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civilboth

Outfall Submergence Check

Determines the percentage of time a stormwater or wastewater outfall is submerged by tidal waters under present-day conditions and a future sea level rise scenario. Uses a sinusoidal tide model h(t) = MSL + A sin(2 pi t / T) with a closed-form solution for the submerged fraction, then converts to hours per day. Applicable to coastal outfall feasibility assessments per MfE Coastal Hazards Guidance 2024 and Australian coastal design practice.

both: The model must reason numerically unaided.

Standards

IPCC AR6 Sea Level Projections MfE Coastal Hazards Guidance 2024

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

01
Template
The reusable contract shown on this page.
02
Scenario
An archetype and site context are sampled.
03
Difficulty tier
Inputs may be hidden at harder tiers.
04
Task prompt
The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

5 inputs

Always given

Included directly in every task prompt.

Outfall invert level m
outfall_invert_level_m
Outfall pipe invert level relative to datum (m AHD or m CD)
-1 – 1.5 m AHD
Mean sea level m
mean_sea_level_m
Present-day mean sea level relative to datum
-0.2 – 0.5 m AHD
Tidal amplitude
tidal_amplitude_m
Tidal amplitude (half the spring tidal range), A = (HAT - LAT) / 2
0.2 – 4 m
Sea level rise
sea_level_rise_m
Projected sea level rise for the design planning horizon
0.1 – 1.2 m

Derived from scenario

Sampled from the scenario and inferable from its description.

Tidal period
tidal_period_hours
Tidal period (typically 12.42 hours for semi-diurnal M2 constituent)
Derived from the archetype scenario. Hidden at hard difficulty.
6 – 25 hours

Scored outputs

5 outputs

Present submergence

present_submergence_percent

Percentage of time outfall is submerged under present-day conditions

Scores if within ±100% of the reference value.

Future submergence

future_submergence_percent

Percentage of time outfall is submerged under future sea level conditions

Scores if within ±100% of the reference value.

Present hours submerged per day

present_hours_submerged_per_day

Hours per day the outfall is submerged (present-day)

Scores if within ±25% of the reference value.

Future hours submerged per day

future_hours_submerged_per_day

Hours per day the outfall is submerged (future)

Scores if within ±25% of the reference value.

Submergence increase

submergence_increase_percent

Absolute increase in submergence percentage from SLR

Scores if within ±100% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

easy

All inputs given

Small tidal range, all parameters given — straightforward substitution into closed-form formula

medium

All inputs given

Larger tidal range with all parameters given — same formula, wider parameter spread

hard

Some inputs hidden

Tidal period hidden — agent must recognise semi-diurnal or diurnal regime from site description

Hidden inputs

Tidal period hourstidal_period_hours

Prompt replacement text

The outfall discharges into {{ archetype.description }} ({{ archetype.site_context }})

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

instruction.md

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior coastal/drainage engineer assessing whether a stormwater outfall will be adversely affected by tidal submergence under present-day and future sea level rise conditions.2 3## Problem4 5Determine the percentage of time a stormwater outfall pipe is submerged by tidal waters under present-day conditions and under a future sea level rise scenario. Calculate submergence as both a percentage and hours per day.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Outfall invert level | {{ outfall_invert_level_m }} | m AHD |12| Present-day mean sea level | {{ mean_sea_level_m }} | m AHD |13| Tidal amplitude (A) | {{ tidal_amplitude_m }} | m |14| Sea level rise projection | {{ sea_level_rise_m }} | m |15{% if tidal_period_hours is defined %}16| Tidal period | {{ tidal_period_hours }} | hours |17{% endif %}18{% if archetype_description is defined %}19 20### Site Conditions21 22{{ archetype_description }}23{% endif %}24 25{% if tool_available %}26## Available Tool27 28An outfall submergence calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:29 30```bash31python3 /workspace/{{ meta.name }}_calc.py --help32```33 34You may use this tool to verify your calculations or compute values directly.35{% endif %}36 37## Required38 39Calculate the following:40 411. Present-day submergence percentage (% of tidal cycle the outfall is submerged)422. Future submergence percentage (after sea level rise)433. Present-day hours per day the outfall is submerged444. Future hours per day the outfall is submerged455. Absolute increase in submergence percentage due to sea level rise46 47## Applicable Standards48 49- MfE Coastal Hazards Guidance 202450- IPCC AR6 Sea Level Projections51 52## Constraints53 54- No internet access is available. Work from engineering knowledge and the provided tool.55- Model the tide as a simple sinusoidal function:56  - h(t) = MSL + A × sin(2π t / T)57  - where MSL = mean sea level, A = tidal amplitude, T = tidal period58{% if tidal_period_hours is not defined %}59  - Use 12.42 hours for semi-diurnal tides or an appropriate period for the tidal regime60{% endif %}61- The outfall is **submerged** when h(t) > outfall invert level62- Use the closed-form solution for the fraction of time a sinusoidal signal exceeds a threshold:63  1. Let x = (z_inv − MSL) / A, where z_inv is the outfall invert level64  2. If x ≥ 1: fraction submerged = 0 (invert always above tide)65  3. If x ≤ −1: fraction submerged = 1 (invert always below tide)66  4. Otherwise: **fraction submerged = 0.5 − (1/π) × arcsin(x)**67- For future conditions, shift MSL by the sea level rise: MSL_future = MSL + SLR68- Hours per day submerged = fraction × 2469- Submergence increase = future % − present %70 71## Output Format72 73Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:74 75```json76{77  "present_submergence_percent": <numeric_value>,78  "future_submergence_percent": <numeric_value>,79  "present_hours_submerged_per_day": <numeric_value>,80  "future_hours_submerged_per_day": <numeric_value>,81  "submergence_increase_percent": <numeric_value>82}83```84 85Write your complete solution to `/workspace/output.md`.86

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Micro tidal estuary

micro_tidal_estuary

Micro-tidal sheltered estuary with small tidal range (< 1 m amplitude)

sydney-harbour-estuaryauckland-waitemata-harbourhobart-derwent-estuary

Parameter ranges

tidal_amplitude_m: 0.2 – 0.5
tidal_period_hours: 12 – 12.5

Meso tidal coast

meso_tidal_coast

Meso-tidal open coast with moderate tidal range (1-2 m amplitude)

gold-coast-broadwaterwellington-harbour-outfallnewcastle-hunter-river

Parameter ranges

tidal_amplitude_m: 0.5 – 1
tidal_period_hours: 12.2 – 12.5

Macro tidal port

macro_tidal_port

Macro-tidal port or river mouth with large tidal range (> 2 m amplitude)

darwin-harbour-outfallbroome-roebuck-baygladstone-harbour-discharge

Parameter ranges

tidal_amplitude_m: 1.5 – 4
tidal_period_hours: 12.3 – 12.5

Diurnal gulf

diurnal_gulf

Diurnal tidal regime with ~24 hour period (Gulf of Carpentaria type)

karumba-gulf-outfallweipa-port-dischargegove-peninsula-outfall

Parameter ranges

tidal_amplitude_m: 0.5 – 1.5
tidal_period_hours: 23 – 25

Example task

sydney-harbour-estuary-micro-tidal-estuary-preview — hard difficulty, some inputs hidden.

Micro-tidal sheltered estuary with small tidal range (< 1 m amplitude). sydney-harbour-estuary. Required outputs: present_submergence_percent, future_submergence_percent, present_hours_submerged_per_day, future_hours_submerged_per_day, submergence_increase_percent

The model sees

Scenario context and visible inputs.

outfall_invert_level_m: -1 to 1.5 m AHD
mean_sea_level_m: -0.2 to 0.5 m AHD
tidal_amplitude_m: 0.2 to 0.5 m
sea_level_rise_m: 0.1 to 1.2 m

Executable tool: outfall-submergence-check_calc.py

The model must infer

Inputs withheld at this difficulty.

Tidal period hours
tidal_period_hours

Stand-in text in the prompt

The outfall discharges into {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "present_submergence_percent": <number>,
  "future_submergence_percent": <number>,
  "present_hours_submerged_per_day": <number>,
  "future_hours_submerged_per_day": <number>,
  "submergence_increase_percent": <number>
}

present_submergence_percent · scored within ±100%
future_submergence_percent · scored within ±100%
present_hours_submerged_per_day · scored within ±25%
future_hours_submerged_per_day · scored within ±25%
submergence_increase_percent · scored within ±100%

Outfall Submergence Check

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Present submergence

Future submergence

Present hours submerged per day

Future hours submerged per day

Submergence increase

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Micro tidal estuary

Meso tidal coast

Macro tidal port

Diurnal gulf

Example task

The model sees

The model must infer

The model must produce