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Calculating a `carbon budget' corresponding to ecological limits can be done in several ways:
1. Dynamic calculation of atmospheric concentrations profiles over time of CO2 and other greenhouse gases that would conform with all of the limits specified using a climate model or an integrated assessment model. The emissions that correspond to CO2 can either be back-calculated using a carbon cycle model, if such a model is not included in the original calculation, or a driven by the ecological constraints on the model run.
Such a calculation requires assumptions be made in relation to the emissions of non-CO2 gases and hence their role in relation to overall radiative forcing.
Whilst this method would have the advantage of sophistication in meeting the rate limits of climate change, and in capturing the response times of the climate system, it has the draw back of complexity, model dependent outcomes and the inability to test the effect of different scientific assumptions such as the climate sensitivity.
2. Static calculation of the atmospheric CO2 concentration corresponding to different temperature limits at equilibrium (or at a specified time in the future). The `carbon budget' can then be back-calculated using carbon cycle models over different time horizons of interest.
The focus here is on committed (or equilibrium) warming which is the increase in temperature once the climate system has come into equilibrium with a given increase in greenhouse gas concentrations. This is important to climate policy for several reasons:
* As a consequence of the inertia of the climate system, whilst atmospheric concentrations are increasing, the observed warming lags behind the committed warming. What this means is that at present, for example, the observed warming is only about 30-50% of the long term committed warming of the increase in greenhouse gases since pre-industrial times. Once atmospheric greenhouse gas concentrations stabilize it will take from several decades to a century for atmospheric temperature to stabilize.
- The large mass of the oceans mean that "sea-level rise will continue at a scarcely unabated rate for many centuries after concentration stabilization and/or the stabilization of global mean temperature."[128] In the case of the lower ecological targets (i.e. 1oC) the sea-level rise after stabilization may not be very large, however in nearly all other cases the sea-level rise after stabilization may be a factor or 2-3 above the rise to the point of stabilization[129].
* A a long-term temperature limit of 1oC mean that global temperature increases may exceed this before atmospheric CO2 levels decline from their peak values. A focus on long term warming commitment levels is thus essential in designing emissions policy.
The static approach to calculating the `carbon budget' has the draw back that rate limits are not driving the calculation, however it does enable easy evaluation of the effects of uncertainties in the climate sensitivity parameter, the role of other gases and in the carbon cycle models. This approach may thus underestimate the allowed carbon budget if the rate of change limits are exceeded as a consequence of delayed action or where the rate of climate change or sea-level rise are the dominant constraints on emissions over the time period of the budget calculation. Nevertheless the static approach does provide a relatively easy means of evaluating an allowed carbon budget to meet long term climate constraints.
Taking these factors into account the static system has been used in the following calculation. It involves several steps which are shown schematically in Figure 13:
* Determining the ultimate atmospheric CO2 concentration corresponding to the warming limit. This involves choosing the climate sensitivity and making assumptions as to the relative role of other greenhouse gases.
* Deciding on the carbon budget time-frame and calculating the carbon emissions that correspond within that time frame, to the warming limits. The warming limits approach adopted here is based on long term equilibrium warming commitment and the time taken to reach this limit may be greater than the time frame over which one wants to compare carbon budgets.
Each of these issues will be discussed below.
The purpose of this part of this work is to provide a simple system for estimating the cumulative carbon emissions budget to the year 2100 that would correspond to specific CO2 concentration stabilization levels. These levels themselves are the product of the ecological limit assumptions and other parameters such as the climate sensitivity and the relative role of other greenhouse gases.
Whilst in principle, having determined an atmospheric CO2 level corresponding to a set of assumptions, one could use an inverse carbon cycle model to calculate the carbon budgets this would be a cumbersome process. Instead an attempt has been made to use the IPCC carbon cycle assessment and a simple calibration technique to arrive at a simple but relatively accurate means of estimating the carbon budgets. Figure 13 Calculating the carbon budget
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For the purposes of the carbon budget calculation it is useful to review several aspects of the IPCC CO2 stabilization calculations. In 1994 the IPCC conducted a carbon cycle model intercomparison process which calculated, amongst other variables, the emissions that correspond to standards CO2 concentration profiles for 350,450, 550, 650 and 750 ppmv.[130]
* Table 17 shows that there is a large range in the estimated emission budget for each CO2 stabilization scenario. For the lower concentration scenarios the range of emissions is quite large in absolute terms relative to the overall budget. The range of the 350 ppmv scenario corresponds to an uncertainty range of plus or minus 25% from the mid-range value. This reduces to an uncertainty range of plus or minus 15% for the 450 ppmv scenario.
* The budgets for the concentration scenarios were reduced by around 7% as a consequence of the incorporation of improved scientific understanding from the 1994 to 1995 IPCC Assessments (Table 17).
* The emissions pathway can affect the overall budget. Table 18 compares the budget for the standard IPCC scenarios and the so-called delay scenarios, where action to change the path of emissions from business as usual is delayed some 5-20 years (see caption to this table for explanation). The effects of the delay scenarios is to increase the total amount of carbon emitted that can be emitted because in the models higher CO2 concentrations lead to larger rates of uptake of carbon by the oceans and the terrestrial biosphere. These effects are largest in the higher concentration cases and are negative from below 450 ppmv. However it is important to remember that delaying action could have other adverse effects, for example, increasing the rate of warming and likelihood of surprises and catastrophes. Figure 14 Fossil CO2 emissions corresponding to the IPCC stabilization scenarios
This figure shows the annual CO2 emissions calculated for the IPCC concentration profiles outlined in Figure 8. In addition the IPCC business as usual emissions scenario (IS92a) is shown. Each of the S scenarios exhibit the same general feature - after a certain period emissions decline ultimately towards a lower level than in 1990. Table 17 Carbon cycle model uncertainties
IPCC 1994 carbon cycle model budgets |
Year of Stabilisation GtC |
Min. GtC |
Average GtC |
Max. GtC |
Range GtC |
IPCC 1994 mid range estimates GtC |
IPCC 1995 mid range carbon cycle estimates GtC |
Diffe -rence GtC |
S350 |
2150 |
258 |
345 |
415 |
157 |
322 |
300 |
-22 |
S450 |
2100 |
606 |
684 |
790 |
185 |
677 |
630 |
-47 |
S550 |
2150 |
860 |
936 |
1047 |
188 |
930 |
870 |
-60 |
S650 |
2200 |
988 |
1083 |
1225 |
237 |
1104 |
1030 |
-75 |
S750 |
2250 |
1207 |
1280 |
1405 |
198 |
1282 |
1200 |
-182 |
This table shows the relative uncertainties in the carbon cycle budgets used to derive the carbon budgets corresponding to the stabilization of atmospheric concentrations of CO2. The range for the 350 ppmv scenario is from 260 to 415 GtC corresponding to fossil emissions of approximately 180-335 GtC (including 80 GtC deforestation) with a mid-range estimate of 220 GtC to the year 2100. The mid range 450 ppmv estimate for fossil emissions would be 550 GtC with a range of 440- 535 GtC. Table 18 Total anthropogenic CO2 emission budgets to 2100: delay vs. immediate action
CO2 stabilization level |
IPCC 95a Immediate action trajectory (GtC) |
IPCC95b Delay trajectory (GtC) |
Difference (GtC) |
% of IPCC95a |
450 ppmv |
630 |
650 |
20 |
3% |
550 ppmv |
870 |
990 |
120 |
14% |
650 ppmv |
1030 |
1190 |
160 |
16% |
750 ppmv |
1200 |
1300 |
100 |
8% |
This table shows the small but significant effects of delay scenarios for CO2 stabilization scenarios. The "delay" scenarios (IPCC95b) defer the point at which emissions are allowed to depart from the business as usual trajectory by some 5-20 years from the almost immediate departure in the standard scenarios (IPCC95a). Note that for the 450 ppmv case the budget is virtually the same for both scenarios. If one views the immediate action and delay trajectories as extrema and the likelihood of adoption of one or the other as more or less random then the trajectory uncertainty is around plus or minus 5-8% for CO2 stabilization in the range of 500-700 ppmv. For lower concentrations there is little difference in the cumulative carbon budgets.
Looking beyond 2100 Figure 15 shows the cumulative emissions for the IPCC "mid-range" carbon cycle model for each of the stabilization scenarios. Except for the 350 ppmv scenarios the cumulative CO2 emissions continue to rise beyond the moment of atmospheric stabilization, although at a much lower rate of increase. As can be inferred from this figure the carbon budget varies by the time period. Figure 16 shows explicitly the way in which the budget period varies by the time over which it is measured.
In relation to the carbon budget corresponding to specific CO2
concentration stabilization levels it is often pointed out that to a first
order estimate the ultimate concentration level determines the cumulative
carbon irrespective of the detail of the emissions over time. Whilst this is
true, Figure 16 also shows that where the time frame to stabilization is
extended over centuries (as it was in the IPCC calculations) the flow of carbon
which maintains the atmospheric CO2 at a certain level, once that
level been reached, is a significant fraction of the overall budget.
Figure 15 Cumulative carbon budget for CO2 stabilization
scenarios
This
figure shows the cumulative emissions that correspond to the IPCC stabilization
scenarios for the period 2000-2350. The black markers show the point at which
atmospheric CO2 is stabilized under each of the scenarios.
In summary, there are quite significant uncertainties in calculating the carbon emissions corresponding to a particular concentration of CO2 deriving from incomplete knowledge of the carbon cycle and other model uncertainties and from incomplete knowledge of the future. Recognised uncertainties are likely to be in the range of plus or minus 25% in the lower concentration range and plus or minus 15% in the mid to higher concentration range over a fixed budgeting period.
In addition the time frame of the integration clearly affects the volume of carbon that can be emitted and still maintain a given atmospheric concentration of CO2. This is particularly relevant limitation on the use of the IPCC stabilization scenarios budgets to 2100 as basis for calculating the carbon budgets to the year 2100 corresponding to arbitrary CO2 concentrations. For all except the 450 ppmv scenario the specified concentration pathway does not coincide in 2100 with the final atmospheric CO2 levels. The implications of this will be outlined in the following section.
The purpose of this exercise is to provide a means of calculating cumulative carbon budget to the year 2100 which would correspond closely with prescribed long term temperature limits. Figure 16 shows the results of several different ways of correlating a carbon budget with an atmospheric CO2 concentration over different time frames and using different methods:
1. Integrated carbon emissions for IPCC CO2 stabilization scenarios to 2250.
This curve is drawn from the IPCC atmospheric CO2 stabilization exercise with the integration period ending in the year in which the 750 ppmv stabilization scenario reaches its maximum concentration. As consequence it overstates the amount of carbon required to raise the atmospheric CO2 concentration to levels below 750 ppmv.
2 Integrated carbon emissions for the IPCC CO2 stabilization scenarios to 2100.
These two curves (2a,b) are drawn from the IPCC atmospheric CO2 stabilization exercise and correspond to the data presented in the 1994 and 1995 IPCC reports as the budget to the year 2100. The only IPCC CO2 stabilization scenario, however, which actually stabilizes CO2 in 2100 is the 450 ppmv scenario. Above this level the CO2 concentrations are assumed not to stabilize until much later (see Table 17) and below this for the 350 ppmv scenario. not until 2150. In other words the IPCC budgets to 2100 do not actually produce, in the year 2100, the long term CO2 stabilization levels that correspond to the long term temperature target.
3. Integrated emissions against actual concentration in 2100.
This curve is based on the calculated concentrations in the year 2100 for a set of relatively smooth emissions profiles using the MAGICC model of Wigley. After 2100 sharp emission reductions would be needed in the case of the higher concentrations in order for atmospheric CO2 levels to be stabilized at the concentrations prevailing in that year. As a consequence the emissions budgets are higher than for 2 above but much lower than for the longer integration periods. The gap between this curve and the higher curves of 1 and 4 is a measure of the budget timeframe effects beyond 2100. Table 19 tabulates the data from which this is drawn and shows that for the 450-750 ppmv scenarios the budget is approximately 50% higher for the 2250 integration than for this method.
For the lower concentrations (close to current the current concentration +/-25 ppmv), which would correspond to strong environmental targets and to a higher climate sensitivity, estimating the carbon budget is more problematic. The dependence on time path is quite critical to the overall budget size. If for example all emissions ceased in the year 2000, the CO2 concentration would be around 315 ppmv in 2100 for a total budget of around 80 GtC. In other words stabilization of atmospheric CO2 at levels that would limit long term warming to one degree or so could not feasibly occur until sometime in the 22nd century. Hence the IPCC concentration profile and emission budget for low (i.e. 350 ppmv) CO2 concentration will be more appropriate for estimating the realistic carbon budget for strong environmental targets.
4. Integrated carbon emissions for IPCC CO2 stabilization scenarios to the year of atmospheric stabilization.
This curve is included for illustrative purposes. It shows that the cumulative emissions to the year of stabilization for each of the scenarios rises gradually to meet the curve for integrated emissions to 2250. Cumulative emissions diverge from the curve for integrated emissions against actual concentrations from above 450 ppmv because the IPCC scenarios specify stabilization at 550 ppmv and above later than 2100. The divergence of this curve from the integrated emissions against actual concentration curve is a measure of the effect of the time frame for stabilization on the budget. Table 19 Cumulative carbon emissions by scenario
Stabilization level ppmv |
1. Year 2250 |
2a Year 2100 - IPCC 1994 |
2b Year 2100 - IPCC 1995 |
3. Year 2100 actual concentration |
350 |
324 |
322 |
300 |
277 |
450 |
978 |
677 |
630 |
676 |
550 |
1525 |
930 |
870 |
1013 |
650 |
1994 |
1104 |
1030 |
1307 |
750 |
2417 |
1282 |
1200 |
1601 |
In summary, having looked at various ways of calibrating a carbon budget for atmospheric CO2 concentrations the IPCC profile may provide the best means of doing this. The budgets correspond to relatively smooth concentration profiles and particularly when used to interpolate for low atmospheric concentrations take account of the fact that concentrations will rise above the final stabilization level before falling back to the level corresponding to the long term environmental target some time in the 22nd century. The limitations of the IPCC budgets are that they underestimate the budgets to 2100 for higher concentration levels above around 500 ppmv by 20-30%. Within the limits of the budget estimation exercise however and taking into account the environmental targets examined this is not a major limitation.
For the purposes of calculating the carbon budgets in this work the central results of the IPCC CO2 stabilization scenarios will be used as the central estimate. Figure 16 Cumulative CO2 budgets by time horizon
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This figure shows several different curves which could be used for calibrating the amount of carbon emissions (CCE) which correspond to a given atmospheric CO2 level. The top curve shows the cumulative emissions to 2250, which is the stabilization year for the 750 ppmv CO2 stabilization scenario, for a mid-range carbon cycle model. Below this is the curve for cumulative emissions to the year of stabilization in the IPCC scenarios. It can be seen that this curve gradually rises to meet the top curve, as the year of stabilization approaches the integration period for the top curve. The difference between these two curves is the carbon emissions required to sustain the concentrations from the year of stabilization to 2250. The middle curve shows the cumulative emissions corresponding to concentrations in the year 2100 calculated explicitly with the MAGICC model of Wigley which compares closely with the mid-range carbon cycle results. The calculation of this curve assumes that each of the concentration can be achieved in 2100 - the IPCC for example assumed that a return to 350 ppmv does not occur until 2150, hence the CCE corresponding to this pathway are higher. The bottom curves show the CCE to 2100 only for the same model reported by the IPCC in 1994 and 1995. These emissions correspond to the 2100 level, not the final CO2 stabilization level, which except for the 450 ppmv case does not occur until later than 2100. In other words, for all except the 450 ppmv case the CCE shown in these two curves do not produce the final concentrations against which they are plotted. Table 20 Total carbon budgets for different time horizons and calibration systems
1oC warming limit |
2oC warming limit | |||||
|---|---|---|---|---|---|---|
Climate Sensitivity |
Budget to 2100 by actual conc. ( GtC). |
IPCC stabilization profiles to 2100 ( GtC) |
IPCC stabilization profiles to 2250 ( GtC) |
Budget to 2100 by actual conc. ( GtC) |
IPCC stabilization profiles to 2100 ( GtC) |
IPCC stabilization profiles to 2250 ( GtC) |
1.5 |
510 |
481 |
682 |
1129 |
933 |
1628 |
2.0 |
365 |
361 |
445 |
832 |
722 |
1106 |
2.5 |
268 |
294 |
314 |
628 |
585 |
807 |
3.0 |
200 |
252 |
241 |
510 |
481 |
600 |
3.5 |
154 |
223 |
191 |
425 |
411 |
462 |
4.0 |
116 |
202 |
154 |
365 |
361 |
363 |
4.5 |
85 |
185 |
125 |
319 |
324 |
289 |
For the 1oC warming limit and with the climate sensitivity greater than around 3oC the calibration system used here for the carbon budget to 2250 based on the IPCC profiles produces a lower CO2 budget than to 2100 for the IPCC profile for that year. This reflects that fact that CO2 emissions need to be "negative" after 2100 to enable atmospheric CO2 levels to fall to the required level. In practice this would mean that between 2100 and 2250 there would have to be significant net afforestation. For example, the difference between the IPCC 2100 budget and the IPCC 2250 budget is around 30 GtC , which can compared with land use emission from 1765 to 1990 of around 180 GtC.
The carbon budget corresponding to a given temperature limit is critically dependent in the assumed climate sensitivity - an increase in the sensitivity from 2.5 to 3.5C reduces the budget to the year 2100 by around 30%, for example. Table 21 shows the carbon budget to the year 2100 for two different warming targets (1oC and 2oC above pre-industrial levels) for the range of IPCC climate sensitivity assumptions. As can be seen from this table and Figure 17, this budget is very sensitive to the assumed climate sensitivity parameter:
* For 1oC limit the total carbon budget is 295 GtC and 223 GtC for the 2.5oC and 3.5oC climate sensitivity values respectively. (In the main body of this report 223 GtC has been rounded up to 225 GtC).
* For a 2oC limit the budget is 585 GtC and 411 GtC for the 2.5oC and 3.5oC climate sensitivity values respectively. (In the main body of this report 411 GtC has been rounded up to 410 GtC). Table 21 Carbon Budget: Climate Targets vs. Climate Sensitivity
Climate Sensitivity (oC at equilibrium for doubling of CO2) |
Carbon Budget for 1oC climate target |
Carbon Budget for 2oC climate target |
||
Total Fossil and Deforestation emissions GtC |
Fossil emissions GtC |
Total Fossil and Deforestation emissions GtC |
Fossil emissions GtC | |
1.5 |
481 |
399 |
933 |
851 |
2.0 |
361 |
280 |
722 |
640 |
2.5 |
295 |
213 |
585 |
503 |
3.0 |
253 |
171 |
481 |
399 |
3.5 |
223 |
142 |
411 |
330 |
4.0 |
202 |
120 |
361 |
280 |
4.5 |
186 |
104 |
324 |
242 |
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This table shows the relationship between climate sensitivity and the carbon budget for two temperature targets. The carbon emissions due to deforestation over period to 1991-2100 are those assumed by IPCC 1994.
To look at the uncertainties in the carbon budget due to the uncertain nature of the climate sensitivity parameter it is useful to consider a sensitivity range of 2.5-3.5oC with central estimate of 3oC. For the 1oC target the uncertainty introduced into the budget of 0.5oC uncertainty in the climate sensitivity is around 15% and for the 2oC target around 20%. Figure 17 Sensitivity of carbon budget to temperature and climate sensitivity
Throughout this work a climate sensitivity of 3.5oC will be used for the calculation of the central estimates of the carbon budgets.
Other greenhouse gases (Methane, nitrous oxide, HFCs and PFCs) add significantly to the greenhouse effect. Inclusion of their contribution reduces the amount of carbon that can be emitted to meet any given warming limit when compared to a CO2 only situation.
For a given set of scientific assumptions a specific CO2 equivalent concentration limit corresponds to a long term equilibrium warming limit. If CO2 were the only gas then CO2 could be emitted until the actual CO2 concentration equalled the CO2 equivalent concentration corresponding to the warming limit. If other greenhouse gases are important then their contribution, in CO2 equivalent concentration, will need to be deducted from the CO2 equivalent concentration limit to arrive at the maximum actual CO2 concentration corresponding to the temperature limit.
In 1990 the effects of the other greenhouse gases, excluding aerosols, amounted to 70% of the direct radiative forcing due to the increase in CO2 278 ppmv in pre-industrial times to 355 ppmv[131]. When the effects of aerosols are included the net effect is negative, offsetting 14% of the CO2 only forcing.
The IPCC 1992 emission scenarios to 2100 explicitly included estimates for the emissions of non- CO2 greenhouse gases. For the IS92a scenario, excluding the effects of aerosols, the radiative forcing in 2100 of other greenhouse gases is 46% of the CO2 only forcing[132]. Under the same scenario if aerosol emissions are held constant at 1990 levels the net radiative effect of the other reduces to 24%.
In the case of the CO2 stabilization scenarios however, emissions of other gases were not estimated. Hence efforts to account for these have usually been based on assuming that these gases add radiative forcing equivalent to an arbitrary fraction of that produced by CO2 alone. Wigley for example has assumed a ratio of 23%[133] closely based apparently on the ratio for the IS92a scenarios in 2100 assuming that aerosol emissions do not increase. Whilst this is lower than the direct forcing ratio from IS92a it is not unreasonable given that efforts to stabilize CO2 concentrations will most likely be associated with strong action on the other greenhouse gases as well. Nevertheless, when one considers that under CO2 stabilization policies SO2 will also be reduced it is apparent that Wigley's assumption may be too low.
In order to better understand this relationship Table 22 shows some examples of the effect of other greenhouse gases on the actual CO2 concentration calculated for a 1 and 2 degree temperature limit. There is a small but significant influence of the assumptions made in relation to the levels of other greenhouse gases.
7.4.1.1.1.1.1.1.1 Table 22 Non-CO2 greenhouse gases and actual CO2 levels
Total radiative forcing as % of CO2 |
100% CO2 only |
110% |
123% |
133% |
150% |
1oC limit - 3.5oC sensitivity |
339 |
333 |
327 |
323 |
317 |
1oC limit - 2.5oC sensitivity |
367 |
358 |
348 |
342 |
334 |
2oC limit - 3.5oC sensitivity |
413 |
398 |
384 |
374 |
362 |
2oC limit - 2.5oC sensitivity |
484 |
460 |
436 |
422 |
402 |
This table shows the effects of other gases on the actual CO2 concentration level corresponding to different warming targets and climate sensitivity values. The percentage of total radiative forcing is relative to CO2 only, hence the second column shows the equivalent CO2 level (i.e. as though CO2 were the only gas) corresponding to the temperature and climate sensitivity in the first column. The column headed 123% is level used by Wigley (1995).
Assuming that policies aimed at stabilization of CO2 concentrations would also address the other greenhouse gases it would be reasonable to estimate that a range of forcing ratios for the other greenhouse gases would be 10-33% using the 23% as a midpoint. From Table 23 it can be seen that this introduces an uncertainty into the carbon budget calculation of around plus or minus 10%. Table 23 Effects of other greenhouse gases on the carbon budget
Total radiative forcing as % of CO2 |
100% |
110% |
123% |
133% |
150% |
1oC limit - 3.5oC sensitivity |
264 |
244 |
223 |
210 |
193 |
1oC limit - 2.5oC sensitivity |
356 |
325 |
294 |
275 |
249 |
2oC limit - 3.5oC sensitivity |
508 |
460 |
411 |
381 |
340 |
2oC limit - 2.5oC sensitivity |
712 |
655 |
585 |
537 |
473 |
This figure shows the effect on the carbon budget of different assumptions in relation to other trace gases. For example under the 1oC limit with a climate sensitivity of 3.5oC the budget ranges from 264 GtC for no other trace gases to 193 GtC if other trace gases contribute a radiative forcing equivalent to 50% of that of CO2. The higher the temperature limit and the lower the climate sensitivity the larger is the effect of other gases on the budget. If the radiative forcing ratio of 123% is assumed to be the central estimate then an uncertainty of +/- 10% in this corresponds to a budget uncertainty of around 7-9%.
For the purposes of this work the relative contribution of greenhouse gases will be assumed to be 23%. It should be borne in mind however that this is at the low end of reasonable assumptions. A higher contribution would reduce the allowed carbon budget corresponding to a given target.
[128] IPCC SAR WG I Chapter 7.
[129] Wigley (1995) op.cit.
[130] Enting et.al. (1994) op.cit.
[131 ]Calculated from data in Kattenburg (1996) op.cit.
[132] See Table 6.4 of Kattenburg et al (1996) op.cit.
[133] Wigley (1995) op.cit.
