It’s hard to find a reputable scientist who denies that human emissions of greenhouse gases are warming the planet and that there will be consequences for human society and the biological health of the planet. There are a few holdouts who, for various reasons, either think humans are not causing warming or that the warming will not have much consequence.

Some members of this vocal minority spend a lot of time trying to convince the public that they are right. They write letters to newspapers, appear in slick movies, give press conferences, promote their views to Congress, and so on. Their high profile gives the public a false sense that there are two relatively equal-sized bodies of experts that cannot agree on climate change; this is not true.



An even smaller subset also tries to publish their views in the scientific literature – the dueling ground for experts. Sometimes these contributions have been useful, adding some nuance to the discussion, but all too often they have proven to be of very poor quality when other scientists have had a chance to dissect them.

A few months ago, I co-authored an article which charted the different quality in scientific output from the Dwindling Few contrarians compared to the majority of experts. My colleague, Dana Nuccitelli, summarized the article here. What we show is that the Dwindling Few have had a very poor track record – having papers rebutted time after time after time because of errors they have made. The low quality of their research has caused journal editors resign, and they have wasted the time of their colleagues who have had to publish the rebuttals to their work.



Well, again this year, I’ve wasted my time (and my colleagues’ time) by rebutting a 2014 paper published by the darling of the Dwindling Few, Roy Spencer. Dr. Spencer wrote a paper earlier this year that used a very simple ocean model to suggest that standard climate models overestimate the Earth’s sensitivity to carbon dioxide increases in the atmosphere. You can see his manuscript here although it is behind a paywall so you will have to shell out about $40 to read it.

Dr. Spencer and his colleague Danny Braswell made a number of basic math and physics errors in the article that call into question their conclusions.



Before we get into the errors, let’s talk about what their model does. They basically treated the ocean like a non-moving fluid and allowed heat to diffuse into the ocean depths. They did allow some mixing in the upper layers through added terms in a one-dimensional equation. The model neglects down-welling or up-welling of waters which occur particularly at the poles. In the end, they end up with a bunch of tunable parameters, which they adjusted so that the model output matches the measured temperature history.

So, what were the errors and poor modeling choices?

The model treats the entire Earth as entirely ocean-covered The model assigns an ocean process (El Niño cycle) which covers a limited geographic region in the Pacific Ocean as a global phenomenon The model incorrectly simulates the upper layer of the ocean in the numerical calculation. The model incorrectly insulates the ocean bottom at 2000 meters depth The model leads to diffusivity values that are significantly larger than those reported in the literature The model incorrectly uses an asymmetric diffusivity to calculate heat transfer between adjacent layers The model contains incorrect determination of element interface diffusivity The model neglects advection (water flow) on heat transfer The model neglects latent heat transfer between the atmosphere and the ocean surface.

Now, simple models like this one can still be useful, even though they necessarily gloss over some details. But some of these errors and omissions are pretty obvious, and would have been easy to fix. For instance, by treating the entire Earth as water covered, Spencer and Braswell omit 30% of the surface of the Earth that’s land-covered, and which heats up faster than the oceans. They then compare the CO 2 sensitivity of their ocean-only model to those obtained from more realistic models — apples and oranges. Furthermore, the application of a very local phenomenon (El Niño) to the entire globe just doesn’t make much sense.



But, I here want to talk about the numerical errors, in particular items 3, 4, 6, and 7. In order to explain what went wrong, I need to talk about the underlying math.

The diffusion equation Spencer and Braswell used has a second derivative of temperature with respect to depth in the water. To solve this equation, the common approach is to break the ocean into a number of finite slabs of water and approximate the derivatives by finite differences. So far, so good. The problems arise when you apply what are called boundary conditions. That is, conditions at the ocean surface and the bottom of the ocean. At both locations, Spencer and Braswell’s approach fails.

First, at the ocean surface, you are required to make calculations at the exact surface. In fact, the physical phenomenon which Spencer and Braswell introduce require actual surface temperatures. However, in their computer program, no surface temperatures were ever determined. They basically transcribed a temperature 25 meters deep into the ocean onto the surface (and no, they didn’t do this because of ocean mixing). At the ocean bottom, Spencer and Braswell insulated the ocean, and thereby did not allow any energy exchange there.

Finally, Spencer and Braswell incorrectly used upstream element-diffusivity values in their heat transfer term. They were obligated to use mean values representing adjacent elements. When we implemented the corrected numerical scheme, the quality of the results dissolved. Once again, Roy Spencer has failed in his attempt to show the Earth is not very sensitive to climate change.

These errors are the sort of thing that could have been avoided by consulting any elementary textbook on heat transfer, or any number of papers that have published similar ocean diffusion models. My colleague and co-author, Dr. Barry Bickmore from BYU described the situation like this,

What our paper shows is that Spencer and Braswell’s model was flawed on a very basic level, in such a way that it could have predicted wildly low climate sensitivity to greenhouse gases. Whatever sensitivity their model predicts, the true value is probably significantly higher, and therefore probably in the range indicated by the IPCC.

Spencer and Braswell might object that their paper says ocean temperature measurements “might not provide a very strong constraint on our estimates of climate sensitivity.” Let’s just say that Roy Spencer forgot to include that little detail when he recently told a U.S. Senate committee, “Our most recent peer-reviewed paper on this subject... has arrived at a climate sensitivity of only 1.3 degree C for a doubling of atmospheric carbon dioxide, based upon a variety of global measurements, including warming of the global oceans since the 1950s.”



In a recent blog post, Dr. Spencer challenged well-known and well-respected Dr. Andrew Dessler to a debate. While the peanut gallery was busy chiding Dessler for not taking the bait, it perhaps is important to remember that the place where scientists debate is in the scientific literature. It is a venue that has not been kind to Dr. Spencer in the past decade or so. We published our latest work in an open-source journal here so that any interested reader can see the results for themselves.

