#### 2.1. The Mathematical Model

In the present study, the mathematical model for estimating isoprene, monoterpenes, and OVOCs emissions in Greece was incorporated into the GIS platform. The mathematical model used for all types of vegetation, describing the emissions flux on an hourly basis is that of [

10]:

where ε is the emission potential (

${\mathsf{\mu}\mathrm{g}\text{}\mathrm{g}}^{-1}{\mathrm{h}}^{-1}$) for any particular species, D is the foliar biomass density (

$\mathrm{g}\text{}\mathrm{dry}\text{}\mathrm{weight}\text{}\mathrm{foliage}\text{}{\mathrm{m}}^{-2}$), and γ is a unit less environmental correction factor representing the effects of short-term (e.g., hourly) temperature and solar radiation changes on emissions. We have to underline that the experiments were conducted using eucalyptus trees (

Eucalyptus globulus L.).

Concerning the estimation of the isoprene emissions, [

14] showed that, to a very good approximation, the short-term (e.g., hourly) variations in emissions could be described by the product of a light-dependent factor and a temperature-dependent factor. So, the environmental correction factor for the isoprene emission is expressed as:

The light-dependent factor is given by:

where a = 0.0027 and

${\mathrm{C}}_{{\mathrm{L}}_{1}}=1.066$ are empirical constants, and L is the PAR flux (

$\mathsf{\mu}\mathrm{mol}\text{}\mathrm{photons}\text{}\left(400\u2013700\text{}\mathrm{nm}\right){\mathrm{m}}^{-2}{\mathrm{s}}^{-1})$.

The temperature-dependent factor is given by:

where R is the gas constant (

$=8.314\text{}\mathrm{J}\text{}{\mathrm{K}}^{-1}\text{}{\mathrm{mol}}^{-1}$),

${\mathrm{C}}_{{\mathrm{T}}_{1}}\left(=\mathrm{95,000}\text{}\mathrm{J}\text{}{\mathrm{mol}}^{-1}\right)$,

${\mathrm{C}}_{{\mathrm{T}}_{2}}=\left(\mathrm{230,000}\text{}\mathrm{J}\text{}{\mathrm{mol}}^{-1}\right)$, and

${\mathrm{T}}_{\mathrm{M}}\left(=314\text{}\mathrm{K}\right)$ are empirical coefficients based upon measurements of three plant species—eucalyptus, aspen, and velvet bean—but which seem to be valid for a variety of different plant species [

14], and finally,

${\mathrm{T}}_{\mathrm{s}}\left(=303\text{}\mathrm{K}\right)$ is the standard temperature. More precisely, the above equation accounts the influence of temperature on electron transport and is a simplified form of the enzyme activation equations [

14]. Initial fits for

${\mathrm{C}}_{{\mathrm{T}}_{1}}$,

${\mathrm{C}}_{{\mathrm{T}}_{2}}$, and

${\mathrm{T}}_{\mathrm{M}}$ (at each light intensity level) revealed no significant trend in the values of three constants with light intensity. The values used represent the best fit for all light intensities and temperature.

Concerning the estimation of the monoterpene emissions, the environmental correction factor suitable for most of the plants is parameterized using the following equation [

14]:

where

$\mathsf{\beta}(=0.09\text{}{\mathrm{K}}^{-1})$ is an empirical coefficient based on non-linear regression analysis of numerous measurements present in the literature.

Recent studies proved that monoterpene emissions from some evergreen oaks and also Norway spruce show a light dependency, which seems to be well described by the isoprene environmental correction factor [

8].

Since the environmental conditions controlling emissions of OVOCs are not entirely understood compared to isoprene and monoterpenes, and given the lack of other information, OVOCs emissions are considered temperature-dependent and the use of Equation (5) is recommended for the estimation of their emissions [

15].

#### 2.2. The Computational Model

In order to produce the NMVOCs emission inventory for Greece on a 6 × 6 ${\mathrm{km}}^{2}$ spatial and a 1hr temporal resolution covering one year, the GIS software (ArcView v10) was used in order to combine a variety of input data: updated satellite land-use data, land-use specific emission potentials, foliar biomass densities, temperature, and solar radiation data. For the calculation of the hourly biogenic emissions, detailed meteorological data for the time period of a whole year (2016) were used. After calculating the hourly emission fluxes, daily, monthly, and yearly emission values were also estimated.

The land use–land cover (LULC) data used in the present study was provided by the United States Geological Survey (USGS) Global LULC version 2.0 Database derived from the 1 km Advanced Very High Resolution Radiometer (AVHRR) data. The USGS classification system includes 25 land cover categories, only 14 of which are found in the area under study (

Figure 1). The different land-use classes emitting BVOC are characterized by one ecosystem type (e.g., Grassland) or a combination of two of them (e.g., Mixed Scrubland–Grassland). The area was divided into cells using a spatial resolution of 6 × 6

${\mathrm{km}}^{2}$ with Lambert Conic Conformal projection. Each cell was checked separately and correction of the LULC category was made if necessary based on the work done by [

5,

16]. As a result, new updated land-use data were used for the year 2016 that depict the all the changes that took place the recent years in Greece and especially the urban areas.

The employment of land-use specific emission potentials and foliar biomass densities for every month covering the whole year is essential for the estimation of isoprene, monoterpenes, and OVOCs. The main references used for the selection of these values were from the recent study of [

17] under the NatAir program (Improving and Applying Methods for the Calculation of Natural and Biogenic Emissions and Assessment of Impacts on Air Quality) for the region of Europe and the neighboring ones. The existing databases were used and updated according to recent experimental findings. Plant species-specific emission factors were updated and recalculated in order to assign foliar biomass densities and emission potentials to commonly observe European vegetation species. Furthermore, the fact that the foliar biomass densities are not constant during the year was taken into account. In order to describe the seasonal variation of the foliar biomass densities, it was necessary to use corrective factors which vary between the different vegetation species according to the study of [

9]. So, appropriate monthly foliar biomass densities were assigned to each land-use category. The maximum monthly foliar biomass densities are observed during May, June, July, August, and September while the minimum ones are observed during December, January, and February. Indicatively, in

Table 1, the values of a winter (January) and a summer month (July) are presented. When a land-use class was characterized by a combination of different vegetation species, it was assumed that the monthly average foliar biomass density is equal to the mean value of the foliar biomass densities of all vegetation types within the land-use category [

9]. Finally, the specific emission potentials for the land-use classes that are a combination of different vegetation types were calculated using the formula:

where

${\mathsf{\epsilon}}_{\mathrm{i}}$ and

${\mathrm{D}}_{\mathrm{i}}$ are the emission potentials and the foliar biomass densities of each vegetation type within the land-use category, and n is the number of vegetation types within the land-use category [

9].

Finally, for the OVOCs, due to lack of reliable experimental data on their emissions, [

9] recommended the use of the uniform emission rate of 1.5

$\mathsf{\mu}\mathrm{g}\text{}{\mathrm{g}}^{-1}{\mathrm{h}}^{-1}$ for the different vegetation species.

Hourly temperature values were provided by the National Observatory of Athens (

www.meteo.gr) from 292 meteorological stations for 2016. The typical temperature diurnal variation for all the stations was produced by calculating the average hourly temperature values of each month of the year. Hourly temperature maps were constructed using the technique of Inverse Distance Interpolation (IDW), thus providing a continuous temperature field covering the area under study.

Solar radiation data have been calculated with the use of an existing methodology [

18] that has been used in the pilot study SENSE of the Geo-Crandle project (

http://geocrandle.eu/en/). It is based on solar irradiance spectra produced via a synergy of satellite data, radiative transfer simulations, and neural network techniques. The method has been validated in [

19] by comparison with ground-based solar radiation measurements. The radiation SENSE output for every month of 2016 having 0.05° latitude by 0.05° longitude spatial resolution and 1 h temporal resolution. Indicatively, in

Figure 2, the mean daily PAR for January and July are presented. Then, with the aid of GIS, these radiation values were adjusted to the area of interest with a spatial resolution of 6 × 6 km

^{2}.

Initially, the hourly biogenic emissions were calculated using the typical temperature and radiation diurnal variation of each month of 2016. Then, the monthly biogenic emissions were estimated by summing up the daily emissions of isoprene, monoterpenes, and OVOCs per month in Greece, and finally, the annual ones were estimated as the sum of the total monthly emissions for 2016 per hydrocarbon.