# Richards Equation Nonlinear Unsaturated Column Transport Solver

> Richards Equation Nonlinear Unsaturated Column Transport Solver is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Simulates nonlinear unsaturated-zone water flow using the Richards equation and returns pressure head profiles and cumulative water flux at sampled timesteps.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B011/nonlinear-unsaturated-richards-conservative-head-water-flux-transcript?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/richards-equation-nonlinear-unsaturated-column-transport-solver-2aa5604d
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_cZvvoT1QDI8_rxdndwur2

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability richards-equation-nonlinear-unsaturated-column-transport-solver-2aa5604d -d '<json body>'
```

Example prompt: Simulate unsaturated column flow using Richards equation for a 10-node soil column with initial pressure heads all at -1.0 m, top boundary at -0.1 m and bottom boundary at -10.0 m, residual water content 0.05, saturated water content 0.45, alpha 0.5, shape exponent 2.0, saturated conductivity 0.01 m/day, cell spacing 0.1 m, timestep 0.001 days, and give me pressure head profiles at steps 4, 8, and 16.

## When to prefer this

Use this endpoint when you need a numerically rigorous solution to the nonlinear Richards equation for variably saturated (vadose zone) soil columns, specifically when you require both pressure head evolution profiles and boundary water flux accounting at precise simulation timesteps. Prefer this over linear or saturated-only flow solvers when capillary effects and partial saturation are physically significant. It is ideal for infiltration modelling, drainage analysis, or water balance verification in geotechnical and environmental hydrology workflows.

## Known failure modes

- Invalid van Genuchten parameters (alpha or n out of physical range) causing convergence failure
- Pressure head boundary values outside [-100, -0.001] m range rejected with validation error
- Sample step indices exceeding 16 or array length outside [1,3] causing schema rejection
- Timestep too large relative to cell spacing causing numerical instability
- Initial pressure heads array length outside [2,12] returning schema validation error
- Missing required fields in the richards data object returning 400 Bad Request
- Insufficient USDC balance or x402 payment failure blocking request

## How this service works

Recover a complete nonlinear unsaturated-column transport artifact and its boundary-to-storage water ledger.

## Output

Returns a structured transcript containing simulated pressure head profiles at each requested sample timestep, corresponding water content distributions derived from the van Genuchten retention model, cumulative water flux through the top and bottom boundaries, and a water storage ledger reconciling volumetric changes over the simulation period.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "richards"
   ],
   "properties": {
    "richards": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "initial_pressure_heads",
        "top_pressure_head",
        "bottom_pressure_head",
        "residual_water_content",
        "saturated_water_content",
        "alpha",
        "shape_exponent",
        "saturated_conductivity",
        "cell_spacing",
        "timestep",
        "sample_steps"
       ],
       "properties": {
        "alpha": {
         "type": "number",
         "maximum": 10,
         "minimum": 0.01
        },
        "timestep": {
         "type": "number",
         "maximum": 1,
         "minimum": 0.0001
        },
        "cell_spacing": {
         "type": "number",
         "maximum": 10,
         "minimum": 0.1
        },
        "sample_steps": {
         "type": "array",
         "items": {
          "type": "integer",
          "maximum": 16,
          "minimum": 0
         },
         "maxItems": 3,
         "minItems": 1
        },
        "shape_exponent": {
         "type": "number",
         "maximum": 4,
         "minimum": 1.2
        },
        "top_pressure_head": {
         "type": "number",
         "maximum": -0.001,
         "minimum": -100
        },
        "bottom_pressure_head": {
         "type": "number",
         "maximum": -0.001,
         "minimum": -100
        },
        "initial_pressure_heads": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": -0.001,
          "minimum": -100
         },
         "maxItems": 12,
         "minItems": 2
        },
        "residual_water_content": {
         "type": "number",
         "maximum": 0.4,
         "minimum": 0
        },
        "saturated_conductivity": {
         "type": "number",
         "maximum": 1,
         "minimum": 0.0001
        },
        "saturated_water_content": {
         "type": "number",
         "maximum": 0.8,
         "minimum": 0.05
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/richards-equation-nonlinear-unsaturated-column-transport-solver-2aa5604d/health.json
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