Simple Models
Humidity
Allen, 1985
I was unable to find the original publication for this formula however the function is defined as such:
def relative_humidity(temperature, min_temp)
rh = np.exp((17.625 * min_temp) / (243.04 + min_temp)) / np.exp((17.625 * temperature) / (243.04 + temperature))
return rh * 100.0
Temperature
Cesaraccio
From Cesaraccio et al. 2001 Int.J. Biometeorol. 161-169
This is a decent estimation of temperature over a day.
Uses Temperature Low and Temperature High for the minimum and maximum values.
Doesn’t support photoperiods across midnight (where sunset < sunrise).
alpha = max_temp - min_temp
to = max_temp - 0.39 * (max_temp - min_temp)
r = max_temp - to
hx = sunset - 4.0
hp = sunrise + 24.0
b = (min_temp - to) / np.sqrt(hp - sunset)
if hx >= time > sunrise:
t = min_temp + alpha * np.sin((time - sunrise) / (hx - sunrise) * np.pi / 2.0)
if hx < time < sunset:
t = to + r * np.sin(np.pi / 2.0 + (time - hx) / 8.0 * np.pi)
if sunset < time <= hp:
t = to + b * np.sqrt(time - sunset)
if time <= sunrise:
t = to + b * np.sqrt(time + 24.0 - sunset)
Sine
Uses a sine wave between Temperature Low and Temperature High, with the trough offset to half an hour after Sunrise, this function ignores Photoperiod
sr_off = 5.5 - (sunrise.hour + (sunrise.minute / 60.0))
f = 2 * np.pi / 24.0
t_avg = (min_temp + max_temp) / 2.0
t_amp = (max_temp - min_temp) / 2.0
t = t_avg - t_amp * np.sin((t + sr_off) * f)