Geoscience is witnessing an era of rapid development of new observational technologies that are producing massive amounts of high dimensional digital data of the natural and built environment at outstanding resolutions. Of particular importance are the increasing dense data sets generated from high resolution airborne laser swath mapping and ground-based LiDAR. These data require the development of novel advanced mathematical and computational methods for the automatic extraction of knowledge relevant to, for example, climate change impact and hazard assessment, including flood and landslide prediction and control. These are very challenging tasks of high societal importance. The goal of this project is to develop modern computational geometric image analysis techniques applicable to geosciences, and in particular, to hydrologic and geomorphologic hazard prediction and control. Specifically, the project aims to study high-resolution, multiscale, and dynamic topography with the goals of extracting: (1) channel networks (which is needed for flood prediction, watershed management, ecosystem analysis, and stream restoration); (2) landslide prone areas (for hazard forecasting); and (3) service roads (which can contribute significant runoff and sediment to streams, causing channel instability and habitat decline). The topographic data and the features they reveal can then be used, in combination with typically much lower resolution data such as precipitation and soil moisture/type, to improve the accuracy of predictive models. This brings yet an additional novelty to the project: namely the simultaneous consideration of multimodality and multiresolution data for knowledge extraction.

The mathematical and computational techniques to be exploited and developed come from the area of geometric non-linear partial differential equations and energy formulations, combined with differential and computational geometry. These modern image analysis tools have been very successful in other imaging disciplines and are now being pioneered into geosciences. A strong interdisciplinary team is put together to address the challenges of analyzing multimodality/multiresolution landscape data, with a combination of expertise in the geosciences and in geometric image analysis, a synergy which provides a unique asset to the proposed project.

The study of earth's topography has fundamental impacts on society, from flood and landslide prevention and control to the understanding of climate change impacts, management of land-use practices, as well as design of roads and other man-made projects in an environmentally sustainable way. The recent availability of high resolution (0.5 m spacing) digital topography from airborne laser swath mapping and ground-based LiDAR offers opportunities to develop a new class of environmental predictive models that explicitly incorporate important features of the landscape and thus enhance the accuracy of predictions. The goal of this project is to develop modern computational geometric image analysis methodologies applicable to hydrologic and eco-geomorphologic hazard prediction and control. Specifically, our project aims to study high-resolution, multiscale, and dynamic topography with the goal of extracting channel networks, channel banks and shapes, floodplains and hazard-relevant features such as landslide prone areas and service roads which contribute to increased sediment production and thus stream habitat deterioration.

The mathematical and computational techniques to be exploited and developed come from the area of geometric non-linear partial differential equations and energy formulations, combined with differential and computational geometry. Specifically, a combination of methodologies ranging from geometric scale-space theory to singularity theory and geometric variational principles, combined with optimal algorithms for computing special curves on surfaces, will be exploited deriving a complete and automatic analysis of the topography at multiple relevant scales.

Landslides in the US and around the world constitute a serious hazard that causes substantial human and financial loss. In the US alone, the estimated loss averages 25 to 50 deaths and approximately $1 billion to $3 billion per year (NRC, 2004). As a result of a Congressional directive, a National Landslide Hazards Strategy, coordinated by the USGS, has been established which calls for focused activities, ranging from basic research to improved policy measures. The future GPM products offer a tremendous opportunity to: (a) advance our understanding of rainfall-induced landslide hazards, (b) develop and test predictive models that incorporate uncertainty and risk, and (c) deploy effective operational forecasting and warning systems over large areas. Specifically, the goal of the proposed research is to evaluate the potential of the GPM products to advance fundamental understanding and enhance our operational ability to predict rainfall-induced landslides. The specific objectives are: (1) develop quantitative understanding of the statistical multiscale properties of space-time rainfall in complex terrain; (2) develop and test multiscale/multisensor merging techniques and a space-time downscaling model to disaggregate rainfall from the GPM scale of 4 km, 3 hrs to scales commensurate with those needed for landslide prediction (~0.1-0.5km; ~0.5-1.0 hrs); (3) build, based on accepted slope stability and hillslope hydrology theories, a process based model for predicting shallow landslides, acknowledging the uncertainty in the rainfall products and in model parameters; and (4) apply the model in an operation context and for enhancing our understanding of the factors that control the spatio-temporal pattern of landslides. The proposed research aims to bridge the TRMM/GPM remote sensing community with the hydro-geomorphology, earth-surface hazards communities for the purpose of improved prediction of rainfall-induced hazards using GPM precipitation products in mountainous regions. Although this proposal does not directly address flood prediction, the proposed physical-statistical downscaling model for orographic precipitation will contribute to the wider use of GPM products for hydrologic applications.