Generating the adjoint model (ADJM) by hand is tedious, time-consuming, and error prone. In most practical applications of data assimilation these days, the derivative codes, including the ADJM, are generated by the automatic differentiation (AD) tools, which evaluate the exact derivative information of a function in terms of a program. Terminologies and methods in AD are introduced, including the practical exclusion of the forward and reverse modes of differentiation. Various AD tools based on two major AD approaches, source transformation and operator overloading, are compiled with their webpages.

Demonstrates how scope ambiguities involving modifiers used in coordinate structures that contain conjoined nouns correlate with different hierarchical structures that can be assigned to the same linear string of words. These different hierarchical structures, which can be clearly represented as tree diagrams, correspond to distinct interpretations, thereby showing how distinct hierarchical syntactic structures reflect a unique interpretation. This analysis is extended to layered coordinations, containing two conjunctions and three conjuncts, where one of these conjuncts is itself a coordinate structure. In these cases, one unique hierarchical structure will correspond to four distinct linear orders, where the interpretation is determined by the hierarchical structure of the construction, and not its linear order. These ambiguous constructions can be disambiguated by employing both with and and either with or.