As an example of my methodology in conducting literature searches, I will use the years 2013 and 2014 as reported in Powell 2016 and shown in bar 12 on the chart on the home page. I used the ISI Web of Science (WoS), a subscription-based, Internet-hosted reference service of Thompson-Reuters to which many academic libraries subscribe. The WoS provides a searchable database of every scientific article published in peer-reviewed journals. I searched as follows:
Web of Science Core Collection
Enhanced Science Index
Publication Years: 2013 and 2014
Document Type: Article
Topics: “global warming” or “global climate change” or “climate change.” (Quotations marks essential)
Remove duplicates by combining searches using the OR command.
I exported the search results to an Excel file. Over a period of many months, I reviewed the titles and abstracts of the articles.

Some points to note:
1. I found that 5 of 24,210 articles rejected anthropogenic global warming [AGW], a rate of 1 in 4,842 or 0.02%. Since two articles had the same author, the rate of rejection by authors is 4 in 69,406 or 1 author in 17,352.

2. To classify an article as a rejection, I looked for a clear statement that AGW is false or that some other process better explains the rise in global temperature. I did not count articles that report some discrepancy, such as the growth in Antarctic sea ice for example, but do not use that discrepancy as the basis for claiming that AGW is false. Any theory has discrepancies, observations that the theory cannot yet explain. They provide the next set of research problems. One discrepancy does not falsify a theory. Note that I did not rule out any articles, but reviewed each that turned up in my search. I did not engage in any abstruse statistics--I just read the titles and abstracts of the articles and made a judgment.

3. I do not directly obtain the percentage who accept AGW, but infer it from the number of abstracts and authors who reject the theory, as explained in my articles in Bulletin of Science, Technology, and Society. Some will argue to the contrary that unless an author explicitly endorses the theory in question, one cannot know whether that author accepts the theory. Hogwash. Surveys of the peer-reviewed literature not only on AGW but on Darwinian evolution, impact cratering, and plate tectonics show beyond a shadow of a doubt that authors seldom endorse the ruling paradigm of their discipline.

4. Some will respond that the website Popular Technology lists “1350+ Peer-Reviewed Papers Supporting Skeptic Arguments Against ACC/AGW Alarmism” and that I failed to count these many articles. But as the title indicates, rather than stating clearly that AGW is false, articles on that site “support arguments” and many do not even do that. Just to take one example, the most recent article (from 2013) on the site under the heading Antarctica is titled “Seismic detection of an active subglacial magmatic complex in Marie Byrd Land, Antarctica.” The abstract ends, “Together, these observations provide strong evidence for ongoing magmatic activity and demonstrate that volcanism continues to migrate southwards along the Executive Committee Range. Eruptions at this site are unlikely to penetrate the 1.2 to 2-km-thick overlying ice, but would generate large volumes of melt water that could significantly affect ice stream flow.” What does this have to do with AGW? Nothing. Magmatic activity does not explain why between 2002 and 2012 Antarctica lost 69 ± 18 gigatons (billion tons) of land ice per year. One might as well say that the hot spot under Yellowstone is responsible for global warming. Note too that the authors of this paper do not mention global warming or climate change. What right do the deniers at Pop Tech have to draw conclusions that the scientists who wrote the original articles did not?

5. I do not claim to have found every peer-reviewed article on anthropogenic global warming that came out during 2013 and 2014. Some may have fallen outside my search criteria. What I do claim is that there is no reason to suppose that such articles have a higher proportion of rejections than those within my search. If I am wrong, anyone can put in the effort and show it.

6. Based on past experience, I know that some will object to my results because, they will say, a given article is “not about global warming” and therefore should not have been included in my database. An example is an article from 2013 titled “Investigation on critical breakdown electric field of hot sulfur hexafluoride/carbon tetrafluoride mixtures for high voltage circuit breaker applications.” It is surely true that if all one knows is the title of this article, it does not appear to be about global warming. But its authors say it is: the first line of the abstract reads, “Sulfur hexafluoride (SF6) gas, widely used in high-voltage circuit breakers, has a high global warming potential and hence substitutes are being sought.” The use of “global warming” in the abstract is the reason this article came up in my WoS search. Rather than deciding for myself whether a given article is “about global warming,” whatever that means exactly, and thus introducing more subjectivity, I let the WoS and authors decide. That way anyone can reproduce my search and I include more articles rather than fewer.

7. Others will say, “But surely it is impossible for anyone to read 24,210 scientific articles.” Probably so. But note that I read only titles and abstracts, not entire articles. And note that Cook et al. (2013) report, “In March 2012, we searched the ISI Web of Science for papers published from 1991–2011 using topic searches for ‘global warming’ or ‘global climate change.’” They read several more in May 2012, for a total of about 12,000. If nine authors can review 12,000 abstracts in little more than one month, one author (me) can review twice that many in two years.

Anyone can get an idea of how long it takes to read these abstracts by downloading and reviewing an Excel database I have prepared that contains a random selection of 300 abstracts from my literature survey for 2014. Download the database here. (Open it in Excel as the Dropbox view may be garbled.) See how many rejections you find and how long it takes you.

The Five Rejecting Articles in 2013 and 2014
So that the reader can understand what the rejecting articles are like, as an example I list below the five articles in my search from 2013 and 2014 that rejected anthropogenic global warming. The citations are as of late April 2016 and exclude self-citations. You can see that although these articles were published in peer-reviewed journals, they had no impact whatsoever on science.

Avakyan, S., 2013. The role of solar activity in global warming. Herald of the Russian Academy of Sciences. 83, 275-285.
Citations: 0
Abstract: "The author associates the recently observed climate warming and carbon dioxide concentration growth in the lower atmospheric layers with variations of solar-geomagnetic activity in global cloud formation and the significant decrease in the role of forests in carbon dioxide accumulation in the process of photosynthesis. The contribution of the greenhouse effect of carbon-containing gases to global warming turns out to be insignificant."
Note: Carbon isotopes show that the growth in atmospheric CO2 did not come from modern deforestation but from ancient plants, i.e., from fossil fuels.

Avakyan, S., 2013. Problems of climate as a problem of optics. Journal of Optical Technology. 80, 717-721.
Citations: 0
Abstract: "This paper discusses the causes of present-day climate changes, obtained at S. I. Vavilov State Optical Institute in recent years. The main conclusions relate to the relationship of the contribution of natural sources (solar-geomagnetic activity) and anthropogenic sources of action on the weather and climate. It is shown that the determining mechanisms for controlling the weather-climatic characteristics are the processes of aerospace physical optics. The main source of the global warming observed in recent decades is an increase in solar activity on a secular scale, the chief channel of action of solar-geomagnetic activity is the control of the condensation-cluster mechanism of cloud nucleation, and the strongest energy effect is the regulation of the thermal radiation fluxes of the underlying surface by optically thin clouds. The greenhouse effect based on carbon-containing gases makes an insignificant contribution to global warming. (C) 2014 Optical Society of America."
Note: This is to say, “It’s the Sun.” But we know it isn’t the Sun because while global temperature has risen, the Sun’s output has stayed about the same.

Gervais, F., 2014. Tiny warming of residual anthropogenic CO2. International Journal of Modern Physics B. 28, 1450095.
Citations: 1
Abstract: "The residual fraction of anthropogenic CO2 emissions which has not been captured by carbon sinks and remains in the atmosphere, is estimated by two independent experimental methods which support each other: the C-13/C-12 ratio and the temperature-independent fraction of d(CO2)/dt on a yearly scale after subtraction of annual fluctuations the amplitude ratio of which reaches a factor as large as 7. The anthropogenic fraction is then used to evaluate the additional warming by analysis of its spectral contribution to the outgoing long-wavelength radiation (OLR) measured by infrared spectrometers embarked in satellites looking down. The anthropogenic CO2 additional warming extrapolated in 2100 is found lower than 0.1 degrees C in the absence of feedbacks. The global temperature data are fitted with an oscillation of period 60 years added to a linear contribution. The data which support the 60-year cycle are summarized, in particular sea surface temperatures and sea level rise measured either by tide gauge or by satellite altimetry. The tiny anthropogenic warming appears consistent with the absence of any detectable change of slope of the 130-year-long linear contribution to the temperature data before and after the onset of large CO2 emissions."

The one citation of this article, and the only citation (excepting self-citations) in this group of five, is by Nicola Scafetta. To learn more about this citation, see here.

Happer, W., 2014. Why has global warming paused? International Journal of Modern Physics A. 29, 14600033.
Citations: 0
No abstract
Note: But global warming did not pause.

Hug, H., 2013. "The Climate Models are inadequate" Heinz Hug queries the Significance of CO2 for Climate Change. Nachrichten Aus Der Chemie. 61, 132-132.
Citations: 0
No abstract but the last paragraph reads,"It is quite evident that there is no correlation between the atmospheric CO2 concentration and water evaporation. The latter does not depend on CO2 but on the water temperature. That, in turn, depends primarily on the screening by clouds which depends on the incoming cosmic radiation which varies with the rhythm of the solar magnetic field, [ref. 7]. This also explains why, without the action of IR-active trace gases there was both a Roman and Medieval climate optimum."
Note: Hug attributes global warming to cosmic radiation, a claim that has been roundly debunked, see here. Nachrichten Aus Der Chemie seems to be a trade publication like our U.S. C&E News. Hug’s article appears on a page headed, “Pro and Contra.” Was this article actually peer-reviewed, or is it an opinion piece? Hug is clearly giving his opinion and provides no new data or information, but rather a mish-mash of long-refuted denier talking points.