**2. Materials and Methods**

In this study, we compare the method for "traditionally" accounted for GHG emissions and the GWP method that is used in the BCCM. By "traditional" accounting, we mean the use of GWP and multiplying this value of GWP with the corresponding amount of GHG emission of the specific pollutant, given in IPCC guidelines for national GHG inventories and Section 2.1 of this article. As a method using the BCCM, we refer to the use of impulse response function and decay of pulse emissions, which is also covered in the latest (fifth) IPCC assessment report [15] given in detail in Section 2.2 of this article.

### *2.1. Method Used in IPCC Guidelines for the National GHG Inventories*

The Intergovernmental Panel on Climate Change (IPCC) has created an internationally agreed methodology for the assessment of GHG emissions from numerous sectors, including agriculture [16]. The assessed GHG emissions (inventories) are used for approximate anthropogenic emissions by sources and removals by sinks of GHGs. Each year, countries, including the EU Member States, submit individual reports on the inventory of national emissions to the United Nations Framework Convention on Climate Change (UNFCCC). These reports are used to account for the current state of the GHG emissions, see global trends, and make forecasts. Moreover, IPCC has accomplished that based on the reports, governments take action towards the mitigation of climate change [2].

The GHGs included in the IPCC guidelines are carbon dioxide (CO2), nitrous oxide (N2O), methane (CH4), and fluorinated gases (HFCs, PFCs, and SF6). To quantify, compare, and analyze the emissions, promote mitigation options, and design sustainable policy strategies, a default emission metric, CO2 equivalent (eq.), has been developed. The CO2 eq. is obtained by multiplying the estimated amount of non-CO2 GHG emission (component i) by a coe fficient of that specific non-CO2 emission for a fixed time horizon (usually 20 or 100 years) and summing the obtained individual CO2 eq. values into an aggregated emission metric. The coe fficient used is known as the global warming potential (GWP)—"an index, based on radiative properties of greenhouse gases, measuring the radiative forcing following a pulse emission of a unit mass of a given greenhouse gas in the present-day atmosphere integrated over a chosen time horizon, relative to that of CO2" [15].

Based on new scientific and technical knowledge, the guidelines have had two major revisions since their 1996-version: "2006 IPCC Guidelines for National Greenhouse Gas Inventories" and the recently adopted "2019 Refinement to the 2006 IPCC Guidelines for National Greenhouse Gas Inventories". As a result of refinement, new sources, and pollutants, and updates to the previously published methods, have been included in the guidelines. Also, the numeric value of the global warming potential has been updated since its first introduction in the early nineties (see Table 1). Changes in the GWP value have been made due to improved scientific knowledge and updated estimates of the energy absorption, lifetime, impulse response functions. Estimates on impulse response functions or radiative e fficiencies of GHGs vary because of changing atmospheric concentrations of GHGs that result in a change in the energy absorption of one additional ton of a gas relative to another [15]. Since GWP of CO2 is used as a reference, GWP of CO2 equals one and remains constant regardless of the used time frame. Therefore, any parameter adjustments for CO2 will a ffect all results of the assessments done for other GHGs [15].


**Table 1.** Global Warming Potential (GWP) values since the first assessment report, unitless [15,17].

1 With climate-carbon feedbacks [15].

The selection of time horizon has a substantial influence on the GWP values; hence, the estimated contribution to the total emissions by the component i [15]. The majority of studies and agreements use the 100-year time horizon. Also, the Kyoto Protocol and the Paris Agreement are based on GWPs from pulse emissions over a 100-year time horizon. And, indeed, for many objectives, the 100-year time horizon is applicable, especially taking into account the long-term e ffects of GHG emissions and the need for long-term modelling of future temperatures. Yet, the 20-year time horizon might be a more appropriate choice for regional/national strategies or mid-term modelling applications as their focus typically is on a much shorter time frame [18]. In addition, tropospheric temperatures that are more relevant for regional/national decision makers may show more rapid changes in radiative forcing, which creates a situation when the choice of a short time horizon is more fitting [19].

Although the use of the GWP is considered a relatively simple and easy-to-use method, in recent years, it has received some criticism. For example, Peters et al. [20] and Ledgard and Reisinger [21] point to the contrary outcomes that frequently are the result of a negligent and only implicit value judgment of the time horizon to be selected. Joos et al. [22] and Tanaka et al. [23] emphasize the importance of the proper selection of the time horizon in the determination of metrics variability, especially for the GWP value given to gases with a relatively short lifetime (e.g., CH4) compared to gases with long lifetimes (e.g., CH2). Cherubini et al. [3] state that uses of GWP values omits impacts from short-term gases and biophysical factors arising from changes in land cover, as well as overlooks the temporal and spatial heterogeneities of the climate system response to GHG emissions. Also, Skytt et al. [18] state that with GWP, a di fficulty exists on how to value CH4 emissions with CO2 and that the use of GWP values provides "static" information expressed as the radiative forcing potential at a specific time horizon. Finally, the phenomenon of overall acceptance and use of the GWP as a metric for GHG emission accounting by policy developers and scientific community is surprising, considering that since its first introduction by the IPCC in the first assessment report [17], it has had no direct estimation of any climate system responses or direct link to policy goals (Myhre et al. [15]; Cherubini et al. [3]). Hence, the potential use of alternative methods have been proposed and extensively discussed in the literature (see, e.g., Cherubini et al. [3], Levasseur et al. [6], and Skytt et al. [18]). In Section 2.2., a method based on the BCCM is presented as an alternative approach for estimating the temporal e ffects of GHGs on the climate system.

### *2.2. Method Used in the Bern Carbon Cycle Model (BCCM)*

The BCCM describes the decay pattern of GHGs in the atmosphere [24], i.e., both the amount and time of emission are considered, as well as the fraction of emissions remaining in the atmosphere from previous emission periods. Moreover, not constant values are taken (as 20 or 100 years), but the e ffect of emissions is estimated as a continuous pattern that considers removals (via sinks) and addition of new emissions to the "stock" of the atmosphere, hence also considering the climate system response to emissions. The BCCM targets several aspects of the climate impact cause-e ffect loop (see Figure 1).

**Figure 1.** The cause-e ffect loop of greenhouse gas (GHG) emissions and climate change in blue given segments of the loop that are studied in this article. Figure adapted from Fuglestvedt et al. [25].

The application of climate impulse response models for GHG emissions has been developed by Levasseur et al. [26] and Joos et al. [22]. The impulse response function (IRFs) are usually used in two ways: to describe the decay of atmospheric concentration of pulse emissions or to express global temperature changes due to pulse radiative forcing [27]. The e ffect of IRF inclusion in the climate response model is graphically represented in Figure 2.

**Figure 2.** Conversion of input data using impulse response function (*IRF*), adapted from Shimako [7].

*Energies* **2020**, *13*, 800

Pulse emission is the emission of 1 kg of pollutants at the time *t* = 0. When pulse emission is released to the atmosphere, it serves as an impulse to the complex set of behavioural reactions that occur in climate systems.

These climate responses are condensed into simplified mathematical models that use impulse response function (*IRF*) [27] given as a response of the temporal temperature to a sudden unit pulse of radiative forcing [28],

$$y\_i(t) = \int\_0^t x\_i(t)IRF\_i(t)dt\tag{1}$$

where *yi(t)* is the environmental impact of the pollutant *i* at the time step *t*, *x* is the emitted amount of the pollutant *i*, and *IRFi* is the impulse response function of the pollutant *i* [29],

$$AGWP\_i(H) = \int\_0^t RF\_i(t)dt = A\_i R\_i \tag{2}$$

where *AGWPi* is the absolute global warming potential of pollutant *i* (W·m<sup>−</sup>2kg−1·year), *RFi* is the radiative forcing occurring due to a pulse emission of pollutant *i* emitted to the atmosphere at time horizon *H* (W·m<sup>−</sup>2). *RF* is the function of specific radiative forcing (*Ai*, <sup>W</sup>·m<sup>−</sup>2kg−1)—the ability to increase *RF* when the unit of the specific pollutant's *i* mass increases in the atmosphere (see Table 2 for numerical values), and the fraction of pollutant's mass remaining in the atmosphere after the pulse emission of the pollutant *i* (*Ri*). The fraction of pollutant's *i* mass remaining in the atmosphere at the time moment *t* (*Ri*(*t*)) is given as a simple exponential decay function:

$$R\_i(t) = \exp(-t/\tau\_i) \tag{3}$$

where τ*i* is the time needed for the pulse emission of pollutant *i* to converge to zero concentration, known as perturbation lifetime (years) [22], for CO2, CH4, and N2O emissions, the pattern of *R* is substantially different over a 1000 years' perspective (see Figure 3).

**Table 2.** Specific radiative forcing (*Ai*), perturbation lifetimes (<sup>τ</sup>*i*), and parameter *ai* values for the calculation of the pollutant's fraction remaining in the atmosphere (*Ri*) [3,15,22,29].


Most of the pollutants follow single exponential decay, while for the CO2, the behaviour is given with more complex equations [22]. Hence, also the fraction of various GHGs remaining in the air varies by nature. As seen in Figure 3, for CH4, the decay is much faster, while almost a quarter of the CO2 emitted in the year 0 is still present in the atmosphere even after 1000 years.

While the perturbation lifetime and specific radiative forcing are known constants for some of the emissions, such as CO2, CH4, N2O, and others (see Table 2 for numerical values). The fraction of CO2 pulse emission remaining in the atmosphere cannot be represented by a single constant and a simple exponential decay function, as in the case of CH4 and N2O. The fraction of CO2 pulse emission remaining in the atmosphere follows approximation by a sum of exponential functions:

$$R\_{CO\_2}(t) = a\_0 + \sum\_{i=1}^{3} a\_i \exp(-t/\tau\_i) \tag{4}$$

Global warming potential for pollutant *i* at time *t* (*GWPi*(*t*)) is calculated by referring absolute global warming potential of the pollutant *i* (*AGWPi*), to the *AGWP* of the reference gas, usually CO2, and integrating it over time period *t*:

$$\text{GWP}\_{i}(t) = \text{AGWP}\_{i}(t) / \text{AGWP}\_{\text{CO}\_{2}}(t) = \int\_{0}^{t} \text{RF}\_{i}(t)dt / \int\_{0}^{t} \text{RF}\_{\text{CO}\_{2}}(t)dt \tag{5}$$

The change of normalized GWP values and absolute GWP values over 100 years in the case of pulse emissions of CO2, N2O, and CH4 are given in Figures 4 and 5, respectively.

**Figure 3.** The fraction of pulse emissions at year zero remaining for greenhouse gas emissions of CO2, N2O, and CH4in 1000 years' time frame.

**Figure 4.** Normalized GWP values as a response to emission of CO2, N2O, and CH4 at year zero. The values are normalized to the maximum value of the corresponding GWP of each gas, unitless.

As can be seen in Figures 4 and 5, the trendlines for the emissions of CH4 and N2O are both of different natures and different magnitude, while CO2 constant values of 1 are assumed.

**Figure 5.** Absolute GWP values as a response to emission of CO2, N2O, and CH4at year zero, unitless.

Global temperature potential for pollutant *i* at time *t* (*GTPi*(*t*)) is calculated by referring absolute global temperature potential of the pollutant *i* (*AGTPi*), to the *AGTP* of the reference gas, usually CO2, and integrating it over time period *t*:

$$GTP\_i(t) = AGTP\_i(t) / AGTP\_{CO\_2}(t) \tag{6}$$

where the absolute global temperature change potential of pollutant *i* in the time horizon *H* (*AGTPi*(*H*), <sup>K</sup>·kg−1) [4,30] is calculated as:

$$AGTP\_i(H) = \int\_0^H RF\_i(t)R\_T(H - t)dt\tag{7}$$

where *RT* is the climate response (K·m2·W−1·kg−1), *H* is the time horizon over which the absolute global temperature change potential is calculated (years). *RT* is given by the sum of exponentials:

$$R\_T(t) = \sum\_{j=1}^{M} (c\_j/d\_j) \exp(-t/d\_j) \tag{8}$$

where *cj* is climate sensitivity (K·(W·m<sup>−</sup>2)−1), and *dj* is response time (years) (see Table 3 for numerical values). In this equation, the first term is the reaction of the mixed layer in the ocean to a forcing; the second term is the reaction of the deep layer in the ocean. Two exponential terms based on Boucher and Reddy for the non-CO2 greenhouse gases and CO2 are given in Equations (9) and (10), respectively.

$$AGTP\_i(H) = A\_i \sum\_{j=1}^{2} \pi c\_j / (\pi - d\_j) \left( \exp(-H/\tau) - \exp(-H/d\_j) \right) \tag{9}$$

$$\begin{split} A G T P\_{CO\_2}(H) &= \begin{array}{c} A\_{CO\_2} \sum\_{j=1}^{2} \left[ a\_0 c\_j \Big( 1 - \exp\left( -\frac{H}{d\_j} \right) \Big) \right. \\ &+ \sum\_{i=1}^{3} \frac{a\_i \tau\_i c\_j}{\tau\_i - d\_j} \Big( \exp\left( -\frac{H}{\tau\_i} \right) - \exp\left( -\frac{H}{d\_j} \right) \Big) \end{array} \tag{10}$$

**Table 3.** Values of the climate sensitivity and response time coefficients [15].


The concept of GTP was first introduced by Shine et al. [4] and further discussed in Shine et al. [31]. The change of normalized GTP values and absolute GTP values over 100 years in the case of pulse emissions of CO2, N2O, and CH4 are given in Figures 6 and 7, respectively.

**Figure 6.** Normalized (**a**) absolute global temperature change potential (AGTP) (**b**) GTP values as a response to emission of CO2, N2O, and CH4 at year zero. The values are normalized to the maximum value of the corresponding AGTP or GTP of each gas, unitless.

**Figure 7.** Absolute (**a**) AGTP and (**b**) GTP (unitless) values as a response to emission of CO2, N2O, and CH4 at year zero.

### *2.3. Case Study—Agriculture Sector in Latvia*

In the agriculture sector, aggregated annual GHG emissions is a commonly used measure to characterize pressures and risks that GHGs produced on an ecosystem. The total rate of GHG emissions given as t CO2 eq. from agriculture per country per year is estimated by following the IPCC guidelines for national GHG inventory [32]. The main contributors to GHG emissions from the agriculture sector are methane (CH4) and nitrous oxide (N2O). Livestock enteric fermentation and addition of fertilizers to soils represent the largest emission sources, livestock manure managemen<sup>t</sup> being a smaller source. In this study, the agricultural GHG emission results obtained and presented by Dace et al. [2] are used. In their study, Dace et al. [2] developed a system dynamics model of the Latvian agriculture sector and followed the IPCC guidelines for national GHG inventories [16] to calculate the sectoral GHG emissions.

The model included the following elements that usually create agricultural systems in the majority of countries: land management, production of livestock and crops, managemen<sup>t</sup> of manure, fertilization of soil, also various decisions, such as choice of the practices of manure managemen<sup>t</sup> and the type of crops produced. Thus, the interlinkages and complexity of the sector were simulated. The model was validated against the historic data and used for making GHG emission projections until 2030. In this study, we use the amount of GHG emissions estimated by Dace et al. [2] (see Figure 8) and apply the two methods provided in Section 2 to compare the obtained results expressed as aggregated GHG emissions in CO2 eq.

**Figure 8.** Annual (**a**) methane and (**b**) nitrous oxide emissions from the agriculture sector in Latvia, 2005–2030 (data from Dace et al. [2]).
