An analysis of the US economy on the basis of personal consumption and other expenditures presents a very different perspective than the *sectoral* and *end use* approaches. In this view, based on data from the Bureau of Economic Analysis, personal consumption expenditures in 2003 accounted for about 70% of the gross domestic product (GDP) while the remaining 30% was shared by government expenditure, investment, and net exports3. Here, US households contributed about 4.17 billion metric tons of CO2 emissions through their consumption of various goods and services – about 71% of the national total emissions of 5.86 billion metric tons4. Based on numbers reported in figure 4, a few key indicators can be calculated for 2003: the energy and CO2 intensities of the economy were 10,058 kJ/\$ and

2 Carnegie Mellon University Green Design Institute. Economic Input-Output Life Cycle Assessment (EIO-LCA), Available from: http://www.eiolca.net 3 For consumption based household emissions, all numbers are for the year 2003 for consistency with the results of economic input-output analysis of embodied energy and carbon reported in Shammin et

4 These calculations are based on data from Table 1.5 of the Annual Energy Outlook 2007 published by

carbon emissions.

al (2010) and Shammin & Bullard (2009).

the EIA and results reported in Shammin & Bullard (2009).

**3. Consumption based household CO2 emissions**

its various organizations including defense (military, air force, navy and various intelligence agencies). Ultimately all these different consumptive activities and related carbon emissions can be linked back to people. They are all intended to provide people with essential and non-essential products (including public infrastructure) and services (including social services and national security). These linkages are not clearly identifiable in the current representation of the *sectoral* analysis of carbon emissions.

## **2.2 The end use approach**

In contrast to the *sectoral* approach, the *end use* approach provides a more detailed overview of micro-level energy use and carbon emissions by US households. Under this approach, the various energy end uses in households are documented and related carbon emissions are quantified. This includes energy used by HVAC systems, cooking, water heating, appliances, lighting, and other devices such as televisions, computers, and other household electronics. EIA routinely conducts the Residential Energy Consumption Survey (RECS) to generate data for *end use* analysis. The results of the *end use* approach is important for understanding the relative magnitudes of energy consumption by different systems within households and identifying opportunities for conservation and efficiency improvements to reduce household GHG emissions. While this approach is crucial for the purposes stated above, it is still limited to direct consumption of energy and related emissions. It provides a more in-depth understanding of residential sector emissions, but does not shed any additional light on the linkages between households and the other economic sectors listed under the *sectoral* approach.

#### **2.3 Towards a more complete accounting of household emissions**

Over the past four decades development of input-out analysis using methods developed by Nobel Laureate Wassily Leontief (Leontief, 1970) has made it possible to use economic input-out analysis to carry out more complete estimates of household energy consumption and carbon emissions. This is based on two related concepts: a) life cycle analysis: a method of estimating the impact of any resources use over its life cycle - from the point of raw material extraction to ultimate disposal of postconsumer wastes; and b) embodied energy (or embodied carbon): energy use or carbon emissions that occur at various stages over the life cycle of products and services that people eventually consume. This is applicable to both direct energy resources (electricity, natural gas, gasoline and other fuel) and non-energy goods and services (food, clothing, entertainment, insurance etc.). The following two examples illustrate this. A life cycle perspective of gasoline demonstrates that it is not just the emissions resulting from burning gasoline in automobiles, but energy is used and carbon emissions occur for finding, drilling, transporting, refining, and marketing gasoline. These add about 25% carbon emissions that are indirectly attributable to gasoline use. Therefore, the embodied CO2 emissions for gasoline is 2.3 kg/liter from direct burning and an additional 0.6 kg/liter from indirect sources – resulting in a total embodied CO2 of 2.9 kg/liter. While this example explains life cycle analysis and embodied emissions for an energy resource, all non-energy goods and services also have similar embodied life cycle emissions. For example, energy related emissions take place throughout the life cycle of the clothes people buy. If all these emissions are added up and normalized for every dollar spent on clothing in the US, the embodied CO2 emissions for clothing amount to 0.43 kg/\$.

its various organizations including defense (military, air force, navy and various intelligence agencies). Ultimately all these different consumptive activities and related carbon emissions can be linked back to people. They are all intended to provide people with essential and non-essential products (including public infrastructure) and services (including social services and national security). These linkages are not clearly identifiable in the current

In contrast to the *sectoral* approach, the *end use* approach provides a more detailed overview of micro-level energy use and carbon emissions by US households. Under this approach, the various energy end uses in households are documented and related carbon emissions are quantified. This includes energy used by HVAC systems, cooking, water heating, appliances, lighting, and other devices such as televisions, computers, and other household electronics. EIA routinely conducts the Residential Energy Consumption Survey (RECS) to generate data for *end use* analysis. The results of the *end use* approach is important for understanding the relative magnitudes of energy consumption by different systems within households and identifying opportunities for conservation and efficiency improvements to reduce household GHG emissions. While this approach is crucial for the purposes stated above, it is still limited to direct consumption of energy and related emissions. It provides a more in-depth understanding of residential sector emissions, but does not shed any additional light on the linkages between households and the other economic sectors listed

Over the past four decades development of input-out analysis using methods developed by Nobel Laureate Wassily Leontief (Leontief, 1970) has made it possible to use economic input-out analysis to carry out more complete estimates of household energy consumption and carbon emissions. This is based on two related concepts: a) life cycle analysis: a method of estimating the impact of any resources use over its life cycle - from the point of raw material extraction to ultimate disposal of postconsumer wastes; and b) embodied energy (or embodied carbon): energy use or carbon emissions that occur at various stages over the life cycle of products and services that people eventually consume. This is applicable to both direct energy resources (electricity, natural gas, gasoline and other fuel) and non-energy goods and services (food, clothing, entertainment, insurance etc.). The following two examples illustrate this. A life cycle perspective of gasoline demonstrates that it is not just the emissions resulting from burning gasoline in automobiles, but energy is used and carbon emissions occur for finding, drilling, transporting, refining, and marketing gasoline. These add about 25% carbon emissions that are indirectly attributable to gasoline use. Therefore, the embodied CO2 emissions for gasoline is 2.3 kg/liter from direct burning and an additional 0.6 kg/liter from indirect sources – resulting in a total embodied CO2 of 2.9 kg/liter. While this example explains life cycle analysis and embodied emissions for an energy resource, all non-energy goods and services also have similar embodied life cycle emissions. For example, energy related emissions take place throughout the life cycle of the clothes people buy. If all these emissions are added up and normalized for every dollar spent on clothing in the US, the embodied CO2 emissions for clothing amount to 0.43 kg/\$.

representation of the *sectoral* analysis of carbon emissions.

**2.3 Towards a more complete accounting of household emissions**

**2.2 The end use approach**

under the *sectoral* approach.

Life cycle analysis – particularly for all products and services in an economy - appears to be a daunting task. This is where Leontief's work on input-output analysis came in handy. Originally developed for macro-economic analysis, Leontief formulated a mathematical process of inverting the complex matrix of all inter-sector transactions in an economy to derive the total final consumption of individual sectors (Leontief, 1970). This allowed for tracking the flow of money through and between sectors in any given year. Robert Herendeen, Bruce Hannon, Clark Bullard, and others associated with the Energy Resources Group at the University of Illinois carried out the seminal work of using Leontief's method to track the flow of money spent on energy resources (or in some cases the physical flows of energy) within the US economy and then converting the results into the physical quantities of energy used by various industries and enterprises. When this data is combined with national consumer expenditure data, one can actually estimate both the energy intensities of products and services and of households of different income groups (Bullard & Herendeen, 1975; Herendeen & Tanaka, 1976; Herendeen, 1978; Herendeen et al., 1981). Notable followup work that builds on this approach has been done by Manfred Lenzen of University of Sydney, Rutger Hoekstra of Statistics Nederlands, and many others who used this approach to not only estimate energy intensities but also carbon emissions and other environmental impacts. Hoekstra (2010) compiled a database of the development of environmental analysis based on Leontief's input-out method. More recent estimates of energy and carbon intensities are reported in Shammin et al (2010), Shammin & Bullard (2009), and Bin & Dowlatabadi (2005). These papers primarily used the Economic Input Output Life Cycle Analysis (EIOLCA) database developed at Carnegie Melon University2. This method now allows for a much more complete and in-depth understanding of household energy use and carbon emissions that can directly be linked to people's behavior and choices. While details on the methods can be found in the papers cited above, figure 3 provides a generic outline of the process of using economic input-output analysis to estimate carbon intensities for goods and services and combining that with consumer expenditure data to derive total household carbon emissions.

## **3. Consumption based household CO2 emissions**

An analysis of the US economy on the basis of personal consumption and other expenditures presents a very different perspective than the *sectoral* and *end use* approaches. In this view, based on data from the Bureau of Economic Analysis, personal consumption expenditures in 2003 accounted for about 70% of the gross domestic product (GDP) while the remaining 30% was shared by government expenditure, investment, and net exports3. Here, US households contributed about 4.17 billion metric tons of CO2 emissions through their consumption of various goods and services – about 71% of the national total emissions of 5.86 billion metric tons4. Based on numbers reported in figure 4, a few key indicators can be calculated for 2003: the energy and CO2 intensities of the economy were 10,058 kJ/\$ and

2 Carnegie Mellon University Green Design Institute. Economic Input-Output Life Cycle Assessment

(EIO-LCA), Available from: http://www.eiolca.net 3 For consumption based household emissions, all numbers are for the year 2003 for consistency with the results of economic input-output analysis of embodied energy and carbon reported in Shammin et al (2010) and Shammin & Bullard (2009).

4 These calculations are based on data from Table 1.5 of the Annual Energy Outlook 2007 published by the EIA and results reported in Shammin & Bullard (2009).

The Role of US Households in Global Carbon Emissions 177

The consumption based perspective on household emissions communicates a very different message to people. It shows that people have the power to directly and indirectly affect a large component of the nations' carbon emissions through behavior and lifestyle changes that would affect their consumption patterns and preferences. People also have the power to affect the remaining 29% of emissions; however, that would require engagement beyond personal choices. Through political activism and voting patterns, people in a democracy have the power to communicate how the government should spend their tax dollars. Regarding domestic investment, increasingly there are options being available to make investment choices on the basis of environmental performance. Finally, export-import policies can be reformed to trade with partners that are more environmentally responsible. None of this is easy; but at least this way of relating people and their behavior with national carbon emissions and mitigation opportunities provides a perspective that is either missing

The most recent results to date for consumption-based carbon emissions for US households are reported in Shammin & Bullard (2009). The methods are based on calculations of energy intensities using input-output analysis described in Shammin et al (2010). These two papers also discuss the assumptions, nuances, and uncertainties associated with this approach. In 2003, the average household in the US spent about \$49,000 of which only 6.5% was spent on direct energy. The total embodied CO2 emission per household was about 37 metric tons of which about 65% was from direct energy. Thus, a small percent of household expenditure is actually responsible for the bulk of its carbon emissions. However, it is also interesting to see that the remainder of household expenditures made on non-energy goods and services were responsible for about 35% of the total embodied carbon emissions by the average household. This is a significant part of household emissions that is associated with life cycle emissions and the linkages between people and the sectors of the economy beyond residential and personal automobiles. The breakdown of total expenditure and total

Shammin & Bullard (2009) reports detailed carbon intensities for all personal consumption categories based on standard classification of the Bureau of Labor Statistics. A list of carbon intensities for major consumption categories is given in table 1. The distribution of carbon emissions between expenditure categories shown in figure 5b and the intensities in table 1 together provide valuable insights into household energy consumption and related

It is important to understand the different implications of the magnitude of CO2 emissions attributable to households (~37 metric tons/household-yr), the percentage share of specific consumption categories (~38% for residential energy), and the above carbon intensities. The total annual carbon emission, which is the grand total derived by summing the products of the carbon intensities and expenditures for individual items as shown earlier in figure 3, is actually the ultimate measure for the carbon footprint of a given household. Energy efficiency and conservation measures are intended to reduce this total emission. It is now a common consensus among most proposals for climate legislation that US needs to reduce

or inadequately addressed in the *sectoral* and *end use* approaches.

**3.1 CO2 emissions by the average US household**

embodied carbon emissions are shown in figure 5a and 5b.

**3.2 CO2 Intensities of consumption categories**

conservation opportunities.

0.55 kg/\$ respectively; annual per-capita emission was 20 metric tons/person; and annual per-household emission was 51 metric tons/household.

Fig. 3. Process of calculating carbon intensities using economic input-output analysis and total household carbon emissions by summing the product of carbon intensity and consumer expenditure data for individual sectors across all *n* consumer items. (Shammin, 2009)

Fig. 4. GDP components, energy use and CO2 emissions for the US economy, 2003. (Based on data from EIA and BEA)

0.55 kg/\$ respectively; annual per-capita emission was 20 metric tons/person; and annual

Energy Intensity of goods & services

Annual expenditures on goods & services

Fig. 3. Process of calculating carbon intensities using economic input-output analysis and total household carbon emissions by summing the product of carbon intensity and consumer expenditure data for individual sectors across all *n* consumer items. (Shammin,

Fig. 4. GDP components, energy use and CO2 emissions for the US economy, 2003.

Carbon intensities from the fuel mix

Bureau of Economic Analysis (BEA) transportation and trade margins

*Ci*

Carbon Intensity of Item *i* [Tonnes/\$]

> Expenditure on Item *i* in \$

2003 US Economy 10.3 Trillion \$

Total US Energy Use (103.6 x 1015 kJ at a cost of 708 billion \$ )

5.69 x 109 metric tons of CO2

*Yi*

*i*

*n*

*i i YCC* 1

> Total Household Carbon Emissions [Tonnes]

per-household emission was 51 metric tons/household.

500 sector I/O data US Dept. of Commerce

I/O analysis using Leontief's method

Bureau of Labor Statistics (BLS) Consumer Expenditure Survey

> Sample households with yearly data

> > Personal Consumption Expenditure (PCE) 7.2 Trillion \$

Domestic Investment Government Expenditures Net Exports 3.1 Trillion \$

(Based on data from EIA and BEA)

2009)

The consumption based perspective on household emissions communicates a very different message to people. It shows that people have the power to directly and indirectly affect a large component of the nations' carbon emissions through behavior and lifestyle changes that would affect their consumption patterns and preferences. People also have the power to affect the remaining 29% of emissions; however, that would require engagement beyond personal choices. Through political activism and voting patterns, people in a democracy have the power to communicate how the government should spend their tax dollars. Regarding domestic investment, increasingly there are options being available to make investment choices on the basis of environmental performance. Finally, export-import policies can be reformed to trade with partners that are more environmentally responsible. None of this is easy; but at least this way of relating people and their behavior with national carbon emissions and mitigation opportunities provides a perspective that is either missing or inadequately addressed in the *sectoral* and *end use* approaches.

## **3.1 CO2 emissions by the average US household**

The most recent results to date for consumption-based carbon emissions for US households are reported in Shammin & Bullard (2009). The methods are based on calculations of energy intensities using input-output analysis described in Shammin et al (2010). These two papers also discuss the assumptions, nuances, and uncertainties associated with this approach. In 2003, the average household in the US spent about \$49,000 of which only 6.5% was spent on direct energy. The total embodied CO2 emission per household was about 37 metric tons of which about 65% was from direct energy. Thus, a small percent of household expenditure is actually responsible for the bulk of its carbon emissions. However, it is also interesting to see that the remainder of household expenditures made on non-energy goods and services were responsible for about 35% of the total embodied carbon emissions by the average household. This is a significant part of household emissions that is associated with life cycle emissions and the linkages between people and the sectors of the economy beyond residential and personal automobiles. The breakdown of total expenditure and total embodied carbon emissions are shown in figure 5a and 5b.

#### **3.2 CO2 Intensities of consumption categories**

Shammin & Bullard (2009) reports detailed carbon intensities for all personal consumption categories based on standard classification of the Bureau of Labor Statistics. A list of carbon intensities for major consumption categories is given in table 1. The distribution of carbon emissions between expenditure categories shown in figure 5b and the intensities in table 1 together provide valuable insights into household energy consumption and related conservation opportunities.

It is important to understand the different implications of the magnitude of CO2 emissions attributable to households (~37 metric tons/household-yr), the percentage share of specific consumption categories (~38% for residential energy), and the above carbon intensities. The total annual carbon emission, which is the grand total derived by summing the products of the carbon intensities and expenditures for individual items as shown earlier in figure 3, is actually the ultimate measure for the carbon footprint of a given household. Energy efficiency and conservation measures are intended to reduce this total emission. It is now a common consensus among most proposals for climate legislation that US needs to reduce

The Role of US Households in Global Carbon Emissions 179

CO2 emissions by 80% or more. This cannot be achieved without significant reductions at the household level. Share of emissions by specific consumption categories is also important because small percent reductions in large categories can result in a bigger difference than large percent reductions in small categories. Finally, carbon intensities indicate how carbon efficient different consumption categories are and provide an explicit basis for comparisons

Average CO2 Intensity (all categories) 0.80 Average CO2 Intensity of Direct Energy 7.53

Average CO2 Intensity of Indirect Energy 0.32

Table 1. CO2 intensities of major household consumption categories.

Natural gas 6.25 Electricity 8.02 Fuel oil and other fuels 8.07 Gasoline and motor oil 6.87

Housing 0.34 Owned dwellings 0.24 Telephone services 0.17 Water and other public services 0.59 Household operations 0.16 Housekeeping supplies 0.34 Household furnishings and equipment 0.33 Housing structure 0.80 Cars and trucks, new 0.46 Cars and trucks, used 0.50 Other vehicles 0.66 Vehicle finance charges 0.14 Maintenance and repairs 0.29 Vehicle insurance 0.07 Vehicle rental, leases, licenses, other charges 0.19 Public transportation 1.38 Food 0.41 Alcoholic beverages 0.33 Tobacco products and smoking supplies 0.13 Apparel, footwear and related services 0.43 Health care 0.14 Personal care products and services 0.27 Entertainment 0.22 Reading/education 0.21 Cash contributions 0.27 Personal insurance and pensions 0.11 Miscellaneous 0.28

**CO2 Intensity (kg/\$)**

across categories.

Fig. 5a. Breakdown of annual expenditures for the average US household in 2003

Fig. 5b. Breakdown of annual CO2 emissions for the average US household in 2003

Food/Alc/Tobacco 12.6%

> Apparel 2.5%

> > Housing 31.0%

Food/Alc/Tobacco 6.9%

> Housing 7.6%

Residential Energy 37.9%

Apparel 1.5%

Residential Energy 3.5%

Auto Fuel 3.0%

1.1%

Auto Purch. Maint 13.9%

Fig. 5a. Breakdown of annual expenditures for the average US household in 2003

Fig. 5b. Breakdown of annual CO2 emissions for the average US household in 2003

5.1% Health Care

Asset Gain

Health Care 5.9%

Public Trans 0.9%

Auto Purch. Maint 6.7%

Public Trans 1.6%

Other 19.8% Asset Gain 6.8%

Auto Fuel 26.9%

Other 4.9%

CO2 emissions by 80% or more. This cannot be achieved without significant reductions at the household level. Share of emissions by specific consumption categories is also important because small percent reductions in large categories can result in a bigger difference than large percent reductions in small categories. Finally, carbon intensities indicate how carbon efficient different consumption categories are and provide an explicit basis for comparisons across categories.

Table 1. CO2 intensities of major household consumption categories.

The Role of US Households in Global Carbon Emissions 181

and housing type (about 44% more for single-family homes compared to apartments). These differences, reported in Shammin et al (2010), are estimated for households with the same income having different demographic and lifestyle configurations. While these differences are for total energy consumption, they would yield very similar differences in total

Fig. 7. Price increases for goods and services consumed by households as percent of annual household income due to different prices of carbon emissions. Here, emission data is for

Consumption based approach to household carbon emissions puts households and the people living in them front and center in exploring ways of reducing national carbon emissions. This requires households to develop a comprehensive strategy for carbon emission reductions that involves specific actions to address the various sources of emissions: direct emissions, indirect emissions, and emissions related to government expenditure, investment, and net exports. A pre-requisite for this is the motivation and willingness by members of any given household to undertake the solutions that apply to them. Literature in environmental psychology has several studies that investigate ways of motivating people to change behavior and adopt conservation and efficiency measures to reduce their carbon footprint (Nolan et al, 2008; Parnell & Larsen, 2005). Examples of successful interventions from some recent research include: innovative ways of providing real time feedback on energy and resource use (Petersen et al 2007; Petersen & Frantz, 2009) and offering financial incentives for reducing resource consumption (Suter & Shammin, 2010). Once households are committed to reduce emissions, they have to balance several

carbon and not CO2 and tonne = metric tons. (Shammin & Bullard, 2009)

**4. The role of households in reducing CO2 emissions**

household carbon emissions as well.

#### **3.3 Predictors of household CO2 emissions**

Energy consumption and related carbon emissions vary across households depending on several key demographic and lifestyle related factors. Household income is the most influential predictor of total household emissions and how those emissions are distributed across various consumption categories. In general, the relationship between income and carbon emissions is non-linear (figure 6) – resulting in regressive impacts on low income households (Shammin & Bullard, 2009).

Fig. 6. Relationship between annual household income and carbon emissions. (Shammin & Bullard, 2009)

There is a large difference in the total annual carbon emissions and the share of indirect carbon emissions between households belonging to the lowest and highest income quintiles. In 2003, the total CO2 emission of the highest quintile (~68 metric tons) was four times higher than that of the lowest quintile (~17 metric tons). At the same time, the share of indirect emission was close to 50% for the highest quintile as opposed to less than 20% for the lowest quintile. The latter has important implications: if price of direct energy resources go up as a result of climate change legislations, the effect on low income households will be disproportionately higher than high income households. Figure 6 shows that if a new capand-trade or carbon tax policy puts a price on carbon emissions at \$100/metric ton, the impact on low income households can be more than 4% of their income as opposed to less than 2% for high income households (Shammin & Bullard, 2009).

Another important predictor of household emissions is the location of residence. Households in rural areas consumed about 17% higher total energy compared to households of the same income level residing in urban locations. Bigger homes, longer commutes, greater use of outdoor power equipment, etc. are typically responsible for this difference. Other predictors that affect total household energy consumption include: family size (about 28% more for a family of 4 compared to single-occupant households), number of cars (about 27% more for a household with two cars compared to households with no cars),

Energy consumption and related carbon emissions vary across households depending on several key demographic and lifestyle related factors. Household income is the most influential predictor of total household emissions and how those emissions are distributed across various consumption categories. In general, the relationship between income and carbon emissions is non-linear (figure 6) – resulting in regressive impacts on low income

Fig. 6. Relationship between annual household income and carbon emissions. (Shammin &

There is a large difference in the total annual carbon emissions and the share of indirect carbon emissions between households belonging to the lowest and highest income quintiles. In 2003, the total CO2 emission of the highest quintile (~68 metric tons) was four times higher than that of the lowest quintile (~17 metric tons). At the same time, the share of indirect emission was close to 50% for the highest quintile as opposed to less than 20% for the lowest quintile. The latter has important implications: if price of direct energy resources go up as a result of climate change legislations, the effect on low income households will be disproportionately higher than high income households. Figure 6 shows that if a new capand-trade or carbon tax policy puts a price on carbon emissions at \$100/metric ton, the impact on low income households can be more than 4% of their income as opposed to less

Another important predictor of household emissions is the location of residence. Households in rural areas consumed about 17% higher total energy compared to households of the same income level residing in urban locations. Bigger homes, longer commutes, greater use of outdoor power equipment, etc. are typically responsible for this difference. Other predictors that affect total household energy consumption include: family size (about 28% more for a family of 4 compared to single-occupant households), number of cars (about 27% more for a household with two cars compared to households with no cars),

than 2% for high income households (Shammin & Bullard, 2009).

**3.3 Predictors of household CO2 emissions**

households (Shammin & Bullard, 2009).

Bullard, 2009)

and housing type (about 44% more for single-family homes compared to apartments). These differences, reported in Shammin et al (2010), are estimated for households with the same income having different demographic and lifestyle configurations. While these differences are for total energy consumption, they would yield very similar differences in total household carbon emissions as well.

Fig. 7. Price increases for goods and services consumed by households as percent of annual household income due to different prices of carbon emissions. Here, emission data is for carbon and not CO2 and tonne = metric tons. (Shammin & Bullard, 2009)

## **4. The role of households in reducing CO2 emissions**

Consumption based approach to household carbon emissions puts households and the people living in them front and center in exploring ways of reducing national carbon emissions. This requires households to develop a comprehensive strategy for carbon emission reductions that involves specific actions to address the various sources of emissions: direct emissions, indirect emissions, and emissions related to government expenditure, investment, and net exports. A pre-requisite for this is the motivation and willingness by members of any given household to undertake the solutions that apply to them. Literature in environmental psychology has several studies that investigate ways of motivating people to change behavior and adopt conservation and efficiency measures to reduce their carbon footprint (Nolan et al, 2008; Parnell & Larsen, 2005). Examples of successful interventions from some recent research include: innovative ways of providing real time feedback on energy and resource use (Petersen et al 2007; Petersen & Frantz, 2009) and offering financial incentives for reducing resource consumption (Suter & Shammin, 2010). Once households are committed to reduce emissions, they have to balance several

The Role of US Households in Global Carbon Emissions 183

reasonably achievable household emissions reduction in the US can be approximately 20%

In addition to the direct emissions, consumption based approach also allows for households to understand, estimate, monitor and reduce indirect carbon emissions. US society has been on a treadmill of consumption for several decades where more consumption is considered a desirable goal. The core message in this approach is that consumption of non-energy goods and services has associated life cycle carbon emissions and thus reducing consumption would help reduce carbon emissions. As shown in table 1, there is very little difference in the carbon intensity of the various consumption categories responsible for indirect carbon emissions. Any reduction in consumption, irrespective of which items are avoided, would yield similar reductions in a household's carbon footprint. Notable exceptions are water and public transportation. Another related issue is rebound effects. If money saved from the reduction of direct energy is re-spent on other goods and services, part of the conservation savings would be offset. For example, if a household saves \$1,500 by conserving direct energy consumption, they would reduce their CO2 emissions by about 11 metric tons. If that money is re-spent on other goods and services, that would generate about 0.5 metric tons of additional CO2 – resulting in a net savings of 10.5 metric tons. For a single household this may appear to be a small effect, but added across the economy this addition amounts to more than 50 million metric tons. This effect can become much larger if this money is re-spent on more carbon

Influencing the components of GDP beyond personal consumption (see figure 4) requires a different approach – since these involve decision making entities that are exogenous to individual households. A democratic society has avenues for people to influence decisions made by the government about how public tax dollars should be spent – through voting patterns, writing letters to representatives, and other types of civic engagement and political activism. If government expenditure on building roads is shifted towards the development of high speed rail or government subsidy to fossil fuels is shifted towards new incentives for renewable energy projects, significant reductions in carbon emissions can be achieved in the government expenditure component. It is also important to note that reductions of direct and indirect carbon emissions by households would not change the carbon intensity of the underlying infrastructure such as the source mix of power generation or transportation driven by internal combustion engines. Reduction in household electricity use would only go so far if more than 80% of the electricity is generated from coal (which is the case in many US states such as Ohio). Through activism and engagement, people have the opportunity to influence a shift from carbon intensive fossil fuel based sources to carbon-neutral or carbonfree renewable sources. This will have a large impact on economy-wide reductions in carbon

In terms of the investment component of GDP, many investment portfolios now make information on environmental performance or carbon offsets available to investors. If more and more people invest in these green stocks, the carbon footprint of investment can go down. Perhaps the most complicated component of GDP for people to influence is net exports – as this involves carbon emissions associated with industries and commercial ventures in other countries. Reforms in trade policies can allow more partnerships with countries, industries and multi-national companies that promote climate friendly operations. If policy is ultimately reflective of the will of the people, then households can

within 10 years if the most effective non-regulatory interventions are used.

intensive choices such as flying to far-away places for family vacations.

emissions.

different approaches to address their total emissions. Throughout this process, households need to monitor their carbon footprint and track their progress in order to achieve most effective results. People are used to budget their income and expenses on a regular basis. Current challenges of climate change require people to go beyond financial budgeting and begin to develop methods to monitor their energy use and carbon emissions. The paradigm shift and associated challenges required for this to become mainstream involve discussions that are beyond the scope of this chapter.

The *end use* approach mentioned earlier provides the basis for reductions of direct emissions for households within the scope of the residential sector and personal transportation subsector. These mostly include direct conservation and efficiency measures that households can take.

*Conservation measures:* these involve reducing carbon intensive behaviors or replacing carbon intensive behaviors with emission-free options. Examples include:

*Efficiency measures:* these involve replacing less efficient equipment with more efficient ones to achieve the same task. Examples include:

The interplay between conservation and efficiency measures is also important to understand. Here, the ultimate goal is to reduce carbon emissions. However, overemphasis on efficiency measures may lead to *Jevon's Paradox* (people replacing inefficient cars with efficient ones and then driving more miles than before to offset or overshoot energy/carbon savings). On the contrary, when conservation and efficiency measures are coupled, households will be able to maximize their emission reductions. Dietz et al (2009) shows that

different approaches to address their total emissions. Throughout this process, households need to monitor their carbon footprint and track their progress in order to achieve most effective results. People are used to budget their income and expenses on a regular basis. Current challenges of climate change require people to go beyond financial budgeting and begin to develop methods to monitor their energy use and carbon emissions. The paradigm shift and associated challenges required for this to become mainstream involve discussions

The *end use* approach mentioned earlier provides the basis for reductions of direct emissions for households within the scope of the residential sector and personal transportation subsector. These mostly include direct conservation and efficiency measures that households

*Conservation measures:* these involve reducing carbon intensive behaviors or replacing carbon

d. making weather appropriate clothing choices indoors and airflow/shade management

*Efficiency measures:* these involve replacing less efficient equipment with more efficient ones

d. replacing incandescent light bulbs with compact fluorescent or light emitting diode

e. taking inventory of household electronics, eliminate unnecessary ones, and using

The interplay between conservation and efficiency measures is also important to understand. Here, the ultimate goal is to reduce carbon emissions. However, overemphasis on efficiency measures may lead to *Jevon's Paradox* (people replacing inefficient cars with efficient ones and then driving more miles than before to offset or overshoot energy/carbon savings). On the contrary, when conservation and efficiency measures are coupled, households will be able to maximize their emission reductions. Dietz et al (2009) shows that

h. regular maintenance of home appliances, HVAC equipment, and automobiles i. installing renewable energy systems in homes such as solar, wind, geothermal, etc. j. building homes that are designed to maximize the use of passive solar energy

intensive behaviors with emission-free options. Examples include:

b. reducing number of daily trips using motorized transportation

e. lowering thermostat setting in winter and raising it in summer

power strips and on/off switches to avoid phantom loads f. using public transportation instead of personal automobile g. replacing fuel-inefficient vehicles with more fuel-efficient vehicles

a. walking/biking instead of using automobiles

c. using clotheslines instead of dryers

instead of using air conditioning

f. lowering water heater temperature g. choosing to live in a smaller home h. choosing to drive a smaller automobile

to achieve the same task. Examples include:

c. using more efficient water heaters

light bulbs

a. upgrading inefficient HVAC systems and appliances b. improving insulation and reducing leakage in homes

that are beyond the scope of this chapter.

can take.

reasonably achievable household emissions reduction in the US can be approximately 20% within 10 years if the most effective non-regulatory interventions are used.

In addition to the direct emissions, consumption based approach also allows for households to understand, estimate, monitor and reduce indirect carbon emissions. US society has been on a treadmill of consumption for several decades where more consumption is considered a desirable goal. The core message in this approach is that consumption of non-energy goods and services has associated life cycle carbon emissions and thus reducing consumption would help reduce carbon emissions. As shown in table 1, there is very little difference in the carbon intensity of the various consumption categories responsible for indirect carbon emissions. Any reduction in consumption, irrespective of which items are avoided, would yield similar reductions in a household's carbon footprint. Notable exceptions are water and public transportation. Another related issue is rebound effects. If money saved from the reduction of direct energy is re-spent on other goods and services, part of the conservation savings would be offset. For example, if a household saves \$1,500 by conserving direct energy consumption, they would reduce their CO2 emissions by about 11 metric tons. If that money is re-spent on other goods and services, that would generate about 0.5 metric tons of additional CO2 – resulting in a net savings of 10.5 metric tons. For a single household this may appear to be a small effect, but added across the economy this addition amounts to more than 50 million metric tons. This effect can become much larger if this money is re-spent on more carbon intensive choices such as flying to far-away places for family vacations.

Influencing the components of GDP beyond personal consumption (see figure 4) requires a different approach – since these involve decision making entities that are exogenous to individual households. A democratic society has avenues for people to influence decisions made by the government about how public tax dollars should be spent – through voting patterns, writing letters to representatives, and other types of civic engagement and political activism. If government expenditure on building roads is shifted towards the development of high speed rail or government subsidy to fossil fuels is shifted towards new incentives for renewable energy projects, significant reductions in carbon emissions can be achieved in the government expenditure component. It is also important to note that reductions of direct and indirect carbon emissions by households would not change the carbon intensity of the underlying infrastructure such as the source mix of power generation or transportation driven by internal combustion engines. Reduction in household electricity use would only go so far if more than 80% of the electricity is generated from coal (which is the case in many US states such as Ohio). Through activism and engagement, people have the opportunity to influence a shift from carbon intensive fossil fuel based sources to carbon-neutral or carbonfree renewable sources. This will have a large impact on economy-wide reductions in carbon emissions.

In terms of the investment component of GDP, many investment portfolios now make information on environmental performance or carbon offsets available to investors. If more and more people invest in these green stocks, the carbon footprint of investment can go down. Perhaps the most complicated component of GDP for people to influence is net exports – as this involves carbon emissions associated with industries and commercial ventures in other countries. Reforms in trade policies can allow more partnerships with countries, industries and multi-national companies that promote climate friendly operations. If policy is ultimately reflective of the will of the people, then households can

The Role of US Households in Global Carbon Emissions 185

arguments presented in this paper. Special thanks go to Robert A. Herendeen at the University of Vermont and Clark W. Bullard at the University of Illinois for their

Bin, S. & Dowlatabadi, H. (2005). Consumer lifestyle approach to U.S. energy use and the

Bullard, C.W. & Herendeen, R.A. (1975). The energy cost of goods and services. *Energy*

Dietz, T., Gardner, G., Gilligan,, J., Stern, P. & Vandenbergh, M. (2009). Household actions

EIA (2011). Annual Energy Outlook 2011. *US Energy Information Agency*. Washington D.C. Herendeen, R.A. (1978). Total energy cost of household consumption in Norway, 1973.

Hoekstra, R. (2010). Towards a complete database of peer reviewed articles on

Nolan, J., Schultz, P., Cialdini, R., Goldstein, N. & Griskevicius, V. (2008). Normative social

Parnell, R. & Larsen, O. P. (2005). Informing the Development of Domestic Energy Efficiency

Petersen, J.E. & Frantz, C. (2009). Employing multiple modes and scales of real-time

Petersen, J. E., Shunturov, V., Janda, K., Platt, G. & Weinberger, K. (2007). Dormitory

Shammin, M., 2009. Embodied Carbon Emissions by US Households: Missing emissions and

Shammin, M., Herendeen, R. A., Hanson, M. & Wilson, E. (2010). A Multivariate Analysis of

environmentally extended input-out analysis. Paper presented at the 18th

influence is underdetected. *Personality and Social Psychology*, Bulletin 34, pp. 913 –

Initiatives: An Everyday Householder-Centered Framework. *Environment and*

feedback to engage, educate, motivate and empower electricity and water conservation. Paper presented at the *Behavior, Energy and Climate Change (BECC)*

residents reduce electricity consumption when exposed to real-time visual feedback and incentives. *International Journal of Sustainability in Higher Education,*

equity impacts of calculators used in carbon offsets. Paper presented at the 5th Bi‐ Annual Meeting of the US Society for Ecological Economics: Science and Policy for

the Energy Intensity of Sprawl versus Compact Living in the US for 2003. *Ecological*

Herendeen, R.A. & Tanaka, J. (1976). Energy cost of living. *Energy*, Vol. 1, pp. 163–178. Herendeen, R.A., Ford, C., & Hannon, B. (1981). Energy cost of living, 1972–73. *Energy*, Vol.

*International Input-output Conference*, June 20 – 25, Sydney, Australia Leontief, W. (1970). Environmental Repercussions and the Economic Structure: An Input-Output Approach. *Review of Economic Statistics*, Vol. 52, pp. 262-277

can provide a behavioral wedge to rapidly reduce US carbon emissions. *Proceedings*

mentorship and collaboration on the research that has made this chapter possible.

related CO2 emissions. *Energy Policy,* Vol. 33, pp. 197–208

*of the National Academy of Sciences*, Vol. 44, pp. 18452–18456

**7. References**

*Policy,* Vol. 3, pp. 268–278

*Energy*, Vol. 4, pp. 615–630

*Behavior,* Vol. 37, No. 6, pp. 787-807

Vol. 8, No. 1, pp. 16-33

meeting, November 15-18, Washington D.C.

*Economics*, Vol. 69, Issue 12, pp.2363–2373

a Sustainable Future, May 31 – June 3, Washington DC.

6, pp. 1433–1450

923.

play a role in paving the way for such transitions from carbon intensive to a low carbon or carbon-free economy.

Finally, reducing carbon emissions is not necessarily about compromises and sacrifices. There are multiple benefits of low carbon lifestyle in a low carbon economy for households. First, humanity is currently threatened by the grim prospect of catastrophic consequences unless human-induced climate change is slowed, halted or reversed. While there are theories about winners and losers in a post climate change world, in reality everyone is at risk as the global economy is now more interconnected than ever before. We have already seen how crisis in East Asian markets had ripple effects throughout the world and how economic downturn in the US is affecting other countries. Locally, households, communities and regions with low carbon footprint will be more resilient against increased prices of carbon intensive energy resources and consequent increases in the price of goods and services. Thus, a more comprehensive and aggressive strategy for reducing carbon emissions by households, particularly in a carbon intensive nation such as the US, makes sense on many levels: for the sustainability of human race, for a healthy environment for future generations, for economic stability, for social security, and for the development of more engaged and resilient communities.

## **5. Conclusion**

The daunting task of combating climate change is a defining challenge of the present generation. Reducing global carbon emissions is the most important aspect of that challenge. The US is a major player in global climate mitigation initiatives – since it is responsible for more than 20% of global carbon emissions. While the residential sector in the US accounts for about 20% of US emissions, this chapter demonstrates that households can directly and indirectly play a very important role in reducing all of the nations' carbon emissions. They have direct control over about 46% of embodied carbon emissions in the US by managing their consumption of energy resources and indirect control over another 25% of emissions by managing their consumption patterns. They can also play a role in influencing the remaining 29% by promoting and/or supporting initiatives to reduce the carbon footprint of energy systems, government expenditures, investment portfolios, and even businesses and industries beyond US borders. They can do this by becoming more engaged citizens and exercising their democratic privileges. The *sectoral* and *end use* approaches used to represent household emissions in the US are important, but limited in terms of helping people fully understand how their lives are connected to all sectors of the economy. The consumption based approach presented in this chapter constitute a more comprehensive accounting of household emissions as it includes embodied carbon over the life cycle of products and services that people consume to support their lifestyle. Most importantly, this approach offers people much more direct ways of relating personal choices with large scale reductions of national carbon emissions. This is a perspective that has the potential to empower people to become proactive agents of change and provide more explicit tools to make a difference in the battle against climate change.

## **6. Acknowledgment**

I would like to acknowledge my co-authors of the two papers (Shammin & Bullard, 2009; Shammin et al, 2010) that formulate the conceptual and analytical basis for the main arguments presented in this paper. Special thanks go to Robert A. Herendeen at the University of Vermont and Clark W. Bullard at the University of Illinois for their mentorship and collaboration on the research that has made this chapter possible.

## **7. References**

184 Greenhouse Gases – Emission, Measurement and Management

play a role in paving the way for such transitions from carbon intensive to a low carbon or

Finally, reducing carbon emissions is not necessarily about compromises and sacrifices. There are multiple benefits of low carbon lifestyle in a low carbon economy for households. First, humanity is currently threatened by the grim prospect of catastrophic consequences unless human-induced climate change is slowed, halted or reversed. While there are theories about winners and losers in a post climate change world, in reality everyone is at risk as the global economy is now more interconnected than ever before. We have already seen how crisis in East Asian markets had ripple effects throughout the world and how economic downturn in the US is affecting other countries. Locally, households, communities and regions with low carbon footprint will be more resilient against increased prices of carbon intensive energy resources and consequent increases in the price of goods and services. Thus, a more comprehensive and aggressive strategy for reducing carbon emissions by households, particularly in a carbon intensive nation such as the US, makes sense on many levels: for the sustainability of human race, for a healthy environment for future generations, for economic stability, for social security, and for the development of

The daunting task of combating climate change is a defining challenge of the present generation. Reducing global carbon emissions is the most important aspect of that challenge. The US is a major player in global climate mitigation initiatives – since it is responsible for more than 20% of global carbon emissions. While the residential sector in the US accounts for about 20% of US emissions, this chapter demonstrates that households can directly and indirectly play a very important role in reducing all of the nations' carbon emissions. They have direct control over about 46% of embodied carbon emissions in the US by managing their consumption of energy resources and indirect control over another 25% of emissions by managing their consumption patterns. They can also play a role in influencing the remaining 29% by promoting and/or supporting initiatives to reduce the carbon footprint of energy systems, government expenditures, investment portfolios, and even businesses and industries beyond US borders. They can do this by becoming more engaged citizens and exercising their democratic privileges. The *sectoral* and *end use* approaches used to represent household emissions in the US are important, but limited in terms of helping people fully understand how their lives are connected to all sectors of the economy. The consumption based approach presented in this chapter constitute a more comprehensive accounting of household emissions as it includes embodied carbon over the life cycle of products and services that people consume to support their lifestyle. Most importantly, this approach offers people much more direct ways of relating personal choices with large scale reductions of national carbon emissions. This is a perspective that has the potential to empower people to become proactive agents of change and provide more explicit tools to make a difference

I would like to acknowledge my co-authors of the two papers (Shammin & Bullard, 2009; Shammin et al, 2010) that formulate the conceptual and analytical basis for the main

carbon-free economy.

**5. Conclusion**

more engaged and resilient communities.

in the battle against climate change.

**6. Acknowledgment**

**9**

*Ukraine*

**The Uncertainty Estimation and Use of**

*1State Enterprise "All-Ukrainian State Scientific and Production Centre for Standardization, Metrology, Certification and Protection of Consumer"*

*2State Enterprise "Ukrainian Scientific-Research and Educational Centre of Standardization, Certification and Problems of Quality" (SE "UkrSREC")*

A global policy for environmental protection is needed and is under discussion. One of the effects of modern global policy for environmental protection includes the multitude of measurements that are part of the process of environment protection, including the estimation of greenhouse gas (GHG) emission. Global climate studies bring together an enormous range of sciences and for a sound model to be developed it is necessary that the data from all these areas be comparable. The only way for this to be assured is for measurements in all areas of science to be made in terms of a well-defined system of units,

Human activities to have major impacts on the global climate change which caused by an increase of GHG in the atmosphere. In general, there is now a demand for people to have confidence in the credibility of the results of measurements because in so many ways decisions based on the data that come from measurements are increasingly seen to have a direct influence on the economy, human health and safety, and welfare. The United Nations (UN) and its member states adopted the UN Framework Convention on Climate Change (UNFCCC). Parties of the UNFCCC must estimate GHG anthropogenic emissions and to

The governing bodies of the World Meteorological Organization (WMO) and of the UN Environment Programme (UNEP) created a body, the Intergovernmental Panel on Climate Change (IPCC), to marshal and assess scientific information on the subject. For monitoring of global climate change and providing reliable data for climate modelling, a Global Atmospheric Watch (GAW) programme has started by the WMO. The UNFCCC is also starting probably the largest environmental monitoring programme in the world. Parties of UNFCCC can estimate GHG emissions in using two general approaches: direct

measurement or proxy data (Velychko O. & Gordiyenko T., 2007a, 2011).

**1. Introduction**

namely the International System of Units (SI).

develop annual national GHG inventories.

Oleh Velychko1 and Tetyana Gordiyenko2

*(SE "Ukrmetrteststandard")*

**Measurement Units in National Inventories of Anthropogenic Emission of Greenhouse Gas**

*Ukraine*

## **The Uncertainty Estimation and Use of Measurement Units in National Inventories of Anthropogenic Emission of Greenhouse Gas**

Oleh Velychko1 and Tetyana Gordiyenko2

*1State Enterprise "All-Ukrainian State Scientific and Production Centre for Standardization, Metrology, Certification and Protection of Consumer" (SE "Ukrmetrteststandard") 2State Enterprise "Ukrainian Scientific-Research and Educational Centre of Standardization, Certification and Problems of Quality" (SE "UkrSREC")*

## **1. Introduction**

186 Greenhouse Gases – Emission, Measurement and Management

Shammin, M. & Bullard, C. (2009). Impact of Cap-and-trade Policies for Reducing

Suter, J and Shammin, M. 2010. Estimating Payback to Residential Energy Efficiency

Annual Meeting, Denver, Colorado, July 25-27, 2010.

2432–2438.

Greenhouse Gas Emissions on U.S. Households. *Ecological Economics*, Vol. 68, pp.

Measures: A Field Experiment. Selected paper prepared for presentation at the Agricultural & Applied Economics Association 2010 AAEA, CAES, & WAEA Joint

> A global policy for environmental protection is needed and is under discussion. One of the effects of modern global policy for environmental protection includes the multitude of measurements that are part of the process of environment protection, including the estimation of greenhouse gas (GHG) emission. Global climate studies bring together an enormous range of sciences and for a sound model to be developed it is necessary that the data from all these areas be comparable. The only way for this to be assured is for measurements in all areas of science to be made in terms of a well-defined system of units, namely the International System of Units (SI).

> Human activities to have major impacts on the global climate change which caused by an increase of GHG in the atmosphere. In general, there is now a demand for people to have confidence in the credibility of the results of measurements because in so many ways decisions based on the data that come from measurements are increasingly seen to have a direct influence on the economy, human health and safety, and welfare. The United Nations (UN) and its member states adopted the UN Framework Convention on Climate Change (UNFCCC). Parties of the UNFCCC must estimate GHG anthropogenic emissions and to develop annual national GHG inventories.

> The governing bodies of the World Meteorological Organization (WMO) and of the UN Environment Programme (UNEP) created a body, the Intergovernmental Panel on Climate Change (IPCC), to marshal and assess scientific information on the subject. For monitoring of global climate change and providing reliable data for climate modelling, a Global Atmospheric Watch (GAW) programme has started by the WMO. The UNFCCC is also starting probably the largest environmental monitoring programme in the world. Parties of UNFCCC can estimate GHG emissions in using two general approaches: direct measurement or proxy data (Velychko O. & Gordiyenko T., 2007a, 2011).

The Uncertainty Estimation and Use of Measurement Units

national inventories.

Fig. 1. The TACCC criteria

terms are provided in Table 1.

(ISO 5725-1, ISO 3534-1).

closeness of agreement between

closeness of agreement between a measured quantity value and a true quantity value of a measurand (VIM

closeness of agreement between a test result and the accepted reference value

indications or measured quantity values obtained by replicate measurements on the same or similar objects under specified conditions (VIM 2007); the closeness of agreement between independent test results obtained under stipulated conditions (ISO 5725-1, ISO

A*ccuracy*:

2007);

*Precision*:

3534-1)

in National Inventories of Anthropogenic Emission of Greenhouse Gas 189

*transparency* (disclosing sufficient and appropriate GHG-related information to allow intended users to make decisions with reasonable confidence); *accuracy* (reducing bias and uncertainties as far as is practical); *completeness* (including all relevant GHG emissions and removals); *consistency* (enabling meaningful comparisons in GHG-related information) and *comparability* (estimates of emissions and removals reported by countries in inventories should be comparable among countries) (ISO 14064-1…3, IPCC 2006). For this purpose, countries should use agreed methodologies and formats for estimating and reporting

*Accuracy*

Completeness Comparability

Definitions associated with conducting an uncertainty analysis include *accuracy*, *precision*, *uncertainty*, and *error* are described in GPG 2000, IPCC 2006, ISO 14064-1…3, VIM 2007, ISO 5725-1, ISO 3534-1 (Velychko O. & Gordiyenko T., 2005, 2007a, 2007b). Comparison of same metrological (and some statistical) and environmental guides and international standards

*Accuracy*:

*Precision*:

Transparency

a general term which describes the degree to which an estimate of a quantity is unaffected by bias due to systematic error (GPG 2000); a relative measure of the exactness of an emission or removal estimate (IPCC 2006); reducing bias and uncertainties as far as is

the inverse of uncertainty in the sense that the more precise something is, the less

closeness of agreement between independent results of measurements obtained under stipulated conditions (IPCC 2006).

practical (ISO 14064-1…3).

uncertain it is (GPG 2000);

Consistency TACCC

**Metrological terms Environmental terms**

Today's global economy depends on reliable measurements and tests, which are trusted and accepted internationally. Metrology is the scientific study of measurement. Measurements have always been essential in supporting international trade and regulation. Metrology delivers the basis for the comparability of test results, e. g. by defining the units of the measurement and by providing traceability and associated uncertainty of the measurement results. Measurement results may be used provided that the corresponding characteristics of measurement uncertainty are known.

The tasks of the Joint Committee for Guides in Metrology (JCGM) are to maintain and promote the use of the Guide to the Expression of Uncertainty in Measurement (known as the GUM) and the International Vocabulary of Metrology (known as the VIM). The JCGM has taken over responsibility for these two documents, who originally published them under the auspices of the International Bureau of Weights and Measures (BIPM), the International Organization of Legal Metrology (OIML), the International Organization for Standardization (ISO), the International Electrotechnical Commission (IEC), the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC), the International Union of Pure and Applied Chemistry (IUPAC), the International Union of Pure and Applied Physics (IUPAP), the International Laboratory Accreditation Cooperation (ILAC).

The General Conference on Weights and Measures (CGPM) adopted SI, for the recommended practical system of units of measurement. The nearly universal use of the SI has brought coherence to all scientific and technological measurements, a worldwide consensus on the evaluation and expression of uncertainty in measurement would permit the significance of a vast spectrum of measurement results in science, engineering, commerce, industry, and regulation to be readily understood and properly interpreted. Many of the quantities, their recommended names and symbols, and the equations relating them, are listed in the international standards ISO/IEC 80000, in which it is proposed that the quantities and equations used with the SI. The IUPAP recognizes the SI for expressing the quantitative results of measurements in physics. The IUPAC serves to advance the worldwide aspects of the chemical sciences and to contribute to the application of chemistry in the service of Mankind (Velychko O. & Gordiyenko T., 2007a, 2010).

Some metrological terms are used in special guides of the IPCC, which to use for preparation of national inventories of GHG. Therefore it is important to compare uncertainty estimation with international ecological and metrological guides, and to consider peculiarities of their using also. It is also important to consider peculiarities of SI units used in those ecological guides.

## **2. The use metrological terms in international environmental guides**

All branches of science and technology need to choose their vocabulary with care. Each term must have the same meaning for all of its users. In order to try and resolve this problem in field of metrology at an international level, eight international organizations developed VIM. The IPCC and the UNFCCC resolved this problem in environmental field.

Throughout the review process, it is asked to assess the quality of the each Party's UNFCCC national inventory submission, with quality being determined by criteria (TACCC – Fig. 1): *transparency* (disclosing sufficient and appropriate GHG-related information to allow intended users to make decisions with reasonable confidence); *accuracy* (reducing bias and uncertainties as far as is practical); *completeness* (including all relevant GHG emissions and removals); *consistency* (enabling meaningful comparisons in GHG-related information) and *comparability* (estimates of emissions and removals reported by countries in inventories should be comparable among countries) (ISO 14064-1…3, IPCC 2006). For this purpose, countries should use agreed methodologies and formats for estimating and reporting national inventories.

#### Fig. 1. The TACCC criteria

188 Greenhouse Gases – Emission, Measurement and Management

Today's global economy depends on reliable measurements and tests, which are trusted and accepted internationally. Metrology is the scientific study of measurement. Measurements have always been essential in supporting international trade and regulation. Metrology delivers the basis for the comparability of test results, e. g. by defining the units of the measurement and by providing traceability and associated uncertainty of the measurement results. Measurement results may be used provided that the corresponding characteristics of

The tasks of the Joint Committee for Guides in Metrology (JCGM) are to maintain and promote the use of the Guide to the Expression of Uncertainty in Measurement (known as the GUM) and the International Vocabulary of Metrology (known as the VIM). The JCGM has taken over responsibility for these two documents, who originally published them under the auspices of the International Bureau of Weights and Measures (BIPM), the International Organization of Legal Metrology (OIML), the International Organization for Standardization (ISO), the International Electrotechnical Commission (IEC), the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC), the International Union of Pure and Applied Chemistry (IUPAC), the International Union of Pure and Applied Physics (IUPAP), the International Laboratory Accreditation Cooperation

The General Conference on Weights and Measures (CGPM) adopted SI, for the recommended practical system of units of measurement. The nearly universal use of the SI has brought coherence to all scientific and technological measurements, a worldwide consensus on the evaluation and expression of uncertainty in measurement would permit the significance of a vast spectrum of measurement results in science, engineering, commerce, industry, and regulation to be readily understood and properly interpreted. Many of the quantities, their recommended names and symbols, and the equations relating them, are listed in the international standards ISO/IEC 80000, in which it is proposed that the quantities and equations used with the SI. The IUPAP recognizes the SI for expressing the quantitative results of measurements in physics. The IUPAC serves to advance the worldwide aspects of the chemical sciences and to contribute to the application of chemistry

Some metrological terms are used in special guides of the IPCC, which to use for preparation of national inventories of GHG. Therefore it is important to compare uncertainty estimation with international ecological and metrological guides, and to consider peculiarities of their using also. It is also important to consider peculiarities of SI

All branches of science and technology need to choose their vocabulary with care. Each term must have the same meaning for all of its users. In order to try and resolve this problem in field of metrology at an international level, eight international organizations developed

Throughout the review process, it is asked to assess the quality of the each Party's UNFCCC national inventory submission, with quality being determined by criteria (TACCC – Fig. 1):

**2. The use metrological terms in international environmental guides**

VIM. The IPCC and the UNFCCC resolved this problem in environmental field.

in the service of Mankind (Velychko O. & Gordiyenko T., 2007a, 2010).

measurement uncertainty are known.

units used in those ecological guides.

(ILAC).

Definitions associated with conducting an uncertainty analysis include *accuracy*, *precision*, *uncertainty*, and *error* are described in GPG 2000, IPCC 2006, ISO 14064-1…3, VIM 2007, ISO 5725-1, ISO 3534-1 (Velychko O. & Gordiyenko T., 2005, 2007a, 2007b). Comparison of same metrological (and some statistical) and environmental guides and international standards terms are provided in Table 1.

The Uncertainty Estimation and Use of Measurement Units

interval containing the set of true quantity values of a measurand with a stated probability, based on the information

means of the mutual dependence of two

the relationship between two or several random variables within a distribution of two or more random variables (ISO

dependence of two variables, equal to the ratio of their covariances to the positive square root of the product of their

PDF

Fig. 2. Relationship between accuracy and precision

random variables (GUM 1993).

measure of the relative mutual

*Coverage interval*:

available (VIM 2007).

*Correlation coefficient*:

variances (GUM 1993).

*Covariance*:

*Correlation*:

3534-1).

**Metrological terms Environmental terms**

in National Inventories of Anthropogenic Emission of Greenhouse Gas 191

*Confidence interval*:

(IPCC 2006).

two variables (GPG 2000).

(GPG 2000, IPCC 2006).

*Correlation coefficient*:

(GPG 2000, IPCC 2006).

Value RV

*Precision*

The *accuracy* and *precision* of individual measurements will depend upon the equipment and protocols used to make the measurements. A measurement system (equipment) is designated valid if it is both *accurate* and *precise*. The relationship between accuracy and precision is shown in Fig. 2 (PDF is probability density function; RV is reference value).

The concept "*measurement accuracy*" is not a quantity and is not given a numerical quantity value (VIM 2007). The term *accuracy*, when applied to a set of test results, involves a

*Covariance*:

*Correlation*:

Table 1. Metrological and environmental guides and international standard terms

*Accuracy*

the range in which it is believed that the true

the true value of the quantity for which the interval is to be estimated is a fixed but unknown constant, such as the annual total emissions in a given year for a given country

a measure of the mutual dependence between

mutual dependence between two quantities

a number laying between –1 and +1 which measures the mutual dependence between two variables which are observed together

value of a quantity lies (GPG 2000);

*Uncertainty*:

quantity (GPG 2000);

amount (ISO 14064-1…3).

*Error*:

(GPG 2000).

2006).

*Random error*:

IPCC 2006).

*Systematic error*:

an uncertainty is a parameter, associated with the result of measurement that characterises the dispersion of the values that could be reasonably attributed to the measured

lack of knowledge of the true value of a variable that can be described as a probability density function characterizing the range and likelihood of possible values (IPCC 2006); parameter associated with the result of quantification which characterizes the dispersion of the values that could be reasonably attributed to the quantified

a general term referring to the difference between an observed (measured) value of a

the difference between the true, but usually

unknown, value of a quantity being estimated, and the mean observed value as would be estimated by the sample mean of an infinite set of observations (GPG 2000, IPCC

the random error of an individual

measurement is the difference between an individual measurement and the above limiting value of the sample mean (GPG 2000,

quantity and its "true" (but usually unknown) value and does not carry the pejorative sense of a mistake or blunder

**Metrological terms Environmental terms**

*Uncertainty*:

5725-1, ISO 3534-1).

*Error*:

3534-1).

2007);

ISO 3534-1).

*Random error*:

3534-1).

*Systematic error*:

non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on

an estimate attached to a test result which characterizes the range of values within which the true value is asserted to lie (ISO

the information used (VIM 2007);

measured quantity value minus a reference quantity value (VIM 2007); the test result minus the accepted reference value (of the characteristic), which is the sum of random errors and systematic errors (ISO 5725-1, ISO

component of measurement error that in replicate measurements remains constant or varies in a predictable manner (VIM

a component of the error which, in the course of a number of test results for the same characteristic, remains constant or varies in a predictable way (ISO 5725-1,

component of measurement error that in replicate measurements varies in an unpredictable manner (VIM 2007); a component of the error which, in the course of a number of test results for the

same characteristic, varies in an unpredictable way (ISO 5725-1, ISO

Table 1. Metrological and environmental guides and international standard terms

Fig. 2. Relationship between accuracy and precision

The *accuracy* and *precision* of individual measurements will depend upon the equipment and protocols used to make the measurements. A measurement system (equipment) is designated valid if it is both *accurate* and *precise*. The relationship between accuracy and precision is shown in Fig. 2 (PDF is probability density function; RV is reference value).

The concept "*measurement accuracy*" is not a quantity and is not given a numerical quantity value (VIM 2007). The term *accuracy*, when applied to a set of test results, involves a

The Uncertainty Estimation and Use of Measurement Units

of the dispersion (ISO 14064-1…3).

is not possible to correct (ISO 3534-1).

Uncorrected arithmetic mean of observations

Correction for all recognized systematic effects

Measurand value due to incomplete definition

Fig. 4. Relationship between error and uncertainty

Uncorrected observations

*Result of measurement*

Remaining error (unknowable)

*Final result of measurement*

(GUM 1993, VIM 2007).

Measurand value

(unknowable)

in National Inventories of Anthropogenic Emission of Greenhouse Gas 193

series of measurements and can be characterized by *standard deviations*. Estimates of other

Uncertainty depends on the analyst's state of knowledge, which in turn depends on the quality and quantity of applicable data as well as knowledge of underlying processes and inference methods (IPCC 2006). Uncertainty information typically specifies quantitative estimates of the likely dispersion of values and a qualitative description of the likely causes

Uncertainty should be distinguished from an estimate attached to a test result which characterizes the range of values within which the expectation is asserted to lie. This latter estimate is a measure of precision rather than of accuracy and should be used only when the true value is not defined. When the expectation is used instead of the true value the

*Systematic measurement error*, and its causes, can be known or unknown. A correction can be applied to compensate for a known systematic measurement error. *Random measurement errors* of a set of replicate measurements form a distribution that can be summarized by its

*Error* of result is the test result minus the accepted RV (of the characteristic). Error is the sum of systematic and random errors. *Systematic error* may be known or unknown; *random error* it

*Quantity Value Variance*

To express of the measurement result is used the expanded measurement uncertainty with a specified coverage interval which does not need to be centred on the chosen measured quantity value. This interval should not be termed "confidence interval" to avoid confusion with the statistical concept and can be derived from an expanded measurement uncertainty

(single observation) (arithmetic mean)

(does not include variance due to incomplete measurand definition)

expectation, which is generally assumed to be zero, and its variance (VIM 2007).

The relationship between error and uncertainty is shown in Fig. 4 (GUM 1993).

components can only be based on experience or other information (ISO 3534-1).

expression "random component of uncertainty" should be used.

combination of random components and a common systematic error or bias component (ISO 5725-1, ISO 3534-1). Estimates should be accurate in the sense that they are systematically neither over nor under true emissions or removals, so far as can be judged, and that uncertainties are reduced so far as is practicable (IPCC 2006).

*Accepted reference value* is a value that serves as an agreed-upon reference for comparison, and which is derived as: a theoretical or established value, based on scientific principles; an assigned or certified value, based on experimental work of some national or international organization; a consensus or certified value, based on collaborative experimental work under the auspices of a scientific or engineering group; when the first three are not available, the expectation of the (measurable) quantity, i.e. the mean of a specified population of measurements.

*Measurement precision* is usually expressed numerically by measures of imprecision, such as standard deviation, variance, or coefficient of variation under the specified conditions of measurement (VIM 2007). *Precision* is the inverse of uncertainty in the sense that the more precise something is, the less uncertain it is (IPCC 2006).

Precision depends only on the distribution of random errors and does not relate to the true value or the specified value. The measure of precision usually is expressed in terms of imprecision and computed as a standard deviation of the test results. Less precision is reflected by a larger standard deviation. "Independent results" means results obtained in a manner not influenced by any previous result on the same or similar test object. Quantitative measures of precision depend critically on the stipulated conditions (ISO 3534-1). The relationship between small or large accuracy and precision is shown in Fig. 3.

Fig. 3. Small or large accuracy and precision (1-small accuracy and large precision; 2-large accuracy and large precision; 3-large accuracy and small precision; 4-small accuracy and small precision)

The parameter (for uncertainty) may be, for example, a standard deviation called standard measurement uncertainty (or a specified multiple of it), or the half-width of an interval, having a stated coverage probability. In general, for a given set of information, it is understood that the measurement uncertainty is associated with a stated quantity value attributed to the measurand (VIM 2007).

*Uncertainty* of measurement comprises, in general, many components. Some of these components may be estimated on the basis of the statistical distribution of the results of a

combination of random components and a common systematic error or bias component (ISO 5725-1, ISO 3534-1). Estimates should be accurate in the sense that they are systematically neither over nor under true emissions or removals, so far as can be judged,

*Accepted reference value* is a value that serves as an agreed-upon reference for comparison, and which is derived as: a theoretical or established value, based on scientific principles; an assigned or certified value, based on experimental work of some national or international organization; a consensus or certified value, based on collaborative experimental work under the auspices of a scientific or engineering group; when the first three are not available, the expectation of the (measurable) quantity, i.e. the mean of a specified

*Measurement precision* is usually expressed numerically by measures of imprecision, such as standard deviation, variance, or coefficient of variation under the specified conditions of measurement (VIM 2007). *Precision* is the inverse of uncertainty in the sense that the more

Precision depends only on the distribution of random errors and does not relate to the true value or the specified value. The measure of precision usually is expressed in terms of imprecision and computed as a standard deviation of the test results. Less precision is reflected by a larger standard deviation. "Independent results" means results obtained in a manner not influenced by any previous result on the same or similar test object. Quantitative measures of precision depend critically on the stipulated conditions (ISO 3534-1).

RV Value

3 4

The relationship between small or large accuracy and precision is shown in Fig. 3.

Fig. 3. Small or large accuracy and precision (1-small accuracy and large precision; 2-large accuracy and large precision; 3-large accuracy and small precision; 4-small accuracy and

The parameter (for uncertainty) may be, for example, a standard deviation called standard measurement uncertainty (or a specified multiple of it), or the half-width of an interval, having a stated coverage probability. In general, for a given set of information, it is understood that the measurement uncertainty is associated with a stated quantity value

*Uncertainty* of measurement comprises, in general, many components. Some of these components may be estimated on the basis of the statistical distribution of the results of a

and that uncertainties are reduced so far as is practicable (IPCC 2006).

precise something is, the less uncertain it is (IPCC 2006).

1

attributed to the measurand (VIM 2007).

2

population of measurements.

PDF

small precision)

series of measurements and can be characterized by *standard deviations*. Estimates of other components can only be based on experience or other information (ISO 3534-1).

Uncertainty depends on the analyst's state of knowledge, which in turn depends on the quality and quantity of applicable data as well as knowledge of underlying processes and inference methods (IPCC 2006). Uncertainty information typically specifies quantitative estimates of the likely dispersion of values and a qualitative description of the likely causes of the dispersion (ISO 14064-1…3).

Uncertainty should be distinguished from an estimate attached to a test result which characterizes the range of values within which the expectation is asserted to lie. This latter estimate is a measure of precision rather than of accuracy and should be used only when the true value is not defined. When the expectation is used instead of the true value the expression "random component of uncertainty" should be used.

*Systematic measurement error*, and its causes, can be known or unknown. A correction can be applied to compensate for a known systematic measurement error. *Random measurement errors* of a set of replicate measurements form a distribution that can be summarized by its expectation, which is generally assumed to be zero, and its variance (VIM 2007).

*Error* of result is the test result minus the accepted RV (of the characteristic). Error is the sum of systematic and random errors. *Systematic error* may be known or unknown; *random error* it is not possible to correct (ISO 3534-1).

The relationship between error and uncertainty is shown in Fig. 4 (GUM 1993).

#### Fig. 4. Relationship between error and uncertainty

To express of the measurement result is used the expanded measurement uncertainty with a specified coverage interval which does not need to be centred on the chosen measured quantity value. This interval should not be termed "confidence interval" to avoid confusion with the statistical concept and can be derived from an expanded measurement uncertainty (GUM 1993, VIM 2007).

The Uncertainty Estimation and Use of Measurement Units

importance of these factors.

statistical uncertainty associated with the resulting emission estimates.

in National Inventories of Anthropogenic Emission of Greenhouse Gas 195

GHG emissions can be measured either directly or indirectly. The indirect approach usually involves the use of an estimation model (e.g., AD and an EF), while the direct approach requires that emissions to the atmosphere be measured directly by some form of instrumentation (e.g., continuous emissions monitor). As the data used in the direct or indirect measurement of GHG emissions are subject to random variation there is always

The uncertainty in this relationship must be considered as well as the accuracy and precision in measurements in the proxy data itself. An uncertainty is a parameter, associated with the result of measurement that characterizes the dispersion of the values that could be reasonably attributed to the measured quantity (GPG 2000). An *uncertainty analysis* of a model aims to provide quantitative measures of the uncertainty of output values caused by uncertainties in the model itself and in its input values, and to examine the relatively

The IPCC guides (GPG 2000, IPCC 2006) use two main statistical concepts: the PDF and *confidence limits*. On Fig. 5 show PDF and cumulative distribution function (CDF) graphs. The PDF describes the range and relative likelihood of possible values; confidence limits give the range within which the underlying value of an uncertain quantity is thought to lie (confidence interval). The IPCC Guides suggest the use of a 95 % confidence interval, which

PDF is a mathematical function which characterizes the probability behaviour of population. It is a function *f*(*x*) which specifies the relative likelihood of a continuous random variable *X* taking a value near *x*, and is defined as the probability that *X* takes a value between *x* and *x+dx*, divided by *dx*, where *dx* is an infinitesimally small number. Most PDFs require one or

The probability that a continuous random variable *X* lies in between the values *a* and *b* is

EF

EF

is the interval that has a 95 % probability of containing the unknown true value.

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00

given by the interval of the PDF, *f*(*x*), over the range between *a* and *b*:

0.50

1.00

PDF

CDF

Fig. 5. PDF (a) and CDF (b) graphs

more parameters to specify them fully.

The level of belief is expressed by the probability, whose value is related to the size of the interval. It is one of the ways in which uncertainty can be expressed. In practice a confidence interval is defined by a probability value, say 95%, and confidence limits on either side of the mean value *x*. In this case the confidence limits would be calculated from the PDF such that there was a 95% chance of the true value of the quantity being estimated by *x* lying between those limits. Commonly limits are the 2.5 percentile and 97.5 percentile respectively (GPG 2000).

The *confidence interval* is a range that encloses the true value of this unknown fixed quantity with a specified confidence (probability). Typically, a 95 % confidence interval is used in greenhouse gas inventories. From a traditional statistical perspective, the 95 % confidence interval has a 95 % probability of enclosing the true but unknown value of the quantity. An alternative interpretation is that the confidence interval is a range that may safely be declared to be consistent with observed data or information. The 95 %confidence interval is enclosed by the 2.5th and 97.5th percentiles of the PDF (IPCC 2006).

Dependencies among input sources will matter only if the dependencies exist between two sources to which the uncertainty in the GHG national inventory is sensitive and if the dependencies are sufficiently strong. For the quantities evaluation of dependence of two or more input sources used the correlation coefficient.

A value of +1 of *correlation coefficient* means that the variables have a perfect linear relationship; a value of –1 of correlation coefficient means that there is a perfect inverse linear relation; and a value of 0 of correlation coefficient means that there is no straight line relation. It is defined as the covariance of the two variables divided by the product of their *standard deviations* (σ). The population standard deviation is the positive square root of the variance*.* It is estimated by the sample standard deviation that is the positive square root of the sample variance (GPG 2000, IPCC 2006).

For the preparation of GHG national inventories used the activity data (AD) and emission factor (EF). *Activity data* is data on the magnitude of a human activity resulting in emissions or removals taking place during a given period of time. Data on energy use, metal production, land areas, management systems, lime and fertilizer use and waste arisings are examples of AD. *Emission factor* is a coefficient that quantifies the emissions or removals of a gas per unit activity. EF is often based on a sample of measurement data, averaged to develop a representative rate of emission for a given activity level under a given set of operating conditions (IPCC 2006).

## **3. Uncertainty estimation in international environmental and metrological guides**

Parties of UNFCCC can estimate GHG emissions in using two general approaches: direct measurement or proxy data. The concept of uncertainty in direct measurements is more consistent with a statistical concept of uncertainty. The statistical issues include precision and calibration of measurement equipment, fraction of population captured, frequency of sampling, etc. In contrast, proxy data is more typically in the form of AD and EF. The proxy data approach requires assumptions as to the relationship between some activity and actual emissions (IPCC 2006).

The level of belief is expressed by the probability, whose value is related to the size of the interval. It is one of the ways in which uncertainty can be expressed. In practice a confidence interval is defined by a probability value, say 95%, and confidence limits on either side of the mean value *x*. In this case the confidence limits would be calculated from the PDF such that there was a 95% chance of the true value of the quantity being estimated by *x* lying between those limits. Commonly limits are the 2.5 percentile and 97.5 percentile respectively

The *confidence interval* is a range that encloses the true value of this unknown fixed quantity with a specified confidence (probability). Typically, a 95 % confidence interval is used in greenhouse gas inventories. From a traditional statistical perspective, the 95 % confidence interval has a 95 % probability of enclosing the true but unknown value of the quantity. An alternative interpretation is that the confidence interval is a range that may safely be declared to be consistent with observed data or information. The 95 %confidence interval is

Dependencies among input sources will matter only if the dependencies exist between two sources to which the uncertainty in the GHG national inventory is sensitive and if the dependencies are sufficiently strong. For the quantities evaluation of dependence of two or

A value of +1 of *correlation coefficient* means that the variables have a perfect linear relationship; a value of –1 of correlation coefficient means that there is a perfect inverse linear relation; and a value of 0 of correlation coefficient means that there is no straight line relation. It is defined as the covariance of the two variables divided by the product of their *standard deviations* (σ). The population standard deviation is the positive square root of the variance*.* It is estimated by the sample standard deviation that is the positive square root of

For the preparation of GHG national inventories used the activity data (AD) and emission factor (EF). *Activity data* is data on the magnitude of a human activity resulting in emissions or removals taking place during a given period of time. Data on energy use, metal production, land areas, management systems, lime and fertilizer use and waste arisings are examples of AD. *Emission factor* is a coefficient that quantifies the emissions or removals of a gas per unit activity. EF is often based on a sample of measurement data, averaged to develop a representative rate of emission for a given activity level under a given set of

**3. Uncertainty estimation in international environmental and metrological**

Parties of UNFCCC can estimate GHG emissions in using two general approaches: direct measurement or proxy data. The concept of uncertainty in direct measurements is more consistent with a statistical concept of uncertainty. The statistical issues include precision and calibration of measurement equipment, fraction of population captured, frequency of sampling, etc. In contrast, proxy data is more typically in the form of AD and EF. The proxy data approach requires assumptions as to the relationship between some activity and actual

enclosed by the 2.5th and 97.5th percentiles of the PDF (IPCC 2006).

more input sources used the correlation coefficient.

the sample variance (GPG 2000, IPCC 2006).

operating conditions (IPCC 2006).

**guides**

emissions (IPCC 2006).

(GPG 2000).

GHG emissions can be measured either directly or indirectly. The indirect approach usually involves the use of an estimation model (e.g., AD and an EF), while the direct approach requires that emissions to the atmosphere be measured directly by some form of instrumentation (e.g., continuous emissions monitor). As the data used in the direct or indirect measurement of GHG emissions are subject to random variation there is always statistical uncertainty associated with the resulting emission estimates.

The uncertainty in this relationship must be considered as well as the accuracy and precision in measurements in the proxy data itself. An uncertainty is a parameter, associated with the result of measurement that characterizes the dispersion of the values that could be reasonably attributed to the measured quantity (GPG 2000). An *uncertainty analysis* of a model aims to provide quantitative measures of the uncertainty of output values caused by uncertainties in the model itself and in its input values, and to examine the relatively importance of these factors.

The IPCC guides (GPG 2000, IPCC 2006) use two main statistical concepts: the PDF and *confidence limits*. On Fig. 5 show PDF and cumulative distribution function (CDF) graphs. The PDF describes the range and relative likelihood of possible values; confidence limits give the range within which the underlying value of an uncertain quantity is thought to lie (confidence interval). The IPCC Guides suggest the use of a 95 % confidence interval, which is the interval that has a 95 % probability of containing the unknown true value.

#### Fig. 5. PDF (a) and CDF (b) graphs

PDF is a mathematical function which characterizes the probability behaviour of population. It is a function *f*(*x*) which specifies the relative likelihood of a continuous random variable *X* taking a value near *x*, and is defined as the probability that *X* takes a value between *x* and *x+dx*, divided by *dx*, where *dx* is an infinitesimally small number. Most PDFs require one or more parameters to specify them fully.

The probability that a continuous random variable *X* lies in between the values *a* and *b* is given by the interval of the PDF, *f*(*x*), over the range between *a* and *b*:

The Uncertainty Estimation and Use of Measurement Units

*n s u A* ,

Type A of GUM 1993 regulated using assessment of uncertainty (components evaluated by statistical methods to a series of repeated determinations) and use

Type B of GUM 1993 regulated using assessment of uncertainty (components evaluated by other means) and use

*B*

*U* is the expanded uncertainty given in

*k* is the coverage factor (typically *k* = 2).

In GUM 1993 the overall uncertainty arising from the combination of type A and type B uncertainties calculated used

2 or

*ui* is the components of uncertainty; *U p* is the expanded uncertainty.

2 2 ˆ ˆˆ *c AB u uu* ,

*i c i uu* 1

*uc* is the total uncertainty;

*m*

*u*

*U*

*k* ,

*s* is the standard deviation; *n* is the number of measurements.

equation:

where:

equation:

where:

Certificate;

equation:

where:

and*U ku p c*

**Metrological guides Environmental guides**

in National Inventories of Anthropogenic Emission of Greenhouse Gas 197

equation:

where:

equation:

where:

where:

*U*

sum of the quantities\*;

them, respectively.

Rule А of GPG 2000 regulated using assessment of uncertainty and use

*total xxx*

Rule B of GPG 2000 regulated using assessment of uncertainty (if impossible use statistical processing) and use

> 2 1 ... *total UUUU n* ,

*Utotal* is percentage of uncertainty in the

*Ui* are percentage of uncertainties associated with each of the quantities.

In IPCC 2006 the overall uncertainty arising from the combination of EF and AD uncertainty calculated used equation:

*UE* is percentage of uncertainties

*U A* is percentage of uncertainties

associated with the AD, so long as *UE* ,

associated with the EF;

*U A* < 60 %\*\*.

\* half the 95 % confidence interval divided by the total and expressed as a percentage; \*\* the 60 % limit is imposed because the rule suggested for *UT* requires σ to be less than about 30 % of the central estimate, and we are interpreting the quoted range as ± 2σ.

Table 2. Uncertainty estimation in metrological and environmental guides

product of the quantities\*;

2

*n*

2 2

2

)( 22 *T UUU AE* ,

*xUxUxU*

11 ,

22

 ... )(...)()(

21

*Utotal* is percentage of uncertainty in the

*i x* and *Ui* are the uncertain quantities and percentage of uncertainties associated with

*nn*

2 2

$$\Pr(a \le x < b) = \bigcap\_{b}^{a} f(\mathbf{x}) d\mathbf{x} \text{ .}$$

The PDF is the derivative (when it exists) of the distribution function (*F*(*x*) for a random variable *X* specifies the probability Pr(*X* ≤ *x*) that *X* is less than or equal to *x*):

$$f(\mathbf{x}) = \frac{dF(\mathbf{x})}{d\mathbf{x}}\,\,\,\,\,\,$$

In practical situations, the PDF used is chosen from a relatively small number of standard PDFs and the main statistical task is to estimate its parameters. Thus, for inventory applications, a knowledge of which PDF has been used is a necessary item in the documentation of an uncertainty assessment (GPG 2000).

Uncertainty information on the EF, AD and other parameters used for the uncertainty analysis must be collected to create PDF (for the Monte Carlo method) or mean and standard deviation of the data (for the error propagation method). As this uncertainty data is collected, the correlations between parameters should also be considered.

The measurement error is one of the first types of uncertainty of GHG emission inventories, which may be: results from errors in measuring, recording and transmitting information; finite instrument resolution; inexact values of measurement standards and reference materials; inexact values of constants and other parameters obtained from external sources and used in the data-reduction algorithm; approximations and assumptions incorporated in the measurement method and estimation procedure; and/or variations in repeated observations of the emission or uptake or associated quantity under apparently identical conditions. Measurement error can be reduced using more precise measurement methods, avoiding simplifying assumptions and ensuring, that measurement technologies are appropriately used and calibrated.

Uncertainties also may be a result of: measurements were attempted but no value was available (missing data); and measurement data are not available either because the process is not yet recognized or a measurement method does not yet exist (lack of completeness). Where a PDF can be identified, sources of uncertainty can be addressed by statistical means (*type A of uncertainty* for GUM 1993). There can be structural uncertainties that are not easily incorporated into a quantitative uncertainty analysis in the form of a PDF. These types of situations are typically outside the scope of statistics (*type B of uncertainty* for GUM 1993).

Comparison of uncertainty estimation in metrological and environmental guides are provided in Table 2 (Velychko O. & Gordiyenko T., 2005; Gordiyenko T. & Velychko O., 2006; Velychko O. & Gordiyenko T., 2007a; Velichko О. N. & Gordienko T. B., 2007c, 2009; Velychko O. M. & Gordiyenko T. B., 2008; Velychko O. & Gordiyenko T., 2009).

The pragmatic approach for producing quantitative uncertainty estimation is using the best available estimates, which are often a combination of measured data, published information, model outputs, and expert judgement. Although uncertainties determined from measured data are often perceived to be mote rigorous than uncertainty estimates based on models, and similarly.

*a b a x b f x dx* .

Pr( ) ( )

variable *X* specifies the probability Pr(*X* ≤ *x*) that *X* is less than or equal to *x*):

is collected, the correlations between parameters should also be considered.

documentation of an uncertainty assessment (GPG 2000).

appropriately used and calibrated.

and similarly.

The PDF is the derivative (when it exists) of the distribution function (*F*(*x*) for a random

( ) ( ) *dF x f x dx* .

In practical situations, the PDF used is chosen from a relatively small number of standard PDFs and the main statistical task is to estimate its parameters. Thus, for inventory applications, a knowledge of which PDF has been used is a necessary item in the

Uncertainty information on the EF, AD and other parameters used for the uncertainty analysis must be collected to create PDF (for the Monte Carlo method) or mean and standard deviation of the data (for the error propagation method). As this uncertainty data

The measurement error is one of the first types of uncertainty of GHG emission inventories, which may be: results from errors in measuring, recording and transmitting information; finite instrument resolution; inexact values of measurement standards and reference materials; inexact values of constants and other parameters obtained from external sources and used in the data-reduction algorithm; approximations and assumptions incorporated in the measurement method and estimation procedure; and/or variations in repeated observations of the emission or uptake or associated quantity under apparently identical conditions. Measurement error can be reduced using more precise measurement methods, avoiding simplifying assumptions and ensuring, that measurement technologies are

Uncertainties also may be a result of: measurements were attempted but no value was available (missing data); and measurement data are not available either because the process is not yet recognized or a measurement method does not yet exist (lack of completeness). Where a PDF can be identified, sources of uncertainty can be addressed by statistical means (*type A of uncertainty* for GUM 1993). There can be structural uncertainties that are not easily incorporated into a quantitative uncertainty analysis in the form of a PDF. These types of situations are typically outside the scope of statistics (*type B of uncertainty* for GUM 1993).

Comparison of uncertainty estimation in metrological and environmental guides are provided in Table 2 (Velychko O. & Gordiyenko T., 2005; Gordiyenko T. & Velychko O., 2006; Velychko O. & Gordiyenko T., 2007a; Velichko О. N. & Gordienko T. B., 2007c, 2009;

The pragmatic approach for producing quantitative uncertainty estimation is using the best available estimates, which are often a combination of measured data, published information, model outputs, and expert judgement. Although uncertainties determined from measured data are often perceived to be mote rigorous than uncertainty estimates based on models,

Velychko O. M. & Gordiyenko T. B., 2008; Velychko O. & Gordiyenko T., 2009).

\*\* the 60 % limit is imposed because the rule suggested for *UT* requires σ to be less than about 30 % of the central estimate, and we are interpreting the quoted range as ± 2σ.

Table 2. Uncertainty estimation in metrological and environmental guides

The Uncertainty Estimation and Use of Measurement Units

*m* is mode (most likely position), subject to *amb* .

by:

distribution is given by:

(GPG 2000).

in National Inventories of Anthropogenic Emission of Greenhouse Gas 199

The *normal* (*or Gaussian*) *distribution* is most appropriate when the range of uncertainty is small, and symmetric relative to the mean. This distribution arises in situations where many individual inputs contribute to an overall uncertainty, and in which none of the individual uncertainties dominates the total uncertainty. The PDF of the normal distribution is given

> 2 ( ) 1 ( ) , for . 2

The *lognormal distribution* may be appropriate when uncertainties are large for a nonnegative variable and known to be positively skewed. If many uncertain variables are multiplied, the product asymptotically approaches lognormality. The PDF of the lognormal

1 ( ) , for 0 . 2

The parameters required to specify the function are: *l* the mean of the natural log transform of the data; and 2 *l* the variance of the natural log transform of the data. The data and information that the inventory compiler can use to determine the input parameters are:

and

*Fractile distribution* is a type of empirical distribution in which judgements are made regarding the relative likelihood of different ranges of values for a variable (GPG 2000).

The rules for *uncertainties propagation* specify how to algebraically combine the quantitative measures of uncertainty associated with the input values to the mathematical formulae used in GHG national inventory compilation, so as to obtain corresponding measures of uncertainty for the output values. The *Monte Carlo analysis* is suitable for detailed category-by-category assessment of uncertainty, particularly where uncertainties are large, distribution is non-normal (non-Gaussian), the algorithms are complex functions and/or there are correlations between some of the activity sets, EF, or both

Simplified estimation of expanded measurement uncertainty for Type A is shown on Fig. 7.

1 2 ( , ,..., ) *Y fXX X m* ,

*fx e x*

*x*

2 2 (ln )

> 2 2 ln 1 *l*

.

*l l*

*x fx e x*

*l*

*l* is mean; 2 variance; and the relationships:

ln *l*

Measurement uncertainty of the values equation is used:

*x*

σ

Probability distribution is a function giving the probability that a random variable takes any given value or belongs to a given set of values. The probability on the whole set of values of the random variable equals 1. Many commonly used PDF distributions of practical important are: uniform; triangular, normal; lognormal; and fractile (Fig. 6).

Fig. 6. Some commonly used PDF models

*Uniform distribution* describes an equal likelihood of obtaining any value within a range. Sometimes the uniform distribution is useful for representing physically-bounded quantities. The PDF of the uniform distribution is given by:

$$f(\mathbf{x}) = \begin{cases} 1 / \, (b - a) \text{, for } a \le \mathbf{x} \le b \, \mu \\ 0 \quad \text{elsewhere,} \end{cases}$$

where:

 *a b* 2 is a mean and; *a b* 12 is the variance.

The *triangular distribution* is appropriate where upper and lower limits and a preferred value are provided by experts but there is no other information about the PDF. The triangular distribution can be asymmetrical. The PDF of the triangular distribution is given by:

$$f(\mathbf{x}) = \begin{cases} 2(\mathbf{x} - a) / \left\{ (b - a)(m - a) \right\}, \text{ when } a \le \mathbf{x} \le m \text{ and } a < m \le b, \\ 2(b - \mathbf{x}) / \left\{ (b - a)(b - m) \right\}, \text{ when } m \le \mathbf{x} \le b \text{ and } a \le m < b, \\ 0 & \text{elsewhere,} \end{cases}$$

where:

*a b*, are minimum and maximum value respectively;

*m* is mode (most likely position), subject to *amb* .

198 Greenhouse Gases – Emission, Measurement and Management

Probability distribution is a function giving the probability that a random variable takes any given value or belongs to a given set of values. The probability on the whole set of values of the random variable equals 1. Many commonly used PDF distributions of practical

Value of variable Value of variable

d) lognormal

Value of variable Value of variable

important are: uniform; triangular, normal; lognormal; and fractile (Fig. 6).

PDF a) uniform PDF b) triangular

c) normal

PDF PDF

quantities. The PDF of the uniform distribution is given by:

e) fractile

Fig. 6. Some commonly used PDF models

PDF

where:

where:

*a b* 2 is a mean and;

*a b* 12 is the variance.

Value of variable

*Uniform distribution* describes an equal likelihood of obtaining any value within a range. Sometimes the uniform distribution is useful for representing physically-bounded

1 /( ), for , ( ) 0 elsewhere,

The *triangular distribution* is appropriate where upper and lower limits and a preferred value are provided by experts but there is no other information about the PDF. The triangular

( ) 2( ) / ( )( ) , when and ,

*f x b x babm m x b a m b*

2( ) / ( )( ) , when and ,

*x a bama a x m a m b*

distribution can be asymmetrical. The PDF of the triangular distribution is given by:

0 elsewhere,

*a b*, are minimum and maximum value respectively;

*f x*

*ba axb*

The *normal* (*or Gaussian*) *distribution* is most appropriate when the range of uncertainty is small, and symmetric relative to the mean. This distribution arises in situations where many individual inputs contribute to an overall uncertainty, and in which none of the individual uncertainties dominates the total uncertainty. The PDF of the normal distribution is given by:

$$f(\mathbf{x}) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(\mathbf{x}-\mu)^2}{2\sigma^2}}, \text{ for } -\infty \le \mathbf{x} \le \infty.$$

The *lognormal distribution* may be appropriate when uncertainties are large for a nonnegative variable and known to be positively skewed. If many uncertain variables are multiplied, the product asymptotically approaches lognormality. The PDF of the lognormal distribution is given by:

$$f(\mathbf{x}) = \frac{1}{\sigma\_l \mathbf{x} \sqrt{2\pi}} e^{-\frac{\left(\ln \|\mathbf{x} - \boldsymbol{\mu}\_l\|\right)^2}{2\sigma\_l^2}}, \text{ for } 0 \le \mathbf{x} \le \infty.$$

The parameters required to specify the function are: *l* the mean of the natural log transform of the data; and 2 *l* the variance of the natural log transform of the data. The data and information that the inventory compiler can use to determine the input parameters are: *l* is mean; 2 variance; and the relationships:

$$\mu\_I = \ln \frac{\mu^2}{\sqrt{\left(\sigma^2 + \mu^2\right)}} \qquad \text{and} \quad \sigma\_I = \sqrt{\ln \left(\frac{\sigma^2}{\mu^2} + 1\right)} \quad . \dots$$

*Fractile distribution* is a type of empirical distribution in which judgements are made regarding the relative likelihood of different ranges of values for a variable (GPG 2000).

The rules for *uncertainties propagation* specify how to algebraically combine the quantitative measures of uncertainty associated with the input values to the mathematical formulae used in GHG national inventory compilation, so as to obtain corresponding measures of uncertainty for the output values. The *Monte Carlo analysis* is suitable for detailed category-by-category assessment of uncertainty, particularly where uncertainties are large, distribution is non-normal (non-Gaussian), the algorithms are complex functions and/or there are correlations between some of the activity sets, EF, or both (GPG 2000).

Simplified estimation of expanded measurement uncertainty for Type A is shown on Fig. 7.

Measurement uncertainty of the values equation is used:

$$Y = f(X\_1, X\_2, \dots, X\_m)\_{\prime\prime}$$

The Uncertainty Estimation and Use of Measurement Units

by means of the equation from Table 2 (GUM 1993).

within the identified uncertainty range.

Table 3. *t*-factors for the 95% confidence level

estimations of emission foul and GHG.

**4. Uncertainty estimation with correlation values**

measurement (the evaluation of type B covariance).

be done by using the Table 3.

in National Inventories of Anthropogenic Emission of Greenhouse Gas 201

The overall standard uncertainty *uc* (Table 2) determined by a combination of uncertainties components; estimation of the expanded measurement uncertainty *U p* may be calculated

Statistical uncertainty in the context of GHG inventories is usually presented by giving an uncertainty range expressed in a percentage of the expected mean value of the emission. This range can be determined by calculating the "confidence limits", within which the underlying value of an uncertain quantity is thought to lie for a specified probability. The "confidence level" determines the probability, that the true value of emission is situated

Determining the *t*-factor *t* (standard error that is to be estimated follows a *t*-distribution) can

**Number of measurements (***n***)** *t***-factor (***t***) for confidence level 95 %**  3 4,30 5 2,78 8 2,37 10 2,26 50 2,01 100 1,98 1,96

Necessity in the analysis of covariance and autocorrelation for the uncertainty estimates of emission foul and greenhouse gases exists. It is importantly to investigate the correlations of the estimated values relevant to emissions as in the context one estimation and the various

If correlation exists between input values then this correlation is essential and can not be ignored. Covariance of input values may be estimated experimentally, on condition of possible the change of input correlated values (the estimation of type A covariance), or with the using of necessary data on the correlation changeability of values which relate to this

In practical cases input values often appear to be correlated, as far as the evaluation of their values is used by the same standards, measuring instruments, standard data and even method of measurement which possess peculiar uncertainty. If direct measurement results

Covariance with the estimations of two input values may be equal to zero or selected as negligible, if: these values are not correlated (values measurement are run repeatedly in various independent experiments, or they present the various estimations of values which made independently); any values may be is accepted as an constant; there is negligible data

Comparison of the uncertainties estimations of input values with correlation in metrological and environmental guides are driven in Table 4 (Velychko O. & Gordiyenko T., 2007b).

are not correlated then calculated value of covariance is expected to be close to zero.

for calculation of covariance related with the estimations of these values.

Fig. 7. Simplified estimation of expanded measurement uncertainty

where:

*X1, …, Xm* are entrance value (direct measured value or other value which have an influence on measurement results);

*m* is quantity values;

*f* is functional dependence type.

Estimation of the standard measurement uncertainty *иА*(*хi*) of measurement *i*-th input values without correlation input values may be calculated by means of the following equation:

$$
\mu\_{\mathcal{A}}(\mathbf{x}\_{i}) = \sqrt{\frac{1}{n\_{i}(n\_{i}-1)} \sum\_{q=1}^{n\_{i}} \left(\mathbf{x}\_{iq} - \overline{\mathbf{x}\_{i}}\right)^{2}},
$$

where:

*iq x* is the measurement results of *i*-th input values;

$$\overline{\mathbf{x}\_i} = \frac{1}{n} \sum\_{q=1}^{n\_i} \mathbf{x}\_{iq} \quad \text{is the arithmetic median of measurement results of } i\text{-th input values.}$$

Fig. 7. Simplified estimation of expanded measurement uncertainty

( )

*iq x* is the measurement results of *i*-th input values;

*X1, …, Xm* are entrance value (direct measured value or other value which have an influence

Estimation of the standard measurement uncertainty *иА*(*хi*) of measurement *i*-th input values without correlation input values may be calculated by means of the following equation:

1

( 1)

is the arithmetic median of measurement results of *i*-th input values.

*A i iq i q i i u x x x n n*

2

,

1

*i n*

where:

where:

1

1 *i n i iq q x x n*

on measurement results); *m* is quantity values;

*f* is functional dependence type.

The overall standard uncertainty *uc* (Table 2) determined by a combination of uncertainties components; estimation of the expanded measurement uncertainty *U p* may be calculated by means of the equation from Table 2 (GUM 1993).

Statistical uncertainty in the context of GHG inventories is usually presented by giving an uncertainty range expressed in a percentage of the expected mean value of the emission. This range can be determined by calculating the "confidence limits", within which the underlying value of an uncertain quantity is thought to lie for a specified probability. The "confidence level" determines the probability, that the true value of emission is situated within the identified uncertainty range.

Determining the *t*-factor *t* (standard error that is to be estimated follows a *t*-distribution) can be done by using the Table 3.

Table 3. *t*-factors for the 95% confidence level

## **4. Uncertainty estimation with correlation values**

Necessity in the analysis of covariance and autocorrelation for the uncertainty estimates of emission foul and greenhouse gases exists. It is importantly to investigate the correlations of the estimated values relevant to emissions as in the context one estimation and the various estimations of emission foul and GHG.

If correlation exists between input values then this correlation is essential and can not be ignored. Covariance of input values may be estimated experimentally, on condition of possible the change of input correlated values (the estimation of type A covariance), or with the using of necessary data on the correlation changeability of values which relate to this measurement (the evaluation of type B covariance).

In practical cases input values often appear to be correlated, as far as the evaluation of their values is used by the same standards, measuring instruments, standard data and even method of measurement which possess peculiar uncertainty. If direct measurement results are not correlated then calculated value of covariance is expected to be close to zero.

Covariance with the estimations of two input values may be equal to zero or selected as negligible, if: these values are not correlated (values measurement are run repeatedly in various independent experiments, or they present the various estimations of values which made independently); any values may be is accepted as an constant; there is negligible data for calculation of covariance related with the estimations of these values.

Comparison of the uncertainties estimations of input values with correlation in metrological and environmental guides are driven in Table 4 (Velychko O. & Gordiyenko T., 2007b).

The Uncertainty Estimation and Use of Measurement Units

imply an expected change in the other.

*Correlation and covariance for entrance value*

the following equation:

the following equation:

1 (, ) ( ) *L i k il kl l l ux x c c u Q*

equations (GUM 1993):

*i c* are sensitivity coefficients;

*y* is estimation of measurable value *Y*; 1 *x x* ,..., *m* are input values ( *i m* 1, ).

where:

where:

are equal 1.

For correlation and covariance with type *А* using

1 (, ) 1 ( 1) ( )( ) *n i k ij i kj k j ux x n n x xx x* .

2

*il c* , *kl c* are sensitivity coefficients respectively; ( ) *u Ql* is standard uncertainty of variables *Ql* .

Uncertainties contribution ( ) *u y i* every input

values *Xi* to uncertainty *u y*( ) using the following

() ( ) *u y c ux i ii* ; 1 2 *i i* , ,..., *m yx YXix x x c*

For direct measurement all sensitivity coefficients

*Uncertainties contribution every input values and sensitivity coefficient*

,

For correlation and covariance with type *B* using

For correlation coefficient (,) *i j rx x* = 1 uncertainties contribution is:

values in metrological and environmental guides are driven in Table 5.

**Metrological guides Environmental guides**

in National Inventories of Anthropogenic Emission of Greenhouse Gas 203

, () () () ( ) ( ) *u y u y u y cux cux i j i j i i j j* ; if the estimates *i x* and *j x* are independent, (,) *i j rx x* = 0, and a change in one does not

Uncertainties aggregation arises of two various processes: aggregation of emissions one gas which complies with the law of propagation of uncertainty; aggregation of emissions bound with several gases. Into second case emission must be result in common scale, and been used for this process consists in the application of Global Warming Potentials (GWP).

Comparison of the emission sources with allowance for correlation and covariance of input

The sample covariance of paired sample

calculated using the following equation

*xi, yi, i = 1,…,n* are items in the sample;

using the following equation (GPG

*ET* is the aggregated emissions; *a* is input quantity (or parameter). Dispersion of tendency for emission two different time *E t*( ) and *Et t* ( ) with *t* using the following equation:

2 2 ( ) 2 (1 ( ))

 *E rt E* . where: *r*(∆*t*) is correlation coefficient

calculated

of random variables *X* and *Y* is

(GPG 2000, IPCC 2006): 2 1 ( )( ) *n xy i i i s x xy y*

,

*x* and *y* are sample means

Sensitivity coefficient

*n*

respectively.

 *E a T* , where:

where:

2000):

Table 5. Comparison of uncertainty contributions in metrological and environmental guides

Some variables which are necessary aggregation, do not are Gauss, large dispersion and correlated with other variables are have. In this case the application of Monte-Carlo method

Table 4. Uncertainty estimation with correlation in metrological and environmental guides

*U*

where:

Using estimation of uncertainty Rule А and use equation (GPG 2000, IPCC 2006):

11 ,

*Utotal* is percentage of uncertainty in the

*i x* , *Ui* are uncertain quantities and percentage of uncertainties associated

Not numerical estimated in GPG 2000

A value of correlation coefficient of +1 means that the variables have a perfect direct straight line relation; a value of –1 means that there is a perfect inverse straight line relation; and a value of 0 means that there is no straight line

It is defined as the covariance of the two variables divided by the product of their

relation (GPG 2000).

standard deviations.

Table 4. Uncertainty estimation with correlation in metrological and environmental guides

*xUxUxU*

22

 ... )(...)()(

21

*total xxx*

sum of the quantities;

with them, respectively.

and IPCC 2006.

2

*n*

*nn*

2 2

**Metrological guides Environmental guides**

*Entrance value is non correlated*  Using estimation of uncertainty in

where:

or

where:

accordance with the law of propagation of uncertainty and use equation (GUM 1993):

2 22 22 2 2 11 2 ( ) ( ) ( ) ... ( ), *u y cu x cu x cu x c m m*

( ) *u xi* , ( ) *u y i* are standard uncertainty input ( *i m* 1, ) and output value respectively; *y*, *i x* are estimations of measurable value *Y*

Using estimation of uncertainty in accordance with the law of propagation of uncertainty

1 1 1 ( ) ()2 (, ) *m m m c ii i j i i j i u y f x u x ux x*