Using fractal downscaling of satellite precipitation products for hydrometeorological applications

The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L»l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (~25-km grid spacing) to the same resolution as the NCEP stage IV products (~4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied. © 2010 American Meteorological Society.

Phase Locked Loop and Modulo Games, The Dogma Loops; and “Finding Ibrida”

This dissertation consists of two independent musical compositions and an article detailing the process of the design and assembly of an electric guitar with particular emphasis on the carefully curated suite of embedded effects.

The first piece, 'Phase Locked Loop and Modulo Games' is scored for electric guitar and a single echo of equal volume less than a beat away. One could think of the piece as a 15 minute canon at the unison at the dotted eighth note (or at times the quarter or triplet-quarter), however the compositional motivation is more about weaving a composite texture between the guitar and its echo that is, while in theory extremely contrapuntal, in actuality is simply a single [superhuman] melodic line.

The second piece, 'The Dogma Loops' picks up a few compositional threads left by ‘Phase Locked Loop’ and weaves them into an entirely new tapestry. 'Phase Locked Loop' is motivated by the creation of a complex musical composite that is for the most part electronically transparent. 'The Dogma Loops' questions that same notion of composite electronic complexity by essentially asking a question: "what are the inputs to an interactive electronic system that create the most complex outputs via the simplest musical means possible?"

'The Dogma Loops' is scored for Electric Guitar (doubling on Ukulele), Violin and Violoncello. All of the principal instruments require an electronic pickup (except the Uke). The work is in three sections played attacca; [Automation Games], [Point of Origin] and [Cloning Vectors].

The third and final component of the document is the article 'Finding Ibrida.' This article details the process of the design and assembly of an electric guitar with integrated effects, while also providing the deeper context (conceptual and technical) which motivated the efforts and informed the challenges to hybridize the various technologies (tubes, transistors, digital effects and a microcontroller subsystem). The project was motivated by a desire for rigorous technical and hands-on engagement with analog signal processing as applied to the electric guitar. ‘Finding Ibrida’ explores sound, some myths and lore of guitar tech and the history of electric guitar distortion and its culture of sonic exploration.