Flood Mapping

Part A — From a Flow to a Flooded Map: Bathtub and Inundation Models

CE 414 Engineering Applications of GIS
Civil & Construction Engineering
Brigham Young University
Dr. Dan Ames

CE 414 · Week 8 — Flood Mapping, Part ALast Updated: 2026-10-09© 2026 Daniel P. Ames · CC BY 4.0

Today's Goals

By the end of class you should be able to:

  • Say what a 100-year flood is, and what it is not
  • Turn a flow into a water level with a rating curve, and a water level into a depth
  • Draw a bathtub flood map, and say when it is the right model
  • Say what FEMA does instead, and why a river needs it
CE 414 · Week 8 — Flood Mapping, Part A

Part 1 — How Big Is the Flood?

CE 414 · Week 8 — Flood Mapping, Part A

One Number a Year

  • A stream gage records flow every few minutes; the annual peak is the largest of each year
  • Provo River at Provo (USGS 10163000): 90 annual peaks, 1903 to 2024
  • The record: 2,520 ft³/s in 1952
  • Every peak is flagged regulated: dams upstream shape every flood
CE 414 · Week 8 — Flood Mapping, Part A

A 100-Year Flood Is a Probability

  • 1% chance every year, not "once a century" — FEMA says 1% annual chance
  • Over a 30-year mortgage: 1 − 0.99³⁰ ≈ 26% chance of at least one
  • FEMA's flows for this reach: 1,475 · 1,810 · 2,065 · 2,325 ft³/s for 10%, 4%, 2%, 1%
CE 414 · Week 8 — Flood Mapping, Part A

Part 2 — From a Flow to a Water Level

CE 414 · Week 8 — Flood Mapping, Part A

The Rating Curve

  • The gage measures gage height; the rating converts it to flow
  • Provo's current rating: 3.42 to 8.00 ft, 6.8 to 2,150 ft³/s
  • Read it backwards for a flood: flow → gage height
  • FEMA's 1% flow is off the top of the rating: that level is an extrapolation
CE 414 · Week 8 — Flood Mapping, Part A

Gage Height Is Not Depth

  • Gage height is read from the staff's own zero, the gage datum
  • Water elevation = datum + gage height
  • Depth = gage height − the zero-flow offset (3.20 ft at Provo)
  • Lab 7 floods the land by depth, so the datum cancels out
CE 414 · Week 8 — Flood Mapping, Part A

Part 3 — Two Ways to Draw the Flood

CE 414 · Week 8 — Flood Mapping, Part A

The Bathtub Model

  • Pick one water elevation; every cell below it is wet
  • Right for lakes and coasts: Lab 6's Lake Powell shorelines were bathtubs
  • One Con on the DEM: Con("DEM" <= 1372.04, 1)
CE 414 · Week 8 — Flood Mapping, Part A

A River Is Not a Bathtub

  • A river's surface slopes downhill with the water
  • One flat elevation drowns the low ground near Utah Lake and never reaches the river upstream
  • At the 1% level: 15.1 km² wet, nearly all of it Utah Lake lowland; it reaches only the river below the gage
CE 414 · Week 8 — Flood Mapping, Part A

What FEMA Does Instead

  • 1-D hydraulics (HEC-RAS): cross-sections, roughness, bridges, and a sloping water surface
  • FEMA's study of this reach: 42 sections inside the Lab 7 area
  • Median 1% depth above the streambed: 1.8 m
  • Accurate, and expensive: one study per reach, redone every few years
CE 414 · Week 8 — Flood Mapping, Part A

Thursday: A Cheaper Way

  • What if every cell knew its height above the river it drains to?
  • Then one depth floods the whole river at once
  • That is HAND, and it is Lab 7
CE 414 · Week 8 — Flood Mapping, Part A

Final Thoughts

Quiz: How Big, How High? Five questions on return periods, rating curves, depth and bathtubs. Scan the code, or open the link under it.

  • Not graded, nothing recorded: a quick check that today's material made sense
  • Most people miss the mortgage question

Before next class

  • Midterm 1 — in the Testing Center, open through Thursday 9:00 pm
  • Lab 7 — Flood Mapping with HAND — due Saturday 11:59 pm — Lab 7
  • Look up a stream gage near your home on the USGS map: what is its largest flow on record?
  • Office hours: calendly.com/dan-ames/office-hours

center

byu-hydroinformatics.github.io/ce414-gis-applications/quizzes/floods/

CE 414 · Week 8 — Flood Mapping, Part A

Tuesday of Week 8, the third of the water weeks: Lab 5 found where the water goes, Lab 6 measured how much a lake holds, and this week asks how high a river rises and what it covers. Today is the hydrology and the simplest flood model; Thursday is HAND and Lab 7. Midterm 1 is open in the Testing Center all week. The title image is three of FEMA's own cross-sections of the Provo River in Provo, with the 1% water surface over the lidar ground.

stamp:begin

stamp:end

Real NWIS peak series (code 6 on every peak: discharge affected by regulation or diversion). The gaps are years with no record. Point at 1983 and 1952: two years above FEMA's 1% flow, which is the next slide's puzzle. Data: the Lab 7 package, peaks_10163000.csv; figure from tools/week08_flood_figures.py.

Blue: the 90 annual peaks ranked and plotted at (n+1)/rank, the simplest empirical return period. Orange: FEMA's published flows for the Provo River "3 miles above tie-in to Utah Lake", Utah County Flood Insurance Study, Table 9 (49049CV001B); the 0.2% flow is 2,935. Ask the room why two measured years sit above FEMA's 1% flow. Answers worth hearing: short records, regulation, a fitted distribution versus the raw ranks. A simple Log-Pearson III fit to this gage's own peaks since 1993 gives about 3,111 ft³/s for the 1% flow (tools/lab07, labeled a teaching approximation, not Bulletin 17C), 34% above FEMA's; two defensible "100-year floods" can differ that much.

The USGS current rating for 10163000 (459 rows; the Lab 7 package, rating_10163000.csv). The dotted lines are FEMA's 10%, 4%, 2% and 1% flows; only the 1% falls in the gray band beyond the last measured row. A rating is built from field measurements, and floods are the hardest flows to measure, so the top of every rating is its least certain part.

Numbers from the USGS site record and the rating file: gage datum 4,493.22 ft NAVD 88; the rating's offset is 3.20 ft (the gage height at which flow would be zero). Lab 7 uses depth above the river, h = gage height − 3.20 ft, converted to meters, which is why Thursday's HAND model never needs the datum. Diagram drawn for this deck (not to scale).

1,372.04 m NAVD 88 is the 1% water elevation at the gage in the Lab 7 stage table (FEMA's 2,325 ft³/s, gage height 8.21 ft, extrapolated above the rating; tools/lab07/package_checks.json). A lake's surface really is flat, so the bathtub is the right model there; that is exactly what Lab 6 did at Lake Powell.

Left panel: every cell of the Lab 7 filled DEM at or below 1,372.04 m, 15.1 km² (tools/week08_flood_figures.py). The Lab 7 page measures the same thing along the river: a bathtub at this level covers only the lowest 4.8 km of the river, below the gage. Right panel: HAND at the same 1% depth, 1.57 km², following the river to the canyon mouth; that is Thursday.

FEMA NFHL cross-section lines for Utah County (effective June 23, 2026; WSEL_REG and STRMBED_EL attributes, converted from feet NAVD 88), sampled against the Lab 7 5 m lidar DEM. Depths range 1.5 to 2.1 m. Section T shows the lidar channel bottom sitting above FEMA's streambed: lidar cannot see through water, and that comes back Thursday.

The HAND raster for the Lab 7 reach (the package chain; 697,608 cells, 0 to 198 m; about 11% of them within 2 m of the river). White means the cell does not drain to the mapped river inside the study area. Let them puzzle over the left panel versus the right one: same terrain, two different "heights".

Four minutes, in pairs. If the room has no signal, put the URL on the board.

Deck written October 9, 2026, for the restructured Week 8 (tools/build_schedule.py). Figures: tools/week08_flood_figures.py (peaks, frequency, rating, FEMA sections, HAND map) and two drawn diagrams (fl-gage-datum.svg, fl-hand-schematic.svg).