Using fractal downscaling of satellite precipitation products for hydrometeorological applications

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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.






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Tao, K, and AP Barros (2010). Using fractal downscaling of satellite precipitation products for hydrometeorological applications. Journal of Atmospheric and Oceanic Technology, 27(3). pp. 409–427. 10.1175/2009JTECHA1219.1 Retrieved from

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Ana P. Barros

Edmund T. Pratt, Jr. School Distinguished Professor Emeritus of Civil and Environmental Engineering

Professor Ana Barros was born in Africa, grew up in Angola and Portugal, and has lived almost all of her adult life in the United States. She attended the Faculty of Engineering of the University of O’Porto where she obtained a summa cum laude Diploma in Civil Engineering with majors in Structures and Hydraulics in 1985, and a M.Sc. degree in Ocean Engineering in 1988 with a thesis focusing on numerical modeling of sediment transport in estuaries and coastal regions. In 1990, Dr. Barros completed and M.Sc. degree in Environmental Science Engineering at the OHSU/OGI School of Science and Engineering. She earned a Ph.D. in Civil and Environmental Engineering from the University of Washington, Seattle in 1993. Her graduate studies were supported in part by fellowships from the Portuguese Foundation for Science and Technology (FCT/JNICT), and NASA’s Graduate Fellowship program.  She is registered with the Portuguese Order of Professional Engineers since 1986. 

 Dr. Barros was in the engineering faculty at the University of Porto, Penn State University, and Harvard University before joining Duke University in 2004. Her primary research interests are in Hydrology, Hydrometeorology and Environmental Physics with a focus on water-cycle processes in the coupled land-atmosphere-biosphere system particularly in regions of complex terrain, the study of multi-scale interface phenomena in complex environments across the Earth Sciences, remote sensing of the environment (precipitation, clouds, soil moisture, and vegetation), climate predictability, extreme events and risk assessment of natural hazards. Prof. Barros is especially proud of having involved dozens of students in undergraduate research, a great majority of which continued their studies to earn graduate degrees in science and engineering.  Over recent years her work has focused on precipitation processes including microphysics and dynamics or orographic precipitation, and land-atmosphere interactions in mountainous regions from the Himalayas to the Andes and the Southern Appalachians including Land-Use Land-Cover Change impacts on regional climate. Her research relies on intensive field and laboratory experiments, large–scale computational modeling, nonlinear data analysis and environmental informatics.

Prof. Barros served in the Space Studies Board of the National Research Council, and in several committees of the Water Science and Technology Board and the Board of Atmospheric Sciences and Climate including the Climate Research Committee, and she was a member of the US National Committee for the International Hydrology Program (IHP) of the UNESCO.  She served as an elected member of the Council of the American Meteorological Society, and serves and served in several committees within the American Meteorological Society and the American Geophysical Union. Prof. Barros was a member of the NOAA’s Climate and Global Change Program and serves or has served in several working groups at NASA, NSF and DOE-ARM. She has been an active member of several professional organizations including the IEEE, ASCE, AGU, AMS, AAAS, EGS, ASEE, and AWRA, and she currently serves in the ASCE committee on Climate Change and Adaptation. Prof. Barros was the Chief Editor of the Journal of Hydrometeorology for five years, and she was an AE of the Journal of Hydrology until 2015 among other editor posts. She has been a Senior Fellow who the Energy and Climate Partnership of the Americas (ECPA) since 2011. 

Prof. Barros received Early Career Investigator awards from NSF and NASA in 1995 and 1996. She was a George W. Merck Faculty Fellow at Harvard University 1999-2003, and Packard Fellow nominee from Penn State University. She received the Prize Foundation A. Almeida in Engineering in 1985, and the Lorenz G. Straub Award for her Ph.D. thesis in 1993, and the NASA GSFC Robert H. Goddard Award (GPM GV Team), Category of Exceptional Achievement in Science in 2014 for contributions in support of the Global Precipitation Measurement Mission.  Dr. Barros is a Member of the ASCE, Senior Member of the IEEE, a Fellow of the American Meteorological Society, and a Fellow of the American Geophysical Union.  She was the AMS Sigma-Xi Distinguished Lecturer 2014-2015.

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