A broad consensus has been reached on the need to adapt the management of our forests to the context of the rapidly changing climate, which resulted in the development of numerous models capable of simulating the impact of the climate change on the forest. The primary goal of this specific endeavor is to propose a novel framework of comparative analysis which could lead to the unique and universal description and mapping of these models. This framework is based on the reduction of the model output to the relatively simplistic information about the presence of the tree species suitable for the forest management i.e. - a binary classifier, making it comparable with the largely available tree presence observations. The framework we propose comes along with a new score, based on the joint use of the Principal Component Analysis and the Co-inertia Analysis, which evaluates the model vis-`avis the corresponding observations with the focus on its phase space dynamics i.e. its dependence on external environmental variables, rather than its spatial precision. The pertinence of the proposed multi-scale approach, suitable for the multi-scale analysis, is demonstrated by conjointly using prototype binary classifiers, designed for this purpose, and two different examples of binary classifiers used in the forest management - climate-dependent tree species distribution models. This work has the ambition to serve as the basis for a potential combination of different models at different spatial scales in order to improve the decision making process in the forest management.