Cluster analysis of climatic characteristics for territorial zoning in the context of climate change: a case study of the Altai Krai

Abstract

The paper presents results of a comparative analysis of climatic
zoning in Altai Krai across three time periods: early (1927-1975), modern (1976-
2024), and full (1927-2024) observation periods based on data from 31
meteorological stations using multivariate statistical methods. A total of 42 climatic
indicators were calculated, including air temperature and precipitation
characteristics, as well as Conrad's continentality index, de Martonne's aridity
index, and Vysotsky-Ivanov's moisture index. The k-means clustering algorithm
was applied with quality assessment using silhouette analysis and the Adjusted
Rand Index (ARI). Significant climate warming was established between the early
and modern periods: mean annual air temperature increased from 1.51±0.60°C to
2.92±0.73°C (+1.41°C), annual precipitation increased from 400±104 mm to
452±116 mm (+52 mm), and Conrad's continentality index decreased from 53.2 to
50.1 (-3.1). Differences in climatic zoning structure were identified: two climatic
zones are optimal for the early and modern periods (silhouette 0.351 and 0.319,
ARI 0.236 and 0.199 respectively), while three zones are optimal for the full period
(silhouette 0.266, ARI 0.201). The emergence of a third transitional zone in the
integral analysis over the entire period reflects the increasing complexity of spatial
climate organization. Mountain-foothill areas demonstrate maximum moisture
(495-555 mm/year), while steppe areas are characterized by maximum warming
and moisture deficit (325-377 mm/year). The first two principal components
explain 75-79% of the variance in climatic characteristics across all periods.
Cartographic analysis confirmed the spatial consistency of identified clusters with
conventional agroclimatic zoning. The results justify the need for periodic updating
of climatic zoning and can be used to develop adaptation strategies for regions and
economic sectors.