This study addresses flood estimation challenges in the Upper Irtysh River basin through comprehensive stochastic hydrological analysis. We evaluate the adequacy of various engineering methods for calculating peak discharges, with each computational approach based on probabilistic models combining: (1) theoretical probability distributions and (2) parameter estimation techniques for limited observational data. Our methodology employs an extensive range of three-parameter probability laws and frequency curve parameterization methods.

The research protocol involved: (i) rigorous stationarity testing of maximum annual discharge time series (for the period 1951-2019), and (ii) development of probabilistic frequency curves. Since conventional stochastic modelling requires stationary series, we developed methodological tools for detecting non-stationarity (particularly linear trends) and adjusting affected series through statistical normalization.

Key findings reveal that a part of studied rivers exhibit statistically significant (p<0.05) non-stationarity in annual peak flows observed as a linear trend. For such rivers, the time series were adjusted to stationary conditions. For all time-series - including the adjusted datasets - we constructed the complete set of considered probability models. From these, optimal models were selected representing different computational approaches: (1) the standard framework recommended by current regulatory documents, and (2) alternative schemes derived through comprehensive synthesis of published research.

Through application of multiple model quality criteria, it has been established that alternative computational schemes yield evidently better results compared to the standard methodology. The analysis further demonstrates that current non-stationarity in time series does not yet substantially affect the magnitude of the most critical design parameter - the 1% exceedance probability discharge. Future regional research should focus on: (1) identifying causes of non-stationarity in annual peak flow series, and (2) developing optimized computational frameworks for non-stationary conditions