22  Water and Energy Balances

Figure from Rodriguez et al. (2010).

22.1 Water balance

A useful source is Nadia Christina Sabeh’s PhD thesis, 2007.

\[ E_V + E_C + E_S + E_T = 0 \]

22.2 Energy balance

\[ Q_R + Q_G + Q_V + Q_S + Q_P + Q_L + Q_H = 0 \]

22.3 Evaporative Cooling

22.4 Potential Evapotranspiration

22.4.1 Penman (1948)

This equation accounts for two main terms: * the first is the available energy flux density, * the second term is the drying power of the air.

\[ PE = \frac{\Delta(R_n-G) + \gamma\cdot 2.6 (1+0.536 u_2)\text{VPD}}{\lambda(\Delta+\gamma)} \]

More about this here.

22.4.2 PyET

Luckily, we don’t have to work very hard to estimate the potential evapotranspiration. We will use the Python library pyet:

• documentation
• github

Using PyET is quite straightforward:

pyet.pm_fao56(tmean,               # mean temperature
              wind,                # wind speed
              rn=rn,               # net radiation
              tmax=tmax,           # max temperature
              tmin=tmin,           # max temperature
              rh=rh,               # relative humidity
              elevation=elevation) # elevation above sea level