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» A list of weather formulas

Modified on Saturday, 11 June 2011 23:59 Categorized as Uncategorized
Taken from http://www.aprweather.com/pages/calc.htm

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Andrew Revering's List of Meteorological Formulas
New formulas will be added providing you submit any formulas you know of that are not listed here.
1° Latitude=  69.125 miles
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Temp(F)=  Tf= (1.8*Tc)+32
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Temp(C)=  Tc= (Tf-32)/1.8
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Kelvin(Tk)=  Tk= 273.15 + Tc
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Temp (Reamur) =  (25/36)(°F-32)
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Temp (Rankine) =  °F + 459.67
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Knots=  Knots= Wind Speed MPH * 0.868976241091
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MPH=  MPH= Knots * 1.15077944802
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Miles=  MI= Kilometers * 0.6214
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Kilometers=  KM= Miles * 1.61
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Kilometers=  KM= Meters / 1000
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Meters=  Meters= Kilometers * 1000
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Meters=  M= Feet * 0.305
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Meters Per Second=  M/S= Knots * 0.5148
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Feet=  Ft= Meters*3.2808
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Inches=  IN= CM / 2.54
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Centimeters=  CM = IN * 2.54
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Pascals(Pa)=  Pa= (Mb*100)
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Kilopascal (Kp)=  Kp= InHg * 3.38638815789
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Millibars(Mb)(Hectopascal)=  Mb= (In*33.86388158)
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Inches of Mercury(InHg)=  InHg= (Mb/33.86388158)
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Dew Point(F) Knowing Tc=  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
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Dew Point(F) Knowing Tf=  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
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Before Winter 2001/2002
Wind Chill(F)=  Wc= 0.0817*(3.71*SQRT(WIND SPEED MPH)+
5.81-0.25*WIND SPEED MPH)*(Tf-91.4)+91.4
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Starting Winter 2001/2002
Wind Chill °F =
T = Air Temperature °F
V = Wind Speed MPH  35.74 + 0.6215 * T - 35.75(V ^ 0.16) + 0.4275 * T (V ^ 0.16)
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Heat Index(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 Simmer Index(SSI)=  SSI= 1.98(Tf - (0.55 - 0.0055(RH))(Tf-58)) - 56.83
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Saturation Vapor Pressure(Mb)=  Es= (6.11*10^(7.5*Tc/(237.7+Tc))
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Vapor Pressure(Mb)=
From Dew Point  E= (6.11*10^(7.5*Tdc/(237.7+Tdc)))
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Vapor Pressure(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)))))
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Specific Humidity(kg/kg)=  SH= (0.622*E)/(Mb-(0.378*E))
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Relative Humidity(%)=  RH= (E/Es)*100
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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))
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Relative Humidity and Dew Point knowing Wet & Dry Bulb Temps Relative Humidity & Dew Point using Wet & Dry Bulb Temps
'Saturation Vapor Pressure 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 PressureRelative Humidity
RH = (E / Es) * 100Dew Point
Tp = -1 * {[ln(E/6.1078) * 219.522] + 307.004} / {[ln(E/6.1078) * 0.556] - 9.59539} --------------------------------------------------------------------------------

Dew Point from just T and 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)
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LCL Height (Estimated FT)=  H= 222(Tf-Tdf)
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LCL Height (Estimated Meters)=  H= 67(Tf-Tdf)
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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 and Parcel 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 --------------------------------------------------------------------------------

Rankine Temperature(R)=  R= Tf+460
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Saturation Mixing Ratio(g/kg)=  Ms= ((Val(Humidity) / 100) / Val(MixingRatio)) * 100
OR MORE ACCURATELY
0.622 * Es/(P - Es)
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Mixing Ratio(g/kg)=  M= RH*Ms/100
&
M= ((0.622*E)/(Mb-E))*1000
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Virtual Temperature(C)=  Tv= ((TemperatureC + 273.16) / (1 - 0.378 * (VaporPressure / StationPressure))) - 273.16
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Lifted Index=  LI= Tc(500mb) - Tp(500mb)
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Showalter Index=  SI= 1) From the 850mb temp, raise a parcel dry adiabatically to the mixing ratio line that passes through the Tdc(850mb)
2) From that point, raise the parcel moist adiabatically to 500mb.
3) SI= Tc(500mb) - Tp(500mb)
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Vertical Totals =  VT= T(850mb) - T(500mb)
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Cross Totals =  CT= Td(850mb) - T(500mb)
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Total Totals=  TT= Tc(850mb) + Tdc(850mb) - 2*Tc(500mb)
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(30 or greater strong thunderstorms)
Deep Convection Index =  DCI= T(850 mb) + Td(850 mb) - LI(sfc-500 mb)
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K Index=  KI= (T850 - T500 ) + Td850 - T dd700Basically double the KI value to calculate the chance of thunderstorms.
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Energy Helicity Index =  EHI= (CAPE * Helicity) / 160000
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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)
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ThetaE (any level) =
[Saturated Potential Temperature]  ThetaE = (Tc + 273.15) * ( 1000 / Mb ) ^ 0.286 + (3 * M)
ORThetaE = (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
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WMAX (Maximum Potential Speed of an Updraft) =  WMAX = (( SQRT(2 * CAPE) ) / 2 ) / 0.5148
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Vertical Velocities can overcome the cap if:  VV > SQRT(2 * CINH)
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Convective Temperature=  CT = CCL Tc *(1000.0/CCL Mb)0.286 * (SFC Mb/1000.0)*0.286
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Maximum Hail Size=  Hail = 2*((3*0.55*1.0033*(MVV*MVV))/(8*9.8*900))*100
MVV = Max Vertical Velocities in M/S
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Normalized CAPE=  NCAPE = CAPE / (ELm - LFCm)
<= 0.1 Weak Updrafts
0.1 - 0.3 Moderate Updrafts
>= 0.3 Strong Updrafts
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How to calculate CAPE
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TQ Index (low top convection potential)=  (T850 + Td850 ) - 1.7 (T700)
> 12 Storms Possible
> 17 Low-Top Storms Possible
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Delta Theta-E=
(Wet Microburst Potential)  (SFCThetaE - LowestMidLevel ThetaE)
>= 20 Wet Microbursts Likely
<= 13 Wet Microbursts Unlikely
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U and V Components of Horizontal 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))
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Speed (Knots) and Direction (Degrees) from U and V Components=  Speed = Sqr(U ^ 2 + V ^ 2) / 0.5148
If V > 0 Then ANG = 180
If U < 0 And V < 0 Then ANG = 0
If U > 0 And V < 0 Then ANG = 360Direction = (180 / PI) * Atn(U / V) + ANG --------------------------------------------------------------------------------

BRN Shear =  0.5 (( 6km AVG U Component) ^ 2)
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Bulk Richardson Number =  BRN= (CAPE / BRN Shear)
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Air Density (km/m3) =  D= (mb*100)/((Tc+273.16)*287)
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Absolute Humidity =  Ah= ((6.11*10.0**(7.5*Tdc/(237.7+Tdc)))*100)/((Tc+273.16)*461.5)
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Station Pressure =  Ps = Altimeter in Inches * ((288 - 0.0065 * Elevation in Meters)/288)^5.2561
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Altimeter Setting =  As = (Station Pressure in MB - 0.3) * (1 + (((1013.25^0.190284 * 0.0065)/288) * (Elevation in Meters/(Station Pressure in MB -0.3)^0.190284)))^(1/0.190287)
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Sea Level Pressure =  SLP = Station Pressure & R-Factor
You most likely will have Altimeter Setting information that needs to first be converted to Station Pressure using the equation above.
You can get historical temperature and dew point information from here. Click 'History Data' --> Enter your location --> Click Custom.
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Pressure Altitude (Ft) =  Ap = (1-(Station Pressure in MB/1013.25)^0.190284)*145366.45  --------------------------------------------------------------------------------The Wind Index (WINDEX) is defined as a parameter, developed by McCann (1994), that indicates the maximum possible convective wind gusts that could occur in thunderstorms. The WINDEX is represented by the following equation:WI = 5[HM*RQ(G^2 - 30 + QL - 2QM)]^0.5where HM is the height of the melting level in km above the ground; G is the temperature lapse rate in degrees C km-1 from the surface to the melting level; QL is the mixing ratio in the lowest 1 km above the surface; QM is the mixing ratio at the melting level; and RQ = QL/12 but not > 1--------------------------------------------------------------------------------
Cap Strength (Lid Strength Index)= Saturated wet bulb potential temperature (Theta-E) between the surface and 500 mb MINUS the maximum saturated wet bulb potential temperature (Theta-E) in the lowest 100 mb of the atmosphere. Note in the formulas below M = Mixing Ratio & WBc = Wet Bulb Temperature in °C.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 - 100
MB = 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 - QwmaxA cap of 2 degrees Celsius or greater is a good inhibitor of convection. A strong cap is can hold energy down too much and thus cause thunderstorms not to break. A weak cap can cause development to occur before enough energy builds up for the cells to become severe. A median of a strong cap and a weak cap (a cap strength from 1-2°C) is generally ideal to allow enough time for energy to build and then break the cap, allowing storms to go severe and possibly tornadic.
--------------------------------------------------------------------------------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 (°C); 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. Values over 300 are considered
a severe producing atmosphere.
Meaux Saturation Pressure Curve Formula
dryr = (dry bulb temperature deg.F) + 459.67  <--conversion to Rankine
Psat = 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 componet
variable...weather influences / conditions have to accounted for!(Note=> the racing industry uses 60 deg F instead of 59 degF as part of
STP ) The raw, uncorrected Horsepower and Torque output is corrected
(standardized) to 29.92 inches Hg. / 60 deg. F / 0.00 % Relative Humidity
through 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 to
determine vapor pressure accuracy to better than a 1/10th inch Hg.,
so I began research 14 years ago at local college libraries on various
weather 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 their
data 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 could
find ......couldn't find one single formula that would "mirror" the
Smithsonian data,..so I began to develop my own formula....in 1995 I
finally finished my formula that does "mirror" Smithsonian data from -60F to
212 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. 343
Abbeville, LA 70510
337-893-1541
This 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 C
RH = Relative Humidity in form 88 not 0.88Optional Variable (for more accuracy):
P = Pressure
or
Constant (with up to 0.2° inaccuracy):
P = 985
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))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))
For questions or comments about these formulas, or if you would like a formula that you don't see listed here, email us: Convective Development
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