of preparatory signal analysis techniques

Our study is a preparatory exercise. We focus on the analysis of uncertainty in greenhouse gas emission inventories. lnventory uncertainty is monitored, but not regulated, under the Kyoto Protocol. For most countries under the Protocol the agreed emission changes are of the same order of magnitude as the uncertainty thai underlies their combined (carbon dioxide-CO 2 equivalent) emissions estimates. We compare six available techniques to analyze the uncertainty in the emission changes that countries agreed to realize by a specified point in time. Any such technique, if implemented, could 'make or break' claims of compliance, especially in cases where countries claim fulfillment of their commitments to reduce or limit emissions. The techniques all perform differently and can thus have a different impact on the design and execution of emission control policies. A thorough comparison of the techniques has not yet been made but is urgently needed to expand the discussion on how to go about dealing with uncertainty under the Kyoto Protocol and its successor.


Introduction
The focus of our study is on the analysis of uncertainty in greenhouse gas (GHG) ernission inventories.lnventory uncertainty is monitored , but not regulated, under the Kyoto Protocol (KP).The aim of our study is to provide a preparatory guide for dealing with uncertainty in the (post-) Kyoto policy process.We cornpare available techniques to analyze uncertain emission changes (alsocalled emission signals) that countries agreed to realize by a specified point in time (com111it111ent year/period).A thorough comparison of the techniques has not yet been made available.Even worse: although highly needed, techniques to analyze uncertain emission signals from various points of view, ranging from signal quality (defined adjustments, statistical significance, detectability, etc.) to the way uncertainty is addressed (trend uncertainty or lota! unce11ainty) are not in place.For most Parties to the Protocol (Annex B countries) the agreed emission changes are of the same order of magnitude as the uncertainty that underlies their combined (COzequivalent) emissions estimates (see Table I).Any such technique, if implemented, could ' make or break ' claims of compliance, especially in cases when countries claim fulfillment oftheir commitments to reduce or limit emissions.
Moreover, as demonstrated by Jonas el al. (2004b, c), Bun andJonas (2006), andHama! andJonas (2008a, b ), these techniques could also be u sed to serve monitoring purposes.Emission changes since 1990 (base year of most Annex B countries) thai are reported annually can be evaluated in an emissions change-versus-uncertainty context rather than an emissions change-only context.This advanced monitoring service is also not provided under the Protocol.1 Jonas el al. (2004a) distinguish between preparatory si gnał ana lysis, m id way signal analysis, and signal analysis in retrospect.Preparatory signal analysis is most advanced.lt allows generating useful information beforehand as to how great unce1tainties can be depending on the level of confidence of the emission signal, or the signal one wishes to detect, and the risk one is willing to tolerate in nor meeting an agreed emission limitation or reduction co111111it111ent.We are aware of at least six different preparatory signal analysis techniques, some of which have been presented at the I s ' International Workshop on Uncertainty in GJ-IG lnventories (Gillenwater el al., 2007; Jonas and Nilsson, 2007;  Nahorski et al., 2007).These techniques need to be scrutinized further, now in a comparative mode, before a discussion on which of them to select can take place.These techniques all agree that uncertainty analysis is a key component of GJ-IG emission analysis.1-!owever, they all perform differently and thus can have a different i111pact on the design and execution of e111ission control policies.Going through this comparative exercise and making this knowledge available is a legacy of the I" International Workshop on Uncertainty in GI-IG lnventories held 2004 in Warsaw, Poland.This exercise is required prior to advancing the discussion on how to go about dealing with uncettainty under the Kyoto Protocol and its successor.
This comparison is technical by nature.We provide necessary definitions and agreements in ' Secdon 2 and an overview of the techniques in Section 3. In Section _:4 we describe each technique in a standardized fashion.J-lowever, mathematical details to and numerical results for all techni~ues are available at: http://www.iiasa.ac.at/Research/FOR/ unc prep.htmI.-Wesummarize our findings in Section 5.

Definitions and Agreements
Spali al foc11s: Ann ex B countries to the Kyoto Protocol (FCCC, 1998).
Tempora/ foc11s: Base year ( t, )-com111it111ent year/period ( 1 2 ) ; we use the year 20 l O as co111mit111ent year with t 2 referring to the te111poral average in net e111issions over the commitment period 2008-2012.
Themaric focus: Emissions and/or re111ovals of the s1x Kyoto GI-IGs, individually or co111bined (FCCC, 1998: Annex A).Grouping of countries: For convenience, the Protocol's Annex B countries are grouped according to their (i) emission limitation or reduction commitments, and (ii) base years (see left side ofTable I).

Uncertainty (i11vento1y dejinition):
A generał and imprecise term which refers to the Jack of certainty (in inventory components) resulting from any causal factor such as unidentified sources and sin ks, lack of transparency, etc. (Pen man et al., 2000: A3. l 9).

Total and trend uncertainty:
The total (or level) uncertainty reflects our real diagnostic emissions accounting capabililies, that is, the uncertainty that underlies our past (base year) as well as our current accounting and that we will have to cope with in reality at some time in the future (commitment year/period).The trend uncertainty reflects the uncertainty of the difference in net emissions between two years (base year and/or commitment year/period) (Jonas and Nilsson, 2007: Section 4).

Conjidence interval:
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.The confidence interval (CI) is a range that encloses the true value ofthis unknown fixed quantity with a specified confidence (probability).Typically, a Cl of95% is used in GHG inventories (IPCC, 2006: Section 3.1.3).

Relative uncertainty (of i11vent01y sources and sinks):
To make all preparatory signal analysis techniques easily applicable, we build on relevant findings of earlier studies which suggest resolving relative uncertainty of inventory sources and sinks only in terms of intervals or classes and referring to their medians.Our definition of relative uncertainty classes (Class I: 0-5%; Class 2: 5-10%; Class 3: I 0---20%; Class 4: 20-40%; and Class 5: >40%) is arbitrary but appears robust.For further details we refer the reader to Jonas and Nilsson (2007: Section 2.4).

CRU Concept
Starting Point: Annex B countries comply with their emission limitation or reduction commitments under the Kyoto Protocol.
Assumptions: (I) The relative uncertainty (p) of a country's net emissions (x) shall be symmetrical and not change over time, i.e., r, = r 2 (:= r ). 4 (2) The absolute change in net e1111ss1ons shall outstrip absolute uncertainty (E) at t2, i.e., Jx, -x 2 J> e 2 .1.13)-it can be stated that this value appears difficult to achieve for quite a few, especially data poor, Annex B countries.
The CRU concept exhibits a dissimilarity between emission limitation ( t;:p < O) and reduction ( t;:P > O).In the case of increasingly stricter Kyoto emission targets, Annex B countries committed to emission limitation must decrease their uncertainties according to this concept; their CR Us decrease ( dKP decreases).In contras!, countries committed to emission reduction do not need to do so; their uncertainties can even increase because their CR Us also increase and can be met more easily ( dKP increases).The opposite is true in the case of increasingly more lenient Kyoto emission targets.Annex B countries committed to emission reduction must decrease their uncertainties in order to satisfy decreasing CRUs ( ~P decreases), while countries committed to emission limitation can even increase their uncertainties because their CRUs also increase and can be met more easily ( dKP increases).
According to this concept the stabilized emissions case ( ~P = O ) should not be allowed-it presupposes zero uncertainty-unless it is ascertained beforehand that relative uncertainties are, or can be expected to be, at least small.

VT Concept
Starting Point: Annex B countries comply with their emission Iimitation or reduction commitments under the Kyoto Protocol.
Assumptions: (I) The relative uncertainty (p) of a country's net emissions (x) shall be symmetrical and not change over time, i.e., r 1 = r 2 (:= r ). (

The answer is given by
where ót is the VT and tł -t 1 the time between base year and commitment year/period, upon which the VT is normalized.
For the numerical result see [!! §!ę,ill,;ili;of the supporting mathematical details available at: http:/ /www.iiasa.ac.at/Research/FOR/unc _prep.html).Moreover, the VT concept corroborates the dissimilarity between emission limitation and reduction, which has already been found for the CRU concept and which is a direct consequence of not demanding a uniform dKr for all countries under the Protocol.While both the VT concept and the CRU concept favor stricter over more lenient Kyoto emission targets in the case of emission reduction ( dKr > O), this is not so in the case of emission limitation ( dKr < O): the two concepts favor more lenient over stricter Kyoto emission targers, which is not in line with the spirit of the Kyoto Protocol.

Und Concept
Storting Point: Annex B countries comply with their emission limitation or reduction commitments under the Kyoto Protocol.
Assumptions: (I) Uncertainties at 1 1 and t, are given in the form of intervals, which take inio account thai a difference (E) might exist between the true (t) but unknown net emissions ( x,) and their best estimates (x).
(2) The relative uncertainty (p) of a country's net emissions is symmetrical and does not change over time, i.e., r, = r, (= r ).

Question:
Approach: Answer: Taking inio account the combined uncertainty at 1 2 and considering chat the true emissions are not known, how much undershooting (Und) is required to limit the risk a that countries overshoot their true emission limitation or reduction commitments?
Quasi-statistical, based on interval calculus (see Figure 3 and Appendix C of the supporting mathematical de tai Is available at: http:!/www.iiasa.ac.at/Research/FOR/unc _prep.html).

Preparatory Signal Analysis Teclmiques
Jonas et al.

Result:
where v approximates (first-order approach) the net (effective) correlation between E 1 and E 2 ; and d'" 00 is the countries' modified (mod) emission limitation or reduction targets defined via and the undershooting U via For the numerical result see  1.13). 7 The table shows that the Und concept is difficult to justify politically in the context of the Kyoto Protocol.Under the Protocol, nonuniform emission limitation or reduction commitments (see dKr values in the second column) were determined 'off the cuff, mean ing that they were deri ved via horse-trading and not resulting from rigorous scientific considerations.The outcome is discouraging.Varying dK P while keeping the relative uncertainty p and the risk u constant exhibits that Annex B countries that must comply with a smaller d KP (they exhibit a small 0:,, 00 ) are better off than countries that must comply with a greater dKr (they exhibit a great0: 000 ). (See, e.g., c( 100 values for p = 7.5% and u= 0.3.)The choice of oKr dominates Equation C-15, while the influence of oKr on U (see Equation C-18) is negligible and does not compensate for agreed deviations in the oKP values.Such a si tuation is not in line with the spirit of the Kyoto Protocol.This situation would be different if the nonunifonnity of the emission limitation or reduction commitments is the outcome of a rigorously ba sed process resulting in a straightforward rul e that applies equally to all countries, as it would be the case, for instance, under the widely discussed contraction and convergence (C&C) approach (e.g. , WBGU, 2003: Section 2.3;Pearce, 2003).Linder such conditions, it would be the undershooting U that matters, not the modified emission limitation or reduction target l~11ut.l•

Und&VT Concepts Combined
Starting Point: Annex B countries comply with their emission limitation or reduction commitments under the Kyoto Protocol.Assumptions: (l) Uncertainties at 1 1 and 1 2 are given in the form of intervals, which take into account that a difference (E) might exist between the true (t) but unknown net emissions ( x,) and their best estimates (x).
(2) The relative unce11ainty (p) of a country's net emissions is symmetrical and does not change over time, i.e., r 1 = r 1 (= r ). 8 (3) The absolute change in net emissions shall outstrip uncertainty at time t ~ 1 2 , i.e., the VT shall be equal to, or smaller than, the maximal allowable VT ( ~t ~ t 2 -t, ).
Systems View: lntra-systems view suited to supp011 inter-systems (top-down) view: Only our real diagnostic capabilities of grasping emissions at any point in time individually-reflected by absolute uncertainty E ( t) -are of interest.
Correlation of uncertainty over time does not matter.

Question:
Approach: Answer: Referring to risk as the strength of the Und concept and to time in detecting an emission signal as the strength of the VT concept, can these concepts be combined (Und&VT) to take advantage of the two?
Quasi-statistical, based on interval calculus (see Figure 4 and Appendix D of the supp011ing mathematical details available at: http:!/www .iiasa.ac.at/Research/FOR/unc _ prep.html ).
The answer comprises four cases depending on how 8"'' , the critical emission limitation or reduction , and 8,r relate to each other (see Figure 4).8";' allows distinguishing between detectable and nondetectable emission changes. 9The complete answer is given by where d,,,od is defined as before (see Equation C-15) and U via UG,r in Cases 2--4 is an initial obligatory undershooting, which is introduced to ensure that detectability is given before Annex B countries are permitted to make economic use of potentia!excess emission reductions.
For the numerical result see  However, this concept reveals a crucial difficulty from a political perspective.The Und&VT concept requires the Protocol's Kyoto emission targets to be corrected for nondetectability through the introduction of an initial obligatory undershooting (UG,,) so thai the countries' emission reductions, not limitations, become detectable (i.e., meet the maximal allowable VT) before the countries are permitted to make economic use of their excess emission reductions.(See, e.g., group I countries in T_ able D-3. ( oK,, = 8%) under Case 2 conditions: the cl,"°" value for p = 15% and a= 0.5 is cl,"°" = dKr + UG,,, = 13% (U= UG,,); that is, the initial obligatory undershooting is UG,, = 13%-8% = 5% .)lt remains to be seen whether this strict interpretation of signal detection will be accepted by Annex B countries as it forces them to strive for detectability (i.e., to make initial investments before they can profit from their economic actions).Notwithstanding, opponents to this concept must realize that the countries' detectability, i.e.: the 'x,.,greater-than-(1-d,r )x,,,' risk (Case I), the 'x,_, -greater-than-(1-d,"' )x, _ , ' risk (Case 2), the ' x,_ 2 -greater-than-(1 + d,n, )x,_ 1 ' risk (Case 3), and the ' x,., -greater-than-(t-(d""-2d,n,))x,_ 1 ' risk (Case 4) of their emission signals can be grasped-and thus priced-although the countries' true net emissions at t, and t 2 are unknown!

GSC #1 Concept
Starting Point: Annex B countries comply with their emiss ion limitation or reduction commitments under the Kyoto Protocol. 11 Assumptions: (I) It is accepted a priori that the true, but unknown, net emissions at t 2 ( x,_ 2 ) can exceed (overshoot) the target emissions commitment ( x 2 ) by some fractional or percentage amount (por p%, respectively).
(2) The relative uncettainty (p) of a country's net emissions is symmetrical and does not change over time, i.e., r, = r, (= r ). 12   (3) The probability distributions for estimated emissions are nonnal and the shape of the emissions probability distribution for each country does not change significantly as emissions change. Preparatory Systems View: lntra-systems view suited to support inter-systems (top-down) view: Only aur real diagnostic capabilities of grasping emissions at any point in time individually-reflected by absolute unce11ainty e(t) -are of interes!.
Correlation of uncertainty over time does not matter.

Question:
~----A~fiproach: _ Figure 5 _ Answer: Result: Can we attain a reasonable level of confidence that countries will have actually achieved the target emissions levels stated in their commitments under the Kyoto Protocol and are in compliance?Thai is: I) Would we consider il acceptable if true emissions will exceed ( overshoot) the target emissions commitment by some fractional or percentage amount?2) How much is thai amount?3) How confident do we want to be in our result?
Statistical (see tfa'µfjfj and fil_pe J@Jc J:Ę;ofthe For the numerical result see [.i!J!lel._Ęillof the supporting mathematical details available at: http://www.iiasa.ac.at/Research/FOR/unc prep.html. Table E-1 lists adjustment (Adj) values as a result of applying Equation E-7 (Case I) , Equation E-8 (Case 2) and Equation E-9 (Case 3).p is treated as parameter as well as the confidence FN or (1 -a) that true emissions do not exceed (overshoot) target emissions by more than p = I\,,, (Cases I and 2) and p = O (Case 3); (i-a) is specified to be 0.9, 0.7 and 0.5.The table shows that the GSC #1 concept is not easy to handle politically in the context of the Kyoto Protocol.Emission reduction (SKr >0) under the GSC #1 concept behaves mirror-inverted to the Und concept as a consequence of nonuniform emission reduction commitments: Varying d'" while keeping the relative uncertainty p and the confidence (1-a.)constant exhibits that Annex B countries thai musi comply with a great dKP (they exhibit a small Adj) are better off than countries that must comply with a small dKP (they exhibit a great Adj). (See, e.g., Adj values for p = 15% and I-a= 0.9 .)However, this is only true if adjustments musi be compensated for by additional emission reductions (undershooting mode) and are not misused by policy and decision-makers to only establish a country comparison in terms of confidence (confidence mode).Then countries that musi comply with a small dKP (they exhibit a great Adj) are better off than countries that must comply with a great dKP (they exhibit a small Adj).This situation would not be in line with the spirit of the Kyoto Protocol.

GSC #2 Concept
Storting Point: Annex B countries comply with their emission limitation or reduction commitments under the Kyoto Protocol. 11 Assumptions: (I) lt is accepted a priori that true emiss ion reductions (increases) fali below (above) the committed level of reductions (increases) by some fractional or percentage amount (por po/o, respectively).
(2) The relative uncertainty (p) of a country's net emissions is symmetrical and does not change over time, i.e., r 1 = ,., (= r ).
(3) The probability distributions for estimated emissions and emission changes are normal and the shape of the emissions and emissions change probability distributions for each country do not change significantly as emissions change.
Systems View: lntra-systems view: Correlation of uncertainty over time matters.

Question:
Can we attain a reasonable level of confidence that countries will have actually achieved the emission changes, measured relative to base-year emissions, stated in their commitments under the Kyoto Protocol and are in compliance?Thai is: I) Would we consider it acceptable if true emission reductions (increases) will fali below (above) the committed level of reductions (increases) by some fractional or percentage amount?
Preparatory Signal Analysis Techniques Jonas et al.
~----A~:proach: _ Figure 6 J Answer: 2) How much is thai amount?3) How confident do we want to be in our result?Cases 3 and 4).6Kr, p and p"'' are treated as parameters, as well as the contidence FN or (1 -a) that true emission reductions (increases) will not fali below (above) the committed level of reductions (increases) by more than p =O.I (Cases I and 2) and p = O (Cases 3 and 4); (1-a) is specified to be 0.9, 0.7 and 0.5.The correlation v is 0.75 (as in Appendix c. of the supporting mathematical details available at: http://www.iiasa.ac.at/Research/FOR/unc prep.html).
The table shows that the GSC #2 concept is also not easy to handle politically in the context of the Kyoto Protocol.Emission reduction (6Kr > O) under the GSC #2 concept behaves, like under the GSC # I concept, mirror-inverted to the Und concept as a consequence of nonuniform emission reduction commitments.Thai is, the GSC #2 concept would not run counter to the spirit of the Kyoto Protocol if applied in the undershooting mode (adjustments must be compensated for by additional emission reductions).But it must be mentioned that, for the given set of parameters (notably, p =O.I and v = 0.75 ), the span between smallest and greatest Adj values is negligible.

Conclusions
We have scrutinized six preparatory signal analysis techniques in a comparative mode.The purpose of this exercise is to provide a basis for discussing on how to go about dealing with uncertainty under the Kyoto Protocol and its successor, and which of the technique(s) to eventually select.The authors of these techniques all agree that uncertainty analysis is a key component of GHG emissions analysis although their perceptions range from using an investigation-focused approach to uncertainty analysis to only improve inventory quality to actually apply a technique, or a combination of techniques, to check compliance.As shown, all techniques perform differently (see Table ~) and can thus have a different impact on the design and execution of emissions control policies.However, what is more important is to realize thai a single best technique cannot yet be identitied (and will, most likely, not exist); the main reason for this being that the techniques suffer from shortfalls that are not scientitic but are related to the way the Kyoto Protocol has been designed and implemented politically.As the two most important shortfalls on the side of policy-making can be identified ( I) the overall neglect of unce1tainty confronting experts with the situation that for most Annex B countries the agreed emission changes are of the same order of magnitude as the unce1tainty that underlies their combined CO2 equivalent emissions; and (2) the introduction of nonuniform emission reduction commitments.The techniques manifest these shortfalls differently: CRU and VT These two concepts exhibit a dissimilarity between countries committed to emission reduction (stricter over more lenient Kyoto emission targets are favored) and emission limitation (more lenient over stricter Kyoto emission targets are favored).

Preparatory Signal Analysis Techniques
Jonas et al.
Und and GSC #2.Yarying c/Kr, the normalized en:1issions change committed under the Kyoto Protocol, while keeping the relative uncertainty p and the risk a constant exhibits that under the Und concept countries thai musi comply with a small dKP (they exhibit a small d,,., 0 ) are better offthan countries that 111ust comply with a great c/Kr (they exhibit a great cf,,, 00 ).Such a situation is not in line with the spirit of the Kyoto Protocol.Emission reduction under the GSC #2 concept avoids this situation if applied in the undershooting 111ode.Countries that must comply with a great cl,P (they exhibit a small Adj) are better off than countries that 111ust comply with a small dKP (they exhibit ag Adj).But it must be mentioned that, for the given set of parameters (notably, p =O.I and v = 0.75 ), the span between smallest and greatest Adj values is negligible.So far, emission reduction and emission limitation under the GSC #2 are not treated uniformly.The GSC #2 concept stil! lacks elear guidelines as to whether or not, and to what extent diminishments in, e111ission reductions shall be accepted under these two regimes.
Und& VT and GSC #1.The Und&VT overcomes situations thai run (Und concept) or can run counter to the spirit of the Kyoto Protocol (GSC # I and GSC #2 concepts if applied in the confidence 111ode).However, by requiring a priori detectable emission reductions, not limitations, the Und&YT concept corrects the Protocol's emission limitation or reduction targets for nondetectability through the introduction of an initial or obligatory undershooting so that the countries' emission signals become detectable before the countries are permitted to make economic use of their excess emission reductions.This, de facto, nullifies the politically agreed targets under the Kyoto Protocol!We do not consider this a realistic scenario.By way of contras!, the GSC # I con ce pt builds on the notion of confidence, not detectability.If applied in the undershooting mode it would not run counter to the spirit of the Kyoto Protocol.Nonetheless, it would en force additional emission reductions, which would be smaller than those under the Und&YT concept but still be considerable and thus also difficult to sell politically.So far, emission reduction and emission limitation under the GSC #1 are not treated uniformly.The GSC # I concept still lacks elear guidelines as to whether or not, and how many, excess emissions shall be accepted under these two regimes.
lt appears very probable thai the first shortfall (emission changes and uncertainty are of the same order of magnitude) will vanish soon as mankind is getting increasingly under pressure to adopt a longer-lasting perspective and to realize greater emission reductions in the mid to long-term.However, we suggest that policy-makers revisit the second shortfall.lf nonuniform, country-specific emission reduction commitments are favored, then these musi be decided on the basis of a straightforward rule thai applies equally and rigorously Io all countries and should not be determined 'off the cuff.Only then can scientists finalize their discussion and give meaningful feedback on which technique(s) to select for the preparatory analysis of uncertainty in the countries' emission changes-and which numerical advantages and disadvantages between countries we then have to accept and tolerate.
http://www.iiasa.ac.at/Research/FOR/unc_prep.html with e,, "'0.03 (typically reported), li,,, = o.os(valid for many Ann ex B countries) and e, = e, "0.075 (see right side of Table I) results in v"' O. 79. 8 The Und&VT concept only considers uncertainty in the commitment year/period, not in the base year (i.e., formally x,., = x, and v =o).However, for reasons of comparability, we continue to abide by the condition of constant relative uncertainty. 9Recalling Equation D-I of the supporting mathematical details available at: http ://1vww.iiasa.ac.at/Research/FOR/u11c prep.html,li,.,. is given by p/(1 +p) in the case li" >0 (emission reduction) and -p/(t -p) in the case li" so (emission limitation).
10 Moreover, by employing a uniform detectability criterion the Und&VT concept partially rectifies (see Cases 2 and 3, the cases of nondetectability before correction) the politically unfavourable situation under the Und concept, under which countries    risk as the strength of the undershooling concept and detectability as the strength of the verification time concept.Depending on how 6.,,, and 6" relate to each other, four cases can be distinguished (see text).These differ in terms of detectability (Cases I and 4) versus nondetectability (Cases 2 and 3) and an initial obligatory undershooting U 0 , , thai is introduced (Cases 2--4) to ensure thai detectability of emission reductions, not increases, is given before Annex B countries are permitted to make economic use of potentia!excess emission reductions.Emission reduction: 8".>o; emission limitation: 8.,.:5 O. Source: Hama! and Jonas (2008b: Figure 4).Here, Case 2 is shown: Given an uncertainty of p%, lhis case requires adjusting a country's emissions es timate at t, upward if we want to be (I-a)% confident that its true emissions do not exceed its Kyoto emissions largel (here referred to as 1) by more than P.,., % .Ernission reduction: 8.,.> O ; emission limitalion: 8".:5 O.    commitment are 1990 (1995) and 92%, respectively.
3) Country Group 2: The US has indicated its intention not to ratify the Kyoto Protocol.
The US reports all its emissions with reference to 1990.However, information on 1990 in its national inventory submissions does not reflect or prejudge any decision that may be taken in relation to the use of 1995 as base year for hydroOuorocarbons (HFCs), perfluorocarbons (PFCs) and sulphur hexafluoride (SF6) in accordance with Anicie 3.8 of the Kyoto Protocol. Figure2 Figure3

Figure 3 :
Figure 3: lllustration of the undershooting concept ( p, = p, ) with the help of norma!probability density functions: Undershooting helps to limit the risk u lhat countries overshoot their true ernission limitation or reduction commitments.Source: Jonas et al. (2007: Figure 11 ); modified.

Fig u re 5
Fig u re 5: lllustralion of the Gillenwater, Sussman and Cohen # l concept ( p, = p,) with the help of the standard norma!probability density function: lt aliows specifying the confidence (1 -a) via F" that a country's true, but unknown, emissions comply with its Kyoto emissions target.Depending on whether or not excess emissions are accepted and favorable compliance conditions exist a priori, three cases are di stinguished.Here, Case 2 is shown: Given an uncertainty of p%, lhis case requires adjusting a country's emissions es timate at t, upward if we want to be (I-a)%

Figure 6 :
Figure 6: llluslration of the Gillenwater, Sussrnan and Cohen #2 concept ( p, = p,) with the help of the standard normal probability density function: lt allows specifying the confidence ( I -a) via F" that a country's true, but unknown, emissions change complies with its commitled change.Depending on whether or not diminished reductions (additional increases) are accepted and favorabie compliance conditions exist a priori, four cases are distinguished.Here, Case 2 is shown: Given an uncertainty of p%, this case requires adjusling a country 's emissions estirnale at t, upward if we want to be ( I -a)% con fi dent its true emission reduction equals at least ( I 00 -p)% of the committed reduction (here referred to as I).Emi ssion reduction: 1\,.> o; emission limitation: 6.,.:5 O.
: BE, CZ, DE, OK, EC(= EU-15; the EU-27 does not have a common Kyata target), EE, ES, FI, GR, IE, LT, LU, LV, MC, NL, PT, SE, UK.Member States of the EU•27 but without individual Kyoto targets: CY, ML.Listed in the Convention's Annex I but not included in the Protocol's Annex 8: BY and TR (BY and TR were not Parties to the Convention when the Protocol was adopted).BY requested becoming an Annex 8 country by amendment to the Kyoto Protocol at CMP 2 in 2006.BY's base years and KP

Table I Table 1 Preparatory Signal Analysis Techniques
Jonas el al.

Table 2
summarizes the major characteristics of the six preparatory signal analysis techniques thai we discuss and compare in .Section4:.These are (I) the critical relative uncertainty (CRU) concept; (2) the verification time (VT) concept; (3) the undershooting (Und) concept; (4) the undershooting and VT (Und&VT) concepts combined; (5) the adjustment of emissions (Gillenwater, Sussman and Cohen-GSC #I) concept; and (6) the adjustment of emission reductions (Gillenwater, Sussman and Cohen-GSC #2) concept.The techniques' individual characteristics are also explained in Section :4.

Table B -
1 lists normalized VTs for all Annex B countries under the Kyoto Protocol.The VT concept provides amore detailed detection perspective for negotiators of the Protocol than the CRU concept presented in ' .Sectfon :• 4,1.lt quantifies in detail what the consequences are in the form of normalized VTs if countries report emissions with relative uncertainties thai are S or> P,n,.
Table C-1 lists O: .... values as a result of applying Eąuation C-15 in combination with Equation C-18.1\r, p and a are treated as parameters, while the correlation v is 0.75 (typical for currently reported unce1tainties; see EEA 2007: Table

Table D -
3 lists cl,"°" values as a result of applying Equation C-15 in combination with: Equation D-5 (Case I), Equations D-8 to D-9 (Case 2), Equations D-12 to D-13 (Case 3), and Equations D-16 to D-18 (Case 4).oKr , p and a are treated as parameters.By employing a uniform detectability criterion, the Und&VT concept overcomes the dissimilarity of both the VT concept and the CRU concept between countries committed to emission reduction ( dKr > O) and emission limitation ( d,r L O), which arises if more lenient or stricter Kyoto emission targets are introduced (see TableA-1 and B-1). 10 (see fjgij_i,fg and ~1?.Pfu~iH!,~f the supporting mathematical details available at: http://www.iiasa.ac.at/Research/FOR/unc prep.html).For the numerical result see TableF-1 of the supporting mathematical details available at: http://www.iiasa.ac.at/Research/FOR/unc prep.html.

Table 1 :
Left: Countries included in Annex B to the Kyoto Protocol (KP) <1nd their emission limitation and reduction commitments.Emissions and/or removals of greenhouse gases (GHGs), or combinations of GHGs, classified according to their relative uncertainty ranges.The bars of the arrows indicatc the dominant uncertainty range for these emissions and removais, while the tops of the arrows point at the neighboring uncertainty ranges, which cannot be excluded but appear less frequently.LULUCF stands for the direct human-induced land use, land-use change, and forestry activities stipulated by Articles 3.3 and 3.4 under the Kyoto Protocol(FCCC, 1998).The arrows are ba.sed on the tota\ uncertainties that are reported for the Member States of theEU-25 (EEA, 2007)and the expertise available at IIASA's Forestry Program (cf.http://www.iiasa.ac.at/Research/FOR/unc bottonmp.html)and elsewhere (e.g., Watson et al., 2000: Sections 2.3.7,2.4.1;Pen man et al., 2003: Section 5.2).Source: Jonas and Nilsson (2007: Table 1 ), modified.