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civilwith-tool

Cerc Longshore Transport

Estimates annual volumetric longshore sediment transport using the CERC formula from the USACE Coastal Engineering Manual and Shore Protection Manual. Calculates wave energy flux at the breaker line and converts it to a sediment transport rate, accounting for wave angle, sediment and water densities, and porosity. Used in coastal engineering to predict littoral drift and inform beach nourishment or breakwater design.

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

Standards

Shore Protection Manual (SPM)USACE 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

6 inputs

Always given

Included directly in every task prompt.

Breaking wave height
breaking_wave_height_m
Significant breaking wave height H_b
0.3 – 5 m
Wave angle at breaking deg
wave_angle_at_breaking_deg
Wave angle at breaking relative to shore-normal alpha_b (positive = left-to-right looking shoreward)
-45 – 45 degrees

Derived from scenario

Sampled from the scenario and inferable from its description.

K coefficient
k_coefficient
CERC empirical transport coefficient K
Derived from the archetype scenario. Hidden at hard difficulty.
0.1 – 1

Optional

Used only when the sampled task needs this part of the contract.

Sediment density
sediment_density_kg_m3
Sediment grain density rho_s
Derived from the archetype scenario. Optional input. Hidden at hard difficulty.
2500 – 2800 kg/m³
Water density
water_density_kg_m3
Water density rho_w
Derived from the archetype scenario. Optional input. Hidden at hard difficulty.
1000 – 1035 kg/m³
Porosity
porosity
In-situ sediment porosity p
Derived from the archetype scenario. Optional input. Hidden at hard difficulty.
0.3 – 0.5

Scored outputs

3 outputs

Energy flux w

energy_flux_w_m

Wave energy flux at breaking (E*Cg)_b in W/m

Scores if within ±3% of the reference value.

Transport rate m3 yr

transport_rate_m3_yr

Volumetric longshore transport rate Q_l (m³/year, absolute value)

Scores if within ±5% of the reference value.

Transport direction

transport_direction

Transport direction: 1.0 = left-to-right, -1.0 = right-to-left (looking shoreward)

Scores if within ±1% 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

Moderate wave height, all parameters given — straightforward CERC formula application

medium

All inputs given

Larger waves, steeper angles, all parameters given — larger numbers but same formula

hard

Some inputs hidden

K coefficient, sediment density, water density, and porosity hidden — agent must infer from site description

Hidden inputs

K coefficientk_coefficient
Sediment densitysediment_density_kg_m3
Water densitywater_density_kg_m3
Porosityporosity

Prompt replacement text

The site is a {{ 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
cerc-longshore-transport_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 coastal engineer specializing in littoral processes and sediment transport.2 3## Problem4 5Calculate the longshore sediment transport rate using the CERC formula (USACE Coastal Engineering Manual / Shore Protection Manual).6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Breaking wave height (H_b) | {{ breaking_wave_height_m }} | m |12| Wave angle at breaking (α_b) | {{ wave_angle_at_breaking_deg }} | degrees |13{% if k_coefficient is defined %}14| CERC transport coefficient (K) | {{ k_coefficient }} | - |15{% endif %}16{% if sediment_density_kg_m3 is defined %}17| Sediment density (ρ_s) | {{ sediment_density_kg_m3 }} | kg/m³ |18{% endif %}19{% if water_density_kg_m3 is defined %}20| Water density (ρ_w) | {{ water_density_kg_m3 }} | kg/m³ |21{% endif %}22{% if porosity is defined %}23| Sediment porosity (p) | {{ porosity }} | - |24{% endif %}25{% if archetype_description is defined %}26 27### Site Conditions28 29{{ archetype_description }}30{% endif %}31 32{% if tool_available %}33## Available Tool34 35A longshore transport calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:36 37```bash38python3 /workspace/{{ meta.name }}_calc.py --help39```40 41You may use this tool to verify your calculations or compute values directly.42{% endif %}43 44## Required45 46Calculate the following:47 481. Wave energy flux at breaking (E × C_g)_b in W/m492. Volumetric longshore transport rate Q_l in m³/year (absolute value)503. Transport direction (1.0 = left-to-right looking shoreward, -1.0 = right-to-left)51 52## Applicable Standards53 54- USACE Coastal Engineering Manual (CEM)55- Shore Protection Manual (SPM)56 57## Constraints58 59- No internet access is available. Work from engineering knowledge and the provided tool.60- Use the CERC formula with breaker index γ_b = 0.78:61  - Breaking depth: d_b = H_b / γ_b62  - Shallow water group velocity at breaking: C_gb = √(g × d_b)63  - Wave energy flux: (E × C_g)_b = ρ_w × g × H_b² × C_gb / 864  - Longshore wave power component: P_ls = (E × C_g)_b × sin(2α_b) / 265  - Immersed weight transport rate: I_l = K × P_ls66  - Volumetric transport rate: Q_l = I_l / ((ρ_s − ρ_w) × g × (1 − p))67  - Convert Q_l from m³/s to m³/year using 365.25 × 24 × 3600 seconds per year68- Use g = 9.81 m/s²69- Transport direction: positive α_b means transport is left-to-right looking shoreward (direction = 1.0); negative α_b means right-to-left (direction = -1.0)70- Report transport_rate_m3_yr as an absolute value71 72## Output Format73 74Show 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:75 76```json77{78  "energy_flux_w_m": <numeric_value>,79  "transport_rate_m3_yr": <numeric_value>,80  "transport_direction": <numeric_value>81}82```83 84Write your complete solution to `/workspace/output.md`.85

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.

Exposed sandy coast

exposed_sandy_coast

High-energy exposed sandy coastline with quartz sand and large oblique swell

nsw-south-coast-swellwa-southwest-capessa-great-ocean-road

Parameter ranges

breaking_wave_height_m: 2 – 4
wave_angle_at_breaking_deg: 10 – 30
k_coefficient: 0.3 – 0.45
sediment_density_kg_m3: 2600 – 2700
water_density_kg_m3: 1020 – 1030
porosity: 0.35 – 0.42

Moderate energy beach

moderate_energy_beach

Moderate-energy beach with medium swell and modest wave angles

sunshine-coast-qldnewcastle-nsw-beachmandurah-wa-coast

Parameter ranges

breaking_wave_height_m: 0.8 – 2
wave_angle_at_breaking_deg: 5 – 15
k_coefficient: 0.32 – 0.42
sediment_density_kg_m3: 2600 – 2700
water_density_kg_m3: 1020 – 1030
porosity: 0.35 – 0.42

Sheltered embayment

sheltered_embayment

Low-energy sheltered embayment with short-period wind waves and fine sand

moreton-bay-qldport-phillip-bay-viccockburn-sound-wa

Parameter ranges

breaking_wave_height_m: 0.3 – 0.8
wave_angle_at_breaking_deg: 5 – 20
k_coefficient: 0.35 – 0.5
sediment_density_kg_m3: 2550 – 2650
water_density_kg_m3: 1020 – 1030
porosity: 0.38 – 0.45

High energy headland

high_energy_headland

High-energy headland-controlled pocket beach with coarse sand and strong oblique waves

byron-bay-nsw-headlandnoosa-heads-qldcape-naturaliste-wa

Parameter ranges

breaking_wave_height_m: 3 – 5
wave_angle_at_breaking_deg: 15 – 45
k_coefficient: 0.2 – 0.35
sediment_density_kg_m3: 2650 – 2800
water_density_kg_m3: 1020 – 1030
porosity: 0.3 – 0.38

Example task

nsw-south-coast-swell-exposed-sandy-coast-preview — hard difficulty, some inputs hidden.

High-energy exposed sandy coastline with quartz sand and large oblique swell. nsw-south-coast-swell. Required outputs: energy_flux_w_m, transport_rate_m3_yr, transport_direction

The model sees

Scenario context and visible inputs.

breaking_wave_height_m: 2 to 4 m
wave_angle_at_breaking_deg: 10 to 30 degrees

Executable tool: cerc-longshore-transport_calc.py

The model must infer

Inputs withheld at this difficulty.

K coefficient
k_coefficient
Sediment density
sediment_density_kg_m3
Porosity
porosity
Water density
water_density_kg_m3

Stand-in text in the prompt

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

The model must produce

The scored JSON answer schema.

{
  "energy_flux_w_m": <number>,
  "transport_rate_m3_yr": <number>,
  "transport_direction": <number>
}

energy_flux_w_m · scored within ±3%
transport_rate_m3_yr · scored within ±5%
transport_direction · scored within ±1%

Cerc Longshore Transport

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Energy flux w

Transport rate m3 yr

Transport direction

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Exposed sandy coast

Moderate energy beach

Sheltered embayment

High energy headland

Example task

The model sees

The model must infer

The model must produce