Analysis of Internal Boundaries and Transition Regions in Geophysical Systems with Advanced Processing Techniques
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
This thesis examines the utility of the Rényi entropy (RE), a measure of the complexity of probability density functions, as a tool for finding physically meaningful patterns in geophysical data. Initially, the RE is applied to observational data of long-lived atmospheric tracers in order to analyse the dynamics of stratospheric transitions regions associated with barriers to horizontal mixing. Its wider applicability is investigated by testing the RE as a method for highlighting internal boundaries in snow and ice from ground penetrating radar (GPR) recordings. High-resolution 500 MHz GPR soundings of dry snow were acquired at several sites near Scott Base, Antarctica, in 2008 and 2009, with the aim of using the RE to facilitate the identification and tracking of subsurface layers to extrapolate point measurements of accumulation from snow pits and firn cores to larger areas.
The atmospheric analysis focuses on applying the RE to observational tracer data from the EOS-MLS satellite instrument. Nitrous oxide (N2O) is shown to exhibit subtropical RE maxima in both hemispheres. These peaks are a measure of the tracer gradients that mark the transition between the tropics and the mid-latitudes in the stratosphere, also referred to as the edges of the tropical pipe. The RE maxima are shown to be located closer to the equator in winter than in summer. This agrees well with the expected behaviour of the tropical pipe edges and is similar to results reported by other studies. Compared to other stratospheric mixing metrics, the RE has the advantage that it is easy to calculate as it does not, for example, require conversion to equivalent latitude and does not rely on dynamical information such as wind fields.
The RE analysis also reveals occasional sudden poleward shifts of the southern hemisphere tropical pipe edge during austral winter which are accompanied by increased mid-latitude N2O levels. These events are investigated in more detail by creating daily high-resolution N2O maps using a two-dimensional trajectory model and MERRA reanalysis winds to advect N2O observations forwards and backwards in time on isentropic surfaces. With the aid of this ‘domain filling’ technique it is illustrated that the increase in southern hemisphere mid-latitude N2O during austral winter is probably the result of the cumulative effect of several large-scale, episodic leaks of N2O-rich air from the tropical pipe. A comparison with the global distribution of potential vorticity strongly suggests that irreversible mixing related to planetary wave breaking is the cause of the leak events. Between 2004 and 2011 the large-scale leaks are shown to occur approximately every second year and a connection to the equatorial quasi-biennial oscillation is found to be likely, though this cannot be established conclusively due to the relatively short data set.
Identification and tracking of subsurface boundaries, such as ice layers in snow or the bedrock of a glacier, is the focus of the cryospheric part of this project. The utility of the RE for detecting amplitude gradients associated with reflections in GPR recordings is initially tested on a 25 MHz sounding of an Antarctic glacier. The results show distinct regions of increased RE values that allow identification of the glacial bedrock along large parts of the profile. Due to the low computational requirements, the RE is found to be an effective pseudo gain function for initial analysis of GPR data in the field. While other gain functions often have to be tuned to give a good contrast between reflections and background noise over the whole vertical range of a profile, the RE tends to assign all detectable amplitude gradients a similar (high) value, resulting in a clear contrast between reflections and background scattering. Additionally, theoretical considerations allow the definition of a ‘standard’ data window size with which the RE can be applied to recordings made by most pulsed GPR systems and centre frequencies. This is confirmed by tests with higher frequency recordings (50 and 500 MHz) acquired on the McMurdo Ice Shelf. However, these also reveal that the RE processing is less reliable for identifying more closely spaced reflections from internal layers in dry snow.
In order to complete the intended high-resolution analysis of accumulation patterns by tracking internal snow layers in the 500 MHz data from two test sites, a different processing approach is developed. Using an estimate of the emitted waveform from direct measurement, deterministic deconvolution via the Fourier domain is applied to the high-resolution GPR data. This reveals unambiguous reflection horizons which can be observed in repeat measurements made one year apart. Point measurements of average accumulation from snow pits and firn cores are extrapolated to larger areas by identifying and tracking a dateable dust layer horizon in the radargrams. Furthermore, it is shown that annual compaction rates of snow can be estimated by tracking several internal reflection horizons along the deconvolved radar profiles and calculating the average change in separation of horizon pairs from one year to the next. The technique is complementary to point measurements from other studies and the derived compaction rates agree well with published values and theoretical estimates.