LIVEdataset aec-bench@releasetasks 552models 18last submission … · built …
civilwith-tool

Rational Method

Computes peak stormwater runoff discharge using the rational method formula Q = C*I*A/360, where C is the runoff coefficient, I is the design rainfall intensity, and A is the catchment area. Applicable to small catchments up to 80 hectares per ARR and HEC-22, widely used for sizing drainage infrastructure in urban and rural settings.

with-tool: The model is given an executable Python calculator script.

Standards

ARRHEC-22

Tags

drainagehydrologyrunoffstormwater

How this task is generated

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

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

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

Inputs

3 inputs

Always given

Included directly in every task prompt.

2

  • Rainfall intensity

    rainfall_intensity_mm_hr

    Design rainfall intensity I

    10 – 300 mm/hr

  • Catchment area

    catchment_area_ha

    Catchment area A

    0.1 – 80 ha

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Runoff coefficient

    runoff_coefficient

    Runoff coefficient C (dimensionless)

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.1 – 0.95

Scored outputs

2 outputs

Peak runoff

peak_runoff_m3_s

Peak runoff Q (m³/s)

Scores if within ±3% of the reference value.

Peak runoff

peak_runoff_l_s

Peak runoff Q (L/s)

Scores if within ±3% 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 catchment, moderate intensity — straightforward application of Q = CIA / 360

medium

All inputs given

Larger catchment with higher intensity — same formula, bigger numbers

hard

Some inputs hidden

Runoff coefficient hidden — agent must infer C from site description

Hidden inputs

  • Runoff coefficientrunoff_coefficient

Prompt replacement text

The catchment is {{ 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
  • rational-method_calc.py

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 civil engineer specializing in hydrology and stormwater drainage.2 3## Problem4 5Calculate the peak stormwater runoff from a catchment using the rational method.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11{% if runoff_coefficient is defined %}12| Runoff coefficient (C) | {{ runoff_coefficient }} | - |13{% endif %}14| Rainfall intensity (I) | {{ rainfall_intensity_mm_hr }} | mm/hr |15| Catchment area (A) | {{ catchment_area_ha }} | ha |16{% if archetype_description is defined %}17 18### Site Conditions19 20{{ archetype_description }}21{% endif %}22 23{% if tool_available %}24## Available Tool25 26A peak runoff calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:27 28```bash29python3 /workspace/{{ meta.name }}_calc.py --help30```31 32You may use this tool to verify your calculations or compute values directly.33{% endif %}34 35## Required36 37Calculate the following:38 391. Peak runoff Q in cubic metres per second (m³/s)402. Peak runoff Q in litres per second (L/s)41 42## Applicable Standards43 44- Australian Rainfall and Runoff (ARR)45- HEC-22 Urban Drainage Design Manual46 47## Constraints48 49- No internet access is available. Work from engineering knowledge and the provided tool.50- Use the rational method equation (SI units):51 - Q = C × I × A / 36052 - where Q is in m³/s, I is in mm/hr, A is in hectares53 - The divisor 360 is the unit conversion factor54- Convert to litres per second: Q (L/s) = Q (m³/s) × 100055- The rational method is valid for catchments up to approximately 80 hectares56 57## Output Format58 59Show 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:60 61```json62{63 "peak_runoff_m3_s": <numeric_value>,64 "peak_runoff_l_s": <numeric_value>65}66```67 68Write your complete solution to `/workspace/output.md`.69

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.

Paved commercial

paved_commercial

Dense commercial area with impervious surfaces

sydney-cbdmelbourne-cbdbrisbane-cbd
Parameter ranges
runoff_coefficient
0.7 – 0.95

Suburban residential

suburban_residential

Suburban residential area with mixed surfaces

sydney-western-suburbsmelbourne-outerperth-northern-suburbs
Parameter ranges
runoff_coefficient
0.3 – 0.5

Low density rural

low_density_rural

Low-density rural or semi-rural area

hunter-valley-ruraldarling-downs-pastoralbarossa-valley
Parameter ranges
runoff_coefficient
0.1 – 0.3

Industrial warehouse

industrial_warehouse

Industrial or warehouse precinct with large roof areas

sydney-western-industrialmelbourne-northern-industrial
Parameter ranges
runoff_coefficient
0.6 – 0.9

Parkland open space

parkland_open_space

Parks, playing fields, and open green space

brisbane-parklandadelaide-parklandscanberra-green-belt
Parameter ranges
runoff_coefficient
0.1 – 0.25

Example task

sydney-cbd-paved-commercial-preview — hard difficulty, some inputs hidden.

Dense commercial area with impervious surfaces. sydney-cbd. Required outputs: peak_runoff_m3_s, peak_runoff_l_s

The model sees

Scenario context and visible inputs.

rainfall_intensity_mm_hr
10 to 300 mm/hr
catchment_area_ha
0.1 to 80 ha

Executable tool: rational-method_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Runoff coefficient

    runoff_coefficient

Stand-in text in the prompt

The catchment is {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "peak_runoff_m3_s": <number>,
  "peak_runoff_l_s": <number>
}
  • peak_runoff_m3_s · scored within ±3%
  • peak_runoff_l_s · scored within ±3%