This is part of the labels / documentation for <a href='http://jcm.chooseclimate.org'>Java Climate Model</a><hr/>

#science		¨oldJCM4 addJCM5		§Note this is old documentation from JCM4, to be updated

Cross-cutting global climate science topics in JCM  <li>@inertia<li>@uncertainty<li>@flowchart<li>@simplemodels
  <hr>For experts note also:  <li>@compareipcc<li>@eigenvec<li>@references
  <hr>Each part of the system is documented in detail in @pan and @mod
  £§usehelpmode
  %%Direct links to some subsections of core-science module documentation are below:  <li>@carbonmodel, @carbonemissions, @sinksdynamic, @sinksbiosphere, @sinksocean, @carbchem  <li>@oghgahowwork, @atchem, @fgases  <li>@radforintro, @radforco2, @radforothgas, @radforaerosol, @radforsolvol, @radfordistrib, @rftemp, @co2eq  <li>@udebmodel, @gcmfit @sealevelicemelt, @sealevelother
  %%  <li>Note also @scale

#uncertainty		¨oldJCM4		§££uncertintro ££uncertjcm ££uncertmixing  ££uncertexample ££uncertburden ££uncertcope ££probabilistic ££uncertfuture

#uncertintro		¨oldJCM4		§It is well known that the weather is instrinsically chaotic. Although much of this variability cancels when considering long-term average climate change, nevertheless other uncertainties arise over such timescales, concerning slow ocean mixing and ice-melt processes, biogeochemical cycles and biospheric feedbacks, and also changes in human society.

So climate prediction will never be an exact science, and any decision based on climate predictions must be a risk judgement. Since the risks depend on a complex combination of uncertainties from many interacting processes, this leads to conflicting advice from "experts" each focusing on specific parts of the whole system.  People may then get the impression that everthing is so uncertain, so why bother to  draw any conclusions at all?

Actually, a clearer picture can emerge, so long as we think carefully about how the various uncertainties fit together. Are they intercorrelated or independent - is the impact of an uncertain factor damped by negative feedbacks with other processes, or amplified by positive feedbacks? Are we more concerned about the uncertainty in the <i>overall</i> climate impacts, or the uncertainty in the relative <i>change</i> in impacts due to a particular mitigation or adaptation policy measure? The net benefit of that particular measure may be clear, even if the overall uncertainty is higher.

#uncertmixing		¨oldJCM4		§For static presentations, without such interactive exploration, uncertainties are often summarised with overall error-range statistics or bands on plots
  However it can be misleading to mix very different kinds of uncertainties in this way, for example:   <li>Calculating a probability estimate for sea-level rise by mixing uncertainties from low probability - high impact processes such as the collapse of the West Antarctic ice-sheet, with high probability lower impact processes, such as thermal expansion. The result would be an in-between number which does not give meaningful information about either type of risk (see @sealevelplot).  <li>Quoting an uncertainty range in in future temperature predictions derived by combining uncertainties in natural climate system processes (as predicted by various global climate models -see @climodmenu), with uncertainty regarding emissions scenarios (considering various future human "world-views", see @aboutsres).   <li>The latter combination may be useful when considering <i>local adaptation</i> policies, but is rather fatalistic in the context of <i>global mitigation</i> policy (the UNFCCC process) which aims to control emissions. -see also @philosophy

#uncertjcm		¨oldJCM4		§How can we present complex interacting uncertainties, avoiding @uncertmixing?
  This interactive web model offers people a unique opportunity to experiment by adjusting parameters themselves. The instant response illustrates cause and effect  -how much difference does each parameter make, and how does this depend on the settings of other parameters? By viewing several plots together, you can also look for feedback processes which may be dampening or amplifying the effect.   <li>See also @flowchart
  Moreover, the options to stabilise greenhouse gas concentration and temperature (including emissions from all gases and aerosols) help to show the importance of scientific uncertainties in the context of inverse calculations (i.e. given a specific climate target, what are the range of possible pathways towards it?).    <li>See @stabilisation, @uncertburden, @stabtemp2c

Of course, the presentation of uncertainty in this model could always be improved  <li>See @uncertfuture

#uncertexample		¨oldJCM4		§Discussion of specific uncertainties for each component of the system is now contained in the documentation for each module/plot. See:  <li>@atco2plot, @carbonstorageplot, @carboncycle  <li>@othgasplot, @fgasplot, @oghga  <li>@radforplot, @radfor  <li>@glotempplot, @heatflux  <li>@oceantempplot,  @sealevelplot, @sealevel  <li>@regclimap, @regcli

However, some factors are more uncertain than others. The table below makes some comparisons:
  <table border=2><tr>  <td>Component</td><td>Better understood</td><td>Less well understood</td></tr><tr>  <td>Emissions</td><td>CO2, F-gases</td><td>CH4, N2O, other gases (especially from soils)</td></tr><tr>  <td>Carbon Cycle</td><td>Ocean sink (physical and chemical)</td><td>Biosphere sink (climate feedback effects)</td></tr><tr>  <td>Atmospheric Chemistry</td><td>F-gases, CH4, N2O </td><td>Ozone and OH feedbacks</td></tr><tr>  <td>Radiative Forcing</td><td>Well-mixed greenhouse gases</td><td>Solar Variability and Aerosols</td></tr><tr>  <td>Temperature</td><td>Ocean warming (except surprise circulation changes)</td><td>Cloud processes and feedbacks ("climate sensitivity")</td></tr><tr>  <td>Sea-level</td><td>Thermal Expansion</td><td>Polar icecaps</td></tr><tr>  <td>Regional Climate</td><td>Average Temperature</td><td>Precipitation and Winds</td></tr><tr>  </tr></table>

It is also important to note that many types of uncertainty <i>cannot</i> be represented in "deterministic" simple climate models such as this one (see @simplemodels). A long-term aim is to investigate the possibility to develop interactive versions of intermediate complexity models incorporating more non-linear feedbacks, and intrinsic and regional variability.

Emissions scenarios are not considered here, as we have some choice about what we emit -see @emitcc, @uncertburden, @philosophy

  %%Naturally there are many different views regarding relative ucnertainties, please tell me your opinions! @contact %%

#uncertfuture		¨fut		§<li>An uncertainty range should be shown for some individual parameters. Suggestions for how best to portray this graphically are welcome! It may be necessary to adjust this range dynamically where uncertainties are not independent.   <li>The @scripting system offers potential for running ensemble calculations testing many parameter combinations. See  @probabilistic, @optimisation  <li>Noting that <i>"Climate change decision making is essentially a sequential process under general uncertainty"</i> (IPCCTAR Synthesis report Q1), how can we try to reach a particular goal such as that specified in @art2 ? One approach may be to investigate @fuzzycontrol strategies</i> incorporating deliberate climate-emissions feedbacks which are more robust against uncertainties. The structure of this model was designed to enable investigation of such feedbacks.

#probabilistic		¨oldJCM4		§££probintro ££probwccc ££probscript

#probintro		¨oldJCM4		§Uncertainty in the carbon-climate system depends on a wide range of interacting parameters. We might be able to constrain the range of uncertainty in future climate impacts (or of emissions, in an inverse calculation), by assigning a probability to each combination of parameters using a score based on the model fit to historical data (or some other criteria), gradually building up a probability density function.  

 Current development of JCM is directed towards a more complex Risk-Analysis framework, more information will be added here later. (see also @stabilisation or @optimisation).

#probwccc		¨oldJCM4		§The analysis receently presented at WCCC in Moscow and subsequent conferences (autumn 2003) combined tens of thousands of variants (of carbon cycle, other gas emissions, forcing and climate model). For this purpose specific compiled java code was added to JCM, since the calculation was too intensive for an interpreted scripting system. This cannot be demonstrated online, however graphics of the results and principles of the calculation are illustrated in the presentations at @linkpres (see also @moscow, @wccc2003, @confpres).

#probscript		¨oldJCM4		§You can use @scripting in JCM to explore uncertainty - <li>@carbonprobscript  <li>@stabprobscript
 illustrate early exploration of probabilistic approach. 

 The following don't assign probabilities, but do explore an ensemble of parameter/model combinations:  <li>@stabtemp2cscript  <li>@stabconc500script

#carbonprobscript		¨dem		§This script explores the range of possible CO2 concentrations produced by one emissions scenario SRES B1, considering various uncertainties in the @carboncyle.

The parameters varied are:  <li>@lucfemit1990 (1300, 1500, 1700, 1900, 2100, 2300 )  <li>@fertbeta (0.187, 0.237, 0.287, 0.337, 0.387 )  <li>@ceddydiff ( 0.5, 1.0, 1.5 )  <li>@chighlat ( 19, 38, 57 )  <li>@csidemix ( 0.0009, 0.0018, 0.0027 )   <li>@asgasex  ( 0.03, 0.06, 0.09 )
  There are thus 6x5x3x3x3x3 = 2430 combinations - so this script takes a long time!
  For each combination it calculates an error function, which is the standard deviation of the difference between the calculated and measured concentrations, between 1750 and 2000.
  If this error function is less than 2.5, it plots a CO2 concentration curve.
  The brightness of the curve depends on the error function, ranging from 1.5 = black, to 2.5 = white.
  £!carbonprobscript
  It takes some time to reach the first curve, so please be patient!
  After a while, you can see a spread of curves, with the blacker ones in the middle.
  Eventually it can be seen, that the range of CO2 concentrations is about 60ppm in 2100, and 100ppm in 2300.

Naturally, when the landuse emissions are higher, the sinks must be higher too. A close examination shows that this algorithm favours combinations with both high landuse emissions and high land sinks, which helps to match the early part of the curve. However beware that the emissions and concentration data for the earlier years are not so accurate, so this factor should also be considered, before drawing conclusions from such analysis.

Note also that the full effect of temperature-carbon feedbacks are not explored here
  <hr>See also @carbonprobscriptinv

#carbonprobscriptinv		¨dem		§This does the same as @carbonprobscript, except that the CO2 concentration is fixed to stabilise at 500ppm in 2125, and the range of CO2 total emissions pathways is plotted.
  £!carbonprobscriptinv
  See also @stabconc, @inverse

#fcnormal		¨oldJCM4		§The key steps of the normal cause-effect sequence are:<ul>  
<li>History<ul>
<li>@history, <li>@calcLUCemit
</ul><li>Scenarios<ul>
<li>@stabilisation or @futbasescen  
<li> @globco2emit and @othgasemit
</ul><li>Biogeochemistry <ul>
<li>@berncarbon
<li>@atchem, @aerosol, @fgas
</ul><li>Global climate<ul>
<li>=>@radfor (all gases come together)
<li>=>@udebclimod 
</ul><li>Impacts<ul>
<li>=>@sealevel 
<li>+@regcli
</ul><li> if  regional analysis needed: <ul>
	<li>£`globco2emit => @shares, @futureLUC, 
	<li>+ climate, impacts=>@costs, @responsibility  
</ul></ul>

This calculation sequence is illustrated by the numbers in the @interacmap. However there are some feedback processes which go the other way (see @interacex)

#fcchanging		¨FIX		§Old doc from JCM4, to be fixed: 

Red arrows on the flowchart indicate cause-effect flows that were changed by your last action (dragging a parameter, selection from menu, etc.). The module directly affected by the parameter is shown with red text. Yellow arrows show dependencies that didn't change.

For example, if @chemfbopt  is enabled, and you also choose "£~stabconc" from @emitmenu, then adjusting climate sensitivity will affect both carbon and emissions, so most of the arrows are red. If it is disabled, adjusting an uncertainty control on the temperature plot (e.g. climate sensitivity) has no effect on carbon or radiative forcing, so the arrows in the upper part are yellow.

Note the model only calculates the components that have changed, and are also needed by visible plots. So you may notice, that the more red arrows there are, the slower the response is.
  See also: @howfast, @struccode

#fcstabsres		¨oldlink		§£§clipolfeedback

#eigenvec		¨oldJCM4		§The carbon and climate models both use about 40 ocean layers (x2 oceans for climate model). If using a simple integration method, the timestep would have to be quite small (e.g. 1 month) in order that the fluxes are much smaller than the box contents, and so the calculation over hundreds of years is rather slow. Therefore in order to get an instant response in the plots as the parameters are dragged by the mouse, a more efficient matrix-eigenvector method has been applied.  <li>See @carboncycle and @heatflux modules , also @howfast
  ££evmethod ££jama ££evmathprinc

#evmethod		¨oldJCM4		§<ul><li>An exact analytical solution   <li>The only approximation is that the change in non-linear fluxes is linear within one timestep.   <li>The timestep can be any size (depending on input data and plot resolution)   <li>The ramp function must be iterated when a non-linear flux is a function of box contents.   <li>Only matrix cells needed for data output or non-linear input are calculated.   <li>Usually more efficient than pulse response function especially with many timesteps.   <li>Unlike PRF, preserves knowledge of all box contents (needed for thermal expansion or depth profiles etc.)   <li>The eigenvectors only need to be recalculated when you change a parameter that alters the linear fluxes (such as internal mixing rates), not when the external emissions change.</ul>

#jama		¨oldJCM4		§Eigenvectors, inverses, etc. are calculated using the convenient Java Matrix Package ("JAMA"), which was developed at MIT, and has simply been bolted onto Java Climate Model.
  See: <a href=math.nist.gov/javanumerics/jama/>math.nist.gov/javanumerics/jama/</a>

#evmathprinc		¨oldJCM4		§<h4>Differential equation</h4>
  Start with a simple differential equation:

dq/dt = -&lambda;q + x

If x changes linearly from x<sub>t</sub> to x<sub>t+dt</sub>, it can be shown that:

q<sub>t+dt</sub> = prop q<sub>t</sub> +  step x<sub>t</sub> + ramp (x<sub>t+dt</sub> - x<sub>t</sub>)

Where:

prop = e<sup>-&lambda;dt</sup>

step = (1 - prop)/&lambda;

ramp = (dt - step)/(&lambda;.dt)
  <hr><h4>System of boxes (n equations)</h4>
  A system of n boxes with diffusive fluxes between them, plus extra non-linear inputs, can be written as:

dQ/dt = R Q + X

Where Q is the vector of box contents, R is an nxn matrix for the fluxes, and X is the vector of extra inputs.

We can diagonalise R:

R = S diag(E) S<sup>-1</sup>

Where S is the matrix of eigenvectors, and diag(E) the diagonal matrix of eigenvalues.

Premultiplying all by  S<sup>-1</sup> gives:

d/dt(S<sup>-1</sup>Q) = diag(E) (S<sup>-1</sup>Q) + S<sup>-1</sup>X

S<sup>-1</sup>Q and S<sup>-1</sup>X are just vectors, with each element of S<sup>-1</sup>Q multiplied by just one eigenvalue,
  so this is just like n simple differential equations as above, with diag(E) providing the &lambda; terms

Now, if we have a lot of equal timesteps, we only need to calculate the n prop, step and ramp functions once, at the beginning.

If we preserve the state information in the form S<sup>-1</sup>Q,
  then the diffusion for each timestep is given just by multiplying each element by it's prop function.

To add the step and ramp functions for extra inputs, we need to calculate S<sup>-1</sup>X,
  but if we have only y boxes with non-linear inputs
  (for example due to carbonate chemistry at the surface of an upwelling-diffusion ocean),
  we only have to multiply out y columns of the nxn matrix S<sup>-1</sup>
  (which we can also premultiply by the step and ramp functions just once at the beginning).

To plot a result, we also need to convert S<sup>-1</sup>Q back to Q by premultiplying with S,
  but if we are plotting only z elements of Q (for example, the contents of the surface layer),
  we only have to multiply z rows of the nxn matrix S.

So if there are t timesteps, we have altogether

 t.n.(1+2y+z) multiplications

(the 2 is for step + ramp functions)

(Note that if (1+2y+z)>n, it might be quicker preserving the state in Q rather than S<sup>-1</sup>Q).
  <hr><h4>Iteration</h4>
  If the X are not just external inputs, but are also dependent on the contents of the box (as with the carbonate chemistry), then we have to iterate. A good first guess is usually that the change in X is the same as in the previous timestep.
  This can still be fast and accurate, providing the assumption that X changes linearly within one timestep is reasonable.

If X is a non-linear function of box contents, it helps to separate out an arbitrary linear part of X and include this within R, so that the remaining non-linear perturbation is as small as possible.
  <hr><h4>Compare with PRF</h4>
  Note that (im)pulse response functions are derived from the same principle:
  an exact PRF for a linear system is derived from the n prop functions as above.
  The difference lies the way of adding it up:

  With PRFs, the fate of each input (X<sub>t</sub>) from every timestep must be calculated seperately for all subsequent timesteps.
  So if there are n boxes and t timesteps, 
  then we have altogether n.t<sup>2</sup> /2 multiplications.

  So this method seems to be slower, so long as t > 8!

(note for comparison y and z must be 1, since PRF can only cope with input and output in one box).

#simplemodels		¨oldJCM4		§JCM uses an efficient Java implementation of simple carbon and climate models, the same as those used to create many of the smooth-curve plots and quoted predictions in the recently published Intergovernmental Panel on Climate Change Third Assessment Report (IPCC-TAR)
  Note this does not mean that it contains the <i>same computer code</i>, only that we try to match the <i>same specification</i>, as described in published scientific papers and IPCC reports.
  You can check the good fit to published data from IPCC by superimposing the data from the WG1-SRES appendix -see @compareipcc
  ---- ===Types of models===
  Note that this is a "simple" model which generates smooth curves, useful for comparing scenarios and understanding key processes. It cannot generate intrinsic climate variability, or regional climate variations, for which it is necessary to use much more sophisticated, but very slow "General Circulation Models" (GCMs).

Between these two extremes are also emerging "Earth System Models of Intermediate Complexity" (EMICS) which may be particularly useful for integrated assessment, for investigating non-linear "surprises", and for simulations over longer timescales (glacial interglacial cycles).

IPCC-TAR considered all these types of model -you can tell the difference by how smooth or "noisy" the plots are.
  ---- ===JCM Model Components===
  The Carbon cycle, Atmospheric chemistry, and Radiative Forcing calculations are based on the Bern model. The temperature and sea-level calculations are based on the Wigley/Raper UDEB model parameterised to fit a range of GCM predictions according to appendix 9.1 of IPCC-TAR-WG1.

Both models incorporate upwelling-diffusion multi-layer oceans to account for the slow uptake of heat and carbon into the deep water. These systems are solved using an eigenvector method which is more efficient than direct integration and more flexible than pulse response functions.

The code also has a flexible modular structure, whose components are only calculated if they are both needed for output, and have changed due to parameter adjustments or feedbacks.

See also   <li>Details of how the calculations are made within the @mod documentation. %%¤adju Note, to explore the details, it is recommended that you switch the version (top panel menu) to "expert" mode!%%  <li>@howfast  <li>@struccode  <li>@aboutjava  <li>@references

#inertia		¨oldJCM4		§££timescaleintro ££timescalescript ££timescaleprocess

#timescaleintro		¨oldJCM4		§Some climate change processes, such as land surface warming in response to radiative forcing, or mixing of the atmosphere, occur within hours or months, whilst others, such as the transfer of heat or carbon to the deep ocean, or the melting of polar icecaps, take centuries or even millenia. Moreover, the deep ocean has a vast capacity to accumulate both heat and carbon.

Consequently, it takes hundreds of years to see the full climate impact of current emissions, and so the timescale in this model extends to 2300 although our planning horizon for specific mitigation or adaptation policy is much shorter (hence the regional scenarios data only extends to 2100).
  So we must bear in mind the great inertia of the system, in order to find effective policy to avoid dangerous climate change.

Also, by experimenting with the options in the emissions menu, you can see that stabilising emissions is not enough to stabilise concentration, stabilising concentration is not enough to stabilise temperature, and it is impossible to stabilise sea-level rise (on this timescale). This is mainly due to the slow accumulation of CO2 and heat in the deep ocean.   <li>See also @stabilisation

#timescalescript		¨dem		§This script makes one plot showing CO2 Emissions, Concentration, Radiative Forcing, Temperature and Sealevel Rise, all on the same axes.
  It's similar to the timescales plot shown in IPCCTAR SYR (see @ipcclinks)
  £!timescalescript
  The units are arbitrary -see scaling factors in the code
  For discussion see @inertia
  This script builds on @blankplot, see also @scripting.

#timescaleprocess		¨oldJCM4		§The atmospheric CO2 concentration is the accumulation of past emissions, minus sinks into the ocean and land plants and soil. Although the processes controlling these sinks are complex so there is no simple "lifetime" for CO2, we can say that CO2 emissions from burning fossil fuels typically remain in the atmosphere for about 100 years. Actually, the atmosphere will always retain a small fraction (which increases the more we emit due to the acidification of seawater), until the fossil fuel may be recreated on geological timescales.   <li>See @atco2plot, @carbonstoreplot
  Most other greenhouse gases are eventually destroyed in the atmosphere, their lifetime ranging from about a decade for methane, to many millenia for some CFCs and SF6. As the atmosphere mixes globally within a few months, these gases can be considered to be almost uniformly distributed.
  Aerosols of sulphate or soot, by-products of fossil fuel combustion, biomass burning, are washed out of the atmosphere by rain and so survive at most few weeks. Tropospheric ozone also has a short lifetime as it is highly reactive. Consequently these are concentrated in more polluted regions.
  The radiative forcing combines the effect of all these gases and aerosols, plus solar variability. RF shows instantaneous heating power rather than accumulated heat, so it is measured in Watts (per m2).   <li>see @othgasplot, @radforplot
  The land surface responds quickly to changes in radiative forcing (both the land and the atmosphere have such a low heat capacity, that these are neglected in this simple energy-balance climate model). The ocean surface however, lags behind due to the slow exchange of heat with the deep ocean.
  If you choose the "expert" complexity level, you can compare the land and ocean temperature changes -notice how the oscillations due to solar variability (you can adjust this from the radiative forcing plot) affect the land more than the ocean.   <li>see @rftemp, @glotempplot
  The surface ocean is only mildly influenced by the warming of the deep ocean, hence if greenhouse gas concentrations are stabilised the temperature rises only slowly (note however, that dramatic changes in the thermohaline circulation, not included in this model, might alter this conclusion!).
  However the deep ocean warming determines the thermal expansion of seawater which is the largest contributor to the sea-level rise. You can see that this only begins to slow down, even centuries after the surface temperature has stabilised.
  Sea-level is also influenced by ice-melt. Some mountain glaciers may melt within a few decades, however it requires thousands of years to melt the polar icecaps. Indeed they are still responding to the warming at the end of the last ice-age.   <li>see @oceantempplot,  @sealevelplot
  Note the different timescales of the climate system are also discussed in IPCC Synthesis report Q5   <li>see @ipcclinks
  Note also that there are many more physical and biogeochemical feedback processes which are not yet included in this model, such as the response of permafrost, ocean phytoplankton, or the thermohaline circulation. Although these are generally slow, a combination of such feedback processes may lead to dramatic surprises on passing critical thresholds.
  <hr><li>For a more symbolic summary, see @calculuscc

#calculuscc		¨oldJCM4		§%%(or why it's so hard to find effective policy solutions)%%

For the mathematically minded, we can say:  <li>&int; represents the time integral  <li>E = Emissions, S = Sinks,   <li>C =Concentration  <li>RF = Radiative Forcing  <li>T<sub>s</sub> = Surface temperature  <li>T<sub>d</sub> = Deep ocean temperature  <li>I = Ice Melt  <li>S = Sea-level rise

then to a first approximation:  <li>C = &int; (E - S) and S = f(C)  <li>RF = f (C) fast  <li>T<sub>s</sub> = f (RF ,T<sub>d</sub>) mainly RF  <li>T<sub>d</sub> = f (&int; T<sub>s</sub>) over centuries  <li>I = f (&int; T<sub>s</sub>) over millenia  <li>S = f (I, T<sub>d</sub>)

If we consider also that emissions reductions depend on cumulative policy actions,  <li>E = f (Pop, Lif, Tec) = f (&int;Pol)  <li>Where:  <li>Pop =Population  <li>Lif =Lifestyle  <li>Tec =Technology  <li>Pol =Policy

Then you can see that  we have a triple time-integral   <li>S = f (&int;&int;&int; Pol)

in going from climate policy to impacts such as sea-level rise (although not to temperature -see  note below).
  Hence it is so difficult to calculate in inverse mode (differentiate) to find the best policy to avoid dangerous impacts.
  Even with a double integral, a kink in the target curve implies an infinite jump in the policy!  <li>See also  @inertia, @inverse, @stabtempdoc

An alternative approach is to devise "fuzzy control" strateges for deliberate climate-policy feedback (as used for an experimental stabilise temperature  method in JCM - see @stabtempfuzzy), but such formulae tend to cause oscillations, which may not be so unrealistic!
  ---- ===Policymake model?===
  The Brazilian government proposed a simple "policymaker model", based on a few differential equations, for the purpose of attributing responsibility for climate change. The first variant assumed that the surface temperature was the integral of the radiative forcing, which is incorrect as the surface has a much shorter "memory" than the deep ocean. However, the formula was improved in the second variant of the Brazilian proposal, whilst retaining some of the mathematical simplicity.

Also, the attribution of responsibility is found to be strongly dependent on the time period both for attributing emissions, and for calculating their future impact, raising issues of integenerational equity. For more on this topic, see: @attribution, @attribution

#compareipcc		¨oldJCM4		§@tarwg1data | @ipccdiff  |  @ipcclinks | @unitbaseline
  ££cipccintro ££tarwg1data ££ipccdiff  ££ipcclinks ££unitbaseline

#cipccintro		¨oldJCM4		§This web model uses an efficient java implementation of simple carbon and climate models with the same specification as used to generate many of the smooth-curve plots used within the IPCC-TAR report.
  Therefore, if we give it the same input (emissions or stabilsation scenarios), and use the same sets of model parameters (ocean mixing, climate sensitivity, etc.), we should get the same output (CO2 concentration or emissions, radiative forcing, temperature, sea-level) as IPCC. This can be checked, by comparing with specific plots and data from IPCC-TAR, as explained below.
  Experts can also check that the model behaves as they would expect, by experimenting with many possible combinations of parameters. For this purpose switch the version (top panel menu) to "expert" mode, and you will see more curves and controls.

#tarwg1data		¨oldJCM4		§The SRES appendix at the end of IPCC-TAR WG1 report contains useful tables of data, giving IPCC predictions of CO2 concentration, radiative forcing, temperature and sea-level rise for the 6 SRES marker scenarios. To help you check the correspondence, this data may be superimposed as small circles on the plots.
  ¤adju To see this, you should do the following:   <li>Press the reset button (top), to get the default set of model parameters.   <li>Choose "SRES no-climate-policy scenarios" from the Mitigation menu (top)   <li>Select "expert" from the complexity menu (top)   <li>Press the "IPCC-data" button (top)   <li>Select a plot to check (CO2 Concentration, Radiative Forcing, Temperature, Sea-level)   <li>Select a scenario from the SRES menu (top)
  The circles should then appear, you should see a good fit to the curves generated by the model. (Of course, the data will not correspond, if you adjusted the model parameters since pressing the reset button!)
  ¤cogs There are also some important technical points to consider when making comparisons:   <li>The IPCC data for temperature and sealevel correspond to the average of the seven GCMs (see Climate Model). You can use the GCM-fit menu on the temperature plot to cycle through the range of models. HadCM3 is now the default option and is quite close to the average, however the difference between models varies between scenarios and is greater for sea-level.   <li>The concentration / radiative forcing data come from the Bern-CC Model and the temperature/ sealevel from the Wigley/Raper model, except that:   <li>The total RF is from the WR model   <li>CO2 RF is shown for both models. However, in the WR Model, the parameter "Radiative Forcing for CO2 doubling" varies with the GCM-fit, whereas in the Bern-CC model this was fixed at 3.71 W/m2. You must set this parameter, to check the CO2 RF data.   <li>You should select the @taro3 parameter (@othgasplot) to use the older formula for tropospheric ozone  <li>These two models used quite different formulae for RF from carbon aerosols. The default (Bern-CC) option scaled to CO emissions is consistent with IPCC Chapter 6 and SRES tables. However you should select the BCOCWig option when comparing temperature / sealevel / total rf. Data is shown for the total of BC+OC according to the WR. The BCOCWig option gives an approximate fit only.   <li>The circles are adjusted, if you move the temperature baseline year.   <li>The baseline year for sealevel rise is 1990 in the data and 1750 in JCM, so the circles are adjusted accordingly.   <li>Circles are not shown in the emissions plots, since the emissions are taken directly from SRES data tables.   <li>You can also choose the older scenario IS92A, but data is not available for all quantities. Also it had to be scaled down to match current emissions, and different models may make different assumptions about this.

#ipccdiff		¨oldJCM4		§---- ===Mathematical Method===
  JCM uses an eigenvector calculation method rather than direct integration, combined with an iteration of the ramp-function for non-linear fluxes. This method finds the exact analytical solution, given the assumption that the non-linear fluxes change linearly within one timestep. The algorithm used by Bern-CC and WR models is different, but the difference should be almost negligible.   <li>See @eigenvec

  ---- ===Terrestrial Biosphere sink===
  The carbon cycle model used here is an older version of the Bern model which uses the same "HILDA" ocean as the Bern-CC model, but a simpler 4-box terrestrial biosphere (as used in IPCC SAR). The Bern-CC (TAR) model incorporates a more sophisticated dynamic vegetation model including several plant types and many grid cells, each with different temperature and precipitation derived from GCM predictions. The temperature feedback tends to lower the biosphere sink (and hence increase the concentration) towards the end of this century. It is planned to develop a fast implemention of the dynamic vegetation model within JCM.<li>See @carboncycle module
  ---- ===Climate-Carbon feedback===
  In this web model, the carbon cycle and climate are directly coupled to achieve the feedback from temperature to carbonate chemistry in the surface ocean. In the IPCC calculations, different models were used for the carbon cycle and temperature. Although both Bern-CC and WR model include some climate-carbon feedbacks, these two models were not directly coupled as they are here. This may result in slight differences, however direct coupling should be preferable.
  ---- ===Sea-level rise due to ice-melt===
  The calculations here are based on simple formulae, parameterised to fit data in Chapter 11 of IPCC-TAR-WG1 (the glacier formula is adapted from that used in the SAR).

#ipcclinks		¨oldJCM4		§---- ===General links===  <li><a href="http://www.grida.no/ipcc_tar/index.htm" target="_new">IPCC-TAR Online at GRID Arendal</a>   <li><a href="http://www.ipcc.ch/"  target="_new">IPCC Homepage</a>  <li><a href="ref.html">JCM References Page</a>
  ---- ===Stabilisation scenarios===
  The formulae for defining the target curve towards a particular stabilisation level
  is derived from the original formulae in the IPCC technical paper of Enting et al 1994 (referred to as "S" "WG1" in IPCC-TAR-SYR). The "WRE "curves are a variant of this with a delayed start, following the IS92A business-as-usual scenario for the first few years.

  In JCM, stabilisation curves start from 2000 (current emissions), whereas the originals started from 1990. As current emissions lie significantly below the IS92A projections, these have been scaled down to fit the current level.

For more information see:  <li><a href="../emit/mitigation.html">Mitigation /Stabilisation scenarios</a>,   <li><a href="../emit/syrspm6.jpg" target="_new">IPCC-TAR-SYR Figure SPM6</a>  <li><a target="_new" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/figts-25.htm">WG1 TS Fig 25</a> WRE stabilisation curves & implied emissions
  ---- ===Radiative forcing===
  The contributions of the minor greenhouse gases and aerosols were derived from figures and data in<li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/338.htm">Chapter 6 of TAR-WG1</a>

Various contributions to RF  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/figts-9.htm">WG1 TS Fig 9</a>  <li>SYR main part Fig 2-2 (not yet available online)  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig6-6.htm">WG1 Ch6 Fig 6-6</a>

Solar and volcano forcing history  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig6-8.htm">WG1 Ch6 Fig 6-8</a>

Useful data table  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/251.htm">WG1 Ch6 Table 6-11</a>
  ---- ===Temperature projections===
  Explaining the climate model parameters  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/371.htm"> WG1 Ch9 Appendix 9.1</a>
  <!--need similar from Ch3 for Carbon!-->

SRES temperatures  <li>SYR SPM3 -SRES projections (not yet available online)  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/figts-22.htm">WG1 TS Fig 22</a>   <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig9-14.htm">WG1 Ch9 Fig 9-14</a>  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig9-15.htm">WG1 Ch9 Fig 9-15</a>

WRE temperatures  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/figts-26.htm">WG1 TS Fig 26</a>  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig9-16.htm">WG1 Ch9 Fig 9-16</a>  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig9-17.htm">WG1 Ch9 Fig 9-17</a>
  ---- ===Sea level rise===

SRES sea-level  <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/figts-24.htm">WG1 TS Fig 22</a>   <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig11-12.htm">WG1 Ch11 Fig 11-12</a>

Note various other plots and tables in   <li><a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/408.htm"> Chapter 11 of TAR-WG1</a>,

Note also <a target="fig" href="http://www.grida.no/adm/dev/ipcc_tar/wg1/fig11-9.htm">WG1 Ch 11 fig 11-9</a>  (uncertainty in different contributions to sea-level)
  ---- ===Timescales of response===
  See Q5 of IPCC SYR regarding timescales of response, especially Figure SPM5.

#references		¨oldJCM4		§££sciref ££dataref

#sciref		¨oldJCM4		§The two papers below (and references therein) describe the calculation methods used in IPCC-TAR, and also implemented in JCM.

  <h4>Bern-CC Model</h4>
  %%(used for @carboncycle, @oghga modules in JCM )%%  <li><b>Global Warming Feedbacks on Terrestrial Carbon Uptake under the IPCC emissions scenarios </b>,
  F.Joos, I.C.Prentice, S.Sitch, R.Meyer, G.Hooss, G.K.Plattner, S. Gerber, K.Hasselmann, Global Biogeochemical Cycles v15 no4, 891-907, 2001

  <h4>Wigley-Raper UDEB model</h4>
  %%(used for @heatflux module in JCM)%%  <li><b>Use of a upwelling-diffusion energy balance model to simulate and diagnose A/OGCM results</b>, S.C.B. Raper, J.M. Gregory, T.J. Osborn, Climate Dynamics v17, p601-13, 2001  <li>See also IPCCTAR-WG1-Ch9 Appendix 9.1

  <h4>Stabilisation scenarios</h4>
  %%(used for @stabilisation scenarios in JCM)%%  <li><b>Future Emissions and Concentrations of Carbon Dioxide, Key
  Atmosphere/Ocean/Land analyses</b>, Enting I.G., Wigley T.M.L., Heimann M., CSIRO Technical paper 1994
  <i><A href="http://www.dar.csiro.au/publications/Enting_2001a0.pdf" target=new>PDF online</a></i>

#dataref		¨oldJCM4		§<li><a href="http://cdiac.esd.ornl.gov/" target="_new">Carbon Dioxide Information Analysis Centre (CDIAC)</a> %%(source of historical CO2 Emissions for each country, combined to make JCM regional data)%%  <li><a href="http://www.rivm.nl/image/" target="_new">RIVM IMAGE model</a> %%(source of regional socioeconomic projections under the IPCC-SRES scenarios)%%  <li><a href="http://ipcc-ddc.cru.uea.ac.uk/" target="_new">IPCC-Data Distribution Centre</a> %%(source of  regional climate GCM data)%%

See also @regiondatasource

#optimisation		¨fut		§This module tries to maximise an economic welfare function (see @costs) by automatically adjusting a set of parameters (depending on @optvariant). For a mulit-dimensional problem involving several parameters, it may have to iterate hundreds of times. 
The code in @optimcaller does this iteration

Note that the author of JCM does not have confidence in the quality of the functions in @costs  Therefore this module should be seen only as an experimental tool to test the methodology and explore sensitivity to some other parameters.

Note that it may be necessary to extend the @model_end_year to get good results

Below is old documentation to be updated
----

The concept of Optimisation is essentially to create a single objective function which one wants to maximise or minimise, given a set of adjustable parameters, and an efficient iterative algorithm to find the best solution.  There are several potential applications of this Â– it may be used for tuning the parameters of natural science models to fit historical data or predictions of more complex models (in which case the objective is to minimise the error - see @probabilistic, @uncertfuture). It may also be used for finding efficient future policy pathways in a 'cost-benefit' style of analysis (note, there are many interpretations of 'efficient' -see @uncertburden, @equity, @peoplefuture).
  Therefore it is proposed to add a general optimisation tool to JCM, to complement the @scripting facility. When there are many free parameters, the shape of the multidimensional objective function may become very complex, so it is important to combine an effective algorithm (possibly the simplex triangle method) with a fast model (see @howfast).  <li>Note that an iterative method is already used for JCM stabilisation scenarios (@stabitmethod). In this case, the future scenario is defined by a few parameters of a mathematical curve formula, rather than by discrete time intervals. This helps to reduce the dimensionality of the problem, and also ensures a smooth transition from current emissions.

</ul>
----