Controversial new climate change results
University of Bristol Press release issued 9 November 2009
New data show that the balance between the airborne and the absorbed fraction of carbon dioxide has stayed approximately constant since 1850, despite emissions of carbon dioxide having risen from about 2 billion tons a year in 1850 to 35 billion tons a year now.
This suggests that terrestrial ecosystems and the oceans have a much greater capacity to absorb CO2 than had been previously expected.
The results run contrary to a significant body of recent research which expects that the capacity of terrestrial ecosystems and the oceans to absorb CO2 should start to diminish as CO2 emissions increase, letting greenhouse gas levels skyrocket. Dr Wolfgang Knorr at the University of Bristol found that in fact the trend in the airborne fraction since 1850 has only been 0.7 ± 1.4% per decade, which is essentially zero.
The strength of the new study, published online in Geophysical Research Letters, is that it rests solely on measurements and statistical data, including historical records extracted from Antarctic ice, and does not rely on computations with complex climate models.
This work is extremely important for climate change policy, because emission targets to be negotiated at the United Nations Climate Change Conference in Copenhagen early next month have been based on projections that have a carbon free sink of already factored in. Some researchers have cautioned against this approach, pointing at evidence that suggests the sink has already started to decrease.
So is this good news for climate negotiations in Copenhagen? “Not necessarily”, says Knorr. “Like all studies of this kind, there are uncertainties in the data, so rather than relying on Nature to provide a free service, soaking up our waste carbon, we need to ascertain why the proportion being absorbed has not changed”.
Another result of the study is that emissions from deforestation might have been overestimated by between 18 and 75 per cent. This would agree with results published last week in Nature Geoscience by a team led by Guido van der Werf from VU University Amsterdam. They re-visited deforestation data and concluded that emissions have been overestimated by at least a factor of two.
###
Here is the abstract from GRL:
Several recent studies have highlighted the possibility that the oceans and terrestrial ecosystems have started losing part of their ability to sequester a large proportion of the anthropogenic CO2 emissions. This is an important claim, because so far only about 40% of those emissions have stayed in the atmosphere, which has prevented additional climate change.
This study re-examines the available atmospheric CO2 and emissions data including their uncertainties. It is shown that with those uncertainties, the trend in the airborne fraction since 1850 has been 0.7 ± 1.4% per decade, i.e. close to and not significantly different from zero. The analysis further shows that the statistical model of a constant airborne fraction agrees best with the available data if emissions from land use change are scaled down to 82% or less of their original estimates. Despite the predictions of coupled climate-carbon cycle models, no trend in the airborne fraction can be found.
Knorr, W. (2009), Is the airborne fraction of anthropogenic CO2 emissions increasing?, Geophys. Res. Lett., 36, L21710, doi:10.1029/2009GL040613.
According to Pat Michaels at World Climate Report:
Dr. Knorr carefully analyzed the record of anthropogenic CO2 emissions, atmospheric CO2 concentrations, and anthropogenic land-use changes for the past 150 years. Keeping in mind the various sources of potential errors inherent in these data, he developed several different possible solutions to fitting a trend to the airborne fraction of anthropogenic carbon dioxide emissions. In all cases, he found no significant trend (at the 95% significance level) in airborne fraction since 1850.
(Note: It is not that the total atmospheric burden of CO2 has not been increasing over time, but that of the total CO2 released into the atmosphere each year by human activities, about 45% remains in the atmosphere while the other 55% is taken up by various natural processes—and these percentages have not changed during the past 150 years)
Here is Figure 1 from the Knorr paper:
Figure 1. The annual increase in atmospheric CO2 (as determined from ice cores, thin dotted lines, and direct measurements, thin black line) has remained constantly proportional to the annual amount of CO2 released by human activities (thick black line). The proportion is about 46% (thick dotted line). (Figure source: Knorr, 2009)
The conclusion of the Knorr paper reads:
Given the importance of the [the anthropogenic CO2 airborne fraction] for the degree of future climate change, the question is how to best predict its future course. One pre-requisite is that we gain a thorough understand of why it has stayed approximately constant in the past, another that we improve our ability to detect if and when it changes. The most urgent need seems to exist for more accurate estimates of land use emissions.
Another possible approach is to add more data through the combination of many detailed regional studies such as the ones by Schuster and Watson (2007) and Le Quéré et al. (2007), or using process based models combined with data assimilation approaches (Rayner et al., 2005). If process models are used, however, they need to be carefully constructed in order to answer the question of why the AF has remained constant and not shown more pronounced decadal-scale fluctuations or a stronger secular trend.
Michaels adds:
In other words, like we have repeated over and over, if the models can’t replicate the past (for the right reasons), they can’t be relied on for producing accurate future projections. And as things now stand, the earth is responding to anthropogenic CO2 emissions in a different (and perhaps better) manner than we thought that it would.
Yet here we are, on the brink of economy crippling legislation to tackle a problem we don’t fully understand and the science is most certainly not settled on.
UPDATE: A professional email list I’m on is circulating the paper, read it here: Knorr 2009_CO2_sequestration
Sponsored IT training links:
We offer incredible 350-050 online training to help you pass HP2-E31 on first attempt. Get up to date 1z0-042 resources for guaranteed success.
John Finn (00:51:51)
although this study from Dr Knorr maintains that the airborne fraction of c02 hasn’t changed, which “runs contrary to climate models”. That implies that airborne Ac02 is 3% (or 1% per year?) whilst natural airborne c02 is still 97%. If so then most of the airborne 30% c02 increase since 1850 isn’t anthropogenic, or so it suggests, and if c0w found in ice in Antarctica is the golden standard of the global average of c02.
I’m open to counter evidence to jaworowski’s view that casts doubts on ice cores, although this study seems to confirm that he might have been right.
Perhaps Ferdinand could read through this, particularly page 736 which gives Greenland ice cores a higher concentration of c02 that corresponding time scales in Antarctica
http://suesam.files.wordpress.com/2008/01/climate-change-re-examined.pdf
Zbignew Jaworowski, MD, PhD, DSc, of the Central Laboratory for Radiation
Protection in Warsaw, Poland, has examined CO2 concentration data. Accordingto Jaworowski, until 1985 the published CO2 concentrations in air bubbles in pre-industrial ice ranged from 160–700 ppm, with an occasional spike to 2450ppm. After 1985, high readings disappeared from publications! Jaworowski gave a flagrant example of data selection from A. Neftel et al. (in Nature), who reported in 1985 that pre-industrial CO2 concentrations from a Byrd, Antarctica, ice core were 330–500 ppm (dots and bars in Figure 8). However, in 1988, also in Nature, and on the same core, only values of 290 ppm or less were reported, in agreement with the ‘‘global warming’’ hypothesis (gray areas in Figure 8)
(Jaworowski, 1997).
Jaworowski also noted that air from ice at Summit, Greenland, deposited
during the last 200 years ranged from 243–641 ppm in CO2. ‘‘Such a wide range reflects artifacts caused by sampling, or natural processes in the ice sheet, ratherthan the variations of CO2 concentrations in the atmosphere’’. G. I. Pearmanet al., in a 1986 paper in Nature, rejected 43% of the CO2 readings, 39% of the methane readings, and 43% of the nitrous oxide readings from the Law Dome,Antarctica, core because they were higher or lower than the politically correctvalues, according to Jaworowski. They decided on a value of 281 ppm for CO2in the pre-industrial period. Air bubbles in a drilling core from 6000-year-old icefrom Camp Century, Greenland, showed a CO2 concentration of 420 ppm, while it was 270 ppm in a supposedly 6000-year-old ice core from Byrd, Antarctica.
it only raises the question as to whether c02 from Antarctic ice cores are the most accurate record of c02 globally over 600,000 years
Ferdinand i’m looking through the siple dome data. It show a recovery from the LIA, or else the beginning of AGW depending on how you see it. However, Between 1935 and 1945 the atmospheric carbon dioxide concentration was constant, or even declined slightly, for reasons unknown. The modern record doesn’t seem to follow a straight curve with fossil fuel emissions
http://www.pnas.org/content/94/16/8343.full.pdf
Ferdinand-
I found this helpful. But the Knorr paper found that the proportion of incremental CO2 removed (not exchanged) by natural processes has been 55% in each year.
So, in your example, 55GtC will go in year 2 as a result of reduced outgassing in the tropics and hungry sinks at the poles. The remaining pink 45GtC will presumably decay at your calculated rate of 4GtC per annum (or does that vary?) giving a half life of about 18 years.
Ferdinand
“But what happens to the total amount of (partially colored) CO2? The exchanges of CO2 between atmosphere and oceans(/vegetation) don’t change the amounts in the atmosphere, as long as the inputs and outputs are equal. ”
this assumes a static input output flow chart. Since you’ve studied ice core’s yourself, the trend shows erratic spikes and dips of c02 over short to long time scales – which doesn’t appear static aerial equilibrium at any time period..
could not sea surface temperatures have something to do with how much c02 can be measured in the atmosphere, and in this respect, is it possible that Antarctica at -40C in ice only shows a regional magnitude?
maksimovich: Have you actually read what I said about Le Quéré? I don’t understand why you’re going on about it. I am saying and have been saying the whole time that Knorr’s results are not at all surprising or controversial (even though it might have some flaws), because nobody thought the AF was changing much over the time period 1850-2000. The only reason I list Le Quéré is to show an example of a paper where they saw hints of ocean uptake reducing in the last decade – to emphasize the fact that AF is expected to increase in the future, not in past as studied by Knorr. Observations (Le Quéré, one or two others) of a less effective ocean sink are preliminary, uncertain, disputed, and applicable only the the last few years, not 1950 or 1960. That you continue to dispute Le Quéré doesn’t detract from my point; it actually helps make it.
The only thing that Knorr does is suggest a different method and slightly different results from Canadell (2007). That isn’t controversial, nor a bombshell. Maybe Canadell will follow up. Maybe not. It’s possible that Knorr’s analysis wasn’t the best, and there might be some very slight trend there. But it’d be very slight, and essentially insignificant, as Canadell originally found anyway.
P Wilson (04:03:48) :
This is worth a read reference removed peaks and troughs from CO2 data:
http://rabett.blogspot.com/2009/10/ian-plimer-is-con-artist-one-of.html
From NOAA:
“Anybody, including Plimer, can download the actual measurement records, complete, warts and all, from our web site http://www.esrl.noaa.gov/gmd/ccgg/iadv/, or http://www.esrl.noaa.gov/gmd/ccgg/trends/ by clicking on the appropriate places. To illustrate how misleading Plimer is I made a plot of 3 years of all hourly data, with 2004 in the middle because Plimer discussed 2004. I have also attached a description of our MLO measurements, which Plimer and anybody else can download from the second web page mentioned above. In the plot, “selected” data means that we have used it in constructing the published monthly mean because those hours satisfy the conditions for “background” measurements. The red stripes are extremely close to the published monthly means. The published data has another step, first from hourly to daily averages, then to monthly, which I did not do here. Also plotted in purple-blue are all non-background data. If one constructs monthly means from ALL data, incl. non-background, one obtains the purple-blue stripes. The differences are only slight, with the seasonal cycle becoming a bit larger due to upslope winds, esp. during the summer.”
The NOAA plot:
http://www.imageuploading.net/image/thumbs/large/plimer-379.jpg
From this it is very obvious that measuring CO2 is currently fraught with problems – wind direction/industrial pollution/measuring errors.
Trying to do this on a few microlitres of gas in a fragile container (ice) must be an order of magnitude more difficult. There will be errors – these need weeding out of published data or the uneducated masses will get confused.
Ferdinand: Good idea to color-label the molecules in the illustration. By tracking the individual molecules that way, people should see that they shouldn’t be fixated on those individual molecules.
As it happens, as you know (from looking at your website), the molecules actually are coded, to an extent, by isotopes. But introducing that data here might only confuse.
Also, Ferdinand: a gentle correction: You keep saying the half-life of the accumulation is some 40 years, not the hundreds used by the IPCC. Again, I’d advise you to double check what they actually say. Here is the exact wording of the IPCC:
“Consistent with the response function to a CO2 pulse from the Bern Carbon Cycle Model (see footnote (a) of Table 2.14), about 50% of an increase in atmospheric CO2 will be removed within 30 years, a further 30% will be removed within a few centuries and the remaining 20% may remain in
the atmosphere for many thousands of years (Prentice et al., 2001; Archer, 2005; see also Sections 7.3.4.2 and 10.4)”
They agree with you on the half life. To see about the longer persistence, I’d refer you to Archer (2005).
Given that the anthropic proportion is only 3% or so, can anybody say what is causing the relatively enormous natural CO2 interchange between the oceans and the atmosphere? And why should it be so exactly repeatable on a year-on-year basis that the 3% of Anthropic CO2 can be measured?
Is it mainly the local changes in the partial pressure of CO2 that cause the interchange? Could it be the action of wind and waves? Of sun-tides and moon-tides? Or the Weather?
BTW that hissing sound from the surf, and from ship’s wakes: could it be the sound of escaping CO2? Has anybody analysed the gas-composition of sea foam?
P Wilson (04:03:48) :
John Finn (00:51:51)
although this study from Dr Knorr maintains that the airborne fraction of c02 hasn’t changed, which “runs contrary to climate models”. That implies that airborne Ac02 is 3% (or 1% per year?) whilst natural airborne c02 is still 97%. If so then most of the airborne 30% c02 increase since 1850 isn’t anthropogenic, or so it suggests, and if c0w found in ice in Antarctica is the golden standard of the global average of c02.
Did you read what I wrote. I think you’re getting confused with percentages. Why are you segegating natural and human CO2. There are natural emissions and human emissions which together make up TOTAL emissions. Then there are absorptions. Currently the TOTAL emsiions are exceeding the absorptions.
In the past
Total Emissions = Natural Emissions and
Total Emissions = Absorptions -> stable CO2 concentrations
Since ~1850 Total Emissions have increased because
Total Emissions = Natural + Human so now we have
Total Emissions > Absorptions -> CO2 goes up.
It just happens to be going up by an amount that is equivalent to 45% of the human emissions.
If we’re going to clarify this, you might need to explain you’re thinking because there appears to be something you don’t quite grasp.
simply because you have to separate the fluxes of natural from anthropogenic, natural being mainly sea exchanges, where seas contain 1000gt at the surface. It seems natural to me that we cannot measure how much c02 air exchanges with oceans according to se surface temperatures, although when its warmer, oceans exhale more. We’re at another relatively high SST at the moment, which means oceans expel more than they absorb, and this increases that carbon cycle. The best we can say is that if nature is responsible for 97% of aerial c02 then we’re responsible for 3%.
i don’t accept that total emissions were fixed before 1850. There are some remarkable spikes and slumps prior to 1840 at decadal and centennial timescales – proxies from stomata during the MWP suggest 400+ppm. so if we take the pre industrial to be
antarctic Ice, which has up to 6,000, or a corrected 4,000 years difference between its ice formation and its c02 capture at a subzero environment then they show more flux than a fixed in/out quantity.
other proxies from Greenland show greater varieties
B E Brill (04:58:19) :
I found this helpful. But the Knorr paper found that the proportion of incremental CO2 removed (not exchanged) by natural processes has been 55% in each year.
So, in your example, 55GtC will go in year 2 as a result of reduced outgassing in the tropics and hungry sinks at the poles. The remaining pink 45GtC will presumably decay at your calculated rate of 4GtC per annum (or does that vary?) giving a half life of about 18 years.
A small addition: the about 4 GtC/year removal of CO2 happens only if you have about 200 GtC (that is about 100 ppmv) higher levels of CO2 in the atmosphere than the normal (temperature dictated) equilibrium. Thus there is not a 55% removal in the second year of the extra 100 GtC injection, but only about 2 GtC (the oceans are limited CO2 transmitters and receivers…). Thus only a few % of the extra mass per year is removed. The 55% is what is removed from the atmosphere today from the human emissions (in quantity, not as anthro CO2 molecules) at 8 GtC/year (45% if you exclude land use changes, as these are quite uncertain)… In the third year the amount removed will be a little smaller, as the CO2 level in the atmosphere now is a little smaller, thus less pressure to move CO2 into the oceans, thus the 4 GtC (at +100 ppmv, 2 GtC at +50 ppmv,…) will reduce over time. This leads to the half life time of about 40 years: 50% removed after 40 years, 75% after 80 years, 87.5% after 120 years,…
In fact it is far more complicated than that (transport to deep oceans is involved, precipitation and solution of carbonates, response of vegetation growth and decay,…), but the general idea is like that.
I know it is difficult to explain… It is a matter of changes in total quantity of CO2 in the atmosphere, caused by the sum of quantities added and removed over a year (that is a full seasonal cycle), while most people mix that up with the quality (the color), of the molecules involved…
carrot eater (06:02:16) :
I have looked at the Archer’s study and the Bern model, but the long tail is only involved if you burn thousands of GtC, that is most oil and lots of coal. In that case, even the deep oceans increase in carbon content, which will be reflected in (near permanent) increased atmospheric CO2 levels.
The current total anthro emissions since 1850 are at less than 0.1% of the deep ocean carbon content, thus not measurable in the deep ocean upwelling. If we should stop our emissions today, that means that the longer term of the Bern model will not materialize at all.
Unfortunately it is the long term CO2 level which is used by some scientists and the media to scare people, without the caveat that it is for extreme amounts of carbon used and that it is ultimately about some 10% of the increase in CO2 which is left (near) forever…
Ferdinand. It is interesting but: What are the actual measured data series for absorbed and exchanged c02, both natural and anthropogenic for the last 10 years? Are there any data sets, or are they just assumed?
Supercritical:
“Is it mainly the local changes in the partial pressure of CO2 that cause the interchange?”
That is the driving force for any such transfer. Any place you see net flux, you should find a difference in partial pressure of CO2 (or chemical potential, if you want to be fancy) between air and surface water. At high latitudes, carbon goes (net) into the ocean waters. At tropical low latitudes, it comes out (net) into the air. You can then follow ocean circulation from there.
In fact, here’s an ocean map. Negative flux means net flux into the ocean.
http://www.ipcc.ch/graphics/ar4-wg1/jpg/fig-7-8.jpg
However, as has been emphasised in this comment thread, CO2 doesn’t just stay as such when it enters the water; plantlife takes it up, and the chemical equilibria favor it forming HCO3-. Even for a small area of surface water, simply applying Henry’s Law won’t get you far; you have to account for the further chemistry and biology.
John Finn (06:28:20) :
yes i read what you wrote, although this study says that there is no change in percentage of the AC02 fraction since 1850. That means that it must be 3% of total c02
Ferdinand: One of Archer’s cases was for an instantaneous release of 1000 Gton. I don’t think that’s an unreasonable amount, do you?
In any case, I’d simply recommend more careful language: the IPCC half-life is about the same as what you say, so why say it isn’t? If you want to say the long tail won’t really materialise unless total emissions reach X, that’s a different point altogether; it’s a point that the simple maths being tossed around here don’t address, since one would need to look at the physical processes more carefully.
P Wilson: This has been said a few times: once the anthro CO2 is released into the air, there’s no point in distinguishing between which exact molecules are ‘natural’ and which are human related. There is simply more carbon in the system, and all the other flows will adjust to that perturbation in various ways, and the extra carbon will accumulate in the various sinks.
If you absolutely insist on labeling molecules, they are to some extent labeled; from the changing balance of carbon isotopes in the atmosphere one can see that fossil fuel-derived carbon is indeed accumulating in the system.
Has anyone studied or even thought about what happens to dissolved CO2 in sea water when the surface of that sea water evaporates into the atmosphere? Does it precipitate as CaCO3, go into the atmosphere as a gas, or both? I think it is the latter but I have no idea what fractions go where. It is a function of the thermodynamics and kinetics of a complex mixture. Some of you smarter folks figure it out.
Fred,
Are you proposing a theoretical exercise in ocean-boiling?
carrot eater,
After following your numerous posts, I am still waiting for your answer to this question: will an increase in CO2 cause a “tipping point” to be reached, where runaway global warming and climate catastrophe result?
Because that is the central question in the entire debate. If CO2 has a relatively minor effect, as seems likely due to the fact that as that minor trace gas increases, the planet continues to cool, then there is no rationale for spending $Trillions on misguided efforts to stop emitting CO2 — especially since it is the developing countries that are currently responsible for the rise.
But if a rise in CO2 will in fact cause the climate to hit a tipping point resulting in catastrophe, where exactly is that point, ± 50 ppmv?
We don’t want to derail our economy based on a scary assumption that there’s a vague ‘tipping point’ somewhere out there. But if there is, there should certainly be an empirical experiment that can be devised showing where we can expect climate doom to begin.
Re: Supercritical
Ha! Ha!
P Wilson (08:48:13) :
John Finn (06:28:20) :
yes i read what you wrote, although this study says that there is no change in percentage of the AC02 fraction since 1850. That means that it must be 3% of total c02
I think you’re missing the point. The source of the atmospheric CO2 is not really relevant. Even if all human emitted CO2 were re-absorbed this just means that the human contribution is being absorbed at the expense of the natural emissions.
Can you really not see this?
P Wilson (08:41:45) :
Ferdinand. It is interesting but: What are the actual measured data series for absorbed and exchanged c02, both natural and anthropogenic for the last 10 years? Are there any data sets, or are they just assumed?
There are two datasets of interest: the (more or less) global CO2 levels and fossil fuel use. The first is measured at a lot of “baseline” places, the second is calculated from fuel sales (by tax accounts). The net amount of natural CO2 over a year can be calculated as the difference between emissions and what is found in the atmosphere. So far the regular amounts.
The fluxes between oceans and atmosphere and vegetation and atmosphere are deduced from O2 and d13C trends: O2 use or production gives an impression of the vegetation decay or growth. The difference in oxygen use from fossil fuel burning gives you how much net vegetation growth/decay happened. d13C is reducing through fossil fuel use and vegetation changes. Again the d13C change due to fossil fuel use can be calculated and the difference is largely due to ocean exchanges (which has a higher d13C level than the atmosphere). Thus measurement series for fossil fuel use, combined with CO2 level trends, oxygen level trends, d13C level trends give you the desired answers. See:
http://www.sciencemag.org/cgi/reprint/287/5462/2467.pdf and
http://www.bowdoin.edu/~mbattle/papers_posters_and_talks/BenderGBC2005.pdf
The atmosphere – oceans/vegetation fluxes have wide margins of error, as the accuracy of the d13C and especially of the O2 measurements is borderline sufficient, but the fluxes and resultant sink capacity are quite clear.
Besides the global trends, there are a lot of local/regional flux measurements, to investigate the amount of CO2 released/absorbed over land (tall towers) and globally (satellites). Two marine stations (Bermuda and Hawai) have long series of carbon items at different depths in the oceans. And a lot of planes, buoys and seaships measure CO2 regularly in the air, ocean surface and deep oceans. These still have very large margins of error, but improved satellite measurements may give better results. See further the different sources of data:
http://www.esrl.noaa.gov/gmd/ccgg/iadv/
and for tall towers e.g.:
http://www.chiotto.org/cabauw.html
for ocean fluxes:
http://www.pmel.noaa.gov/pubs/outstand/feel2331/maps.shtml
Fred H. Haynie (09:55:44) :
Has anyone studied or even thought about what happens to dissolved CO2 in sea water when the surface of that sea water evaporates into the atmosphere? Does it precipitate as CaCO3, go into the atmosphere as a gas, or both? I think it is the latter but I have no idea what fractions go where. It is a function of the thermodynamics and kinetics of a complex mixture. Some of you smarter folks figure it out.
Every type of molecule acts on its own respective to evaporation and condensation (water) or dissolving/releasing (CO2), near independent of each other. But as higher temperature both involve more evaporation (water) and a higher partial pressure (CO2), the equatorial band shows both more CO2 release and more evaporation. The same near the poles: colder temperatures give more precipitation than evaporation and CO2 is more readily absorbed.
Precipitation of CO2 as carbonate has more to do with plant life: coccoliths use bicarbonate dissolved in the ocean water to form calcite skeletons. Some of this calcite sinks after the death of the plants.
Smokey:
I hope this tangent does not distract from the topic, as there might be still a couple loose ends here about the carbon cycle.
Runaway global warming? No. To me, ‘runaway’ means the oceans boil off. Not happening; not a term that should be used.
Tipping points? Well, an summertime ice-free Arctic by the end of this century would be an interesting result. Combine that with the possibility of permafrost releasing methane, and you’d have trouble getting back to where you came from, even if you did cut emissions. Does that count as a ‘tipping point’?
But really, what you’re asking after is the impacts on humans, and I simply don’t study that side much. I’m sure there’ll be various impacts on the food supply and ecosystems (including in the ocean) in general, as well as sea level rise. How will they adjust, how will we adjust, and how much would it all cost in economic terms? What does it really matter if a bunch of species go extinct? These aren’t things I spend much time on; one only has so much time. If you want the ‘IPCC’ view, don’t ask me, read the IPCC reports (WG2 and 3), and things like the Stern report. Then, you can read neverending arguments about things like discount rates.