Abstract
Given weak empirical evidence for global warming, climate scientists fall back on climate models to provide the strongest case for climate change. Although computer models of the atmosphere and oceans are solidly grounded in physics, there remains too much that is arbitrary. It is necessary to provide a path of future carbon dioxide emissions before climate models can forecast a future climate scenario. Emission scenarios rely on projections of population and income growth, convergence of per capita incomes between rich and poor countries, technological change, resource availability, et cetera. Not only are the assessment models used to develop emission scenarios spotty, but they assume significant convergence in incomes; indeed, for scenarios that lead to the highest temperature forecasts, the least well off on Earth have per capita incomes that exceed those of rich countries today. Then four types of climate models are described, and a simple energy balance model is used to demonstrate the sensitivity of results to model parameters. Finally, the validity of climate models is considered in greater detail with answers provided to the following questions: How sensitive are numerical solutions of nonlinear models to changes in starting values, solution algorithms and so on? Do climate modelers follow standard guidelines for making forecasts? Do predictions from climate models accord with observation?
Science is the belief in the ignorance of experts – Richard Feynman, Nobel Physicist
Unfortunately, scientific research can be suitably slanted to support just about anything. – William Dembski, mathematician and proponent of Intelligent Design, in The End of Christianity (Nashville, TN: BH Publishing, 2009, p. 161)
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Notes
- 1.
The discussion of the storylines is based on the Summary for Policymakers (IPCC 2000).
- 2.
This illustration comes from Spencer (2010).
- 3.
The values of the constants are as follows: c = 299,792,458 m/s; h = 6.626068 × 10−34 m2∙kg/s; k = 1.3806504 × 10−23 J/K, where J refers to Joules (1 J = 1 W∙s) and K to Kelvin (−273.15 K = 0 °C). The Boltzmann constant equals the gas constant (= 8.314472 J/K/mol, where mol refers to moles) divided by the Avogadro constant (= 6.626068 × 1023 mol−1), and links the macroscopic and microscopic worlds. Unlike k and h, however, σ is not a universal constant of physics as it depends on the geometry of the situation (see Gerlich and Tscheuschner 2009, p.21).
- 4.
Other than the 11-year solar cycle, the IPCC does not identify any other event or cause that might contribute to solar flux. This is examined further in Chap. 5.
- 5.
- 6.
The choice of λ (climate sensitivity) here follows standard practice but should not be confused with the λ (wavelength) used in equation (4.1), which also follows standard practice.
- 7.
Factor f B cannot be added or multiplied, so it has no real mathematically-useful function.
- 8.
Notice that equation (4.15) is identical to (1.4) in McGuffie and Henderson-Sellers.
- 9.
See http://unfccc.int/resource/brazil/climate.html (viewed June 17, 2010).
- 10.
Pierrehumbert (2011) argues to the contrary, attributing one-third of the greenhouse effect to the small amount of carbon dioxide in the atmosphere. But he ignores entirely cloud albedo, indicating that a reduction in atmospheric CO2 would “ultimately spiral Earth into a globally glaciated snowball effect” as clouds disappeared, while rising CO2 would do the opposite.
- 11.
It should be noted that this is extremely speculative; indeed, Beilman et al. (2009) find that thawing of the permafrost might actually promote an increase in peat carbon sequestration.
- 12.
- 13.
A discussion can be found at http://www.drroyspencer.com/2009/02/what-about-the-clouds-andy/(posted February 21, 2009, viewed September 2, 2010). There Roy Spencer points out that there are two components to the energy radiative balance: (1) absorbed/reflected solar, shortwave (SW) radiation; and (2) emitted infrared, long-wave (LW) radiation. He argues that Dessler et al. (2008) and the IPCC models only take into account the LW radiation (in which case he gets identical results). However, they ignore SW radiation, which leads to the negative as opposed to positive feedback from water vapor.
- 14.
This implies that a fine-grid (2° latitude × 2° longitude) model, with 20 vertical layers, a 20-min time step, and projecting climate 50 years into the future must keep track of 851,472,000,000 different values of one variable alone!
- 15.
For example, the Mount St Helen’s eruption of May 18, 1980, led to enhanced 1980–1981 crop yields in the Palouse region of eastern Washington. Volcanic ash absorbed and held moisture, which aided crop growth in this moisture constrained region.
- 16.
Although our approach is similar to that of Spencer (2010), we employ somewhat different assumptions and a more complex method for addressing randomness of solar and ocean radiative fluxes.
- 17.
An excellent discussion of a mean-reverting stochastic process is provided in Dixit and Pindyck (1994, pp.60–79).
- 18.
As discussed in Chap. 5, some solar physicists argue that changes in the sun’s activities and its magnetic field can impact the Earth’s climate. These cycles operate much like a mean-reverting stochastic process and could be modeled that way, but the rate of reversion would be longer as would the time horizon required to investigate some of the sun’s cycles.
- 19.
Examples include Norway’s Nobel physicist Ivar Giaever and a group of 54 noted physicists led by Princeton’s William Happer (see ‘The Climate Change Climate Change’ by K.A. Strassel, Wall Street Journal, June 26, 2009 at http://online.wsj.com/article/SB124597505076157449.html, viewed August 26, 2010). Happer provided testimony before the U.S. Senate Environment and Public Works Committee (chaired by Barbara Boxer) on February 25, 2009. Highly regarded physicist Harold Lewis withdrew his membership in the American Physical Society (APS) because of their 2007 pro-anthropogenic global warming stance; Giaever resigned in 2011 for the same reason. Both recommend that APS withdraw the statement as it is blatantly false and a black mark on the association (see http://wattsupwiththat.com/2010/11/06/another-letter-from-hal-lewis-to-the-american-physical-society/#more-27526 viewed November 14, 2010). Other physicists include Freeman Dyson, James Wanliss (2010), a group led by Danish physicist Henrik Svensmark (see Chap. 5), Russian solar physicist Vladimir Bashkirtsev (and almost all other solar physicists), German physicists Gerlich and Tscheuschner (2009), the Italian Nicola Scafetta (2010), Dutch physicist Cornelis de Jager, and the Hungarian Miskolczi (2007). Other scientists have also been critical of climate models, including geologists such as Ian Plimer (2009).
- 20.
A wonderful novel by Giles Foden (2009) gives some notion of the problems forecasting future climate because of difficulties in measuring and predicting turbulence in the real world.
- 21.
An example is found in van Kooten et al. (2011). The problem involves finding the optimal level of ducks to hunt given various degrees of wetland protection. As discussed by the authors, a very slight change in the estimated parameter on a double-logarithmic function led to a difference in the optimal number of ducks that the authority might permit hunters to harvest in a season from about 1.5 million to over 30 million. A change in functional form, on the other hand, prevented any solution from being realized. Yet, the model involved no more than three nonlinear equations.
- 22.
Green and Armstrong (2007) examine the climate models described in Chapter 8 of the IPCC’s Working Group I report, and conduct a forecasting audit. They chose this chapter because, compared to Chapter 10, it provides more “useful information on the forecasting process used by the IPCC to derive forecasts of mean global temperatures” (p.1006). Despite this, Chapter 8 was “poorly written, … writing showed little concern for the target readership … [and] omitted key details on the assumptions and the forecasting process that were used” (p.1007). While the authors of Chapter 8 (IPCC WGI 2007) claimed that the forecasts of future global temperatures are well founded, the language used through the chapter was imprecise and the message conveyed lack of confidence in the projections (p.1012).
- 23.
K.E. Trenberth, ‘Predictions of climate’, Climate Feedback at (viewed July 21, 2010): http://blogs.nature.com/climatefeedback/2007/06/predictions_of_climate.html
- 24.
On December 10, 2009, the Met Office predicted that 2010 would be the warmest year on record (see http://www.metoffice.gov.uk/corporate/pressoffice/2009/pr20091210b.html viewed February 18, 2010). But, as we have seen, NASA attempts to refute the notion that recent temperatures are flat or declining.
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van Kooten, G.C. (2013). Emission Scenarios and Climate Modeling. In: Climate Change, Climate Science and Economics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4988-7_4
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