About Representing Spatial Data Uncertainty
This menu is an interface to explore the modeling, propagation, and representation of spatial data uncertainty on GIS applications. It allows you to link uncertainty models to GIS applications and identify and understand the spatial component of the uncertainty in those application results.
Two spatial datasets are included. One is a 90 meter resolution raster DEM for the Goleta 7.5' quadrangle. The second is a 90m resolution raster land cover data set derived from California Gap data for the Goleta 7.5' quadrangle. It has been reclassified to include just four classes, urban, agriculture, scrub, and wetland.
You can learn more about either dataset by pressing the "About Model" button in the appropriate box. You can view the original data by pressing the "Original" button. You can view the 10 simulations of either dataset by pressing the "Cinema Verite" button. Each simulation represents the real world better than the original DEM or land cover data.
The large box at the bottom of the window allows you to select one of three GIS application models that can be run on this data. Choose between the sea level rise model, landslide risk model, or banana suitability model. You can read about these GIS models by pressing the "About Model" button below the one you're interested in.
Once you've selected a model, you can view the outcome of the model for the Goleta quadrangle. Press the "No Uncertainty Info" to run the model on the original DEM and landcover dataset. Processing and display of the results takes about 20 seconds.
Alternatively, the GIS application model can be run on the 10 DEM realizations and the 10 landcover realizations for a total of 100 realizations. Processing these takes some time and is not done in real time in this demonstration. Individually, each of these 100 realizations presents a more plausible picture than the results of the "No uncertainty info" model. Press the "Cinema Verite" button to view a "movie" of 10 of the 100 realizations that were generated.
Results across the 100 realizations can be summarized using a probability map. Press the "Probability Map" button to view a map showing the probability of occurrence for each cell. Cell values in this map range from 0, meaning that this cell was not identified in any realization, to 100, meaning that all realizations identified this cell.
Developed by Ashton Shortridge, 1999.
The digital elevation model used for this research is a subset of the Los Angeles West USGS one-degree DEM. It was clipped to the Goleta, CA 7.5' quadrangle, projected into Universal Transverse Mercator, and resampled to a cell resolution of 90 meters. Elevation ranges from one meter near the coast to 918 meters in the northern, mountainous portion of the quadrangle.
We can characterize the quality of the DEM for the Goleta area by using an accurate set of 250 spot elevations scattered across the quadrangle. The error at those 250 locations can be summarized as roughly normal with a mean of 11.9 meters (indicating the DEM is on average 12 meters above the true surface) with a standard deviation of 23.9 meters.
A geostatistical uncertainty model was developed using this set of spot heights. The model employs a variogram to measure the spatial dependence of error. Ten error surfaces were generated for the quadrangle using gaussian simulation in the Gstat software package*. Each surface matched the statistical qualities of the spot elevation set. Back in Arc/Info, these were added to the original DEM to produce realizations of the terrain surface. They more closely match the properties of the actual terrain than the original data.
Click on the button marked "Original" to view the original DEM. Click on the button marked "Cinema Verite" to view a movie of the 10 terrain realizations.
* See Gstat for more on this geostatistics freeware.
About the Landcover Uncertainty Model
The landcover data used for this research is a subset of the California GAP dataset. It was clipped to the Goleta, CA 7.5' quadrangle, projected into Universal Transverse Mercator, and resampled to a cell resolution of 90 meters. The data set was reclassified to a much simpler 4-class scheme than the original GAP land cover.
We can characterize the quality of this data for the Goleta area
by using a more accurate classification of the quadrangle developed by
Ken McGwire at UCSB. The difference between the accurate classification
and the GAP data is summarized in the form of a confusion matrix:
| Scrub | Wetland | Agriculture | Urban | |
| Scrub | 0.9095 | 0.0016 | 0.0364 | 0.0525 |
| Wetland | 0.0 | 0.9251 | 0.0 | 0.0749 |
| Agriculture | 0.1650 | 0.0 | 0.7875 | 0.0475 |
| Urban | 0.0976 | 0.083 | 0.0536 | 0.8405 |
The rows indicate the class of the GAP map, while the columns indicate the actual value. For example, a cell classified as agriculture in the GAP map has a 79 percent chance of actually being agriculture, a 17 percent chance of actually being scrub, and a 5 percent chance of actually being urban. Note that the matrix is not symmetrical.
The simulation model uses this confusion matrix to generate realizations of what the actual surface might be. This surface is then smoothed with Grid's FOCALMAJORITY filter to introduce spatial autocorrelation.
Click on the button marked "Original" to view the original GAP landcover data set. Click on the button marked "Cinema Verite" to view a movie of the 10 land cover realizations.
About the Sea Level Rise Risk Model
The earth may be warming up because of increasing concentrations of greenhouse gasses in the atmosphere. Temperature increases, particularly in the higher latitudes, may cause ice melt in quantities sufficient to raise sea level by significant amounts in the next century. What impact could such a rise have on people living near the coast?
This model identifies urban areas in Goleta at risk of inundation. The critical elevation is 6 meters. This value reflects a potential 2 meter rise in sea level and a 4 meter storm/flood surge. The form of the model in map algebra is simply:
Area_at_Risk = (Elevation < 6 AND Landcover == Urban)
This model was run on the original DEM and landcover data. Then, it was run on each one of the 100 possible combinations of the 10 simulated DEMs and the 10 simulated land cover grids. These 100 maps give us a probablistic sense of what areas are at risk, given the quality of the input data. The information from the 100 maps can also be summarized in a probability map.
Click on the button marked "No Uncertainty Info" to run the model and view an output map of the areas the model identified at risk using the original DEM and land cover set. Click on the button marked "Probability Map" to view a map summarizing the number of times each cell was both urban and inundated. Polygons surrounding areas predicted to flood using the original DEM and GAP data are overlain for comparison. Click on the button marked "Cinema Verite" to view a movie of 10 (of 100) model realizations.
About the Landslide Risk Model
Part of Santa Barbara's appeal is the great mountain wall which rises just behind the city, forming a green backdrop on the Channel. Views from the crest and slopes of the Santa Ynez mountains are unmatched. However, landslides on those slopes are a very real hazard. Given the population growth in the area, are urban areas encroaching on unstable terrain?
This model identifies urban areas in Goleta which are at risk for landslides. A more complete model might include a variety of soil attributes and hydrologic characteristics, but here we use only slope and land cover. Areas with slope greater than 12 degrees. The form of the model in map algebra is:
Area_at_Risk = (slope (DEM) > 12) AND Landcover == Urban)
This model was run on the original DEM and landcover data. Then, it was run on each one of the 100 possible combinations of the 10 simulated DEMs and the 10 simulated land cover grids. These 100 maps give us a probablistic sense of what areas are at risk, given the quality of the input data. The information from the 100 maps can also be summarized in a probability map.
Click on the button marked "No Uncertainty Info" to run the model and view an output map of the areas the model identified at risk using the original DEM and land cover set. Click on the button marked "Probability Map" to view a map summarizing the number of times each cell was both urban and high slope. Polygons surrounding areas predicted as high slope using the original DEM and GAP data are overlain for comparison. Click on the button marked "Cinema Verite" to view a movie of 10 (of 100) model realizations.
About the Banana Suitability Model
Bananas in Goleta?! In fact there was a small commercial banana grove on Highway 101 between Santa Barbara and Ventura. the owners claim it is the northernmost in California. The major reason for the lack of banana-culture (outside of UC Santa Cruz) is the gusty winds along the coast, which shred the banana plant's fragile leaves.
Prospects for growing bananas in Goleta would appear to be brightest in those areas matching the following conditions. First, the area must be agricultural. Second, it must be fairly level, on gentle southward facing slopes. Third, it must be sheltered from strong winds, particularly from the west.
This model identifies such areas. It is the most complex of the three models presented. The form of the model in map algebra is:
Suitable_Area = (Landcover == Agriculture OR Scrub AND
slope(DEM) < 5 AND
(aspect(DEM) = -1 OR 145 < aspect(DEM) < 225) AND
(focalmean (DEM, wedge, 5, 100, 260, data) > DEM + 7)
The first line of this model tests landcover and slope. The second line checks that the aspect of the terrain is either level or facing within 35 degrees of south. The third line checks that the average height of the cells lying to the west of the target cell is at least 7 meters higher than the elevation of the target cell.
This model was run on the original DEM and landcover data. Then, it was run on each one of the 100 possible combinations of the 10 simulated DEMs and the 10 simulated land cover grids. These 100 maps give us a probablistic sense of what areas are at risk, given the quality of the input data. The information from the 100 maps can also be summarized in a probability map.
Click on the button marked "No Uncertainty Info" to run the model and view an output map of the areas the model identified as suitable using the original DEM and land cover set. Click on the button marked "Probability Map" to view a map summarizing the number of times (out of 100) each cell was identified as suitable. Polygons surrounding areas predicted suitable using the original DEM and GAP data are overlain for comparison. Click on the button marked "Cinema Verite" to view a movie of 10 (of 100) model realizations.