The latest analysis is known as the Stern report. From chapter one, on climate science:

Climate models use the laws of nature to simulate the radiative balance and flows of energy and materials. These models are vastly different from those generally used in economic analyses, which rely predominantly on curve fitting. Climate models cover multiple dimensions, from temperature at different heights in the atmosphere, to wind speeds and snow cover. Also, climate models are tested for their ability to reproduce past climate variations across several dimensions, and to simulate aspects of present climate that they have not been specifically tuned to fit.

I think that few economists would concede that we “rely predominantly on curve fitting.”

The accuracy of climate predictions is limited by computing power. This, for example, restricts the scale of detail of models, meaning that small-scale processes must be included through highly simplified calculations. It is important to continue the active research and development of more powerful climate models to reduce the remaining uncertainties in climate projections.

I seriously doubt that computing power is the binding constraint in climate modeling. My guess is that you could raise the computing power by a factor of 10 without increasing the reliability of the models. My guess is that the binding constraints are lack of data and the large number of unknown processes.

Several studies have estimated climate sensitivity by benchmarking climate models against the observed warming trend of the 20th century

In other words, curve fitting.

The distributions share the characteristic of a long tail that stretches up to high temperatures. This is primarily because of uncertainty over clouds and the cooling effect of aerosols. For example, if cloud properties are sensitive to climate change, they could create an important addition feedback. Similarly, if the cooling effect of aerosols is large it will have offset a substantial part of past warming due to greenhouse gases, making high climate sensitivity compatible with the observed warming.

In other words, our understanding is limited by more than just mere computing power.

The main conclusion of the report:

Using the results from formal economic models, the Review estimates that if we don’t act, the overall costs and risks of climate change will be equivalent to losing at least 5% of global GDP each year, now and forever. If a wider range of risks and impacts is taken into account, the estimates of damage could rise to 20% of GDP or more.

In contrast, the costs of action – reducing greenhouse gas emissions to avoid the worst impacts of climate change – can be limited to around 1% of global GDP each year.

One percent of global GDP is a lot–close to one trillion dollars. My guess is that if you think outside the box, you can eliminate global warming for a lot less money. Suppose you told scientists and engineers to come up with a way to monkey around with chemicals and stuff to reduce global average temperature. My guess is that the total cost of that approach, including research and implementation, would be only a few billion bucks, give or take.

Fighting man-made climate change with more man-made climate change almost has to be more cost-effective than fighting man-made climate change by trying to de-industrialize. But it would not satisfy the religious and political longings that are at the heart of the global warming crusade.