A Methodology for Fitting the Time Series of Snow Depth on the Arctic Sea Ice

Abstract

Snow depth is an important geophysical variable for investigating sea ice and climate change, which can be obtained from satellite data. However, there is a large number of missing data in satellite observations of snow depth. In this study, a methodology, the periodic functions fitting with varying parameter (PFF-VP), is presented to fit the time series of snow depth on Arctic sea ice obtained from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). The time-varying parameters are obtained by the independent point (IP) scheme and cubic spline interpolation. The PPF-VP is validated by experiments in which part of the observations are artificially removed and used to compare with the fitting results. Results indicate that the PPF-VP performs better than three traditional fitting methods, with its fitting results closer to observations and with smaller errors. In the practical experiments, the optimal number of IPs can be determined by only considering the fraction of missing data, particularly the length of the longest gaps in the snow-depth time series. All the experimental results indicate that the PPF-VP is a feasible and effective method to fit the time series of snow depth and can provide continuous data of snow depth for further study.

Research on outlier detection in CTD conductivity data based on cubic spline fitting

“…x is any depth between x 1 and x n . f x,i represent the interpolation coefficients, once the IP are determined, the interpolation coefficients can be calculated (Wang et al, 2019). y i (i=1,2,…, n) are assumed fitted conductivity data corresponding to IP, and are initially unknown quantities.…”

“…(2) Cubic spline fitting Please refer to Appendix A of Wang et al (2019) for the computation of the spline interpolation coefficients f x,i of eq (2.1). It should be noted that the IP selected by Wang et al are uniformly distributed, namely h i =x i+1 −x i and a i+1 = h i h i +h i+1 , i=1,2, …,n−1, are invariants, and a i+1 (i=1,2,…,n−1)= 1/2.…”

“…Therefore, h i and a i+1 are variables in this paper. For the specific derivation process, we further refer interested readers to Wang et al (2019) and the Supplementary Material of this paper.…”

“…Based on this physical constraint, a fitting function can help construct the marine elements, and the difference between the observed value and the fitted data larger than the given threshold will be discriminated as outliers (Tan et al, 2021). The cubic spline fitting function has become an extremely important numerical fitting method due to its good stability and smoothness, and it has achieved good application results in data analysis (Jiang et al, 2018;Jin et al, 2018;Zong et al, 2018;Wang et al, 2019;Xu et al, 2021). Based on the above situation, this paper aims to propose an outlier detection method based on Cubic Spline Fitting.…”