A multi-criteria framework for assessing the natural resource potential of agricultural landscapes using Harrington’s generalized desirability function

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.