The basic idea behind the development of a CTM emulator is to run a number of anthropogenic emission control scenarios (the “Scenario experiments” below) and to analyse the response of the system in order to find a predictable pattern [

17,

18]. If such a pattern exists, it can be used to simulate the response of the system for all other possible emission scenarios, thus saving time and computational costs, within errors which magnitudes clearly depend on the goodness of fitting model used to approximate the response function.

#### 2.1. Simulation of the Hg_{anthr} Atmospheric Cycle

The simulation of the atmospheric cycle of Hg

_{anthr} was performed using the global Hg-CTM model ECHMERIT [

13,

14].

Two sets of experiments were conducted, where Hg

_{anthr} emissions were tagged according to their source region, as reported in the HTAPv2 experiment (

http://www.htap.org/) (see

Figure 1), to allow the source apportionment of the subsequent Hg

_{anthr} deposition. The Hg

_{anthr} emissions were included in the model from three different anthropogenic inventories, referred to here as AMAP [

21], EDGAR [

22], and STREETS [

23,

24].

Firstly, the emission fields were mapped to the HTAPv2 mask at their original resolution using the large fraction area method, they were then interpolated onto the ECHMERIT T42 horizontal grid (roughly 2.8° by 2.8° at the equator) using the mass conserving remapping method; both methods are available in the Climate Data Operators (CDO) [

25] package. Finally, the emissions were distributed vertically (up to 10 hPa), at run time, using the relevant prescribed height distribution, mapping them to Standardized Nomenclature for Air Pollutants (SNAP) and using the distribution in Simpson et al. [

26] or evenly injecting them within the Planetary Boundary Layer (PBL) (see De Simone et al. [

10] for details).

A spin-up period of 4 years was employed for both sets of runs, and the results from the fifth year, namely 2010, were then considered for the analysis.

A BASE run is shared by both sets of experiments and includes an Hg oxidation mechanism driven by O

_{3}/OH fields, imported from the Mozart model [

27], and Hg

_{anthr} emissions from AMAP/UNEP [

21].

The first set of experiments, the “Characterising experiments”, aims only to define and characterise the Hg

_{anthr} atmospheric cycle to provide robust constraints of confidence intervals of the contributions to deposition in each receptor region. To this aim, a number of parameters, model assumptions, and inventories were varied, covering a reasonable range of uncertainties known to influence the Hg atmospheric cycle. All these runs, although leading to changes in Hg surface concentration and deposition fields, were demonstrated to be statistically indistinguishable between each other when compared with the available field measurements, as described in [

10].

A number of runs were conducted employing different Hg_{anthr} emission height distributions (APBL), as well as different Hg_{anthr} speciation ratios, only as ${Hg}_{\mathrm{(g)}}^{0}$ (NSP0), or emitted at a ratio ${Hg}_{\mathrm{(g)}}^{0}$:Hg^{II}_{(g/p)} 50/50 (NSP50).

Years with different meteorological characteristics were also simulated to evaluate the effects of changing atmospheric transport conditions, (BASE-2005 and BASE-1998). They were selected according to opposite values of major climatic indices which result in different circulation and precipitation patterns [

28,

29].

Due to uncertainties of the atmospheric Hg oxidation pathway [

30,

31,

32], a run was performed considering an oxidation mechanism based on Bromine (BRTO) (from p-Tomcat [

33,

34]).

Finally, two runs including, respectively, EDGAR and STREETS inventories were run to explicitly account for the uncertainties regarding Hg_{anthr} emissions.

A summary of the runs performed within the scope of the Characterising experiments is reported in

Table 1 below.

A bootstrap analysis [

35] was then used to evaluate the average Hg

_{anthr} deposition in each receptor region due to each source region and to determine the relative confidence intervals, following the procedure described in De Simone et al. [

4].

The second set of experiments, defined as “Scenario experiments”, represents the core of the present study. The runs belonging to this set were performed using only the AMAP/UNEP [

21] emission inventory, since for the scope of this study we want to simulate the response of Hg

_{anthr} deposition to Hg

_{anthr} emission perturbations using this inventory.

To simplify the emission control simulations, we assumed a decrease of the number of Hg

_{anthr} species emitted. Gaseous elemental mercury (

${Hg}_{\mathrm{(g)}}^{0}$) and reactive mercury (Hg

^{R}) were taken into account. The latter as a lumped species representing oxidised mercury (

${Hg}_{\mathrm{(g)}}^{2}$) and particle bounded mercury Hg

_{(p)}, both considered to be emitted with a constant ratio as in AMAP/UNEP [

21]. Reduction changes were simulated (BaseR20 to BaseR80), as were different ratios of

${Hg}_{\mathrm{(g)}}^{0}$:Hg

^{R} (BaseS00 to BaseS100), leaving all other model parameters and assumptions equal to those in the BASE run. The runs of Scenario experiments, listed in

Table 2, were used to build the HERMES emulator, as described in the following

Section 2.2.

#### 2.2. Building the HERMES Emulator

The scope of this study is to provide a CTM emulator, HERMES, to calculate new Hg_{anthr} deposition fluxes for each receptor related to Hg_{anthr} emission perturbation(s) in one or more source regions. The characteristics of the Hg_{anthr} emission amount and speciation ratio, can be controlled, thus simulating the adoption of available abatement techniques. The HERMES emulator output is a new Hg_{anthr} deposition value for each receptor. To achieve this, the deposition fields resulting from the Scenario experiment ECHMERIT runs were fitted using the best model available.

Since Hg in the CTM model is due only to the anthropogenic emissions (i.e., Hg

_{anthr} species are neither created nor destroyed within the model), the deposition in the model domain cells resulting from Hg

_{anthr} emission reduction (runs BaseR20 to BaseR80) is directly proportional to the reduction (adjusted

${R}^{2}$ ∼ 1). Therefore, the Hg

_{anthr} deposition in the receptor region

r due to the emission reduction in the source region

s, namely

$DE{P}_{r,s}^{Red}$, is calculated by HERMES as follows

where

$INPU{T}_{s}^{Red}$ is the Hg

_{anthr} emission reduction in the source region

s as a percentage (0–100%), and

$DE{P}_{r,s}^{BASE}$ is the Hg

_{anthr} deposition, in the receptor region

r due to the source region

s, in the unperturbed scenario (BASE run).

A linear model is also sufficient (adjusted

${R}^{2}$ ∼ 1) to describe the Hg

_{anthr} deposition resulting from emission speciation perturbation runs(BaseS00 to BaseS100) and Hg

_{anthr} deposition in the receptor region

r due to the emission speciation perturbation in the source region

s,

$DE{P}_{r,s}^{Spec}$, is,

where

$INPU{T}_{s}^{Spec}$ represents the ratio between

${Hg}_{\mathrm{(g)}}^{0}$ (0 = 100%) and Hg

^{R} (1 = 100%);

${A}_{s,r}^{Spec}$ and

${B}_{s,r}^{Spec}$ are the coefficients of the linear equation and represent the deposition of Hg

_{anthr} in the receptor region

r due to the emission in source region

s in the case where Hg

_{anthr} is totally gaseous and the rate at which the deposition changes as the contribution of reactive mercury increases.

From relation (

1) between

$DE{P}_{r,s}^{Red}$ and

$INPU{T}_{s}^{Red}$, the following polynomial can be derived relating the deposition

$DE{P}_{r,s}^{HERMES}$, in the receptor region

r due to the change of Hg

_{anthr} in both terms of emission reduction (

$INPU{T}_{s}^{Rec}$), and speciation (

$INPU{T}_{s}^{Spec}$) in the source region

s:

with all variables as defined above.

Equation (

3) represents the core of the of HERMES emulator, and for ease of use it is implemented in a spreadsheet file available in the Supporting Information.

The new deposition value,

$DE{P}_{r,s}$, is finally compared to the relative bounds at 95% confidence interval (CI) at either tail (see

Table 3), with indications if it falls outside the bounds, as further described below.

By the way the experiments were designed, the HERMES emulator calculates the $DE{P}_{r,s}^{HERMES}$, in the receptor region r due to the perturbation(s) of Hg_{anthr} emission in the source region s, nominally after one year following the emission perturbation(s).

Moreover, since we included for this analysis only the Hg emissions from anthropogenic activities, Equations (

1) and (

2) represent processes that are perfectly linear, as demonstrated by a number of tests regarding the goodness of fit (adjusted

${R}^{2}$ ∼ 1, residuals plots and significance of model regression test based on ANOVA at

$\alpha $ = 0.01). The equations fit perfectly the response of the Hg

_{anthr} deposition to control scenarios of Hg

_{anthr} emissions, in terms of reduction and speciation, respectively, and therefore, they must not be regarded as simple linearisation of the response function.

Since the core Equation (

3) is a simple combination of Equations (

1) and (

2), it means that HERMES can simulate the output of any ECHMERIT runs actually without errors. Indeed, the only differences are negligible, in the order of Kgs, and are just due to the numerical or computational errors in CTM sampling and/or fitting algorithm.