Optimal Selection Criterion for Runoff Component Models Based on Benefit-Risk Balance - DING Xiao-ling, HU Wei-zhong, TANG Hai-hua, LUO Bin, FENG Kuai-le (长江科学院院报)
[Objectives] Identification of runoff components is a key aspect of hydrological analysis and is crucial for understanding the evolution patterns of watershed water resources. Traditional runoff component models are often constructed based on the criterion of maximizing the extraction accuracy of deterministic components for the runoff series of a given length. However, a unified criterion for selecting model forms that adapt to variations in runoff series length over time is still lacking, making it difficult to determine the types of runoff components and the order of their separation during modeling. To address this, this study proposes a selection criterion for runoff component models based on the balance between benefits and risks. [Methods] Based on the diagnosis and quantitative description of evolution characteristics such as mutations, trends, and periodicities using time-series variability detection methods—the Mann-Kendall test, sliding T-test, Pettitt test, Standard Normal Homogeneity test, Buishand test, and periodogram—different forms of linear superposition models were developed by combinations and extraction sequences of the identified components, such as mutation, trend, and periodicity. These models were then employed to dynamically identify the components of runoff sequences with varying lengths. The accuracy of deterministic component identification was used to represent the “benefits” achieved by the model in runoff component recognition, while the magnitude of fluctuations in model accuracy under varying runoff sequences (i.e., stability) was regarded as the “risk”. A weighting coefficient representing the decision-maker’s preferences was introduced as a balancing variable to construct a benefit-risk balance indicator. Subsequently, runoff component models were optimized based on the criterion of minimizing this benefit-risk balance indicator. [Results] Using the runoff sequence from 1956 to 2010 at the Pingshan Station on the lower reaches of the Jinsha River as a case study, variable-length runoff sequences (with sample sizes ranging from 30 to 55) were constructed, starting from 1956 and ending in any year from 1986 to 2010. Runoff component identification was conducted under different model forms, and the proposed benefit-risk balance criterion was applied for model selection analysis. The results indicated mutual offsetting among components such as mutations, trends, and periodicities in the runoff sequence, and the same runoff sequence could be characterized by multiple models, each representing distinct compositional forms of runoff components. Runoff component identification was jointly influenced by both the model form and the sequence length; models with higher identification accuracy exhibited relatively lower stability when responding to changes in sequence length. For instance, models incorporating periodic components demonstrated superior fitting accuracy compared to those containing only trend or mutation terms, which in turn outperformed multi-year average models, while the stability of accuracy changes followed the opposite trend. If the decision-making objective was to achieve a more adequate fitting, models that sequentially separate mutations and periodic components are prioritized; conversely, if the objective was to maintain more stable accuracy with varying sequence lengths, models that identify only mutation or trend terms were more advantageous. [Conclusions] A novel approach is proposed in this study for selecting component models of variable-length runoff sequences by balancing identification accuracy (benefit) and stability (risk). Both the accuracy and stability indicators proposed in the criterion can be flexibly defined according to decision-making needs, facilitating decision-makers in comprehensively considering their preferences for model accuracy and stability under varying conditions to optimize model selection.