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First:

Climate models don't "predict." They project what will happen given a set of initial conditions (and may include several scenarios). And they have done that very well.

Some are still "under the mistaken impression that concern about global warming is based on climate models, which in reality play little role in our understanding -- our understanding is based mainly on how the Earth responded to changes of boundary conditions in the past and on how it is responding to on-going changes."- Dr. James Hansen

Part of the problem here stems from people either misunderstanding or deliberately misrepresenting how predictive models work. Many people have the unrealistic expectation that the observed data need to be a near perfect match for the prediction line, but that’s not actually how things work.

Why can we understand climate?

It’s based upon basic physics which follows the same principles as other laws of nature.

“The physics we use to understand the earth’s climate system is the same physics that explains how stoves, fridges, airplanes and more work. And most people don’t really have a problem with the physics of non-linear fluid dynamics and radiative transfer that have been well understood for decades, even centuries.” (Climate scientist Katharine Hayhoe.)

Long term predictions have been accurate.. There is a very simple reason for this:

Some people argue that climate models are unreliable if they don't make perfect short-term predictions. However, a number of unpredictable influences such as ocean and solar cycles have short-term influences on climate. Over the long term, these effects average out, which is why climate models do so well at long-term predictions.

IPCC explains this difference here:

IPCC confirms that short term internal climate variability, in any given 15-year period is hard to predict.

"For the period from 1998 to 2012, 111 of the 114 available climate-model simulations show a surface warming trend larger than the observations"

Then they confirms their CMIP5 models are accurate and explains recent 15-year period short term predictions, showing a surface warming trend larger than the observations, was because of El Ninò:

"There is hence very high confidence that the CMIP5 models show long-term GMST trends consistent with observations, despite the disagreement over the most recent 15-year period. Due to internal climate variability, in any given 15-year period the observed GMST trend sometimes lies near one end of a model ensemble, an effect that is pronounced in Box TS.3, Figure 1a, b as GMST was influenced by a very strong El Niño event in 1998."

https://www.ipcc.ch/pdf/assessme...

Reality check december 2018:

"Twenty years ago in Nature we concluded that recent warming was unprecedented in at least six centuries" (https://www.nature.com/articles/33859

This year in Nature, scientists concluded it's unprecedented in at least eleven millennia
(
https://www.nature.com/articles/nature25464

Here are some more actual predictions from Global Climate Models all of which have proven correct:

1. That the globe would warm, and about how fast, and about how much.

2. That the troposphere would warm and the stratosphere would cool.

3. That nighttime temperatures would increase more than daytime temperatures.

4. That winter temperatures would increase more than summer temperatures.

5. Polar amplification (greater temperature increase as you move toward the poles).

6. That the Arctic would warm faster than the Antarctic.

7. The magnitude (0.3 K) and duration (two years) of the cooling from the Mt. Pinatubo eruption.

8. They made a retrodiction for Last Glacial Maximum sea surface temperatures which was inconsistent with the paleo evidence, and better paleo evidence showed the models were right.

9. They predicted a trend significantly different and differently signed from UAH satellite temperatures, and then a bug was found in the satellite data.

10.The amount of water vapor feedback due to ENSO.

11. The response of southern ocean winds to the ozone hole.

12. The expansion of the Hadley cells.

13. The poleward movement of storm tracks.

14. The rising of the tropopause and the effective radiating altitude.

15. The clear sky super greenhouse effect from increased water vapor in the tropics.

16. The near constancy of relative humidity on global average.

17. The expanded range of hurricanes and cyclones--a year before Cyclone Catarina showed up off the coast of Brazil, something which had never happened before.

Climate Models - OSS Foundation

LETS LOOK AT THE MODELS:

CLIMATE MODELS HAVE BEEN VERY ACCURATE:

Worrisome first quarter of 2017 climate trends » Yale Climate Connections

" the close match between projected and observed warming since 1970 suggests that estimates of future warming may prove similarly accurate."

A study in the journal Science Advances, joins a growing body of literature that suggests the models are on track after all. And while that may be worrisome for the planet, it’s good news for the scientists working to understand its future. Climate models are even more accurate than you thought The difference between modeled and observed global surface temperature changes is 38% smaller than previously thought. Global climate models aren’t given nearly enough credit for their accurate global temperature change projections. As the 2014 IPCC report showed, observed global surface temperature changes have been within the range of climate model simulations.

Factcheck: Climate models have not 'exaggerated' global warming

Slow climate mode reconciles historical and model-based estimates of climate sensitivity

Robust comparison of climate models with observations using blended land air and ocean sea surface temperatures

https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2015GL064888

IPCC:

Comparing CMIP5 & observations

A global perspective on CMIP5 climate model biases

NASA scientist Gavin Schmidt:

Comparing what climate scientists said in the early 80s with today:

Comparing what climate scientists said in the early 80s with today:

Listening to James Hansen on Climate Change, Thirty Years Ago and Now

30 years ago global warming became front-page news – and both Republicans and Democrats took it seriously

The First Climate Model Turns 50, And Predicted Global Warming Almost Perfectly

Modeling the Earth's climate is one of the most daunting, complicated tasks out there. If only we were more like the Moon, things would be easy. The Moon has no atmosphere, no oceans, no icecaps, no seasons, and no complicated flora and fauna to get in the way of simple radiative physics. No wonder it's so challenging to model! In fact, if you google "climate models wrong", eight of the first ten results showcase failure. But headlines are never as reliable as going to the scientific source itself, and the ultimate source, in this case, is the first accurate climate model ever: by Syukuro Manabe and Richard T. Wetherald. 50 years after their groundbreaking 1967 paper, the science can be robustly evaluated, and they got almost everything exactly right.

The effects and dangers of human made climate change was well known and understood by the US military and the president already in the 1960s.

Fifty years ago: The White House knew all about climate change

On November 5, 1965, President Lyndon B. Johnson’s White House released “Restoring the Quality of our Environment”, a report that described the impacts of climate change, and foretold dramatic Antarctic ice sheet loss, sea level rise, and ocean acidification.

https://goo.gl/ufDL5Z

That 1965 White House report stated:

Carbon dioxide is being added to the earth’s atmosphere by the burning of coal, oil, and natural gas at the rate of 6 billion tons a year. By the year 2000 there will be about 25 percent more CO2 in our atmosphere than present.”[…] “This will modify the heat balance of the atmosphere to such an extent that marked changes in climate, not controllable through local or even national efforts, could occur.

On the 50th anniversary of the White House report, CO2 concentrations in the atmosphere are indeed at 399 ppm: 25 percent over 1965 levels, exactly as predicted 50 years ago.

http://ourchildrenstrust.org/sit...

Scientists warned the President about global warming 50 years ago today | Dana Nuccitelli

BONUS:

Q&A: How do climate models work?

https://www.carbonbrief.org/qa-h...

There is an excellent description of climate models evaluation in the following IPCC report:

http://www.ipcc.ch/pdf/assessmen...

If anything else, I suggest you read page 600-601 that address how reliable current models are.

The last paragraph states:
"In summary, confidence in models comes from their physical basis, and their skill in representing observed climate and past climate changes. Models have proven to be extremely important tools for simulating and understanding climate, and there is considerable confidence that they are able to provide credible quantitative estimates of future climate change, particularly at larger scales. Models continue to have significant limitations, such as in their representation of clouds, which lead to uncer- tainties in the magnitude and timing, as well as regional details, of predicted climate change. Nevertheless, over several decades of model development, they have consistently provided a robust and unambiguous picture of significant climate warming in re-sponse to increasing greenhouse gases."

Gilles Fecteau's answer to Is Freeman Dyson correct when he says that climate modelling experts are deluded?


BONUS 2 - NEW SCIENCE ON CLIMATE SENSITIVITY:

With the increased knowledge on climate sensitivity added , there is every reason to believe future climate models will be even better:

A new study by Kate Marvel, Gavin Schmidt, Ron Miller, and Larissa Nazarenko at the NASA Goddard Institute for Space Studies appears to have found the answer. They drew upon previous research by Drew Shindell and Kummer & Dessler, who identified a flaw in studies taking the energy budget approach. Those studies had assumed that the Earth’s climate is equally sensitive to all forcings.In reality, as world-renowned climate scientist James Hansen noted in a 1997 paper, some forcings are more efficient at causing the Earth’s surface temperature to change than others. Those in which the effects are focused in the northern hemisphere tend to be more efficient, for example. [...] The NASA study shows that the previous estimates were indeed biased low, and correcting for that bias brings them into agreement with estimates using other approaches. A number of independent studies using near-global satellite data find positive feedbackand high climate sensitivity. [...] Climate sensitivity is a measure of how much our climate responds to an energy imbalance. The most common definition is the change in global temperature if the amount of atmospheric CO2 was doubled. If there were no feedbacks, climate sensitivity would be around 1°C. But we know there are a number of feedbacks, both positive and negative. So how do we determine the net feedback? An empirical solution is to observe how our climateresponds to temperature change. We have satellite measurements of the radiation budget and surface measurements of temperature. Putting the two together should give us an indication of net feedback.

Less than 2 °C warming by 2100 unlikely The likely range of global temperature increase is 2.0–4.9 °C, with median 3.2 °C and a 5% (1%) chance that it will be less than 2 °C (1.5 °C). Population growth is not a major contributing factor. Our model is not a ‘business as usual’ scenario, but rather is based on data which already show the effect of emission mitigation http://policies.Net positive feedback is confirmed by many different lines of evidence.

Spread in model climate sensitivity traced to atmospheric convective mixing

A Less Cloudy Future: The Role of Subtropical Subsidence in Climate Sensitivity

The Impact of Global Warming on Marine Boundary Layer Clouds over the Eastern Pacific—A Regional Model Study

Greater future global warming inferred from Earth’s recent energy budget.

Tan I, Storelvmo T, and Zelinka MD: Observational constraints on mixed-phase clouds imply higher climate sensitivity. Science 352(6282):224–27, 2016.

Shaffer G, Huber M, Rondanelli R, and Pepke Pedersen JO: Deep-time evidence for climate sensitivity increase with warming. Geophysical Research Letters 43(12):6538–45, 2016.

Armour KC: Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks. Nature Climate Change 7(5):331–35, 2017

The most likely value of ECS constrained by different lines of evidence is 3 °C, not lower than that.Knutti R, Rugenstein MA, and Hegerl GC: Beyond equilibrium climate sensitivity. Nature Geoscience 10:727–736, 2017.

Greater future global warming inferred from Earth’s recent energy budgethttps://www.nature.com/articles/nature24672

All the models and evidence confirm a minimum warming close to 2°C for a doubling of atmospheric CO2 with a most likely value of 3°C and the potential to warm 4.5°C or even more. Even such a small rise would signal many damaging and highly disruptive changes to the environment. In this light, the arguments against reducing greenhouse gas emissions because of climate sensitivity are a form of gambling.

Papers on climate sensitivity estimates

https://agwobserver.wordpress.com/2009/11/05/papers-on-climate-sensitivity-estimates/

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