Week 6 is two decks that share the eight-step delineation workflow between them. This one is Tuesday: Lab 5 introduced, then what a watershed is and why we manage water by them, then the first three steps (the DEM, Fill, Flow Direction) cell by cell, starting from last week's slope and aspect. Thursday's deck (Part B, watershed-delineation-b.md) picks up at flow accumulation, finishes the eight steps and the Lab 5 model, then delineates a watershed by hand and with StreamStats.

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One goal per question on the closing quiz (Which Way Does Water Go?), in the same order. The map at right: where Rock Canyon's water goes, nested from the Lab 5 basin up to the Great Salt Lake subregion. The thread for today: first what a watershed is and why its boundary matters, then the first three steps of computing that boundary from a DEM. Thursday finishes the computation.

Two minutes, not twenty: this is the lab's problem statement in one slide, so that everything this week has somewhere to land. The map at right is the lab's example baseline layout — 29 subwatersheds at a threshold of 5,000 cells. The three things to say out loud: the outlet is one the student places, the model runs from a DEM extract the lab provides (no download hunt), and the report template has every graded item as a heading. StreamStats is a check in the lab (Step 13) as well as Thursday's in-class activity. The last part, Step 14, is the one students underestimate: four runs of the model, one table.

Before the algorithm, what the algorithm is for.

"Potential flow path network" is the honest phrase: the algorithm returns where water would go on this surface, which is not the same as where a channel exists. That gap is why validation against mapped hydrography matters. The five panels are this week's chain on Lab 5's Rock Canyon data — today gets as far as flow direction, Thursday finishes it, rendered in ArcGIS Pro: the DEM, flow direction, flow accumulation, the streams and basin, and the subwatersheds.

Powell's definition is quoted in full on the source slide; it is paraphrased here. Read the original aloud if you want it. The engineering definition and Powell's social one describe the same boundary and are worth contrasting.

One click shows the question. Let them answer before you offer any of these: a river shared by two or three states is a river they fight over, so basin-shaped states would have kept most allocation disputes inside one government; the people who use a stream would also govern the land that feeds it, so upstream grazing, logging or diversion would be the same community's problem as downstream supply; and settlement would have followed the water that could support it, which in the arid West is the binding limit. Powell's 1890 map of the arid region divided the West into drainage basins rather than rectangles. Congress ignored it. A century of interstate water compacts and litigation followed — the Colorado River is the example students will know. Background reading: https://brandonletsinger.com/biography/the-united-watershed-states-of-america-a-biography-of-john-wesley-powell/

The bridge from "we can compute a boundary" to "the boundary is the unit management decisions get made in." Permits, TMDLs, restoration budgets and stormwater plans are all organized by watershed. The three photos are three kinds of Utah watershed with people in them: a Wasatch mountain headwater (a National Trails Day crew on the Mount Olympus trail, Salt Lake Valley below), a valley river through the cities (canoeing the Jordan River, which carries Utah Lake's outflow — and so Rock Canyon's water — to the Great Salt Lake), and a desert canyon (slickrock at Indian Creek in southeastern Utah, Colorado River basin). Ask what a person does in each one that changes the water downstream. Sources, all public domain: https://commons.wikimedia.org/wiki/File:National_Trails_Day_2012_along_the_Mt._Olympus_Trail_on_the_Uinta-Wasatch-Cache_National_Forest_(11955210566).jpg (USDA Forest Service, Intermountain Region); https://commons.wikimedia.org/wiki/File:Canoeing_on_the_Jordan_River_(34395055581).jpg and https://commons.wikimedia.org/wiki/File:Hike_-_Indian_Creek_(30848535156).jpg (Bureau of Land Management – Utah).

One click shows the question; ask it after walking the figure. The answer is yes, everyone does: every point on land drains somewhere, so every address sits inside some watershed. The next slide shows how to name the one you live in. An oblique 3D view of Rock Canyon in ArcGIS Pro, looking east from above Provo, with Lab 5's basin (yellow), stream links (blue) and subwatersheds (thin white lines) draped on imagery. Walk it from the outlet: the outlet at the trailhead, the main stem up the canyon, the tributaries, one subwatershed, up to the divide along the ridgeline and the highest point at Provo Peak. Everything inside the yellow line drains to the one red point at the bottom; everything outside it, even a few meters over the ridge, goes somewhere else. Labels are placed from the Lab 5 data (tools/week06_figures.py, anatomy).

The numbers are HUCs, hydrologic unit codes. The USGS (U.S. Geological Survey, part of the Department of the Interior) maintains the Watershed Boundary Dataset with the USDA Natural Resources Conservation Service; it is the national standard set of drainage boundaries, and the same layer StreamStats and the National Hydrography Dataset are built against. The code is read left to right like an address: the first two digits are the region, and every further pair narrows it down, so you can tell from the number alone that 160202030505 sits inside 16020203. The level names (region, subregion, basin, subbasin, watershed, subwatershed) are the WBD's own; "HUC8" or "HUC12" is how practitioners usually say them. Powell, earlier in this deck, was the USGS's second director. These are the USGS Watershed Boundary Dataset units that contain the Rock Canyon trailhead, pulled live from the WBD map service and drawn in ArcGIS Pro: Great Basin Region (HUC2 16), Great Salt Lake subregion (HUC4 1602, about 74,300 km²), Jordan basin (HUC6 160202), Provo subbasin (HUC8 16020203, about 1,770 km²), Outlet Provo River watershed (HUC10 1602020305, about 332 km²), and Rock Canyon-Provo River subwatershed (HUC12 160202030505, about 50 km²). The Lab 5 basin, 25.2 km², sits inside that HUC12. Each code extends its parent by two digits — the nesting is in the number. The point to land: Rock Canyon's water ends up in the Great Salt Lake, which is where next week starts.

The hydrologic cycle, drawn as a budget for one watershed — Rock Canyon's real outline from Lab 5. Precipitation in; evapotranspiration out; streamflow out at the outlet; deep groundwater out across the bottom; the difference is the change in storage (snowpack, soil water, groundwater). Ask which of these terms a DEM can tell you about. Only one, and only partly: where the water that becomes streamflow will go — the flow paths, the divide, and the outlet. Every other term needs other data: gages, weather stations, soil and snow surveys.

Three things a watershed does, drawn on the same real basin: it collects, stores and releases water; it carries sediment and dissolved chemistry downstream, so the channel carries more the closer it gets to the outlet (line width is drawn from each link's real contributing area); and its streams and their banks are the habitat network. The water budget, the sediment and chemical budget and the biotic structure all use the watershed as their accounting boundary — the argument for computing the boundary carefully (tools/week06_processes_svg.py).

The first three of the eight steps: the elevation surface, Fill, and Flow Direction, done on paper and in Excel before ArcGIS Pro does them at scale. Thursday picks up at step 4, flow accumulation.

This roadmap slide comes back at every step, today and Thursday, each time with the current step highlighted. Step 1: get the elevation data, mosaic tiles together if the area of interest spans more than one, and project into a coordinate system with real ground units so cell size means something.

Point out that "DEM" in this course almost always means the square grid, but the definition is broader. The distinction matters in step 1: a TIN or a contour set has to be converted to a grid before any of the following steps will run. The map is the Lab 5 DEM, 10 m cells around Rock Canyon, colored by elevation over its own hillshade and rendered in ArcGIS Pro.

Step 2. In ArcGIS Pro this is the Fill tool in the Spatial Analyst Hydrology toolset.

Two clicks. The first shows the question and the arrow at the pit in the left profile: in the real world, what happens here? Let them answer. Water ponds; it fills the hollow until it spills over the low point on the rim (the right-hand profile), or it soaks in or evaporates if it never fills. The second click: some pits are real (a pond, a closed basin, a sinkhole, the Great Salt Lake itself) and some are artifacts of how the DEM was made — interpolation, a bridge or culvert the DEM does not show, rounding. Fill treats them all the same, which is why it has an optional z-limit for keeping the deep ones. Water routed into an unfilled pit has nowhere to go, so flow accumulation downstream of it collapses and the stream network breaks into disconnected pieces. The figure is a real 650 m west-east profile of the Lab 5 DEM through the deepest pit Fill found, a closed hollow high in the mountains east of Rock Canyon: its bottom at 2,677.5 m is raised to the spill level, 2,691.0 m, 13.5 m deep (tools/week06_pit_fill_figures.py). The callouts are click-to-reveal fragments: press the right arrow or space to show each.

Left: the same transect as a chart, original against filled. The filled surface sits above the original exactly where the original dipped, and nowhere else: Fill raises elevations, it never lowers them. Right: a close-up of the map in ArcGIS Pro, about 1.8 km by 1.2 km around that pit, with every cell Fill raised colored yellow (a few centimeters) to red (3 m or more). At this zoom each 10 m cell is visible: the pit itself is the red block on the transect, and the small yellow and orange patches around it are shallow pits, most raised by less than a meter. Across the whole Lab 5 DEM Fill raised about 12,900 cells; inside the Rock Canyon basin only 43 cells changed, the deepest by 2.35 m. This pit, 13.5 m deep, lies outside the basin. (Lab 5 check values.)

Step 3, the heart of the method, and the step the Excel activity walks through by hand.

This is the ordinary Slope and Aspect pair in ArcGIS Pro: the third-order finite difference (Horn's method), written exactly as on last week's "Slope: 3rd-order finite difference" and "Aspect" slides — Z1 to Z8 around the center Z0, C the cell size, dZ/dy positive toward the top of the window (north). Cardinal neighbors count double; the center cell Z0 is never used. Slope is the magnitude of the gradient; aspect is its direction as a compass bearing, clockwise from north. Run on the nine cells on the next slide (C = 10 m), dZ/dx = 1.495 and dZ/dy = 0.535, which give 57.8 degrees slope and 250.3 degrees aspect: the values ArcGIS Pro 3.7.1's Slope and Aspect tools reported for that cell (checked against tools/lab05/d8_patch.json). Esri's documentation writes the same formulas with the cells lettered a to i and dz/dy taken toward the south; the answer is identical. The window figure is tools/week06_d8_svgs.py. Next slide: why hydrology does not use this answer.

These are nine real cells of the Lab 5 DEM (after Fill), the top-left corner of the lab's Figure B. The aspect, 250 degrees, is what ArcGIS Pro's Aspect tool reports for the center cell (250.3) — the plane fit from the previous slide. D8 asks a simpler question: which single neighbor has the steepest drop? West falls 8.9 m over 10 m; southwest falls 18.5 m over 14.1 m, which is steeper, so all of this cell's water goes southwest (code 8). Ask the room which D8 direction is closest to 250 degrees: west (270) is 20 degrees away, southwest (225) is 25. D8 still picks southwest, because it compares single drops from the center cell and the aspect plane smooths over the whole window without ever looking at the center — the deep cell at the lower left pulls harder on D8 than on the plane. That is why the Excel activity asks for both.

One click shows the question; ask it after working the example. What to draw out: standard slope fits a plane to all eight neighbors (weighted, the center never used) and reports the steepness of that plane in any of 360 directions; hydrologic slope is the single steepest drop from the center cell to one of its eight neighbors, so it uses the center cell, keeps one neighbor instead of averaging, and can only point in eight directions. On the same cell the two can give different steepness and different directions, as the previous slide showed. Work this one live. The trap students fall into is comparing raw elevation differences and picking the diagonal because 19 is bigger than 15. Slope is rise over run, and the run is longer on the diagonal. The 30 here is the cell size in meters.

Credit: figure adapted from the watershed delineation course materials of D. Maidment, University of Texas at Austin.

The point to land: the number does not go in the neighbor, it goes in the center cell, and it says where that cell's water goes. Reading it clockwise from east: 1 = east, 2 = southeast, 4 = south, 8 = southwest, 16 = west, 32 = northwest, 64 = north, 128 = northeast. Powers of two are used so that more than one direction could in principle be summed into one value, which is how the tool reports unresolved flat areas. Students only need to read a code back to a compass direction. If anyone has used TauDEM or GRASS: those number the same eight directions differently, so a flow-direction grid made in one package cannot be routed in another; regenerate it in the software you route with. Drawn by tools/week06_d8_svgs.py.

Hand out or project a small elevation grid and have students compute the steepest-descent neighbor for each interior cell, then write the Esri direction code. Doing it once by hand is what makes the Flow Direction tool make sense. It sits here, after the encoding and before the flow direction grid, so students have every piece they need and then see the grid they just built by hand.

Left: a schematic grid drawn two ways, the direction as an arrow and the same grid as Esri codes. Have students check one or two cells against the encoding on the pour-point slide. Right: a real flow-direction raster: ArcGIS Pro's Flow Direction on the filled Lab 5 DEM, about 600 m by 400 m of Rock Canyon's slopes, each 10 m cell colored by its D8 code. The point is the texture: neighboring cells share a direction, and the bands are hillslopes draining the same way. The lower right is a slope facing north and northwest (codes 32 and 64).

Credit: figure adapted from the watershed delineation course materials of D. Maidment, University of Texas at Austin.

Connect every cell to the neighbor its arrow points at and the whole grid becomes a tree: every cell has exactly one downstream neighbor, and many upstream ones. Every remaining step in the workflow, Thursday's whole deck, is a question you ask about this tree.

Credit: figure adapted from the watershed delineation course materials of D. Maidment, University of Texas at Austin.

Four minutes, in pairs, then a show of hands on the D8 item: the code is a label for a direction, not a measurement, and it is written in the cell the water leaves. The Fill item is the other one worth a word out loud: real sinks exist, and Fill does not know the difference. If the room has no signal, put the URL on the board; the items read aloud just as well.

Revision notes (2026-10-05, later): dropped the "Remember This Map?" population-cartogram slide (too much of a diversion before Powell); added click-to-reveal questions on Powell (why basin-shaped states), on the Rock Canyon anatomy slide (do you live in a watershed?) and on hydrologic slope (how it differs from standard slope); cut "Why Watersheds Are Important" to bullets and replaced the field-visit photo with three public-domain Utah photos (mountain, valley, desert); added the USGS, Watershed Boundary Dataset and HUC-level explanation to the nesting slide; rewrote the standard slope and aspect slide in Week 5's notation (Z0 to Z8, dZ/dx and dZ/dy kernels, the textbook aspect formula), which reproduces ArcGIS Pro's 57.8 and 250.3 degrees on the Lab 5 cells.

Restructure notes (2026-10-05): Week 6 was re-cut so both decks carry half of the eight steps. Part A now opens with the watershed theory (Parts 1 of the old Thursday deck: what a watershed is, Powell, why they matter, anatomy, nesting, water balance, functions) and runs steps 1 to 3, the DEM to flow direction. Part B opens at flow accumulation, finishes the steps and the Lab 5 model, then does the hand-versus-StreamStats delineation. Dropped from Part A: the "Three Settings That Decide Lab 5" slide (it leaned on Fill, snapping and the threshold before any were taught), the "Watershed Delineation" big-question slide, and the non-Esri (TauDEM, QGIS, GRASS) D8 encoding slide (and, from Part B, the TauDEM flow-accumulation convention slide); the title slide's "adapted from" credit line was removed, and slides whose figures were traced from D. Maidment's (UT Austin) course materials now carry a Credit note instead. The decks were renamed watershed-delineation-a and -b to match the other two-part weeks. Rebuilt: the slope-and-aspect slide (crisp window figure plus the slope and aspect formulas as MathJax), the pour-point figure (a center cell with a question mark and eight coded arrows), the pit-fill map (zoomed on the pit), and the two flow-direction grid slides combined into one. The Excel activity moved to just before the flow direction grid.

Split notes (2026-10-01): the deck was split in two for Tuesday and Thursday. Part 1 (the mechanics) stays here under the same file name, so the Learning Suite link for Tuesday still works; Parts 2 and 3 (the theory and the hand-versus-StreamStats activity) moved to what-is-a-watershed.md. Rebuilt in ArcGIS Pro from Lab 5's data by tools/week06_figures.py: the elevation surface, the flow-direction grid, the threshold comparison (replacing the ArcView 200-cell screenshot), the grid-code link figure, the 10 m drainage-path map (replacing the 30 m scanned-topo figure), the labeled subwatersheds, and the subwatersheds on imagery.

Conversion notes (2026-09-03): Source deck "CE 414 Week 6 - Watershed Delineation.pptx", 57 slides, none hidden. All 57 source slides are represented; 62 slides here (source slide 1 became the title slide, source slide 38 — a bare "Day 2" text slide — became the Part 2 divider, and five slides were added: Today's Goals, the Part 1 and Part 3 `lead` dividers, a Lab 5 preview, and Before Next Class). No slides dropped. The nine "Summary of Steps" slides are near-duplicates that each highlight a different step; all nine are kept as roadmap markers with the active step in bold, and are intentionally text-only. Source slides 2 and 3 carry the same student-at-a-computer illustration; slide 2 now uses the workflow diagram instead, so the illustration appears once. The workflow diagram appears twice by design (preview on the big-question slide, payoff on "Example Model"). Shape-built slides (D8 grids, flow accumulation grids, slope equations, annotated StreamStats captures) were re-rendered from the PDF at 200 dpi and cropped, since the underlying art is PowerPoint shapes or WMF that browsers cannot display. Stale ArcView-era screenshots kept and flagged: ws-flow-direction-arcview.jpg, ws-streams-200-cell-threshold.png, ws-vectorized-streams-gridcode.png, ws-subwatersheds-stream-segments.png. ws-delineated-subwatersheds-streams.png is only 203x161 px in the source and is soft on a projector. Open instructor decisions are marked TODO(instructor): the 200-cell threshold's "18 hectares or 13.5 acres" unit mismatch (kept verbatim), a scale/resolution sensitivity question, validation against the NHD or StreamStats, the reading chapter, and the ocwatersheds.com citation link. TODO(graphic) marks four slides that need real captures or figures; no images were generated. Schedule links carry VERIFY comments. Software wording: the source already says ArcGIS Pro on the hands-on slides; no ArcGIS 9 / ArcMap / ArcToolbox wording was found in the text, only in the legacy screenshots.