# Chapter 8 Sub-daily atmospheric temperature and radiation variation

After estimating leaf phenology (chapter 4) and simulating the main hydrological processes (chapter 5), the advanced water balance model (chapter 7) starts simulating subdaily processes, which include energy balances and photosynthesis/transpiration. In order to properly simulate these processes it is important to consider sub-daily variations in temperature and radiation. Here we detail how sub-daily estimates of above-canopy air temperature and atmospheric incoming radiation are derived from daily input values.

## 8.1 Above-canopy air temperature

Above-canopy air temperature ($$T_{atm}$$, in $$^\circ C$$) diurnal variations are modeled assuming a sinusoidal pattern with $$T_{atm} = T_{\min}$$ at sunrise and $$T_{atm} = (T_{\min}+T_{\max})/2$$ at sunset. Air temperature varies linearly between sunset and sunrise . Sunrise and sunset hours are determined from latitude and sun declination (see section 4.2 of the reference manual for package meteoland).

## 8.2 Incoming diffuse and direct short-wave radiation

Daily global radiation ($$Rad$$, in $$MJ \cdot m^{-2} \cdot d^{-1}$$) is assumed to include both direct and diffuse short-wave radiation (SWR). Using latitude information and whether is a rainy day, this quantity is partitioned into instantaneous direct and diffuse SWR and PAR for different daily substeps. Values of instantaneous direct and diffuse SWR and PAR above the canopy ($$I_{beam}$$ and $$I_{dif}$$, in $$W \cdot m^{-2}$$) are calculated using the methods described in Spitters et al. (1986), which involve comparing daily global radiation with daily potential radiation. All these calculations are performed using routines in package meteoland (see details in section 4.6 of the reference manual for this package).

Once the above-canopy air temperature for a given time step is known, instantaneous long-wave radiation (LWR) coming from the atmosphere ($$L_{atm}$$, in $$W \cdot m^{-2}$$) can be calculated following Campbell & Norman (1998): $$$L_{atm} = \epsilon_{a} \cdot \sigma \cdot (T_{atm} + 273.16)^{4.0}$$$ where $$T_{atm}$$ is air temperature, $$\sigma = 5.67 \cdot 10^{-8.0}\,W \cdot K^{-4} \cdot m^{-2}$$ is the Stephan-Boltzmann constant and $$\epsilon_{a}$$ is the emmissivity of the atmosphere, calculated using: $\begin{eqnarray} \epsilon_{a} &=& (1 - 0.84 \cdot c) \cdot \epsilon_{ac} + 0.84 \cdot c \\ \epsilon_{ac} &=& 1.72 \cdot \left(\frac{e_{atm}}{T_{atm} + 273.16} \right)^{1/7} \end{eqnarray}$ where $$e_{atm}$$ is the average daily water vapor pressure (in kPa; see 2.5) and $$c$$ is the proportion of clouds ($$c=1$$ in rainy days and $$c=0$$ otherwise).