Where have all the GDDs gone

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Where have all the GDDs gone?

• Roger Littlejohn
• Colin Boswell
• Alison Rutherford

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and where have they come back from?
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What are growing degree days?

• GDDs measure the amount by which the temperature
  in a plant growth environment exceeds a
  threshold value.
• If the temperature is less than the threshold
  there is assumed to be no growth, therefore no
  GDDs.
• GDDs are accumulated over the growing year, and
  used as an indication of which species are likely
  to thrive in a given environment.

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Mathematically

• where Temp measures daily temperature
• ? is a suitable threshold, e.g. in our case 5C
  or 10C
• Temp(1) lt ?
• and i is summed over days.

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Or from the Web

• Explanation of Growing Degree Days
• Accumulated degree days above a specified
  temperature .
• All Growing Degree Days (GDD) are calculated
  using the formula (Tmax Tmin)/2 - B GDD
  where B represents a base temperature value of
  40 or 50 degrees Fahrenheit.
• http//www.mrsars.usda.gov/morris/weather/gdd.htm

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Oops!!

• Explanation of Growing Degree Days
• Accumulated degree days above a specified
  temperature .
• All Growing Degree Days (GDD) are calculated
  using the formula ((Tmax Tmin)/2 B)
  GDD where B represents a base temperature value
  of 40 or 50 degrees Fahrenheit.
• http//www.mrsars.usda.gov/morris/weather/gdd.htm

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http//www.inniskillin.com/vineyard/index.asp?loca
tionvineyard

• The following chart shows the median growing
  degree days above 10C in the major cool climate
  viticulture regions, measured in
  CelsiusGeisenheim, Germany 1050Epernay,
  France (Champagne) 1050Hawke's Bay, New
  Zealand 1200Roseburg, Oregon 1250Geneva,
  Switzerland 1250Beaune, France
  (Burgundy) 1315Niagara, Canada
  (Ontario) 1426Oliver, Canada (British
  Columbia) 1423Yakima,Washington 1426Napa,
  California 1450Healdsburg, Sonoma,
  California 1755

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http//www.cropssouthland.co.nz/pdf(GDDs above
4C)
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How is daily temperature measured. 1.?

• Traditionally daily mean temperature is
  estimated byTmm(TmaxTmin)/2
• Traditionally temperature was measured using a
  max-min thermometer, so this was a natural thing
  to do.
• It shouldnt actually be called mean, because
  it isnt.
• This is how GDD are defined.

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How is daily temperature measured. 2.?

• A natural progression on this (for a statistician
  uninitiated in agronomics) is to use true daily
  mean temperature Tm
• GDDs are still calculated on a daily basis.

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How is daily temperature measured. 3.?

• Modern thermometers can log (functions of)
  temperature at any instant or over any preset
  interval, e.g., instantaneous every minute, max
  and min every hour, etc.
• This makes it natural to sum or integrate (a
  function of) temperature over the day. Denote
  this by TI.

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How is daily temperature measured?

• I had made a lot of GDD calculations based on
  calculations 2. and 3. before I realized it was
  not standard.
• Care is needed in determining exactly what the
  logger is measuring, e.g., the maximum over 24
  hours of instantaneous hourly temperatures is not
  the daily maximum temperature.

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Are traditional and modern methods compatible?

• If the diurnal temperature pattern is
  sinusoidalTmm Tm TI
• But GDD is a non-linear function of temperature,
  so it transpires that GDDI GDDmm GDDmby a
  small but systematic amount.

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Is daily temperature sinusoidal?

• Loggers were positioned at 20 sites on 3
  properties in the MacKenzie Basin.
• Within each property the sites were in an
  altitudinal sequence.
• Some sites were paired, with sunny and shady
  aspects at the same altitude.
• Hourly air and soil temperatures were measured
  over 3 years.
• Lots of missing values.

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Is daily temperature sinusoidal?
Mean Temperature over sites and days of year
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Is daily temperature sinusoidal?

• In this environment a sinusoidal curve does not
  give a good fit.
• The night-time temperature is quite stable,
  almost constant on average in some cases.
• The day-time temperature peaks more sharply than
  the sine curve.

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Is daily temperature sinusoidal?

• The interaction of annual and daily cycles was
  modelled by a complex harmonic model.
• Fitted values from this model were used for
  reporting, as they covered all missing values.
• Residuals were used as indications of localized
  variation from overall means.
• I also used fitted values in some GDD
  calculations, but this is not appropriate.

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Daily fitted mean air and soil temperature by
month for site 1
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Daily fitted mean air temperature by month for
site 1
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Conclusion

• The overall diurnal temperature pattern is not
  sinusoidal.
• The daily mean temperature is systematically less
  than the average of the maximum and minimum.

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How does this affect calculating GDDs?

• How Temp(i) is calculated
• daily mean of max and min within hours of each
  day (close to traditional GDDmm)
• daily mean of instantaneous hourly
  temperatures(GDDm)
• hourly instantaneous or averaged over hour,
  summed over day.

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How does this affect calculating GDDs?
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Example Site 4
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Example Site 10
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Paired t-test for methods 1 and 2

• In general GDDmm gt GDDm

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Example Site 4
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Example Site 4
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Remarks

• Using the daily mean rather than the max-min
  average substantially reduces the number of GDDs.
• The size of this effect depends on the threshold
  and environment.

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Paired t-test for methods 1 and 3

• In general GDDmm gt GDDm

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Comparing methods 1 and 3

• Over all sites GDDI is close to GDDmm or larger
• There is no universal bias factor (as before)
• A closer investigation shows seasonal biasesGDDI
  gt GDDmm in springGDDI lt GDDmm in summer.

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Mean of all sites GDD above 5 C
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Mean of all sites GDD above 10 C
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Spline fit for all sites and average over sites
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Data for all sites and average over sites
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Data for all sites and average over sites

• There are sytematic bias factors
• In spring and autumn GDDI gt GDDmm 0

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Data for all sites and average over sites

• There are sytematic bias factors
• In summer GDDI lt GDDmm

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Conclusions

• The GDD methodology has justified its reputation
  as a rather murky field of science
• It has been developed using a technology that is
  now outdated
• Using daily mean, rather than average of max
  min, leads to a systematic negative bias of
  10-15 over a year, which may impact on a
  decision-making process.
• Integrating temperature above a threshold within
  a day is exposed to different bias factors in two
  different seasons these may cancel to some
  extent.

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What to do about it?

• Because its very entrenched in industry, its
  best to stick with the old definitions
• Care is needed to measure the correct quantities
  and calculate the correct derived variables
  according to those definitions
• Scientific work relating plant growth to
  environmental variables will operate using
  correspondingly more sophisticated physiological
  measurements and mathematical models.