Signals as departures from random walks.

We study statistics of data ranking, focusing on the recently discovered distribution-invariant discrete eigenvalue spectrum for an independent and identically distributed (IID) process. We employ a variant of a cumulative distribution function in rank and time that maps the sampling variability for an IID process onto a set of random walks. This mapping admits confidence bounds on whether the residual (data with signal removed) arises solely from IID sampling variability.

Extraction of unknown signals in arbitrary noise.

We devise a general method to extract weak signals of unknown form, buried in noise of arbitrary distribution. Central to it is signal-noise decomposition in rank and time: only stationary white noise generates data with a jointly uniform rank-time probability distribution, U(1,N)×U(1,N), for N points in a data sequence. We show that rank, averaged across jointly indexed series of noisy data, tracks the underlying weak signal via a simple relation, for all noise distributions.

Detection of unknown signals in arbitrary noise.

We devise a simple method for detecting signals of unknown form buried in any noise, including heavy tailed. The method centers on signal-noise decomposition in rank and time: Only stationary white noise generates data with a jointly uniform rank-time probability distribution, U(1,N)×U(1,N), for N data points in a time series. Signals of any kind distort this uniformity.

Spatial and temporal variability in desert dust and anthropogenic pollution in Iraq, 1997-2010.

Unlabelled: Satellite imaging has emerged as a method for monitoring regional air pollution and detecting areas of high dust concentrations. Unlike ground observations, continuous data monitoring is available with global coverage of terrestrial and atmospheric components. In this study we test the utility of different sources of satellite data to assess air pollution concentrations in Iraq.

Spatial scales of pollution from variable resolution satellite imaging.

The Moderate Resolution Imaging Spectroradiometer (MODIS) provides daily global coverage, but the 10 km resolution of its aerosol optical depth (AOD) product is not adequate for studying spatial variability of aerosols in urban areas. Recently, a new Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm was developed for MODIS which provides AOD at 1 km resolution. Using MAIAC data, the relationship between MAIAC AOD and PM(2.

Prediction of daily fine particulate matter concentrations using aerosol optical depth retrievals from the Geostationary Operational Environmental Satellite (GOES).

Unlabelled: Although ground-level PM2.5 (particulate matter with aerodynamic diameter < 2.5 microm) monitoring sites provide accurate measurements, their spatial coverage within a given region is limited and thus often insufficient for exposure and epidemiological studies.