R Package for harmonic modelling of time-series data

R Package for harmonic modelling of time-series data

April 23, 2020

Sentinel-2 NDVI time-series over the Steigerwald. Left: Original satellite scenes after cloud, cloud shadow and snow maksing. Right: Interpolated time-series using a harmonic modelling.

In order to fully exploit the monitoring potential of the satellite systems, challenges such as noise and data gaps must be effectively addressed. These quality losses are mainly caused by sensor artifacts, clouds, cloud shadows and other weather conditions (Verbesselt et al., 2012). In the context of time series analysis, harmonic modeling is a powerful tool to fill these gaps and reduce noise by smoothing the original signal (de Jong et al., 2011).

For that purpose, I created an R-package rHarmonics which enables the user to perform a harmonic analysis on a given time-series data set.

To calculate the harmonic fitted curve of a periodic signal, ordinary least squares regressions are computed using coupled sine and cosine curves on time-series data. The underlying algorithm which is based on Shumway & Stoffer (2017) equations 4.1 – 4.2 can be seen below:

MODIS NDVI time-series data together with a harmonic fitted curve using 3 cylces per year.



Literature:

de Jong, R., de Bruin, S., de Wit, A., Schaepman, M. E., & Dent, D. L. (2011). Analysis of monotonic greening and browning trends from global ndvi time-series. Remote Sensing of Environment, 115 (2), 692–702.

Shumway, R. H., & Stoffer, D. S. (2017). Time series analysis and its applications: with r examples. Springer.

Verbesselt, J., Zeileis, A., & Herold, M. (2012). Near real-time disturbance detection using satellite image time series. Remote Sensing of Environment, 123 , 98–108.

you may also like:

Contribution at SilviLaser Conference in Quebec

Contribution at SilviLaser Conference in Quebec

At SilviLaser 2025 in Québec City, PhD candidate Julia Rieder (EORC, University of Würzburg and staff member of EO4CAM) presented her work on "European Beech under Drought: Effects of Topography, Competition and Soil Water Availability." Her study uses LiDAR to reveal...

EORC at Remote Sensing Symposium in Darmstadt

EORC at Remote Sensing Symposium in Darmstadt

On 2 October 2025, Dr. John Friesen and Dr. Julian Fäth from the Earth Observation Research Cluster (EORC) at the University of Würzburg and staff members of EO4CAM took part in the symposium "Vom Orbit zur Entscheidung: Satellitenfernerkundung in der...

New Team Member at the EORC: Sonja Mass

New Team Member at the EORC: Sonja Mass

Sonja Maas joined the Earth Observation Research Cluster (EORC) in October 2025 as a research assistant for the EO4CAM project. After finishing her bachelor's degree in forestry, Sonja Maas enrolled in the EAGLE M.Sc. program at the University of Würzburg, where she...

EAGLE MSc Student Isabella Metz Wins Prestigious IFHS Student Award

EAGLE MSc Student Isabella Metz Wins Prestigious IFHS Student Award

We are delighted to share the exciting news that our MSc student Isabella Metz has been awarded the 2025 International Federation of Hydrographic Societies (IFHS) Student Award for her outstanding research on: “Analysis of Uncertainties for Error Detection and...

Josipa Subotic joined as a DBU fellow

Josipa Subotic joined as a DBU fellow

We are delighted to welcome Josipa Subotić to the Earth Observation Research Cluster as a DBU fellowship visiting researcher. Since September 2025, she has been working on her project “Detection of Snow Surfaces in the Alps Using Multispectral Satellite Images and...