**3. Methodology**

The measurement of the Earth's energy budget can be conducted through remote sensing. A review by Liang et al. [5] has mentioned that there are several components to be calculated. The first formula was to get the surface energy balance and this is the sum of soil heat flux (G), sensible heat flux and latent heat flux. The latent heat flux is derived from the product of latent heat evaporation of water and the rate of evaporation of water.

$$\mathbf{R}\_n = \mathbf{G} + \mathbf{H} + \lambda \mathbf{E} \mathbf{T} \tag{1}$$

Rn is the representation of all-wave net radiation.

However, remote sensing has presented another perspective, where the net radiation is the sum of shortwave net radiation and long wave net radiation (which is represented in **Figure 1**).

#### **Figure 1.**

*The diagram depicts an overall movement of solar energy where the energy dissipates into space, being retained on the surface of earth and those reflected by the atmosphere. Courtesy of the NASA global precipitation measurement education.*

$$\mathbf{R}\_{\rm n} = \mathbf{R}\_{\rm n}^{s} + \mathbf{R}\_{\rm n}^{l} + \left(\mathbf{1} - \alpha\_{\rm sw}\right)\mathbf{F}\_{\rm d}^{s} + \mathbf{F}\_{\rm d}^{l} - \mathbf{F}\_{\rm u}^{l} = \left(\mathbf{1} - \alpha\_{\rm sw}\right)\mathbf{F}\_{\rm d}^{s} + \mathcal{E}\mathbf{F}\_{\rm d}^{l} - \sigma\varepsilon\mathbf{T}\_{\rm s}^{4} \tag{2}$$

The equation above will then include all the other factor that will affect the energy balance. The net radiation is simply the sum of shortwave net radiation ( ) *s Rn* and long wave net radiation ( ) *<sup>l</sup> Rn* . However, the incoming waves will then be affected by the albedo on earth.

Hence, the second part of the equation WHERE the product of the difference in surface shortwave broadband albedo (1−α *sw* ) and the shortwave downward flux incident on the surface ( ) *<sup>s</sup> Fd* , in addition to the difference between the longwave downward ( ) *<sup>l</sup> Fd* and upwelling radiation ( ) *<sup>l</sup> Fu* will give the all-wave net radiation.

The third part of the equation will then include the Stefan-Boltzmann's constant (σ) . The product of (1 ) *<sup>s</sup>* −α *sw d F* is then added to the product of surface longwave broadband emissivity ( ) . The product of and the skin surface temperature ( ) <sup>4</sup> *Ts* will be deducted and this gives the all-wave net radiation.

The remote sensors on the satellite have been used to measure the Total Solar Irradiance. The sensors from previous studies have allowed scientists to estimate solar constant. Remote sensing on the satellite has the ability to sense the net radiation at the top of the atmosphere. The data recorded includes both spatial and temporal scales. Remote sensing have been used to record the amount of energy that is received at the top of the atmosphere. The conserved energy can then be calculated and be accounted. Different surface of the Earth will then have different rate of energy exchange. Therefore, the change in energy balance will affect the climate.

The loss of grassland have been measured by the proportion where it covers the globe. Grasslands that have been lost regionally will then be measured by various units such as kilometres square (km<sup>2</sup> ) and hectares (ha) on a larger scale. To understand further on how the grassland is affected by climate change and other factors, it can be measured with the annual changes in carbon stocks in grassland. Therefore,

$$
\Delta \mathbf{C}\_{GG} = \Delta \mathbf{C}\_{GGLB} + \Delta \mathbf{C}\_{GG\text{solts}} \tag{3}
$$

The annual change in carbon stocks is measures in tonnes of carbon per year and is derived from the sum of annual change in carbon stocks in living biomass ( ) ∆*CGGLB* and annual change in carbon stocks in soils ( ) ∆*CGG soils* in grassland. However, with this use of formula, to calculate the change of carbon stocks in different region will then take into account of the specific grassland type (*i*), the climatic zone (*c*) and the management regime (*m*). Since the ∆*CGGLB* can be affected by different factors, regional grassland carbon stock can then be calculated with:

$$
\Delta \mathbf{C}\_{\text{GGLB(c,t,m)}} = \left( \Delta \mathbf{B}\_{\text{perminal}} + \Delta \mathbf{B}\_{\text{grasses}} \right) \times \mathbf{CF} \tag{4}
$$

*CF* is at the default of 0.5. where the change is the product of carbon fraction of dry matter (CF) to the sum of change in above- and belowground perennial woody biomass (∆*Bperennial*) and below ground biomass of grasses ( ) ∆*Bgrasses* .

Therefore, to accurately place the equation with the inclusion of the type of grassland, the climatic zone the grassland is in and the management regime that the grassland have been placed under:

$$\mathbf{C}\_{GG} = \left[ \left( \Delta \mathbf{B}\_{\text{permissible}} + \Delta \mathbf{B}\_{\text{graases}} \right) \times \mathbf{CF} \right] + \Delta \mathbf{C}\_{GG\text{solts}} \tag{5}$$

Inventory system could also be set up to record clear data of the plants present, the climatic patterns and the management regime where animals that are grazing or being managed by humans efforts to conserve grassland.
