<p>The assessment of the natural resource potential (NRP), as a multi-criteria function of the agroclimatic, pedological, biological, land, and water resources of agricultural landscapes, constitutes a complex challenge involving variables of differing physical nature and dimensional scales. Traditional additive scoring models suffer from compensatory masking, where abundance in one environmental resource artificially obscures a critical deficit in another. The aim of this study is to overcome this limitation by developing a novel non-compensatory hierarchical mathematical framework for NRP assessment, utilizing a geometrically aggregated Harrington generalized desirability function as the core analytical engine. The study employs systems analysis, deterministic non-linear transformations, and mathematical modeling validated against long-term environmental data across spatial and temporal dimensions, disaggregated by natural zones and administrative districts of the Ayagoz District (Abai Oblast, Kazakhstan). The constructed framework successfully operationalizes a multi-level index where twenty heterogeneous natural indicators are transformed into a single continuous, dimensionless scale [0, 1]. By using geometric rather than additive aggregation, the framework strictly complies with ecological boundary conditions, ensuring that if any vital resource subsystem drops below a critical threshold, the entire integral potential deterministically decreases. The resulting models shift land evaluation from discrete, subjective expert scoring matrices to a continuous computational space, generating highly objective, evidentially valid, and spatially explicit cartographic and numerical outputs. The application of this framework to the agro-landscapes of the Ayagoz District demonstrates three definitive advantages: first, it eliminates the mathematical errors inherent in additive indexing; second, it allows each specific resource parameter to be scaled in strict accordance with its non-linear ecological limits; and third, it enables direct translation of the quantitative integral index into qualitative modal categories of desirability for regional land-use optimization. The conceptual and methodological novelty lies in the advancement of landscape-evaluation theory through the transition from compensatory matrices to a rigid, ecologically grounded non-compensatory architecture. For the first time, Harrington’s algorithm is restructured into a multi-tiered, hierarchical system that mathematically reflects the ecological laws of the minimum (Liebig) and tolerance (Shelford) at a landscape scale. It conceptualizes the natural system not as a static sum of assets, but as a dynamic, information-driven cascade where hydrological and pedogenic constraints sequentially filter and determine the final expression of biological and agricultural productivity. The resulting mathematical platform provides a scalable, machine-compatible instrument for digital land-use management and automated environmental monitoring. The spatial–temporal modeling outputs serve as predictive tools for agricultural planning, allowing regional authorities to simulate resource degradation risks and optimize the ecological reproduction of semi-arid agricultural landscapes under climate instability.</p>