The deliverable D2.1 presented a comprehensive set of computational patterns derived from dwarfs and representative computations of the models participating in the ESCAPE-2 project. Each computational pattern derived a set of language elements that would be necessary to express that type of computations in a way that language elements are minimal, orthogonal, simple and non redundant. This document provides a full and formal specification of the high-level intermediate representation (HIR) for weather and climate applications. A full specification is presented as a set of concepts following the language elements identified in D2.1. They are organized as a tree to represent a full program. Each concept captures a specific information of a the computational patterns supported by the DSL toolchain. The semantic of each node is described as well as its properties and children nodes that it supports. The HIR serves as an interface between a language frontend (D2.2) and the implementation of a compiler toolchain that generates an efficient, parallel and optimized implementation of a model described using a concise and compact frontend language.