# West Castle Alpine Monitoring System

# Diurnal Earth-Atmosphere Energy Balance

The diurnal Earth-Atmosphere energy balance (Q*), represents the limit to the available energy source or sink[1]. The variables of interest are incoming shortwave solar radiation (*K*↓), reflected shortwave solar radiation (*K*↑), incoming longwave radiation emitted from the atmosphere (*L*↓), and outgoing longwave radiation (*L*↑) emitted from the Earth surface. The pattern of incoming short-wave radiation is controlled by the azimuth (Ω) and zenith (Z) angles of the Sun relative to the horizon, with a maximum at local solar noon. We can clearly see this phenomenon in graphics bellow. The reflected shortwave radiation is directly proportional to the incoming shortwave radiation and the surface albedo:

As a first approximation, we can assume the surface albedo to be constant through the day[1]. We know that the surface transmissivity is 0 for shortwave radiation, therefore the amount of incident shortwave not reflected is absorbed. We define the net shortwave radiation as follows:

The energy emitted (*E)* by a body, termed *radiant flux*, is described by the Stefan-Boltzmann law:

Where:

ε0 is the emissivity

is Stefan Boltzmann Constant of Proportionality; 5.6 x 10-8 Wm-2K-4

T0 is the surface temperature in Kelvin (K)

*E *is the radiantflux; defined as the rate of flow of radiation (W) from a unit area (m2) of a plane surface into the overlapping hemisphere. The *flux density* is defined as the radiant flux per unit area (Wm-2).

We can now define *irradiance*,* emittance*, *and reflectance*, as the *radiant flux density*; the electromagnetic energy incident upon, emitted by, or reflected off of a surface (respectively). In accordance with the conservation of energy, radiation incident upon a surface will either be transmitted through, reflected from the surface, or absorbed, and thus we define a set of dimensionless radiative properties of the substance[1]; transmissivity ψ_{λ}, reflectivity (albedo) α_{λ}, and absorptivity ξ_{λ}, such that:

In accordance with the Stefan-Boltzmann Law, the incoming long wave radiation is dependent upon the distributions of temperature, water vapour, and carbon dioxide. If these atmospheric properties have low diurnal variability, we can assume the incoming longwave radiation to be relatively constant throughout the day. The ground surface with emissivity less than 1 will radiate longwave radiation according to:

Taking the difference we can calculate the long-wave radiation budget:

We can now calculate the daytime net all-wave radiation budget (Q*):

During the evening when incoming shortwave radiation is not present the net all-wave radiation budget is such that:

During the day, when the net short-wave gain exceeds the net long-wave loss, we expect to see a radiant energy surplus at the surface. Conversely, in the evening when the absence of solar input does not offset the net longwave loss, we expect to see a surface deficit. The ground surface surrounding each of the MET stations vary, -coniferous forest (a=0.8-0.1), silt-loam (a=0.2-0.3)*, and shale (a=0.2), for the Valley, Mid-Mountain, and Ridge MET stations respectively- and therefore each site represents a slightly different albedo. Thus, we expect to see both the reflected shortwave and outgoing longwave radiation vary at each station, while both the long and shortwave incoming radiation are spatially invariant. However, we expect to see spatial variance among these variables during the presence of cloud cover. The data collected from the MET stations clearly demonstrates these phenomena. Figures I,II show a relatively similar solar input, while the reflected shortwave radiation is considerably greater at the Mid-Mountain Station. The above albedo values were derived through *eq.I*, and verified using Table I. This calculation involved a threefold data preprocess. First, the values for incoming shortwave radiation equal to zero (sun down), were removed. Second, following the cosine law of illumination, we removed values for incoming shortwave radiation that were collected at times where the azimuth and zenith angles where large. Specifically values acquired between 20:00 through 7:00 (the following day), which also took into account the lunar illumination experienced mostly at the Ridge location. Finally, the average of remaining calculated values was taken. I is important to note that the emissivity values for common natural surfaces (Table.I), differ by a small amount. Specifically soils, grass, and coniferous trees, the common ground cover surrounding the CMR MET stations, vary by only 0.09. Thus we can conclude, that the spatially variant values of Q*, depend on surface albedo and surface temperature of the reflecting/emitting body. Surfaces with low albedo such as the coniferous trees beneath the valley MET station are far better absorbers than the dry soil surrounding the Mid-Mountain MET station. Barring the small amount of sensible heat loss and latent heat of vaporization due to the process of evapotranspiration, we expect a high surface temperature (*T0*), and therefore a large increase in net shortwave radiation should correlate to a large loss in net longwave radiation.

* 2.5yr 5/4 Reddish Brown - Munsell Soil Chart

1 Oke, T.R.: ‘Boundary layer climates’ (Routledge, 2002. 2002)