LIVEdataset aec-bench@releasetasks 552models 18disciplines 5last submission … · built …

civilboth

Wave Shoaling

Transforms deep-water wave height to nearshore conditions by computing shoaling coefficient K_s and refraction coefficient K_r, yielding H = H_0 * K_s * K_r. Uses the Fenton and McKee (1990) explicit dispersion relation approximation to avoid iterative wavelength solutions, and applies Snell's law for wave angle refraction per the USACE Coastal Engineering Manual.

both: The model must reason numerically unaided.

Standards

Fenton & McKee 1990 USACE Coastal Engineering Manual (CEM)

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

4 inputs

Always given

Included directly in every task prompt.

Deep water wave height
deep_water_wave_height_m
Deep-water significant wave height H_0
0.3 – 8 m
Nearshore depth
nearshore_depth_m
Water depth at the nearshore location d
0.5 – 30 m

Derived from scenario

Sampled from the scenario and inferable from its description.

Wave period
wave_period_s
Wave period T
Derived from the archetype scenario. Hidden at hard difficulty.
3 – 18 s
Deep water wave angle deg
deep_water_wave_angle_deg
Deep-water wave crest angle to bottom contour theta_0
Derived from the archetype scenario. Hidden at hard difficulty.
0 – 80 degrees

Scored outputs

3 outputs

Shoaling coefficient

shoaling_coefficient

Shoaling coefficient K_s (dimensionless)

Scores if within ±3% of the reference value.

Refraction coefficient

refraction_coefficient

Refraction coefficient K_r (dimensionless)

Scores if within ±3% of the reference value.

Nearshore wave height

nearshore_wave_height_m

Nearshore wave height H (m)

Scores if within ±5% 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

Normal incidence with moderate depth — all parameters given, straightforward calculation

medium

All inputs given

Oblique approach or reef shelf — all parameters given, refraction effects significant

hard

Some inputs hidden

Wave period and approach angle hidden — agent must infer from site description

Hidden inputs

Wave period swave_period_s
Deep water wave angle degdeep_water_wave_angle_deg

Prompt replacement text

The site 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

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 engineer specializing in wave mechanics and nearshore transformations.2 3## Problem4 5Determine the wave transformation from deep to shallow water at a coastal site. Calculate the shoaling coefficient, refraction coefficient, and the resulting nearshore wave height.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Deep-water wave height (H₀) | {{ deep_water_wave_height_m }} | m |12{% if wave_period_s is defined %}13| Wave period (T) | {{ wave_period_s }} | s |14{% endif %}15| Nearshore depth (d) | {{ nearshore_depth_m }} | m |16{% if deep_water_wave_angle_deg is defined %}17| Deep-water wave angle to contour (θ₀) | {{ deep_water_wave_angle_deg }} | degrees |18{% endif %}19{% if archetype_description is defined %}20 21### Site Conditions22 23{{ archetype_description }}24{% endif %}25 26{% if tool_available %}27## Available Tool28 29A wave shoaling calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:30 31```bash32python3 /workspace/{{ meta.name }}_calc.py --help33```34 35You may use this tool to verify your calculations or compute values directly.36{% endif %}37 38## Required39 40Calculate the following:41 421. Shoaling coefficient K_s (dimensionless)432. Refraction coefficient K_r (dimensionless)443. Nearshore wave height H (m)45 46## Applicable Standards47 48- USACE Coastal Engineering Manual (CEM)49- Fenton & McKee (1990) explicit wavelength approximation50 51## Constraints52 53- No internet access is available. Work from engineering knowledge and the provided tool.54- Use the following procedure:55  1. **Deep-water wavelength**:56     - L₀ = g × T² / (2π)57     - where g = 9.81 m/s²58  2. **Local wavelength** via Fenton & McKee (1990) explicit approximation:59     - σ = 2π / T60     - kd = (σ² × d / g) × [coth((σ² × d / g)^(3/4))]^(2/3)61     - where coth(x) = 1 / tanh(x)62     - k = kd / d, L = 2π / k63     - This avoids iterative solution of the dispersion relation (< 1.5% error).64  3. **Phase and group velocity**:65     - C = L / T (local phase celerity)66     - n = 0.5 × (1 + 2kd / sinh(2kd))67     - C_g = n × C (local group velocity)68  4. **Deep-water group velocity**:69     - C_g0 = g × T / (4π)70  5. **Shoaling coefficient**:71     - K_s = √(C_g0 / C_g)72  6. **Refraction** via Snell's law:73     - C₀ = L₀ / T (deep-water phase celerity)74     - sin(θ) / C = sin(θ₀) / C₀75     - K_r = √(cos(θ₀) / cos(θ))76  7. **Nearshore wave height**:77     - H = H₀ × K_s × K_r78 79## Output Format80 81Show 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:82 83```json84{85  "shoaling_coefficient": <numeric_value>,86  "refraction_coefficient": <numeric_value>,87  "nearshore_wave_height_m": <numeric_value>88}89```90 91Write your complete solution to `/workspace/output.md`.92

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.

Open coast normal

open_coast_normal

Open coast with waves arriving nearly perpendicular to shoreline

gold-coast-open-beachbondi-beach-nswcottesloe-beach-wa

Parameter ranges

deep_water_wave_height_m: 1 – 4
wave_period_s: 8 – 14
nearshore_depth_m: 2 – 10
deep_water_wave_angle_deg: 0 – 10

Oblique approach

oblique_approach

Coast with waves arriving at a significant oblique angle

byron-bay-headlandnoosa-heads-refractionport-stephens-oblique

Parameter ranges

deep_water_wave_height_m: 1 – 5
wave_period_s: 6 – 14
nearshore_depth_m: 2 – 15
deep_water_wave_angle_deg: 20 – 45

Sheltered bay

sheltered_bay

Semi-enclosed bay with reduced wave energy and moderate refraction

jervis-bay-nswmoreton-bay-qldprincess-royal-harbour-wa

Parameter ranges

deep_water_wave_height_m: 0.3 – 2
wave_period_s: 4 – 10
nearshore_depth_m: 1 – 8
deep_water_wave_angle_deg: 10 – 35

Reef shelf

reef_shelf

Shallow reef platform with rapid depth transition and strong refraction

ningaloo-reef-wagreat-barrier-reef-outerheron-island-reef

Parameter ranges

deep_water_wave_height_m: 1 – 6
wave_period_s: 8 – 16
nearshore_depth_m: 0.5 – 5
deep_water_wave_angle_deg: 5 – 40

Example task

gold-coast-open-beach-open-coast-normal-preview — hard difficulty, some inputs hidden.

Open coast with waves arriving nearly perpendicular to shoreline. gold-coast-open-beach. Required outputs: shoaling_coefficient, refraction_coefficient, nearshore_wave_height_m

The model sees

Scenario context and visible inputs.

deep_water_wave_height_m: 1 to 4 m
nearshore_depth_m: 2 to 10 m

Executable tool: wave-shoaling_calc.py

The model must infer

Inputs withheld at this difficulty.

Wave period s
wave_period_s
Deep water wave angle deg
deep_water_wave_angle_deg

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "shoaling_coefficient": <number>,
  "refraction_coefficient": <number>,
  "nearshore_wave_height_m": <number>
}

shoaling_coefficient · scored within ±3%
refraction_coefficient · scored within ±3%
nearshore_wave_height_m · scored within ±5%

Wave Shoaling

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Shoaling coefficient

Refraction coefficient

Nearshore wave height

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Open coast normal

Oblique approach

Sheltered bay

Reef shelf

Example task

The model sees

The model must infer

The model must produce