Derivation of low flow distribution functions using copulas

• The method of deriving copula-based low flow distributions is proposed.
• Statistical dependence is detected among the characteristics of low flow event.
• Copula-based derived distributions can perform well against observations.
• Choice of marginal distributions is important in copula-based derived distribution.
• It is useful to study the impacts of climate change/human activities on low flows.

SummaryDerivation of low flow distribution using recession functions has been introduced in previous studies, but without taking into consideration the statistical dependence structure between the characteristics of low flow event, i.e. the duration of dry spell t and the recession parameter k. Low flow data of three basins in China with different climates demonstrate that statistical dependence actually exists between t and k. A copula-based derived distribution is proposed in this paper to take full account of this internal dependence within the low flow event. The proposed derived distribution can be flexibly constructed using a wide variety of copula functions and marginal distributions. Four types of copula functions (i.e. Student, Clayton, Gumbel, and Frank), each with twelve combinations of marginal distributions, are all employed to derive low flow distributions to find out which component, copula function or marginal distribution, has the most impact on the performance of derived low flow distributions in fitting the observed data. It turns out that the capability of this copula-based derived distribution is strongly influenced by the choice of marginal distribution, while different copula functions have more than negligible impacts on the tails’ goodness-of-fit. Student copula is preferred to model the chosen (t, k) samples with both lower and upper tail dependence. But the copula-based derived distribution is not recommended to describe low flow samples with long lower tails. The performance of the copula-based derived distributions is compared with that of the derived truncated Weibull distribution whose parameters are also process-oriented but without considering the statistical dependence structure of (t, k) in low flow events. The results highlight that the copula-based derived distribution is more flexible and can more reasonably describe both the upper and lower tails of low flow series than the derived truncated Weibull distribution. Two traditional fitted distributions, fitted truncated Weibull distribution and fitted Pearson Type III distribution, are also applied to describe the low flow series to evaluate the capability of the copula-based derived distribution. The fitted Pearson Type III distribution always provides highest accuracy, while copula-based derived distributions perform comparably given the appropriate marginal distributions and copula function. In general, the copula-based derived distribution can be a potential attractive alternative in low flow frequency analysis, for it can be used in studying the impacts of climate change and human activities on the frequency of low flows.