw)    e  = 1.58 - 0.066*(25-18.21) = 1.64 kPaThe exact answer for Tw is about 17.95C    EW(18.0) = 2.07 kPa;  e = 1.60 kPa    EW(17.9) = 2.05 kPa;  e = 1.58 kPa    EW(17.95) = 2.06 kPa; e = 1.59 kPaThus,    ERROR  e = [(1.64 - 1.58)/1.58]*100 = 3.1%    ERROR Tw = [(18.2-17.95)/17.95]*100 = 1.4%2. EXAMPLE      X M P L    X M P L    X M P L    X M P L>Hello:->I am looking for the algorithm to convert wet/dry bulb temperatures to />from rH (and moisture content as well, for that matter).>I know the Psychometric charts, but they are difficult to use accurately>in software. Anyone have a pointer to appropriate equations?>Thanks in advance! (Spehro Pefhany)Answer(I shall find a formula in SI units, please be patient, BeK)pw = psf  - p * A * (theta - thetaf)theta: dry bulb temp., Kelvin or Celsiusthetaf: wet bulb temp.,   "psf: Saturation pressure at temp thetaf, see 1.), in Torr (mm Hg)pw: Vapor pressure of ambient air, in Torr (mm Hg)p: pressure of ambient air, in TorrA: optimally (see below) 0.66 * 10e-3 * (1/C)3.) The short way round:We're in your backyard: p = 755 Torr, 0 C < theta < 50 C.pw = psf - k (theta - thetaf)phi = pw/psfphi: relative humidity.k= p*A = 0.5 Torr/degreeHigher temperatures:   thetaf about 60 C: k is about 0.52   thetaf about 80 C: k is about 0.53(Formula suggested by A. Sprung, 1888)3. EXAMPLE      X M P L    X M P L    X M P L    X M P LThis question is _often_ asked:>I have the air pressure (p), the temperature (T) and the >relative humidity (rH) and want to calculate the specific humidity>(i.e. the mass of water vapour to the humid air)?First: This air pressure that you have, is actually the total pressure,i.e. it is the sum of the pressure of the dry air (pair) PLUS the sharefrom the water vapour (pw).Then calculate the saturation pressure (es) from one of the formulas givenabove.Then multiply by the relative humidity (rh). This gives you the ambientwater vapour pressure, (e).Then the specific humidity is given by the following formula:        R         L        erho =  --- -----------------        R   p + e(R / R - 1)         W         L   WWHERE:        R / R  = 0.62197   (see the example for the mixing ratio)         L   W4. EXAMPLE      X M P L    X M P L    X M P L    X M P L> Could somebody send or post the method, or fomula, used to calculate> dewpoints.  I have hunted the local library but am unable to find it.Here it is:Td = B / ln(A * 0.622 / w p)where:B = 5420 KA = 2.53 E8 kPaw = water vapor mixig ratiop = local pressure5. EXAMPLE      X M P L    X M P L    X M P L    X M P L>I'm wondering if anyone could please give me the formula for the>calculation of dewpoint temperature given relative humidity, current>temperature, and station pressureFirst calculate the saturation vap. pres. es (Pa) at temperature T(oC):es = 610.78 * exp {A T / (T + B) }  where es in Pa, A = 17.2694 and B = 237.3 for T>0 otherwise 265.5.Then calculate the actual vapour pressure e (Pa) using e = rH / 100 * eswhere rH is the rel.hum in %. Finally invert the equation for es sincee = es(Td). The dewpoint temperature Td (oC) is then obtained fromTd = B  f / { 1 - f  }where f = ln ( e / 610.78 ) / A(Based on Monteith and Unsworth, 1990, Principles of EnvironmentalPhysics, sec.ed., Arnold, London, 291pp.  ISBN 0-7131-2931-X. Note however that their equation 2.25 for Td is wrong)N.J. Bink6. EXAMPLE      X M P L    X M P L    X M P L    X M P LI need some help with calculating RH. Our control system allows us to read> dry bulb temp and enter the specific humidity (g/kg of dry air). We are> looking for a formula to calculate a RH setpoint to use for control. As> the dry bulb temp changes the system would calculate the new RH setpoint> to maintain the same specific humidity.I propose and easy solution.We start with the formula for the mixing ratio:        0.622 * e   w = -----------         p - eand transform it with the formulas for the Saturation vapor pressure (es),resulting in:           w0 * p   rH = ----------------        es(T)*(1 + w0)where:p is the total measured pressure andw0 is the specific humidity (w) at the start of the run, which issupposed to stay constant.To give an example with the same starting conditions as in the exampleabove, see the following table:rel.err.      w'         rh'      es(T)       T1.1%      0.016      60%      2.645      221.3%      0.016      56%      2.810      231.4%      0.016      53%      2.985      241.6%      0.016      50%      3.169      251.8%      0.016      47%      3.363      262.1%      0.016      44%      3.567      272.3%      0.016      42%      3.781      28As you can see w' equals w0, but the relative humidity changes of course.NBBy now you should be able to solve your undergraduate humidity calculationsreally by yourselves. But, looking at the text for the mixing ration, givenabove, most of you could have gained knowledge of this formula byyourselves, I guess.4)Literature hints:For the book and paper aficionados of the readers check out this:'If your really interested in this stuff, I (Kerry Anderson) suggestthe book "Atmospheric Thermodynamics" by Irabarne and Godson."'But unfortunately I learned this book is out of stock(amazon.com). Instead I could recommend:"Fundamentals of Atmospheric Dynamics and Thermodynamics"Paperback, Amazon.com Price: $29.00; Published byWorld Scientific Pub Co. Publication date: May 1992ISBN: 9971978873"Most introductory texts on meteorology will have one or two paragraphs on the matter." (K Anderson)"(Based on Monteith and Unsworth, 1990, Principles of EnvironmentalPhysics, sec.ed., Arnold, London, 291pp.  ISBN 0-7131-2931-X. Note however that their equation 2.25 for Td is wrong)."N.J. Bink"My sources (other than experience) are all German books(Thomas Prufer):"(ue equals u&uml;, BeK)Lueck, Winfired: Feuchtigkeit - Grundlagen, Messen, Regeln.Muenchen: R. Oldenbourg, 1964. Good basics.Sonntag, D.: Hygrometrie: Ein Handbuch der Feuchtigkeitsmessung inLuft und anderen Gasen. (6 vols.) Berlin: Akademie, 1966 - 1968Also contains a very detailed description of nearly everything on themarket in 1966-68.Heinze, D.: Einheitliche, methodische Beschreibung vonGasfeuchte-Messverfahren. Dissertation an der Technischen HochschuleIlmenau, 1980Comprehensive block and signal diagrams with the Laplace functions (!)of nearly all humidity measurement methods. Nearly unobtainable,unfortunately.(Thomas Prufer)5)Committment:This ONA was collected and provided to you by Bernd Kuemmel(bek@mmf.ruc.dk).I admit to have used especially the willing help and the contributionsof the of the following people:Pierre-Alain Dorange, Forrest M. Mims III, Kerry Anderson, Len Padilla,Ralf Haessler, Pieter Haasbroek, Terry Howell, David F Palmer, Thomas Prufer, N.J. Bink, Richard Harvey, Spehro Pefhany, and of course -Ilana Sternduring the ongoing improvement of the ONA.                         Yours sincerely                          Bernd Kuemmel6)Outlook:I have put other peoples warnings on psychrometers now before the examples, I have also included some NET readings peeking to other sites withinformation on the subject, BeK.7)Signature:       Bernd Kuemmel + bek@mmf.ruc.dk + VOX: +45 46 75 77 81 * 2275       IMFUFA, Roskilde University Centre, PB 260, DK-4000 Roskilde         Disclaimer: They do not necessarily agree with all this.

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