Recent assessments of the Intergovernmental Panel on Climate Change (IPCC) and the U.S. National Academy of Sciences have concluded that that there is compelling scientific evidence of a pronounced human effect on global climate. Much of this evidence arises from so-called "fingerprint" studies. These seek to identify model-predicted climate-change patterns in observational data. The basic premise in such studies is that each of the different forcing factors affecting climate has a unique climatic signature. Climate "fingerprinting" frequently involves the use of optimization techniques to enhance the detectability of the searched-for signal. Application of these techniques requires a reduction in the dimensionality of the detection problem, usually by means of Empirical Orthogonal Functions (EOFs) or spherical harmonics. Issues related to optimization and signal detection are discussed here, using the recent example of changes in the height of the tropopause (the transition zone between the troposphere and stratosphere). The final portion of the talk addresses questions that may be of mutual interest to statisticians and atmospheric scientists. Examples include determination of the so-called "truncation dimension" (the EOF subspace in which signal-to-noise characteristics are optimized), and assessment of whether the climate response to external forcing is linear.