Exact answer known1D · free surfaceCandidate

Backwater up a sewer

Does a high water level at the outlet back up the right distance?

Test A1D-005
Chow (1959)
Version 1.0.0

Right answer: Exact solution · Chow (1959)
Results: 5 models · closest 0.024 % off · see them ↓
Must: keep every manhole and pipe depth within 2 cm

Sketch, not to scale.

The model file

The suite writes this EPA SWMM 5 input file from the test's inputs. Each engine's own copy, as it ran, is in Run it yourself under its result below.

Download A1D-005.inp 3 KB Open it on the map →

On the map: click any element to see its line in the file and every engine's result there over time.

What happens

A kilometre of 1.2 m sewer drains to an outlet whose level is held high (as by a river in flood). Water backs up through twenty manholes, its depth falling gradually towards normal depth upstream, along an exactly integrated curve.

Why it matters

Outfalls into rivers and the sea are often submerged. How far the backwater reaches decides which basements and gullies flood.

A good model must

keep every manhole and pipe depth within 2 cm
pass the full inflow down every pipe

Exact answer and models

Water level along the sewer

The outfall holds the water high; it backs up through the manholes towards normal depth upstream.

Point at the chart to read every model's value; click a name to hide or show it.

Difference from the exact answer at every manhole and pipe

Shaded: the pass limit, ±20 mm.

Point at the chart to read every model's value; click a name to hide or show it.

How models did

In rank order: by each model's percent difference from the right answer, the largest over the test's accuracy checks (lower is better; results within 10 % of each other share a rank). Mass error, timing and NSE are shown beside it, not folded in. Each model runs the same inputs. Compare them in the results viewer →

Rank	Model	Difference	Largest difference in	Run time
1=	Hydra urban drainage	0.024 %	Worst depth error	0.18 s
1=	OpenSWMM 6 dynamic wave	0.025 %	Worst depth error	0.60 s
1=	SWMM 5.1.15 previous release	0.025 %	Worst depth error	0.25 s
1=	EPA SWMM 5.2.4 dynamic wave	0.025 %	Worst depth error	0.25 s
5	OpenSWMM 6 finite volume	0.31 %	Worst depth error	1.0 s

Hydra

Hydra 17 (NEER AI, Rust): its urban-drainage engine on the SWMM data model, run through its CLI with default settings

#1= 0.024 % off

Run time, finest grid: 0.18 s · INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: swmm (DYNWAVE routing, network.json as a SWMM input file)

Worst depth error

• 0.29 mm off

0.024 % of the 1.2 m pipe diameter

Typical flow error

• < 0.0001 % off

Scored with method 3.0 · Score card: Hydra urban drainage (17.0.0/4.1.1)

Run it yourself

Hydra urban drainage (17.0.0/4.1.1) · runs on Linux · produced by scripts/run_drainage_cases.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
HYDRA=$(python scripts/fetch_hydra.py .hydra)  # the pinned Hydra 17 CLI
python scripts/run_drainage_cases.py A1D-005 --engines hydra-uds --hydra-exe "$HYDRA"

The model files the suite wrote for this run (.zip, 1.2 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

The test itself (inputs, exact answer, checks): A1D-005.zip. Check the score card with benchmark1d2d verify-card: its signature by the suite's public development key shows the card has not changed since it was written, not who wrote it.

OpenSWMM 6

OpenSWMM Engine v6 (HydroCouple's SWMM 6, pre-release) with dynamic-wave routing

#1= 0.025 % off

Run time, finest grid: 0.60 s · INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: swmm (DYNWAVE routing, network.json as a SWMM input file)

Worst depth error

• 0.3 mm off

0.025 % of the 1.2 m pipe diameter

Typical flow error

• < 0.0001 % off

Scored with method 3.0 · Score card: OpenSWMM Engine v6 dynamic wave (6.0.0a4.dev1)

Run it yourself

OpenSWMM Engine v6 dynamic wave (6.0.0a4.dev1) · runs on Linux · produced by scripts/run_drainage_cases.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python -m venv .venv-openswmm
.venv-openswmm/bin/python -m pip install "openswmm==6.0.0a4.dev1" numpy
python scripts/run_drainage_cases.py A1D-005 --engines openswmm-dw --openswmm-python .venv-openswmm/bin/python

The model files the suite wrote for this run (.zip, 1.2 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

SWMM 5.1.15

EPA SWMM 5.1.15, the release before 5.2: on the parity tests compared with SWMM 5.2.4, on the exact tests scored like any other engine

#1= 0.025 % off

Run time, finest grid: 0.25 s · INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: swmm (DYNWAVE routing, network.json as a SWMM input file)

Worst depth error

• 0.3 mm off

0.025 % of the 1.2 m pipe diameter

Typical flow error

• < 0.0001 % off

Scored with method 3.0 · Score card: EPA SWMM 5.1.15

Run it yourself

EPA SWMM 5.1.15 · version data5.1.15 · runs on Linux · produced by scripts/run_drainage_cases.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python3.10 -m venv .venv-swmm51 && .venv-swmm51/bin/python -m pip install "swmm-toolkit==0.10.0"  # EPA SWMM 5.1.15
python scripts/run_drainage_cases.py A1D-005 --engines swmm515 --swmm51-python .venv-swmm51/bin/python

The model files the suite wrote for this run (.zip, 1.2 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

EPA SWMM 5.2.4

EPA SWMM 5.2.4 with dynamic-wave routing; on the channel tests, the channel is written as one conduit per grid cell

#1= 0.025 % off

Run time, finest grid: 0.25 s · INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: swmm (DYNWAVE routing, network.json as a SWMM input file)

Worst depth error

• 0.3 mm off

0.025 % of the 1.2 m pipe diameter

Typical flow error

• < 0.0001 % off

Scored with method 3.0 · Score card: EPA SWMM 5.2.4

Run it yourself

EPA SWMM 5.2.4 · runs on Linux · produced by scripts/run_drainage_cases.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python scripts/run_drainage_cases.py A1D-005 --engines swmm524

The model files the suite wrote for this run (.zip, 1.2 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

OpenSWMM 6

OpenSWMM Engine v6 with its new explicit finite-volume routing (FLOW_ROUTING FV): one cell per conduit on the channel tests, its default cells per pipe on the drainage networks

#5 0.31 % off

Run time, finest grid: 1.0 s · INTEL(R) XEON(R) PLATINUM 8573C, 2 cores, 15.6 GB, Linux 6.17.0-1022-azure (GitHub Actions (github-hosted, ubuntu24))

Settings: swmm (FV routing, network.json as a SWMM input file)

Worst depth error

• 3.7 mm off

0.31 % of the 1.2 m pipe diameter

Typical flow error

• < 0.0001 % off

3.7 mm. With one cell per pipe (FV_MIN_CELLS 1, as on the channel tests) it is 2.2 cm off; the default subdivides each pipe.

Scored with method 3.0 · Score card: OpenSWMM Engine v6 finite volume (6.0.0a4.dev1)

Run it yourself

OpenSWMM Engine v6 finite volume (6.0.0a4.dev1) · runs on Linux · produced by scripts/run_drainage_cases.py in track-a.yml.

git clone https://github.com/scott-jeffers/benchmark1d2d && cd benchmark1d2d
git checkout 71dc10fc07a9
python -m pip install -e ".[dev,engines]"
python -m venv .venv-openswmm
.venv-openswmm/bin/python -m pip install "openswmm==6.0.0a4.dev1" numpy
python scripts/run_drainage_cases.py A1D-005 --engines openswmm-fv --openswmm-python .venv-openswmm/bin/python

The model files the suite wrote for this run (.zip, 1.2 KB): the exact inputs the solver read (one folder per grid, where the test has several), with their SHA-256.

Not run yet: InfoWorks ICM, MIKE+ (MOUSE), PCSWMM, XPSWMM, Flood Modeller, HEC-RAS

Run it and add yours →

Status of this test

Candidate. To become frozen it needs: maintainer review recorded.

Download inputs (.zip)Check your results in the browser Cite this test View on GitHub

Technical details for reviewers Checks, reference, inputs, sources

Checks and why each limit was chosen

Check	Difference measured as a percentage of	Latest	Why this check
profile_depth Linf of h · in the score	of the 1.2 m pipe diameter	–	Worst manhole or pipe depth within 2 cm. A link–node model represents each 50 m pipe by its end heads and a mid-pipe depth, a second-order discretisation of the profile whose error here is a few millimetres; the rest is the section tables.
pipe_flow L2 of Q · in the score	already a percentage	–	Pipe flows within 0.5 % of the inflow.
convergence not applicable	–	–	A link–node network with a closed-form (or 1e-11 integrated) reference at fixed elements: there is no grid to refine.

Reference

Exact solution from references.drainage.backwater.

Promotion checklist

Only frozen tests have fixed inputs and answers. This list is computed from the manifest and the published score cards; the rules are in the method.

✓Data licence verifiedfor candidateanalytic-public
✓All inputs availablefor candidateall committed or fetched by SHA-256
✓Reference (truth) availablefor candidateanalytic generator
✓Every tolerance justifiedfor candidateeach gating criterion has a rationale
✓A published run passesfor frozen5 passing score card(s)
✓Order of accuracy shownfor frozennot applicable: A link–node network with a closed-form (or 1e-11 integrated) reference at fixed elements: there is no grid to refine.
✓Two independent codes passfor frozenpassing codes: EPA SWMM 5.1.15, EPA SWMM 5.2.4, Hydra urban drainage, OpenSWMM Engine v6 dynamic wave, OpenSWMM Engine v6 finite volume
✗Maintainer review recordedfor frozenno maintainer review recorded

Inputs

File	Role	Format	SHA-256	Get it
`inputs/network.json`	network	json	`880838ccb4e0…`	Download

About this test

Physics

Twenty 1.2 m circular pipes (50 m each, \(n = 0.013\), slope 0.001) carry 0.6 m³/s to an outfall held 1.0 m above its invert. Normal depth is 0.59 m and critical depth lower, so the flow is subcritical and the outfall level backs up an M1 profile,

\[ \frac{dy}{dx} = \frac{S_0 - S_f}{1 - Fr^2}, \quad S_f = \frac{n^2Q^2}{A^2R^{4/3}},\ Fr^2 = \frac{Q^2 T}{g A^3}, \]

integrated upstream from the outfall, pipe by pipe, with an adaptive eighth-order Runge–Kutta method (DOP853, relative tolerance \(10^{-11}\)). The manholes have no losses and the inverts are continuous, so depth is continuous through every manhole. A pipe's reference depth is the profile at its midpoint.

What it checks

Gradually varied flow in a network: friction, the circular section and the convective term together. A link–node model represents each pipe by its end heads and a mid-pipe depth; on 50 m pipes that costs a few millimetres at most.

Citation

Chow, V. T. (1959). Open-Channel Hydraulics. McGraw-Hill. Rossman, L. A. (2017). SWMM Reference Manual Volume II – Hydraulics. EPA/600/R-17/111.

Sources

Chow, V. T. (1959). Open-Channel Hydraulics.
Rossman, L. A. (2017). Storm Water Management Model Reference Manual Volume II – Hydraulics (EPA/600/R-17/111). www.epa.gov/water-research/storm-water-management-model-swmm

Test A1D-005_backwater_through_manholes · version 1.0.0 · data licence analytic-public