Evaluating hydrology preservation of simplified terrain representations

We present an error metric based on the potential energy of water flow to evaluate the quality of lossy terrain simplification algorithms. Typically, terrain compression algorithms seek to minimize RMS (root mean square) and maximum error. These metrics fail to capture whether a reconstructed terrain preserves the drainage network. A quantitative measurement of how accurately a drainage network captures the hydrology is important for determining the effectiveness of a terrain simplification technique. Having a measurement for testing and comparing different models has the potential to be widely used in numerous applications (flood prevention, erosion measurement, pollutant propagation, etc). In this paper, we transfer the drainage network computed on reconstructed geometry onto the original uncompressed terrain and use our error metric to measure the level of error created by the simplification. We also present a novel terrain simplification algorithm based on the compression of hydrology features. This method and other terrain compression schemes are then compared using our new metric

3D oceanographic data compression using 3D-ODETLAP

This paper describes a 3D environmental data compression technique for oceanographic datasets. With proper point selection, our method approximates uncompressed marine data using an over-determined system of linear equations based on, but essentially different from, the Laplacian partial differential equation. Then this approximation is refined via an error metric. These two steps work alternatively until a predefined satisfying approximation is found. Using several different datasets and metrics, we demonstrate that our method has an excellent compression ratio. To further evaluate our method, we compare it with 3D-SPIHT. 3D-ODETLAP averages 20% better compression than 3D-SPIHT on our eight test datasets, from World Ocean Atlas 2005. Our method provides up to approximately six times better compression on datasets with relatively small variance. Meanwhile, with the same approximate mean error, we demonstrate a significantly smaller maximum error compared to 3D-SPIHT and provide a feature to keep the maximum error under a user-defined limit

COMPUTER SIMULATION OF OVERTOPPING OF LEVEES

There have been many cases of earth embankment failures, for example, Hurricane Katrina in 2005, where breaching occurred and devastated the surrounding population. Levee failures are preventable by a better understanding of the ways in which these embankments are designed and fail. The objective of this research is to protect levees against future failures. This paper studies various overtopping quantities and durations to represent the same level of levee erosion hazard. This study is based on experimental results of steady flows on the land side of a levee. The effect of water flow has been investigated and a comparison has been done between rills formations and erosion time for various water flows. Results showed that the pictures of digital simulations and real photographs which have been taken during tests in the laboratory are in a good concordance. Ha habido muchos casos de fallos de terraplén, por ejemplo, el huracán Katrina en 2005, en el cual se produjo una ruptura, devastando la población de los alrededores. Las fallas de diques se pueden prevenir, y es un objetivo de esta investigación alcanzar una mejor comprensión de las maneras en que estos diques se diseñan y fallan, a fin de poder protegerlos contra futuros fallos. Este documento desarrolla y recomienda equivalencias preliminares de combinaciones acumulativas de varias cantidades de desbordamiento y las duraciones asociadas que representan el mismo nivel de riesgo de erosión del dique. Las metodologías se basan en los resultados experimentales de flujos constantes en el lado seco de un dique. El efecto del flujo de agua se ha estudiado específicamente en esta investigación, y se ha hecho una comparación entre las formaciones de surcos y el tiempo de erosión para distintos flujos de agua

Measuring terrain distances through extracted channel networks

This paper initiates a forensic analysis of the causes of levee failures by analyzing and extracting information from a sequence of elevation data. This is a crucial step in bettering the design and construction of levees and dams. (Fully diagnosing failures usually requires knowledge beyond the geometry of the levee, such as weather conditions and material properties). We use results from computer simulations of levee overtopping for training data. The simulations use smoothed particle hydrodynamics coupled with a well-known erodibility model. Using the sequential nature of our data, we extract important channel networks that form as the soil is scoured away. We present a series of metrics to measure the distance between channel networks to assist in determining the critical threshold value used to extract important channels from the flow network. Methods for determining this ideal threshold have gone mainly unexplored, and so we present a comparison of various threshold values and how closely they identify matching channel networks on sequential terrains. These threshold values allow us to identify important properties of the terrain that form its fingerprint, a way of characterizing the geometry of the terrain. Our method for fingerprinting terrain is an important step toward the diagnosis of levee failure from digital elevation data

Simulating Levee Erosion with Physical Modeling Validation

This paper studies rill and gully initiation and propagation on levees, dams, and general earth embankments. It specifically studies where these erosion features occur, and how long a particular embankment can sustain overtopping before breaching and catastrophic failure. This contrasts to previous levee erosion analysis, which has primarily concerned the final effects of erosion, such as soil loss, depth of scour and breach width. This paper describes the construction of scaled-down physical models of levees composed of different homogeneous sands, as well as sand-clay mixtures, and their laboratory testing. A 3-D laser range scanner captured the surface features of the physical model, before and after erosion. The resulting data is utilized in developing digital simulations of the rill erosion process. Those simulations combine 3-D Navier-Stokes fluid simulations and a segmented height field data structure to produce an accurate portrayal of the erosive processes, which will be validated by physical modeling

Quantitative analysis of simulated erosion for different soils

Levee overtopping can lead to failure and cause catastrophic damage, as was the case during Hurricane Katrina. We present a computer simulation of erosion to study the development of the rills and gullies that form along an earthen embankment during overtopping. We have coupled 3D Smoothed Particle Hydrodynamics with an erodibility model to produce our simulation. Through comparison between simulations and between simulation and analogous laboratory experiments, we provide quantitative and qualitative results, evaluating the accuracy of our simulation

Parallel ODETLAP for terrain compression and reconstruction

We introduce a parallel approximation of an Over-determined Laplacian Partial Differential Equation solver (ODETLAP) applied to the compression and restoration of terrain data used for Geographical Information Systems (GIS). ODET-LAP can be used to reconstruct a compressed elevation map, or to generate a dense regular grid from airborne Light Detection and Ranging (LIDAR) point cloud data. With previous methods, the time to execute ODETLAP does not scale well with the size of the input elevation map, resulting in running times that are prohibitively long for large data sets. Our algorithm divides the data set into patches, runs ODET-LAP on each patch, and then merges the patches together. This method gives two distinct speed improvements. First, we provide scalability by reducing the complexity such that the execution time grows almost linearly with the size of the input, even when run on a single processor. Second, we are able to calculate ODETLAP on the patches concurrently in a parallel or distributed environment. Our new patchbased implementation takes 2 seconds to run ODETLAP on an 800 × 800 elevation map using 128 processors, while the original version of ODETLAP takes nearly 10 minutes on a single processor (271 times longer). We demonstrate the effectiveness of the new algorithm by running it on data sets as large as 16000 × 16000 on a cluster of computers. We also discuss our preliminary results from running on an IBM Blue Gene/L system with 32,768 processors

Validation of Erosion Modeling: Physical and Numerical

The overall intent of this research is to develop numerical models of erosion of levees, dams and embankments, validated by physical models. The physical models are performed at 1-g and at high g\u27s using a geotechnical centrifuge. The erosion is modeled in detail, from beginning to end, that is from the time the levee is overtopped until the levee is breached. Typical quantities measured as a function of time are the depth, width and volume of rills, number of junction points, are the rills straight or meandering, sediment transport quantities, and finally breach. This data can be obtained from the numerical modeling, but is difficult to obtain from the physical modeling. Video images indicate the physical modeling agrees quite well with the numerical modeling. A comparison has also been done between observed breaching width and the FEMA new formula for both 1-g and centrifuge tests