Propagation of positional error in 3D GIS: estimation of the solar irradiation of building roofs

Abstract

While error propagation in GIS is a topic that has received a lot of attention, it has not been researched with 3D GIS data. We extend error propagation to 3D city models using a Monte Carlo simulation on a use case of annual solar irradiation estimation of building rooftops for assessing the efficiency of installing solar panels. Besides investigating the extension of the theory of error propagation in GIS from 2D to 3D, this paper presents the following contributions. We (1) introduce varying XY/Z accuracy levels of the geometry to reflect actual acquisition outcomes; (2) run experiments on multiple accuracy classes (121 in total); (3) implement an uncertainty engine for simulating acquisition positional errors to procedurally modelled (synthetic) buildings; (4) perform the uncertainty propagation analysis on multiple levels of detail (LODs); and (5) implement Solar3Dcity – a CityGML-compliant software for estimating the solar irradiation of roofs, which we use in our experiments. The results show that in the case of the city of Delft in the Netherlands, a 0.3/0.6 m positional uncertainty yields an error of 68 kWh/m²/year (10%) in solar irradiation estimation. Furthermore, the results indicate that the planar and vertical uncertainties have a different influence on the estimations, and that the results are comparable between LODs. In the experiments we use procedural models, implying that analyses are carried out in a controlled environment where results can be validated. Our uncertainty propagation method and the framework are applicable to other 3D GIS operations and/or use cases. We released Solar3Dcity as open-source software to support related research efforts in the future.

Keywords:

• error propagation
• uncertainty
• CityGML
• 3D GIS
• photovoltaic potential

Acknowledgements

We thank the anonymous reviewers whose comments improved the quality of the manuscript. We are grateful to Marko Gulin (University of Zagreb), Parag Wate and Volker Coors (University of Applied Sciences Stuttgart), and Paula Redweik (University of Lisbon) for their help while developing the software prototype. Further, we are thankful to the developers of the libraries that have been used: Nathan Charles (Solpy), Elwood C. Downey (XEphem), and Brandon Rhodes (PyEphem).

ORCID

Filip Biljecki http://orcid.org/0000-0002-6229-7749

Gerard B.M. Heuvelink http://orcid.org/0000-0003-0959-9358

Hugo Ledoux http://orcid.org/0000-0002-1251-8654

Jantien Stoter http://orcid.org/0000-0002-1393-7279

Notes

1. https://pypi.python.org/pypi/pyephem/ and http://www.clearskyinstitute.com/xephem/

2. http://github.com/nrcharles/solpy

Additional information

Funding

This research was supported by the Dutch Technology Foundation STW, which is part of the Netherlands Organisation for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs (project code: 11300).