关键词: 水位流量关系, 非线性最小二乘法, Box-Cox变换, 极大似然估计法, 对数变换

Abstract: The nonlinear least squares (NLS) is widely used in stage-discharge curve fitting. The logarithmic transformation used by NLS, however, sometimes cannot play the role of stabilizing the variance with no consideration of the heteroskedasticity, which leads to unreliable parameters and flow rates estimated in stage-discharge relation. To overcome this limitation, the Box-Cox transformation was adopted and the maximum likelihood estimation method (MLE) was used to estimate the parameters of the transformed model. Results show that compared with the logarithmic transformation model in NLS, the stability variance based on the Box-Cox transformation model can be better obtained, more favorable for normal distribution. It is also found that the logarithmic transformation model is a special case of the Box-Cox transformation model. Therefore, the Box-Cox transformation model could more reasonably infer the stage-discharge relation and has a wider application range in practical applications.

Key words: stage-discharge relation, non-linear least square, Box-Cox transform, maximum likelihood estimation, logarithmic transform