<p>Your question is fairly broad, and slightly vague so I don't know if I will be able to answer it in one go. If you would like any clarification, let me know.</p>

<h2>How are predictions made?</h2>

<p>The basic process generally used for probabilistic forecasting of the global climate is something like:</p>

<ol>
<li>Take one or more general circulation models (GCMs), and run multiple simulations over the projection period.

<ul>
<li>GCMs are models that attempt to replicate the physics of the climate system, including land and ocean processes. They can not replicate the physics <em>exactly</em>, because:

<ol>
<li>they operate on scales of a few hundred meters at minimum, and so physical processes (which usually operate on <em>much</em> smaller scales) are scaled up and parameterised to work on the larger scale; and </li>
<li>because for some of the physical processes (especially those that have to be parametrised to larger scales), there is not enough data to adequately fit them. When this happens, those model parameters are usually <em>calibrated</em> - a large number of runs are made, with different values for those parameters, and then the best parameter values are chosen.</li>
</ol></li>
<li>Usually, you run the model for some period prior to the projection period, so that you can compare that to observations (spin-up period).</li>
<li>You need to provide input data to the model. Mostly, this just consists of solar forcing (changes in the sun's output), as well as expected greenhouse gas (GHG) emissions, and aerosol emissions (both human and volcanic).</li>
<li>Simulation output is in the same format as your observational data, and generally includes all of the important variables - temperature, precipitation, etc.</li>
</ul></li>
<li>Put all of those simulations in an ensemble.

<ul>
<li>Often, simulations are "bias corrected", which usually means they are changed so that the model average matches the observation average over some period prior to the projection period - this might be the last 30-40 years. This is to allow for model drift (which is mostly chaotic, and can happen in any direction).</li>
<li>The distribution of the simulations in the ensemble is used to create probabilistic projections. For example, each simulation has a mean global annual temperature. You could make the assumption that the errors in the simulations are normally distributed (over the ensemble), and so make an estimate of that distribution, and use that to make probabilistic estimates. This is basically saying that if ~50% of the models are over a certain temperature, you expect that (assuming the models, the input data, and assumptions they are based on are reliable*) there's a 50% chance that the global annual temperature of the earth would be over that temperature. A similar process can be used for the maximum temperature, or any other variable, and any statistics, including extremes indices. <strong>None of these predictions is a single value - they are always probabilistic, although it's probably quite common for only the mean of that distribution to be reported</strong>.</li>
<li>How you combine the information from the simulations in the ensemble is somewhat up to you. The basic method is as described above, and uses minimal assumptions about the data. It's also common for researchers to use a weighting methodology to estimate the ensemble mean, for example performance-based weighting, where models that perform better over the period before the projection are weighted more highly, with the assumption that they will perform better over the projection period too. Or you could weight based on model independence (if you're using multiple models), by weighting models that are less like other models more highly, in order to minimise bias from particular types of models (e.g. Bishop and Abramowitz 2013). <em>[I have a paper in review at the moment that investigates the efficacy of some of these methods, I'll link to it when it comes out]</em></li>
<li><strong>Can this process predict changes in 1000-year events</strong>? Yes, potentially, even when the projection period is usually more like 100 years. This is because 1 in 1000-year events are actually defined inversely - that is, they are thought to have a 0.1% chance of occurring <em>in any given year</em>. If your ensemble projects over 100 years, but has 100 simulations, then there are 10,000 years in which that a 1 in 1000 might occur. If you see it occurring 20 times, or 4 times, then you might get suspicious that things are changing. You probably need more than that to get a statistically significant result, but there are ensembles out there that are <em>really</em> big (e.g. Stainforth et al, 2005, which had 2,578 simulations totalling over 100,000 simulated
years, and  I think some of the <a href="http://www.climateprediction.net" rel="nofollow">ClimatePrediction.net</a> have tens of thousands of simulations). Even without those large ensembles, if you assume particular distributions of extreme events where probability is a simple function of extremeness (e.g. Log-normal distribution or similar), then you can probably say something about large extremes based on the change in behaviour of less extreme events. Unfortunately, I am not aware of any experiments that look at the likely changes to very extreme events.</li>
</ul></li>
</ol>

<p>* Model reliability is obviously a fairly active field of debate and research. Suckling and Smith (2012) indicates that GCM-based ensembles are better than basic statistical models, but probably not currently much better than some more advanced statistical models. However, that still means that they're at least on-par with the best options we have for forecasting, unless you're in to reading chicken entrails.</p>

<h2>References</h2>

<ul>
<li>Bishop, C.H. &amp; Abramowitz, G., 2013. Climate model dependence and the replicate Earth paradigm. Climate Dynamics, 41(3-4), pp.885–900. Available at: <a href="http://link.springer.com/article/10.1007/s00382-012-1610-y" rel="nofollow">http://link.springer.com/article/10.1007/s00382-012-1610-y</a> [Accessed September 17, 2013].</li>
<li>Stainforth, D.A. et al., 2005. Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature, 433(7024), pp.403–406. Available at: <a href="http://www.nature.com/nature/journal/v433/n7024/abs/nature03301.html" rel="nofollow">http://www.nature.com/nature/journal/v433/n7024/abs/nature03301.html</a>.</li>
<li>Suckling, E.B. &amp; Smith, L.A., 2013. An Evaluation of Decadal Probability Forecasts from State-of-the-Art Climate Models*. Journal of Climate, 26(23), pp.9334–9347. Available at: <a href="http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00485.1" rel="nofollow">http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00485.1</a> [Accessed January 8, 2015].</li>
</ul>

CC BY-SA 3.0
2015-01-08T06:14:11.727Z
nice answer! just regarding the last point (Can this process predict changes in 1000-year events?) it may be worth defining what you mean by members.
Isopycnal Oscillation
CC BY-SA 3.0
2015-01-08T06:16:06.270Z
@IsopycnalOscillation: thanks, changed that to simulations.
naught101
CC BY-SA 3.0
2015-01-10T07:27:26.010Z
Thank you very much for the detailed answer, it is very helpful and informative! There are some points which are not yet clear, thus I extended the OP (there is not enough space here). Thank you for your help in advance.
rozsasarpi
CC BY-SA 3.0
2015-01-12T02:57:55.107Z
@Arpi: I don't think that this method of asking questions is very useful in this format. Your original question was already huge, and hard to follow, and this makes it worse. You are better off asking separate questions, and keeping them as small and self-contained as possible. It makes the information more re-usable for other people, as well as giving other people a chance to answer questions that they might be more qualified for. You can reference those new questions from this question, reference this question from them as well.
naught101
CC BY-SA 3.0
2015-01-12T06:51:02.477Z
Thank you for the suggestion, I opened a [new question](http://earthscience.stackexchange.com/questions/4248/can-climate-models-reliably-predict-meteorological-extremes).
rozsasarpi
CC BY-SA 3.0
2015-01-08T06:05:50.640Z
2016-05-01T02:09:46.330Z
2016-05-01T02:09:46.330Z
naught101
<p>What is the accepted methodology to predict future climatic extremes using the results of climate models?</p>

<p>I have recently read a report about <strong>climatic extremes considering climate change</strong> (MICE, 2002). The report says that researchers fitted extreme value distributions (<a href="http://en.wikipedia.org/wiki/Generalized_extreme_value_distribution" rel="nofollow noreferrer">generalized extreme value</a>, <a href="http://en.wikipedia.org/wiki/Generalized_Pareto_distribution" rel="nofollow noreferrer">generalized Pareto</a>) to the intensity of predicted, future climatic actions, e.g. rain, snow, wind. Applying these models, events with a large <a href="http://en.wikipedia.org/wiki/Return_period" rel="nofollow noreferrer">return period</a> are used to assess the impact of climate change. Additionally, there is a recent Nature article by O’Gorman which also deals with future extreme events, particularly snow.</p>

<p>Considering that the predictions (projections per scenarios) can be made only in probabilistic terms. I would like to know how these predictions are made, what methodology are they using? I mean the actual climatic data, not the extreme value (statistical) analysis of them. For extreme value analysis, annual or more frequent maxima can/could be used. It is quite dubious that climate models would predict monthly or annual maxima of rain/snow for a certain region, up to the end of this century (or are climate models so sophisticated?).
Someone told me that on this site (<a href="http://esgf-data.dkrz.de/esgf-web-fe/" rel="nofollow noreferrer">Earth System Grid Federation</a>) there is an example of daily predicted snow data (this can be downloaded).</p>

<p>So, my main question is <strong>how this data, these predictions, are produced. What are the underlying assumptions of the models?</strong> Can these 100-year long simulations be used to predict extreme events within a 100 to 1000 year return period (these are common in engineering practice).</p>

<p>As far as I know, the climate models contain 'accurate' models (where the phenomenon is described by differential equations) and 'approximate' models (where empirical models are used). I guess the actual amount of precipitation for a given region belongs to the latter; in this case how uncertain are these models? (Surely the 'accurate' models have large uncertainty as well, but perhaps less).</p>

<hr>

<p>I have an engineering background and I am interested in the effect of extreme climatic events on the reliability of structures; especially considering climate change. In order to study this, it would be great to know how reliable are the climate predictions regarding extreme events. If the probability distribution (or more complex probabilistic model of the actions) is given, the reliability of a structure (system) can be directly calculated. However, I am quite suspicious about the extremes predicted by the climate models.</p>

<p>It is quite hard to navigate through the thousand pages reports and find the probably one page long section which would answer my question. I would highly appreciate if someone could explain the main aspects of methodology, basic assumptions or point me to specific references, any help regarding the original question is welcomed.</p>

<hr>

<p>MICE (2002). <a href="http://www.cru.uea.ac.uk/projects/mice/mice.pdf" rel="nofollow noreferrer">Modelling the Impact of Climate Extremes</a>. Description of Work</p>

<p>Paul A. O’Gorman. (2014). <a href="http://www.nature.com/nature/journal/v512/n7515/full/nature13625.html" rel="nofollow noreferrer">Contrasting responses of mean and extreme snowfall to climate change</a>. Nature. Volume 512. 7515.  p. 416-418.</p>

<hr>

<p><strong>Extension of the question:</strong></p>

<p><a href="https://earthscience.stackexchange.com/questions/4248/can-climate-models-reliably-predict-meteorological-extremes">Can climate models reliably predict meteorological extremes?</a></p>

CC BY-SA 3.0
2015-01-10T07:28:35.270Z
@SabreTooth Thank you for the link and for drawing attention to this question by offering the bounty!
rozsasarpi
<meteorology><climate-change><precipitation><climate-models>
What is the methodology to analyze future climatic extremes using the results of climate models?
rozsasarpi
# What is the methodology to analyze future climatic extremes using the results of climate models?

(Asked by: username_0 on 2014-11-13)

What is the accepted methodology to predict future climatic extremes using the results of climate models?

I have recently read a report about **climatic extremes considering climate change** (MICE, 2002). The report says that researchers fitted extreme value distributions ([generalized extreme value](http://en.wikipedia.org/wiki/Generalized_extreme_value_distribution), [generalized Pareto](http://en.wikipedia.org/wiki/Generalized_Pareto_distribution)) to the intensity of predicted, future climatic actions, e.g. rain, snow, wind. Applying these models, events with a large [return period](http://en.wikipedia.org/wiki/Return_period) are used to assess the impact of climate change. Additionally, there is a recent Nature article by O’Gorman which also deals with future extreme events, particularly snow.

Considering that the predictions (projections per scenarios) can be made only in probabilistic terms. I would like to know how these predictions are made, what methodology are they using? I mean the actual climatic data, not the extreme value (statistical) analysis of them. For extreme value analysis, annual or more frequent maxima can/could be used. It is quite dubious that climate models would predict monthly or annual maxima of rain/snow for a certain region, up to the end of this century (or are climate models so sophisticated?).
Someone told me that on this site ([Earth System Grid Federation](http://esgf-data.dkrz.de/esgf-web-fe/)) there is an example of daily predicted snow data (this can be downloaded).

So, my main question is **how this data, these predictions, are produced. What are the underlying assumptions of the models?** Can these 100-year long simulations be used to predict extreme events within a 100 to 1000 year return period (these are common in engineering practice).

As far as I know, the climate models contain 'accurate' models (where the phenomenon is described by differential equations) and 'approximate' models (where empirical models are used). I guess the actual amount of precipitation for a given region belongs to the latter; in this case how uncertain are these models? (Surely the 'accurate' models have large uncertainty as well, but perhaps less).

---

I have an engineering background and I am interested in the effect of extreme climatic events on the reliability of structures; especially considering climate change. In order to study this, it would be great to know how reliable are the climate predictions regarding extreme events. If the probability distribution (or more complex probabilistic model of the actions) is given, the reliability of a structure (system) can be directly calculated. However, I am quite suspicious about the extremes predicted by the climate models.

It is quite hard to navigate through the thousand pages reports and find the probably one page long section which would answer my question. I would highly appreciate if someone could explain the main aspects of methodology, basic assumptions or point me to specific references, any help regarding the original question is welcomed.

---

MICE (2002). [Modelling the Impact of Climate Extremes](http://www.cru.uea.ac.uk/projects/mice/mice.pdf). Description of Work

Paul A. O’Gorman. (2014). [Contrasting responses of mean and extreme snowfall to climate change](http://www.nature.com/nature/journal/v512/n7515/full/nature13625.html). Nature. Volume 512. 7515. p. 416-418.

---

**Extension of the question:**

[Can climate models reliably predict meteorological extremes?](https://earthscience.stackexchange.com/questions/4248/can-climate-models-reliably-predict-meteorological-extremes)

**Tags:** meteorology, climate-change, precipitation, climate-models

> **Comments:**
> **username_0**: @SabreTooth Thank you for the link and for drawing attention to this question by offering the bounty!  

---

## 1 answers

### Answer by username_1 on 2015-01-08. Score: 14 | Accepted answer

Your question is fairly broad, and slightly vague so I don't know if I will be able to answer it in one go. If you would like any clarification, let me know.

## How are predictions made?

The basic process generally used for probabilistic forecasting of the global climate is something like:

1. Take one or more general circulation models (GCMs), and run multiple simulations over the projection period.
   * GCMs are models that attempt to replicate the physics of the climate system, including land and ocean processes. They can not replicate the physics *exactly*, because:
     1. they operate on scales of a few hundred meters at minimum, and so physical processes (which usually operate on *much* smaller scales) are scaled up and parameterised to work on the larger scale; and
     2. because for some of the physical processes (especially those that have to be parametrised to larger scales), there is not enough data to adequately fit them. When this happens, those model parameters are usually *calibrated* - a large number of runs are made, with different values for those parameters, and then the best parameter values are chosen.
   * Usually, you run the model for some period prior to the projection period, so that you can compare that to observations (spin-up period).
   * You need to provide input data to the model. Mostly, this just consists of solar forcing (changes in the sun's output), as well as expected greenhouse gas (GHG) emissions, and aerosol emissions (both human and volcanic).
   * Simulation output is in the same format as your observational data, and generally includes all of the important variables - temperature, precipitation, etc.
2. Put all of those simulations in an ensemble.
   * Often, simulations are "bias corrected", which usually means they are changed so that the model average matches the observation average over some period prior to the projection period - this might be the last 30-40 years. This is to allow for model drift (which is mostly chaotic, and can happen in any direction).
   * The distribution of the simulations in the ensemble is used to create probabilistic projections. For example, each simulation has a mean global annual temperature. You could make the assumption that the errors in the simulations are normally distributed (over the ensemble), and so make an estimate of that distribution, and use that to make probabilistic estimates. This is basically saying that if ~50% of the models are over a certain temperature, you expect that (assuming the models, the input data, and assumptions they are based on are reliable\*) there's a 50% chance that the global annual temperature of the earth would be over that temperature. A similar process can be used for the maximum temperature, or any other variable, and any statistics, including extremes indices. **None of these predictions is a single value - they are always probabilistic, although it's probably quite common for only the mean of that distribution to be reported**.
   * How you combine the information from the simulations in the ensemble is somewhat up to you. The basic method is as described above, and uses minimal assumptions about the data. It's also common for researchers to use a weighting methodology to estimate the ensemble mean, for example performance-based weighting, where models that perform better over the period before the projection are weighted more highly, with the assumption that they will perform better over the projection period too. Or you could weight based on model independence (if you're using multiple models), by weighting models that are less like other models more highly, in order to minimise bias from particular types of models (e.g. Bishop and Abramowitz 2013). *[I have a paper in review at the moment that investigates the efficacy of some of these methods, I'll link to it when it comes out]*
   * **Can this process predict changes in 1000-year events**? Yes, potentially, even when the projection period is usually more like 100 years. This is because 1 in 1000-year events are actually defined inversely - that is, they are thought to have a 0.1% chance of occurring *in any given year*. If your ensemble projects over 100 years, but has 100 simulations, then there are 10,000 years in which that a 1 in 1000 might occur. If you see it occurring 20 times, or 4 times, then you might get suspicious that things are changing. You probably need more than that to get a statistically significant result, but there are ensembles out there that are *really* big (e.g. Stainforth et al, 2005, which had 2,578 simulations totalling over 100,000 simulated
     years, and I think some of the [ClimatePrediction.net](http://www.climateprediction.net) have tens of thousands of simulations). Even without those large ensembles, if you assume particular distributions of extreme events where probability is a simple function of extremeness (e.g. Log-normal distribution or similar), then you can probably say something about large extremes based on the change in behaviour of less extreme events. Unfortunately, I am not aware of any experiments that look at the likely changes to very extreme events.

\* Model reliability is obviously a fairly active field of debate and research. Suckling and Smith (2012) indicates that GCM-based ensembles are better than basic statistical models, but probably not currently much better than some more advanced statistical models. However, that still means that they're at least on-par with the best options we have for forecasting, unless you're in to reading chicken entrails.

## References

* Bishop, C.H. & Abramowitz, G., 2013. Climate model dependence and the replicate Earth paradigm. Climate Dynamics, 41(3-4), pp.885–900. Available at: <http://link.springer.com/article/10.1007/s00382-012-1610-y> [Accessed September 17, 2013].
* Stainforth, D.A. et al., 2005. Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature, 433(7024), pp.403–406. Available at: <http://www.nature.com/nature/journal/v433/n7024/abs/nature03301.html>.
* Suckling, E.B. & Smith, L.A., 2013. An Evaluation of Decadal Probability Forecasts from State-of-the-Art Climate Models\*. Journal of Climate, 26(23), pp.9334–9347. Available at: <http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-12-00485.1> [Accessed January 8, 2015].

> **Comments:**
> **username_2**: nice answer! just regarding the last point (Can this process predict changes in 1000-year events?) it may be worth defining what you mean by members.  
> **username_1**: @username_2: thanks, changed that to simulations.  
> **username_0**: Thank you very much for the detailed answer, it is very helpful and informative! There are some points which are not yet clear, thus I extended the OP (there is not enough space here). Thank you for your help in advance.  
> **username_1**: @Arpi: I don't think that this method of asking questions is very useful in this format. Your original question was already huge, and hard to follow, and this makes it worse. You are better off asking separate questions, and keeping them as small and self-contained as possible. It makes the information more re-usable for other people, as well as giving other people a chance to answer questions that they might be more qualified for. You can reference those new questions from this question, reference this question from them as well.  
> **username_0**: Thank you for the suggestion, I opened a [new question](http://earthscience.stackexchange.com/questions/4248/can-climate-models-reliably-predict-meteorological-extremes).  

---

