The Rumsfeld knowledge matrix – which spans the knowledge categories “known knowns,” “known unknowns,” and “unknown unknowns” – is used to illustrate the process of model improvement. Two new knowledge subcategories – “poorly known unknowns” and “well-known unknowns” – are introduced to distinguish between accuracy of parameterizations. A distinction is made between “downstream benefits” of parameterizations, which improve prediction skill, and “upstream benefits,” which improve understanding of the phenomenon being parameterized but not necessarily the prediction skill. Since new or improved parameterizations add to the complexity of models, it may be important to distinguish between essential and nonessential complexity. The fourth knowledge category in the Rumsfeld matrix is “unknown knowns” or willful ignorance, which can be used to describe contrarian views on climate change. Contrarians dismiss climate models for their limitations, but typically only offer alternatives born of unconstrained ideation.

Dynamical downscaling uses high-resolution regional climate models (RCMs) to bias-correct and downscale global climate model output.This chapter discusses the models and methods used in dynamical downscaling. It provides an overview of the basic physics used in RCMs, and how this is similar to and differs from that used in global models. It also discusses the methods and metrics used to evaluate RCMs, and how projections from RCMs can be used to assess climate impacts at the regional scale

The normal distribution is the most widely used continuous distribution, but many of its relevant properties are a little bit advanced for an undergraduate course. Hence, Part IV introduces some of these advanced topics. This chapter devotes itself to properties of normal distributions: single- and multivariate normal distributions, moment and canonical parameterizations, sum and product, geometry and the Mahalanobis distance, and conditional distributions. We also show that with these properties, some algorithms will become much easier to understand. We use parameter estimation and the Kalman filter as two such examples.