Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network
This study utilized a max-stable process (MSP) model with a dependence structure defined via a non-Euclidean distance metric, with the goal of modelling extreme flood data on a river network. The dataset was composed of mean daily discharge observations from 22 United States Geological Survey stream...
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MDPI AG
2023-12-01
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| Series: | GeoHazards |
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| Online Access: | https://www.mdpi.com/2624-795X/4/4/30 |
| _version_ | 1797380943929933824 |
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| author | Brian Skahill Cole Haden Smith Brook T. Russell |
| author_facet | Brian Skahill Cole Haden Smith Brook T. Russell |
| author_sort | Brian Skahill |
| collection | DOAJ |
| description | This study utilized a max-stable process (MSP) model with a dependence structure defined via a non-Euclidean distance metric, with the goal of modelling extreme flood data on a river network. The dataset was composed of mean daily discharge observations from 22 United States Geological Survey streamflow gaging stations for river basins in Missouri and Arkansas. The analysis included the application of the elastic-net penalty to automatically build spatially varying trend surfaces to model the marginal distributions. The dependence model accounted for the river distance between hydrologically connected gaging sites and the hydrologic distance, defined as the Euclidean distance between the centers of site’s associated drainage areas, for all stations. Modelling the marginal distributions and spatial dependence among the extremes are two key components for spatially modelling extremes. Among the 16 covariates evaluated for marginal fitting, 7 were selected to spatially model the generalized extreme value (GEV) location parameter (for each gaging station’s contributing drainage basin, its outlet elevation, centroid x coordinate, centroid elevation, area, average basin width, elevation range, and median land surface slope). The three covariates selected for the GEV scale parameter included the area, average basin width, and median land surface slope. The GEV shape parameter was assumed to be constant throughout the entire study area. Comparisons of estimates obtained from the spatial covariate model with their corresponding “at-site” estimates resulted in computed values of 0.95, 0.95, 0.94 and 0.85, 0.84, 0.90 for the coefficient of determination, Nash–Sutcliffe efficiency, and Kling–Gupta efficiency for the GEV location and scale parameters, respectively. Brown–Resnick MSP models were fit to independent multivariate events extracted from a set of common discharge data, transformed to unit Fréchet margins while considering different permutations of the non-Euclidean dependence model. Each of the fitted model’s log-likelihood values indicated improved fits when using hydrologic distance rather than Euclidean distance. They also demonstrated that accounting for flow-connected dependence and anisotropy further improved model fit. In this study, the results from both parts were illustrative; however, further research with larger datasets and more heterogeneous systems is recommended. |
| first_indexed | 2024-03-08T20:44:15Z |
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| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-08T20:44:15Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | GeoHazards |
| spelling | doaj.art-e9659931df2448d2b01f8e3873f313aa2023-12-22T14:11:30ZengMDPI AGGeoHazards2624-795X2023-12-014452655310.3390/geohazards4040030Marginal Distribution Fitting Method for Modelling Flood Extremes on a River NetworkBrian Skahill0Cole Haden Smith1Brook T. Russell2Coastal and Hydraulics Laboratory, Engineer Research and Development Center, U.S. Army Corps of Engineers, Vicksburg, MS 39180, USARisk Management Center, Institute for Water Resources, U.S. Army Corps of Engineers, Lakewood, CO 80228, USASchool of Mathematical and Statistical Sciences, Clemson University, Clemson, SC 29634, USAThis study utilized a max-stable process (MSP) model with a dependence structure defined via a non-Euclidean distance metric, with the goal of modelling extreme flood data on a river network. The dataset was composed of mean daily discharge observations from 22 United States Geological Survey streamflow gaging stations for river basins in Missouri and Arkansas. The analysis included the application of the elastic-net penalty to automatically build spatially varying trend surfaces to model the marginal distributions. The dependence model accounted for the river distance between hydrologically connected gaging sites and the hydrologic distance, defined as the Euclidean distance between the centers of site’s associated drainage areas, for all stations. Modelling the marginal distributions and spatial dependence among the extremes are two key components for spatially modelling extremes. Among the 16 covariates evaluated for marginal fitting, 7 were selected to spatially model the generalized extreme value (GEV) location parameter (for each gaging station’s contributing drainage basin, its outlet elevation, centroid x coordinate, centroid elevation, area, average basin width, elevation range, and median land surface slope). The three covariates selected for the GEV scale parameter included the area, average basin width, and median land surface slope. The GEV shape parameter was assumed to be constant throughout the entire study area. Comparisons of estimates obtained from the spatial covariate model with their corresponding “at-site” estimates resulted in computed values of 0.95, 0.95, 0.94 and 0.85, 0.84, 0.90 for the coefficient of determination, Nash–Sutcliffe efficiency, and Kling–Gupta efficiency for the GEV location and scale parameters, respectively. Brown–Resnick MSP models were fit to independent multivariate events extracted from a set of common discharge data, transformed to unit Fréchet margins while considering different permutations of the non-Euclidean dependence model. Each of the fitted model’s log-likelihood values indicated improved fits when using hydrologic distance rather than Euclidean distance. They also demonstrated that accounting for flow-connected dependence and anisotropy further improved model fit. In this study, the results from both parts were illustrative; however, further research with larger datasets and more heterogeneous systems is recommended.https://www.mdpi.com/2624-795X/4/4/30flood frequency estimationspatial extremestrend surfacesvariable selectionspatial dependenceriver distance |
| spellingShingle | Brian Skahill Cole Haden Smith Brook T. Russell Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network GeoHazards flood frequency estimation spatial extremes trend surfaces variable selection spatial dependence river distance |
| title | Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network |
| title_full | Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network |
| title_fullStr | Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network |
| title_full_unstemmed | Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network |
| title_short | Marginal Distribution Fitting Method for Modelling Flood Extremes on a River Network |
| title_sort | marginal distribution fitting method for modelling flood extremes on a river network |
| topic | flood frequency estimation spatial extremes trend surfaces variable selection spatial dependence river distance |
| url | https://www.mdpi.com/2624-795X/4/4/30 |
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