Comparison of linear and cubic spline methods of interpolating lake water column profiles

Abstract

Two commonly used methods of interpolating lake water column profiles—two‐point linear interpolation and cubic spline interpolation—were compared, and their relative performance assessed using “leave‐k‐out” cross‐validation. Artificial “pseudo‐gaps” of various sizes were created in measured water column profiles of four representative variables (water temperature, oxygen concentration, total phosphorus concentration, and chloride concentration) from the Lake of Zurich by removing measured data from the profiles. The pseudo‐gaps were then filled using each of the two interpolation methods. The performance of each interpolation method was assessed based on the root mean square error, mean bias error, and maximum absolute bias error of the interpolated values in relation to the original measured values. The performance of the interpolation methods varied with depth, season, and profile shape. When the profiles were homogeneous both methods performed well, but when the profiles were heterogeneous, linear interpolation generally performed better than cubic spline interpolation. Although the data generated by cubic spline interpolation were less biased than those generated by linear interpolation, there were more instances of extreme errors. The results of this study suggest that linear interpolation is generally preferable to cubic spline interpolation for filling data gaps in measured lake water column profiles.