{"uid":"cap_cZvvoT1QDI8_rxdndwur2","slug":"richards-equation-nonlinear-unsaturated-column-transport-solver-2aa5604d","name":"Richards Equation Nonlinear Unsaturated Column Transport Solver","description":"Recover a complete nonlinear unsaturated-column transport artifact and its boundary-to-storage water ledger.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B011/nonlinear-unsaturated-richards-conservative-head-water-flux-transcript?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"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}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_AoJt3lPnU317TWIBDTfEE","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Simulates nonlinear unsaturated-zone water flow using the Richards equation and returns pressure head profiles and cumulative water flux at sampled timesteps.","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Soil infiltration front tracking","prompt":"Run a Richards equation simulation for a sandy loam column with 8 cells, initial pressure heads all at -5 m, top boundary -0.05 m (ponded), bottom boundary -50 m, residual water content 0.03, saturated water content 0.40, alpha 1.5, shape exponent 2.5, saturated conductivity 0.5 m/day, cell spacing 0.2 m, timestep 0.0005 days, and sample at steps 0, 8, and 16 — I need to see how the wetting front advances."},{"title":"Drainage flux ledger for field lysimeter","prompt":"Model drainage through a 12-cell unsaturated soil column under gravity drainage: initial heads -2 m everywhere, top boundary -2 m, bottom boundary -80 m, theta_r 0.08, theta_s 0.42, alpha 0.3, n 1.8, Ks 0.02 m/day, spacing 0.15 m, timestep 0.001 days, sample steps 4 and 16, and return the cumulative water flux at the bottom boundary."},{"title":"Vadose zone pressure redistribution check","prompt":"I need to verify pressure head redistribution in a 6-node vadose zone column after a rainfall event: initial heads ranging from -10 to -1 m, top head -0.5 m, bottom head -20 m, residual content 0.06, saturated content 0.38, alpha 0.8, shape exponent 1.6, saturated conductivity 0.08 m/day, cell spacing 0.5 m, timestep 0.0002 days, sample at steps 2 and 10 — give me the full transcript with water storage changes."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:41:06.348Z","isFirstParty":false,"canonicalSlug":"richards-equation-nonlinear-unsaturated-column-transport-solver-2aa5604d"}