Parameter uncertainty can be obtained exactly by assuming normal distribution of a parameter in linear regression, but not in nonlinear regression. However, relatively less work has focused on the nonlinear parameter uncertainty estimates using spreadsheet packages. For these reasons, estimation of parameter uncertainties is significant for nonlinear parameter estimates. Parameter uncertainty can be used to judge the degree of reliability of the parameter estimates, which is important to making decisions for environmental management. It is also expressed as the standard error of the mean by assuming normal distribution of parameter values. It is usually expressed as an interval of parameter values at a certain confidence level, say, 95%. Different observations are usually obtained when experiments are repeated, resulting in different values of parameters. Parameter uncertainty refers to lack of knowledge regarding the exact true value of a quantity (Tong et al. For these reasons, spreadsheets such as Microsoft Excel are widely suggested to make nonlinear parameter estimation (Harris 1998 Smith et al. In addition, spreadsheets have the merits of wide accessibility and powerful computation in terms of fitting nonlinear models. However, spreadsheet techniques are easier to learn than other specialized mathematical programs for nonlinear parameter estimation, because no programming skills are needed in spreadsheets to develop their own parameter estimation routines (Wraith and Or 1998). As a result, there are many software packages (such as SAS and MathCAD) that implement nonlinear parameter estimation. Nonlinear relationships are common in natural and environmental sciences (Wraith and Or 1998 Luo et al.
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