These are works I have found useful in exploring the world of climate modeling. Some items are listed in more than one category.
Archer, David. 2007. Global Warming: Understanding the Forecast. Malden, MA: Blackwell Pub.
Edwards, Paul N. 2010. A Vast Machine: Computer Models, Climate Data, and the Politics of Global Warming. Cambridge, Mass.: MIT Press.
Handel, M. D., and J. S. Risbey. 1992. An annotated bibliography on the greenhouse effect and climate change. Climatic Change 21:97–255.
Kaper, Hans, and Hans Engler. 2013. Mathematics and Climate. Philadelphia, PA: Society for Industrial and Applied Mathematics.
Manabe, Syukuro. 1997. Early development in the study of greenhouse warming: the emergence of climate models. Ambio 26(1):47-51.
McGuffie, Kendal, and Ann Henderson-Sellers. 2005. A Climate Modelling Primer. Third edition. Chichester, UK: J. Wiley.
McGuffie, Kendal, and Ann Henderson-Sellers. 2001. Forty years of numerical climate modelling. International Journal of Climatology 21:1067–1109.
Neelin, J. David. 2011. Climate Change and Climate Modeling. Cambridge: Cambridge University Press.
Trenberth, Kevin E. (editor). 1993. Climate System Modeling. Cambridge: Cambridge University Press.
Weart, Spencer R. 2008. The Discovery of Global Warming. Revised and expanded edition. Cambridge, Mass.: Harvard University Press.
Arrhenius, Svante. 1896. On the influence of carbonic acid in the air upon the temperature of the ground. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (fifth series) 41(251):237–276.
Callendar, G. S. 1938. The artificial production of carbon dioxide and its influence on temperature. Quarterly Journal of the Royal Meteorological Society 64:223–237.
Crawford, Elisabeth. 1997. Arrhenius' 1896 model of the greenhouse effect in context. Ambio 26(1):6-11.
Fourier, Joseph. 1827. Mémoire sur les temperatures du globe terrestre et des espaces planétaires. Mémoires de l’Academie Royale des sciences de l’Institut de France 7:569–604.
Rodhe, Henning, Robert Charlson, and Elisabeth Crawford. 1997. Svante Arrhenius and the greenhouse effect. Ambio 26(1):2-5.
Tyndall, John. 1861. On the absorption and radiation of heat by gases and vapours, and on the physical connection of radiation, absorption, and conduction. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science (fourth series) 22:169–194.
Budyko, M. I. 1969. The effect of solar radiation variations on the climate of the Earth. Tellus 21:611–619.
Kasahara, Akira, and Warren M. Washington. 1967. NCAR global general circulation model of the atmosphere. Monthly Weather Review 95:389–402.
Manabe, Syukoro, Joseph Smagorinsky, and Robert F. Strickler. 1965. Simulated climatology of a general circulation model with a hydrologic cycle. Monthly Weather Review 93:769–798.
Manabe, Syukoro, and Kirk Bryan. 1969. Climate calculations with a combined ocean-atmosphere model. Journal of the Atmospheric Sciences 26(4):786–789.
Phillips, Norman A. 1956. The general circulation of the atmosphere: A numerical experiment. Quarterly Journal of the Royal Meteorological Society 82:123–164.
Schneider, Stephen H., and Tevi Gal-Chen. 1973. Numerical experiments in climate stability. Journal of Geophysical Research 78(27):6182–6194.
Sellers, William D. 1969. A global climatic model based on the energy balance of the earth-atmosphere system. Journal of Applied Meteorology 8:392–400.
Smagorinsky, Joseph, Syukuro Manabe, and J. Leith Holloway, Jr. 1965. Numerical results from a nine-level general circulation model of the atmosphere. Monthly Weather Review 93(12):727–768.
Benestad, Rasmus E. 2013 preprint. Validating an old physics-based back-of-the-envelope climate model with state-of-the-art data. http://arxiv.org/abs/1301.1146.
Budyko, M. I. 1969. The effect of solar radiation variations on the climate of the Earth. Tellus 21:611–619.
Schneider, Stephen H., and Tevi Gal-Chen. 1973. Numerical experiments in climate stability. Journal of Geophysical Research 78(27):6182–6194.
Sellers, William D. 1969. A global climatic model based on the energy balance of the earth-atmosphere system. Journal of Applied Meteorology 8:392–400.
Bader, David, et al. 2014. Accelerated Climate Modeling For Energy: Project Strategy and Initial Implementation Plan. http://climatemodeling.science.energy.gov/sites/default/files/publications/acme-project-strategy-plan_0.pdf
Community Earth System Model. Web site. Accessed 2014-10-08. http://www2.cesm.ucar.edu/
Hansen, J., I. Fung, A. Lacis, D. Rind, S. Lebedeff, R. Ruedy, and G. Russell. 1988. Global climate changes as forecast by Goddard Institute for Space Studies three-dimensional model. Journal of Geophysical Research 93(D8):9341–9364.
Kasahara, Akira, and Warren M. Washington. 1967. NCAR global general circulation model of the atmosphere. Monthly Weather Review 95:389–402.
Manabe, Syukoro, Joseph Smagorinsky, and Robert F. Strickler. 1965. Simulated climatology of a general circulation model with a hydrologic cycle. Monthly Weather Review 93:769–798.
Manabe, Syukoro, and Kirk Bryan. 1969. Climate calculations with a combined ocean-atmosphere model. Journal of the Atmospheric Sciences 26(4):786–789.
Manabe, Syukoro, and R. T. Wetherald. 1975. The effects of doubling the CO2 concentration on the climate of a general circulation model. Journal of the Atmospheric Sciences 32:3–15.
Phillips, Norman A. 1956. The general circulation of the atmosphere: A numerical experiment. Quarterly Journal of the Royal Meteorological Society 82:123–164.
Fraedrich, Klaus, Heiko Jansen, Edilbert Kirk, Ute Luksch and Frank Lunkeit. 2005. The Planet Simulator: Towards a user friendly model. Meteorologische Zeitschrift 14:299–304. See also http://edilbert.github.io/PLASIM/
McGuffie, Kendal, and Ann Henderson-Sellers. 2005. A Climate Modelling Primer. Third edition. Chichester, UK: J. Wiley.
Climate Interactive C-Learn Simulation. Web site. Accessed 2014-10-08. http://www.climateinteractive.org/tools/c-learn/simulation/
CliMT: An object-oriented Climate Modeling and diagnostics Toolkit. Web site. Accessed 2014-10-08. http://people.su.se/~rcaba/climt/
Petersen, Christopher. Global Equilibrium Energy Balance Interactive Tinker Toy. Web site. Accessed 2014-10-08. http://icp.giss.nasa.gov/education/geebitt/index.html
Chandler, Mark, Linda Sohl, Jian Zhou, and Sarah Tortorici. Educational Global Climate Modeling. Web site. Accessed 2014-10-08. http://edgcm.columbia.edu/
Java Climate Model. Web site. Accessed 2014-10-08. http://jcm.climatemodel.info/
UCAR Center for Science Education. The Very, Very Simple Climate Model. Web site. Accessed 2014-10-08. http://scied.ucar.edu/simple-climate-model
Barnes, Nick, and David Jones. 2011. Clear climate code: Rewriting legacy science software for clarity. IEEE Software 28(6):36–42.
Easterbrook, Steve M., and Timothy C. Johns. 2009. Engineering the software for understanding climate change. Computing in Science and Engineering 11(6):65–74.
Easterbrook, Steve M., Paul N. Edwards, Venkatramani Balaji, and Reinhard Budich (editors). 2011. Climate Change: Science and Software. IEEE Software 28(6).
Held, Isaac M. 2005. The gap between simulation and understanding in climate modeling. Bulletin of the American Meteorological Society 86:1609–1614.
Rugaber, Spencer, Rocky Dunlap, Leo Mark, and Sameer Ansari. 2011. Managing software complexity and variability in coupled climate models. IEEE Software 28(6):43–48.
Palmer, T. N., F. J. Doblas-Reyes, A. Weisheimer, G. J. Shutts, J. Berner, J. M. Murphy. 2008 preprint. Towards the probabilistic earth-system model. http://arxiv.org/abs/0812.1074
Palmer, T. N. 2014. More reliable forecasts with less precise computations: a fast-track route to cloud-resolved weather and climate simulators? Philosophical Transactions of the Royal Society A 372:20130391.
Kwasniok, Frank. 2014. Enhanced regime predictability in atmospheric low-order models due to stochastic forcing. Philosophical Transactions of the Royal Society A 372:20130286.
Macilwain, Colin. 2014. A touch of the random. Science 344:1221–1223.
Rougier, Jonathan, and Michael Goldstein. 2014. Climate simulators and climate projections. Annual Review of Statistics and Its Application 2014(1):103–123.