Derived Meterological Variables

The following derived variables are available when extracting meteorological data from the e-RA Data Extraction Tool, from ROTHMET, WOBMET and BROOMET.

All the measured variables required to calculate the derived variables are automatically extracted. Click on the 'Calculate Variables' button once the measured variables have been extracted, for your desired date range. You can also set a limiting base temperature TLIM, for calculating degree days above or below a base temperature. If this is not set, 0 degrees C is set as the default base temperature.

To get the full benefit of this calculated variables feature use either Google CHROME or FrontMotion Firefox.

  • DDA: Day Degrees Above a base temperature (TLIM) (°C)
  • DDB: Day Degrees Below a base TLIM (°C)
  • ACCDDA: Accumulated Day Degrees Above TLIM (°C)
  • ACCDDB: Accumulated Day Degrees Below TLIM (°C)
  • SMD: Potential Soil Moisture Deficit (mm)
  • PSMD: Accumulated Potential Soil Moisture Deficit (mm)
  • RELH: Relative humidity at 0900 GMT (% value of saturation value)
  • EVAPG: Evaporation over Grass (mm)
  • EVAPW: Evaporation over Water (mm)
  • VAP: Vapour pressure (mb)

Variables calculated if values are missing:

  • WINDRUN: Run of wind in 24h, 0900GMT to 0900GMT (km/24 hours)
  • DEWP: Dew point (°C)
  • RAD: Radiation (J/m2 or MJ/m2 or J/cm2)

Other definitions:

  • AVTEMP: Average temperature (°C)
  • TRANGE: Temperature range (°C)
  • TMIN: Daily minimum temperature (°C)
  • TMAX: Daily maximum temperature (°C)
  • TLIM: The (arbitrary) limiting or base temperature (set by user) (°C)
  • WETB: Wet bulb temperature (°C)
  • DRYB: Dry bulb temperature (°C)
  • WINDSP: Wind speed at 0900GMT (m/s)
  • RAIN: Rainfall in 24h, 0900GMT to 0900GMT (mm)
  • RDUR: Rainfall duration, 0900GMT to 0900GMT (h)
  • SUN: Hours of sunshine (h)

Calculation of Temperature derived Items:

TRANGE = TMAX - TMIN : Range (°C)

AVTEMP = (TMAX+TMIN)/2 : Average temperature (°C)

Calculation of DDA Day Degrees Above a base temperature (TLIM)


If TMAX <= TLIM then DDA = 0

If (TMAX - TLIM) >= (TLIM - TMIN) then DDA = (TMAX - TLIM)/2 - (TLIM - TMIN)/4

If none of the above then DDA = (TMAX - TLIM)/4

Calculation of DDB Day Degrees Below a base temperature (TLIM)

If TMIN >= TLIM then DDB = 0 in (°C)


If (TMAX - TLIM) >= (TLIM - TMIN) then DDB = (TLIM - TMIN)/4

If none of these then DDB = (TLIM - TMIN)/2 - (TMAX - TLIM)/4


Accumulated day degree data: this is a running total, and an arbitrary start date has to be provided.

Note: these calculations are provided from the standard found in the Energy Efficiency Office (1985).

Calculation of wind run (WINDRUN)

WINDRUN is usually measured so this is only to be used if the data is missing.

WINDRUN = WINDSP * 86.4 (this is conversion from m/s to km/24 hours).

Calculation of actual Vapour pressure (VAP), Dewpoint (DEWP) and saturated vapour pressure (SVAP)

At Rothamsted these are calculated within the datalogger after Buck (1981) and Allen et al (2006).

At Woburn these are have been calculated within the datalogger since the station was automated in 1999 as described by Campbell Scientific Technical Note 16 (2005), using formulae based on studies by Lowe (1977). Before automation, the assumption is that the equations of Buck (1981) werre used alongside those of the Met Office (1964) and Allen et al (2006), as shown below for Rothamsted.

Calculation of actual vapour pressure (VAP):

At Rothamsted this is after Buck (1981) and Allen et al, (2006):

If WETB > 0, VAP= 6.1375*EXP(17.502*WETB/(240.97+WETB))-0.799*(DRYB-WETB)

If WETB <= 0, VAP=6.1389*EXP(22.452*WETB/(272.55+WETB))-0.720*(DRYB-WETB)

At Woburn VAP has been calculated within the datalogger from Relative Humidity (RELH) and DRYB only since Dec 2009, based on Campbell Scientific Technical Note 16 (2005) and Lowe (1977):



SVAP = Saturated vapour pressure for the air temperature range of -50°C to +50°C

Calculation of dew point (DEWP)

At Rothamsted this is calculated after Buck (1981):

DEWP= 240.97*LOGn (VAP/6.1375)/(17.502-LOGn(VAP/6.1375))

At Woburn, DEWP has been calculated within the datalogger from DRYB and WETB and RELH after Lowe (1977).

Calculation of Relative Humidity, RELH

SVAP = Saturated vapour pressure

VAP = Actual vapour pressure (see above)

SVAP = 6.1375*EXP(17.502*DRYB/(240.97+DRYB)) (Buck, 1981)

RELH = 100 * (VAP/SVAP)

Definitions and intermediate calculations for RAD, EVAPG, EVAPW and PSMD

Cos, sin and tan have the usual trigonometric meanings

Sqrt the square root function

nday_val is the day number (Julian date) of the record in question e.g. 1st Feb. = 32

days_in_year ordinarily is 365, but 366 in a leap year

stn_latitude is the latitude of the station in question: Rothamsted = 51.81°N

Woburn = 52.017 °N Brooms Barn = 52.267 °N.

hrday is the maximum amount of sunshine in hours, that a latitude can receive. (i.e. cloudless all day)

sunfr is the sun fraction, the ratio of recorded hours of sun to the maximum possible

HMM is the evaporation term from net radiation over grass

EA_GRASS is the evaporation term from humidity differences over grass

EA_WATER is the evaporation term from humidity differences over water

angnd = (6.28318 *(nday_val - days_in_year + 193))/days_in_year

csd = cos(angnd)

snd = sin(angnd)

cs2d = (csd + snd)*(csd - snd)

sn2d = 2*csd*snd

sndecl = 0.00678 + (0.39762*csd)+(0.00613*snd)-(0.00661*cs2d)-(0.00159*sn2d)

csdecl = sqrt(1 - sndecl*sndecl)

csl = cos((stn_latitude*3.14159)/180)

snl = sin((stn_latitude*3.14159)/180)

cshass = (-0.014544 - (snl*sndecl))/(csl*csdecl)

snhass = sqrt(1 - cshass*cshass)

hass = atan(snhass/cshass) if hass < 0 then hass = hass + 3.14159

hrday = hass*24/3.14159

sunfr = SUN/ hrday

Evaporation Items

Exp is the exponential function (ex)

** is the exponentiation function (xn)

d0g is a correction factor for grass: 0.75

d1g is a correction factor for grass: 1

d0w is a correction factor for water: 0.95

d1w is a correction factor for water: 0.5

c1 is a constant: 4.0621 * 10-7

c2 is a constant: 3.721432778 x 107

The relative humidity (RELH) expresses the degree of saturation of the air as a ratio of the actual (VAP) to the saturation (Es) Vapour pressure at the same temperature (from Allen et al, 2006)

Es = 6.1078 * exp((17.269 * AVTEMP) / avt) (Es = saturated vapour pressure at Avtemp) Note that these values are not exactly the same as for SVAP.

avt = AVTEMP + 237.3

Es = 6.1078 * exp((17.269 * AVTEMP) / avt) (Es = saturated vapour pressure at Avtemp)

delta = (4097.93 * Es) / (avt * avt)

sunfr = SUN/ hrday

fnt2 = (0.0048985 * (AVTEMP + 273.0) ** 4) *(0.47- (0.065 * sqrt(VAP))) * (0.17 + 0.83 * sunfr)

ev1 = c1 * delta

Calculation of Radiation (RAD) (only to be used if data is missing)

inv = 1.00011 - (0.03258*csd)-(0.00755*snd)+(0.00064*cs2d)+(0.00034*sn2d)

RAD = (0.16+(0.62*(((SUN)/hrday))))*c2*inv*((csl*csdecl*snhass) + (snl*sndecl*hass))

NB: The calculated value for radiation should be divided by 1,000,000 to express MJ rather than joules of energy.

Calculation of Evaporation over grass (EVAPG)

EA_GRASS = 0.2625 * ((6.1078 * exp((17.269 * AVTEMP)/(237.3 + AVTEMP)) - (VAP)* (d1g + (WINDRUN* .0062137)))

if EA_GRASS < 0 then EA_GRASS = 0

hj_g = d0g * (1000000 * RAD) - fnt2

EVAPG = ( (hj_g * ev1) + (0.66 * EA_GRASS )) / (delta + 0.66)

HMM = (hj_g * ev1)/ 0.66

Calculation of Evaporation over water (EVAPW)

EA_WATER = 0.2625 * ((6.1078 * exp((17.269 * AVTEMP)/(237.3 + AVTEMP)) - (VAP)*(d1w + (WINDRUN * 0.0062137)))

if EA_WATER < 0 then EA_WATER = 0;

hj_w = d0w * (1000000 * RAD) - fnt2

EVAPW = ((hj_w * ev1) + (0.66 * EA_WATER )) / (delta +0.66)

The calculation of EA, HMM, EVAPG and EVAPW are described in detail in Berry (1964).

Calculation of Potential Soil Moisture Deficit (PSMD)

PSMD = PSMD + EVAPG - RAIN (Not negative)

Where PSMD is the accumulated SMD so far.

PSMD is an accumulated value, starting at the value for soil moisture deficit for start of range.

This measures the loss of moisture in the soil; and while the daily value may be significant it is usually calculated over some months at least. Technically it is an accumulation, and into the summer will usually show a net loss. The value can never be negative, as if precipitation exceeds evaporation together with any deficit to date, this forms runoff and contributes to surface water flow.

Prepared by Margaret Glendining and Claudia Underwood, June 2010, with advice from Tony Scott. Updated December 2016 by Tony Scott. Based on the BITS Metdata Web Manual, extracted Oct 2009, and the old e-RA webpages, 1997. For further details, contact the e-RA Curators.

Key References


  • Reda, I. and Andreas, A.(2008) "Solar Position Algorithm for Solar Radiation Applications. ", ,


  • Allen, R.G. , Pereira, L.S. , Raes, D. and Smith, M.(2006) "FAO Irrigation and Drainage Paper 56, Crop Evapotranspiration,", , 33-40


  • Campbell_Scientific(2005) "Calculating Dew Point from RH and Air Temperature. ", Technical Note 16, Campbell Scientific. , ,
  • Campbell_Scientific(2005) "Calculating Sunshine Hours from Pyranometer/Solarimeter Data. ", Technical Note 18, Campbell Scientific , ,


  • Energy_Efficiency_Office(1985) "Fuel Efficiency Booklet No 7, Degree days. Energy Efficiency Office, Dept of Energy,"





  • Berry, G.(1964) "Evaluation of Penman's natural evaporation formula by electronic computer", Australian Journal of Applied Science, 15, 61-64
  • Meteorological_Office(1964) "Hygrometric Tables (Part II, Second Edition), Stevenson Screen Readings, Degree Celsius (reprinted 1971). HMSO, London (Met.O. 265b), U.D.C. 5551.501. 42:551.571"
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