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Transcript of Flow Direction
Contaminants Upslope area:
The total catchment area above a point
Distributed quantity that directly depends on flow direction Flow Direction How is is calculated? Deterministic 8 (D8) (O'Callaghan and Mark 1984) Implementation Jordan Dornbierer GIS Flow Direction Comp Sci Hydrology Where will I flow? Important component in modeling hydrologic processes that predict the spatial distribution of:
Erosion Threshold determination for channel network extraction Multiple Flow Directions (MD8) (Quinn et al. 1991, Freeman 1991) Where will I flow? Dispersion (Siebert and McGlynn 2007) Triangular Single Direction (D∞) (Tarboton 1997) (Tarboton et al. 1991) No "one size fits all" for threshold.
Support area (upslope area) threshold
based on break point of log-log plot of slope
vs contributing area. Breakpoint corresponds with spatial transition from convex
hillslopes to concave valleys.
Can be difficult to set a single threshold for a network
that spans significantly heterogeneous terrain.
Tarboton et al. in agreement with Montgomery and Dietrich 1988 paper we read. Slope inversely proportional to contributing area.
Tarboton essentially looking for the smallest support area for which known channel network geomorphology "laws" no longer hold. TI - topographic index
a - upslope area per unit contour length
β - local slope
d - soil storage deficit
M - constant characterizing rate at which conductivity decreases with depth
T(0) - transmissivity of soil when saturated to surface
q - subsurface flow per unit width
**distributed vs. lumped** TOPMODEL "model...attempts to combine the advantages of simple lumped parameter models with the important distributed effects of variable contributing areas and flow routing..." (Beven and Kirkby 1979) "There are two very simple ideas at the heart of TOPMODEL: that downslope subsurface flows can be adequately represented by a succession of steady-state water table positions, and that there is an exponential relationship, between local storage (or water table level) and downslope flow rate." (Quinn et al. 1991) America's next? Where does the water go? Overland flow 10.5% @ 108⁰ 10.5% @ 108⁰ 10.5% @ 108⁰ 12% @ 124⁰ 3.3% @ 90⁰ 3.3% @ 180⁰ 9.4% @ 135⁰ 10% @ 90⁰ 2.4% @ 45⁰ Triangular Multiple Direction (MD∞) (Seibert and McGlynn 2007) Divergent Hillslope (Seibert and McGlynn 2007) (Seibert and McGlynn 2007) (Tarboton 1997) Most existing algorithms are variations on a theme: *One input - Elevation *Format - DEM grid (Moore et al. 1991) Some of the drawbacks that arise due to the DEM's gridded nature may be minimized by increasingly higher resolution DEMs. Simple, straightforward structure
(2/3 of spatial data is embedded in matrix structure) Widely available "Raster is faster but vector is correcter..." 30m --> conterminous US
10m and 3m --> parts of US 1) Preprocessing of DEM to remove pits.
2) Calculation of flow directions.
3) Calculation of flow accumulation (upslope area). Pit (aka sink, depression, minima) - closed area surrounded by higher elevation, with no outlet "the nemesis of determining hydrologic flow directions" (Jenson and Domingue 1988) Pits are usually the due to "noise" in the DEM and result in disconnected drainage networks. Resolving Pits: 1) Fill (Jenson and Domingue 1988) 2) Outlet breaching (Martz and Garbrecht 1999) (Tarboton 2012) Dept of Geography - UNL Intro to flow direction Applications Existing algorithms New method: Concept Where will I flow? 3) Carving (Soille et al. 2003) *Minimize impact to original DEM
*Areas of low relief are most troublesome Raster Vector A physically based, variable contributing area model of basin hydrology (Beven and Kirkby 1979) Where will I flow? 3x3 Window What's happening upstream? Investigate incorporation of upslope influence
into calculation of downslope flow direction **Conservation of momentum** Determining flow at a cell requires knowledge of upslope flow directions and upslope flow accumulations Overview: (Seibert and McGlynn 2007) Why DEM grids? (Martz and Garbrecht 1999) Implementation: ArcGIS Python NumPy Free and open source programming language
Used extensively in geoprocessing scripting
Lots of third-party extensions Numerical Python.
Good for high level math and working with
multi-dimensional arrays. array([[ 481., 479., 479., 480., 481.],
[ 480., 478., 478., 480., 481.],
[ 478., 476., 476., 479., 480.],
[ 476., 475., 475., 478., 479.],
[ 475., 475., 475., 476., 477.],
[ 475., 475., 475., 475., 476.],
[ 475., 475., 475., 475., 476.],
[ 473., 474., 474., 474., 475.],
[ 473., 474., 475., 475., 475.],
[ 473., 474., 476., 476., 476.]], dtype=float32) No output or applications without... 0 ≤ direction < 360°
Dispersion limited to 2 cells. The question that is not being asked: DEM = Digital Elevation Model Spatially Heterogeneous
Variables vs. Lumped quantity (Beven and Kirkby 1979) What happens upstream matters. Mean basin storage deficit based on lumped water balance (precipitation, evapotranspiration, outflows) at successive time steps. When is a grid cell part of a stream? Slope ∝ 1/Contributing Area (Seibert and McGlynn 2007) Future Work:
Incorporate TI = ln(a/tanβ) into resolution of upstream vs downstream vectors.
E.g. High TI --> High upstream weight
Upslope influence already contained in elevation data?
Amplified flowpaths? Flood modeling? 5ft 2ft 30ft slope = 3/30 = 10% Plan View Profile View 1) momentum = mass * velocity
velocity = speed & direction "not a fixed model structure but rather a collection of concepts for distributed hydrological modelling to be used where they appear appropriate" (Quinn et al. 1991) (Dunne et al. 1975) upslope area - surrogate for mass and speed 2) downslope direction determined by existing method **Not symbolized Questions? import arcpy
import numpy A New Type of Flow Direction Algorithm