Nature of project: **theory**, software

Available to students on full-time physics degree schemes or joint students.

Space-borne experiments aboard satellites often generate remotely sensed data that maps to the surface of a celestial body. This data typically consists of samples with varying resolutions and geometries dependent on the relative position and orientation of the satellite and the subject under observation. In order to analyse, interpret and/or present the data it can be necessary to remap the data from these erratic samples to a regular grid or lattice, such as evenly spaced latitude and longitude. Any errors in the data, explicit or otherwise, can also be remapped into the new structure through error propagation and the equation(s) governing the remapping process. Naturally, experiments also often require the data to undergo some form of mathematical manipulation to test hypotheses or perform other analyses.

Given these two processes, a question that is the focus of this project logically follows: If errors propagate through the remapping process and the data requires manipulation, does it reduce the propagated error to perform the manipulations prior to remapping the results, or should the original data be remapped and only then manipulated?

For example, the C1XS instrument aboard Chandrayaan-1 satellite mission to orbit the moon used the X-rays released by the most energetic solar flares to perform X-ray fluorescence spectroscopy of the moon's surface. The resulting data contained counts corresponding to the relative abundance of metallic elements in the surface material. The ratio of different element counts indicates the mineral composition of the surface, and if this data were mapped to latitude and longitude a geological map of the surface could be produced. However, should the counts be remapped to the lat-long grid and then the ratio computed? Or, should the ratio be computed using the original sample counts, and then the ratios remapped to the grid?

This project focuses on an analytical analysis of the error propagation through combinations of remapping and manipulating functions. Using conditions derived by the supervisor, students needs to derive the answer to the question above for the chosen functions. The student would need to analyse simple manipulation functions (including products, ratios, exponential, logarithmic and trigonometric functions) and remapping functions (e.g. sums, weighted means, etc.).

*A successful project will develop beyond the above in one/some of the following directions:*

There are various possibilities for extension to the base project activities described. These include the graphical analysis of the derived results, the generation of artificial data to test against the derived results and, at its most challenging, the partial generalisation of the derivation.

When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.

*This project is only available as a Y3 project.*

Please speak to **Tom Knight** if you consider doing this project.

*Initial literature for students:*

- M. Grande et al. 2009: The C1XS X-ray Spectrometer on Chandrayaan-1. Planetary and Space Sci., 57, 717-724.
- J.A. Carter, 2012: Lunar Surface Composition From X-ray Fluorescence Spectroscopy. Aberystwyth University [Thesis].
- P.W. Jones, 1999: First- and Second-Order Conservative Remapping Schemes for Grids in Spherical Coordinates. Mon. Wea. Rev., 127, 2204–2210.
- M. Barbarella, M. Fiani, A. Lugli, 2017: Uncertainty in Terrestrial Laser Scanner Surveys of Landslides. Remote Sens., 9, 113.

This is a novel project and the difficulty is somewhat dependent on the extent to which the student advances the analysis. The supervisor will need to introduce the topic, but the subsequent analysis can be driven by the student. Given the theoretical nature of the project, it would be beneficial for students to have confidence in their mathematical skills.

milestone | to be completed by |
---|---|

An understanding of the context and derived conditions of the project | end of October |

To have identified and prioritised the functions to analyse | end of November |

Demonstrated the error propagation through those functions. | end of February |

Extended the analysis to cover (at least one) of the extensions described. | Easter |