AbstractWhen comparing climate models to observations, it is often observed that the mean over many models has smaller errors than most or all of the individual models. This paper will show that a general consequence of the nonintuitive geometric properties of high-dimensional spaces is that the ensemble mean often outperforms the individual ensemble members. This also explains why the ensemble mean often has an error that is 30% smaller than the median error of the individual ensemble members. The only assumption that needs to be made is that the observations and the models are independently drawn from the same distribution. An important and relevant property of high-dimensional spaces is that independent random vectors are almost always orthogonal. Furthermore, while the lengths of random vectors are large and almost equal, the ensemble mean is special, as it is located near the otherwise vacant center. The theory is first explained by an analysis of Gaussian- and uniformly distributed vectors in high-dimensional spaces. A subset of 17 models from the CMIP5 multimodel ensemble is then used to demonstrate the validity and robustness of the theory in realistic settings.
Journal of Climate – American Meteorological Society
Published: Feb 28, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.
All for just $49/month
Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.
Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.
It’s easy to organize your research with our built-in tools.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera