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:

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)

If TMIN >= TLIM then **DDA** = AVTEMP - 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

If TMIN >= TLIM then **DDB** = 0 in (°C)

If TMAX <= TLIM then **DDB** = TLIM - AVTEMP

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

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

**ACCDDA & ACCDDB**

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).

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).

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.

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**=6.107799961+DRYB*(4.436518521*10^{-1}+DRYB*(1.428945805*10^{-2}+DRYB*(2.650648471*10^{-4}+DRYB*(3.031240396*10^{-6}+DRYB*(2.034080948*10^{-8}+6.136820929*10^{-11}*DRYB)))))

**VAP** = RELH * SVAP/100

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

**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)

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

Exp is the exponential function (e^{x})

** is the exponentiation function (x^{n})

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 10^{7}

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

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).

**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.

*2008*

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

*2006*

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

*2005*

- Campbell_Scientific(2005) "Calculating Dew Point from RH and Air Temperature. ",
- Campbell_Scientific(2005) "Calculating Sunshine Hours from Pyranometer/Solarimeter Data. ",

*1985*

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

*1981*

- Buck, A.L.(1981) "New equations for computing vapor-pressure and enhancement factor",
*Journal of Applied Meteorology*,**20**, 1527-1532

**DOI: 10.1175/1520-0450(1981)020<1527:NEFCVP>2.0.CO;2**

*1977*

- P.R.Lowe(1977) "An Approximating Polynomial for the Computation of Saturation Vapor Pressure",
*Journal of Applied Meteorology*,**16**, 100-103

**DOI: 10.1175/1520-0450(1977)016<0100:AAPFTC>2.0.CO;2**

*1967*

- Murray, F.W.(1967) "On the computation of saturation vapor pressure. ",
*Journal of the American Meteorological Society*,**6**, 203-204

**DOI: 10.1175/1520-0450(1967)006<0203:OTCOSV>2.0.CO;2**

*1964*

- Berry, G.(1964) "Evaluation of Penman's natural evaporation formula by electronic computer",
*Australian Journal of Applied Science*,**15**, 61-64

https://members.optusnet.com.au/gberrycons/GB%20Web_files/Pub%204.pdf - 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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For further information and assistance, please contact the e-RA curators, Sarah Perryman and Margaret Glendining using the e-RA email address: era@rothamsted.ac.uk