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.

Reply on RC1

“…Linear and Stineman interpolation, and weighted moving average had responses similar to each other in terms of the median error and range of outliers in response to varied rates of missingness in the data, while spline interpolation produced a far greater range of outliers for all sites (over 5 times greater at FOT and CARIACO). This was also exhibited in the BATS time series assessment where the flexibility of the spline interpolation led to a tendency to overestimate seasonal maxima and minima, as observed in other comparative studies (North and Livingstone, 2013). Stineman interpolation performed better than basic spline interpolation by providing greater constraint, but no better than linear interpolation, despite the increased flexibility.…”

From dimictic to monomictic: Empirical evidence of thermal regime transitions in three deep alpine lakes in Austria induced by climate change

“…First, we used linear interpolation to generate vertical profiles with a 1‐m resolution over depth per sampling event (i.e. vertical interpolation; see North & Livingstone, ). Values at the edge, that is, surface and bottom, were filled with the closest measurement when not available.…”

Application of Multivariate Techniques for Spatial Drought Modelling using Satellite Rainfall Estimate

“…The zoo package (Zeileis and Grothendieck 2005) in R was used to carry out linear interpolation in the case of missing precipitation data. Point linear interpolation is calculated using the values measured on either side of the missing data (North and Livingstone 2013). The drought index was calculated based on the principles identi ed by Byun and Wilhite (1999) for each of the grid cells retrieved from the CPC data.…”