Global radiation

Daily global radiation \( G \) from extraterrestrial radiation \( G_{ext} \) and minimum and maximum temperature:

\[ G = 0.17 \cdot (T_{max} - T_{min})^{0.5} \cdot G_{ext} \]

If minimum and maximum temperature are not provided, the cloudiness attribute is used:

\[ G = (1 - cloudiness) \cdot G_{ext} \]

Subdaily global radiation \( g \): Hour of sunrise: \( hr_{sunrise} \) Hour of sunset: \( hr_{sunset} \) For \( hr_{sunrise} <= hr <= hr_{sunset} \)

\[ g = ((-cos(2.0 * \pi * (hr - hr_{rise}) / daylength) + 1.0) / daylength) * (24 * G); \]

Note: To calculate daily climate input from a sub-daily data source, use the arithmetic mean of the radiation values from all sub-daily time steps where radiation is greater than zero. Exclude any sub-daily time steps with zero radiation from this calculation.

Relative humidity

\[ vps := f(T) \]

If vapour pressure deficit is given:

\[ rh = 100 \left( 1 - \frac{vpd}{vps} \right) \]

If vapour pressure deficit is not given, the following assumptions are made:

• Saturated conditions at \( T_{min} \) (i.e., condensation at night time).
• Constant amount of water during the day

Mean temperature

...

Vapor pressure deficit

\[ vps := f(T) \]

If relative humidity is given:

\[ vpd = vps \left(1 - \frac{rh}{100} \right) \]

If relative humidity is not given, the following assumptions are made:

• Saturated conditions at \( T_{min} \) (i.e., condensation at night time).
• Constant amount of water during the day

  \begin{eqnarray*} vps_{min} := f(T_{min}) \\ vpd = vps - vps_{min} \end{eqnarray*}

  If daily vpd is given, subdaily vpd is derived by:

  \begin{eqnarray*} vps_{daily} := f(T_{daily}) \\ vps_{subdaily} := f(T_{subdaily}) \\ vp_{daily} = vps_{daily} - vpd_{daily} \\ vpd_{subdaily} = vps_{subdaily} - vp_{daily} \end{eqnarray*}

Order

Synthesizing climte follows an order reflecting dependencies among record items. Topological sorting is non-trivial due to varying dependencies.

• Air pressure
• Precipitation
• Wind speed
• Extraterrestrial radiation
• Mean temperature
• Max temperature
• Min temperature
• Vapour pressure deficit
• Relative humidity
• Longwave radiation