This chapter records remaining design work and the implemented subsets that precede it. Planned Chapters 2 through 9 describe formulations the shipped engine executes; this chapter records the ones it does not — designed and not built, or built with a stated gap between what the code does and what its design or the literature says it should — so that a plan file cited in a commit, a warning met in a report, or a limitation stated in an earlier chapter can be followed to its record. Planned means designed and not built, whatever the plan's own optimism; Experimental means in the code and usable, with the gap named. Every section names its plan of record by path; the plans are not part of the manual, and the code is the source of truth where they disagree. The hydraulic half of the same record is Hydraulics Chapter 10.

Section	Formulation	Plan of record	Status
10.1	Groundwater transport in the mesh aquifer, the hydrology side — bulk transport and named sources implemented; remaining extensions below	Groundwater-transport design, 2026-09-04 (Quality Chapter 11 §11.2); `ROADMAP.md` §2.3	Experimental
10.2	LID controls as storage nodes, the hydrology side	`plans/LID_StorageNode_Redesign.md`; `ROADMAP.md` §6	Planned
10.3	LID detailed output	`plans/LID_DETAIL_OUTPUT_PLAN_2026-08-13.md`	Planned
10.4	The non-Gardner recharge closures and the benchmarks that would promote them	`plans/TWO_ZONE_GROUNDWATER_EXPLICIT_LTS_PLAN_2026-08-15.md` §9 steps 4, 7, 13, 18; `plans/TWO_ZONE_GROUNDWATER_FV_INTEGRATION_PLAN.md` §5	Experimental
10.5	`MODE PER_SUBCATCH` for the mesh aquifer	`plans/TWO_ZONE_GROUNDWATER_EXPLICIT_LTS_PLAN_2026-08-15.md` §9 steps 8, 22	Experimental

Table 10-1 Formulations recorded in this chapter

10.1 Groundwater transport in the mesh aquifer, the hydrology side

The six [GW_*] authoring sections are registered, validated and written back, but they no longer have a single "parsed but inert" status. The active two-zone kernel carries bulk SAT/UNSAT species stores, hydraulic transfers, linear sorption, dispersion and first-order decay. Section: [GW_INITIAL_QUALITY] seeds SAT/UNSAT with GLOBAL < TAG < CELL precedence. Section: [GW_SOURCES] now applies named injection/extraction and native species forcing, with actual water/species budgets, HDF5 results and native restart persistence.

Source FLOW is total m³/s, area-weighted for GLOBAL/TAG and local for CELL; SCALE multiplies flow and independent MASS loading without scaling CONC twice. Linear series use absolute model time and endpoint hold. Native pollutant MASS is mg/s, ug/s or count/s for MG/L, UG/L or #/L. Groundwater age is seconds. Extraction is availability-limited and removes existing dissolved quality.

Initial LAYER quality is refused by active bulk transport; explicit SIGMA LAYERED transport provides separate layer inventories. Hydraulic HEAD/FLOW edges bind groundwater boundary quality, and selected porous thermal/reaction profiles are implemented. Standalone CPU passive pollutant/age CLOSED_FORM/ENSLAVED/SIGMA aquifers also support coupled surface RK2; reactions, heat and borrowed owners retain first-order coupling. See Hydrology Chapter 9 and docs/design/groundwater-transport.md for the current contracts and qualification limits; the older design below does not establish runtime capability.

What the design intends. The plan of record moves every species class the project carries through the two-zone aquifer of Chapter 9: pollutants with retardation, dispersion and first-order decay; MSX species of Quality Chapter 8 under a new SUBSURFACE reaction scope; water age; and temperature with conduction. In the saturated zone the state is species mass in the cell's water, \(n h_g A C\), and the balance is

\[ R_f\,\frac{\partial (n h_g C)}{\partial t} = -\nabla\cdot(\mathbf{q}\,C) + \nabla\cdot\bigl(n h_g \mathbf{D}\,\nabla C\bigr) + S_C - \lambda\, n h_g C, \qquad R_f = 1 + \frac{1-n}{n}\,\rho_s K_d \]

with \(\mathbf{D}\) from molecular diffusion and longitudinal and transverse dispersivities on the Darcy velocity. In the unsaturated zone closure A's single store is a well-mixed reactor fed at the surface-water concentration and drained by \(q_0\) at its own; closure B's σ layers carry a one-dimensional vertical advection on the column's own ALE fluxes, first-order upwind, plus vertical dispersion. Heat follows the same pattern with effective properties taken from the actual moisture state,

\[ (\rho c)_{eff}\,\frac{\partial T}{\partial t} = -\rho_w c_w\,\nabla\cdot(\mathbf{q}\,T) + \nabla\cdot\bigl(\lambda_{eff}\,\nabla T\bigr) + \sum S_H, \qquad (\rho c)_{eff} = \theta\,\rho_w c_w + (1-n)\,\rho_s c_s \]

a vertical conduction chain from the surface boundary through the layers to a geothermal or fixed deep boundary, lateral conduction on the saturated edges, and latent removal where evapotranspiration takes water — solutes stay behind (evapoconcentration). Advection is not a solver of its own: each volume flux the kernel books in fireGwFaces and fireGwCells (§9.9) carries a tuple of species mass, age-volume and enthalpy at the donor's concentration, so conservation across the tier ladder is inherited from the kernel and proved once.

Coupling to the surface transport. Infiltration enters the top of the column at the 2D cell's water concentration where the cell is inundated and at the rainfall or runon concentration otherwise; rejected infiltration and the Dunne return flow of §9.7 go back up at the top layer's concentration; the node–aquifer exchange of §9.6 carries the tuple in both directions, so exfiltration takes mass and heat out of a node and groundwater inflow brings the aquifer's in. That replaces the constant groundwater concentration, temperature and age the legacy aquifer supplies at the node seam today — on positive groundwater flow only, with exfiltration carrying nothing — which the plan would migrate to [GW_INITIAL_QUALITY] * SAT rows on open, as initial conditions rather than eternal constants.

Implementation boundary. SubsurfaceTransportState and the groundwater transport in SubsurfaceSolver now exist and operate on both bulk zones. GwSourceResolver and GwSourceForcing provide operational named forcing; the former blanket inert warning is obsolete for an active aquifer. The fuller σ-layer transport and thermal/reaction formulation described above remains a design record, not a claim that every [GW_*] thermal option is consumed. Experimental

10.2 LID controls as storage nodes, the hydrology side

The LID controls of Quality Chapter 6 are subcatchment attributes: a unit occupies a fraction of its subcatchment, its layers form a downward cascade — surface to soil by infiltration, soil to storage by percolation at field capacity, storage to underdrain by an orifice law on the storage depth alone — and it hands its outflow on through the runon mechanism as a flow rate, never a head. The plan of record's problem statement is that this cannot express anything hydraulic: a saturated downstream unit cannot throttle the one above it, a control structure between units has no place in the topology, and an underdrain beneath a surcharged pipe keeps draining because its driving head is one-sided.

What changes for hydrology. The LID unit becomes a node of the network — a storage node (Section: [STORAGE]) carrying a new [LID_LAYERS] attribute that gives each layer a fractional depth, porosity, conductivity and moisture limits — and takes over the water balance the subcatchment used to run for it: its own rainfall and evaporation on its surface, inflow by runon from the contributing area (the existing mechanism; no new hydrological machinery), and a head resolved at every hydraulic step. The media layer keeps a hydrological model, a kinematic-wave reduction of Richards' equation that drops the matric-potential gradient on the argument that engineered media drain by gravity,

\[ \frac{\partial\theta}{\partial t} = \frac{\partial}{\partial z}\,K(\theta), \qquad K(\theta) = K_s\left(\frac{\theta}{\theta_s}\right)^{n} \]

discretised by the method of lines into \(N\) sublayers, \(d\theta_i/dt = (q_{i-1} - q_i)/\Delta z_i\) plus any link sink mapped to that elevation, every flux limited to the water the sublayer holds, \(q_i = \min\bigl(K(\theta_i),\ (\theta_i - \theta_r)\,\Delta z_i/\Delta t\bigr)\). No retention curve is needed: the node's head partitions the profile into a saturated lower zone whose head is the node's and an unsaturated upper zone governed by moisture content alone, and percolation at the media base is free drainage at \(K(\theta_N)\) above field capacity. The two domains keep their own clocks — the media on the hydrological step, the gravel layer (the storage node itself) and its links on the hydraulic step — joined by the slowly varying percolation flux.

What stays. The eight layered unit types, [LID_CONTROLS] and [LID_USAGE] (Section: [LID_CONTROLS], Section: [LID_USAGE]) and the subcatchment cascade remain the default representation, by the roadmap's compatibility clause; the storage-node form is an alternative a modeller would opt into for the units whose behaviour is hydraulic. The other half of the design — the porosity-corrected storage curve, the underdrain as an offset orifice with the network's head on its far side, overflow as a weir, chains as ordinary node–link topology — is hydraulic and recorded in Hydraulics Chapter 10, §10.8.

The status is design recorded, no implementation. No [LID_LAYERS] parser, no LID node type and no kinematic media solver exists in src/; the plan's code sketches target the legacy C sources and would be re-sited. The LidLayerSpeciesData block that is in the tree is the per-layer species state of the quality transport, not this design. Planned

10.3 LID detailed output

Legacy SWMM writes, for every [LID_USAGE] row whose ninth field names a file, a per-unit report at the runoff step: fourteen tab-separated columns — date, elapsed time, then total inflow, evaporation, surface infiltration, pavement percolation, soil percolation, storage exfiltration, surface runoff and drain outflow as rates, and surface, pavement, soil-moisture and storage levels — with dry spells compressed to their first and last rows. The modern engine parses that field, resolves it as a path, round-trips it through the input writer, the GeoPackage tables and the C API, and reads it nowhere: a model that names report files silently produces none. The only LID output today is the cumulative LID Performance Summary of the .rpt.

What the plan would report. One twelve-variable record per unit per instant — the eight rates in internal ft/s, the four depths in ft, soil moisture dimensionless — converted once at the sink boundary, to three sinks selected in [REPORT] (Section: [REPORT]): legacy-compatible per-unit files written by a runoff-step recorder immediately after the LID step, so they are byte-comparable with legacy; one consolidated tab-delimited file keyed by subcatchment and unit, written at the report step with rates averaged over the report interval and no dry-period compression; and GeoPackage result time series under a new LID object type. Two producers rather than one because LID advances at the runoff step and snapshots are built at the report step. The keys the plan proposes, LID_DETAIL (NONE, UNITS, FILE or ALL) and LID_FILE, are not parsed by this release.

Nothing has shipped: no LidDetailRecorder, LidOutputPlugin, fillLidSnapshot, rpt_* retention arrays or lid_unit_count snapshot field exists in src/. Of the four blockers the plan's survey recorded, the one it made a blocking Phase 0 — LID layer parameters never unit-converted, so a report would print the wrong internal state — has since been fixed: the LID solver now converts every layer parameter out of the deck's display units at initialisation. The others stand as far as the tree shows: the three inter-layer fluxes have no retention arrays, the plan found evap_loss and infil_loss to mean different things in different unit types, and the cadence mismatch above is structural. Planned

10.4 The non-Gardner recharge closures and the benchmarks that would promote them

Chapter 9 §9.3 states the caveat and §9.11 carries it. Of the four soil laws, Gardner's quasi-steady recharge across the water table is Qu and Duffy's equation 22 verbatim, (9-3), and is verified against it. Russo, Brooks–Corey and van Genuchten use the engine's generalisation (9-5),

\[ q_0 = \frac{\bar K}{\sigma(L)}\,\bigl[\sigma(L) - \tilde h_u\bigr], \qquad \bar K = K\!\left(\psi = \tfrac12 L\right) \]

whose equilibrium ( \(q_0 = 0\) at hydrostatic storage) and sign are the law's own and whose rate — the conductivity at the column's mean suction over the law's equilibrium storage — is a modelling choice the code makes explicit rather than a published closed form. It reduces to Gardner's order and limits, which is the consistency it rests on, and no more. The header names what would license it — "Plan step 18's closure-ladder benchmark and step 4's HYDRUS-1D comparison" — and until those run the three laws carry Experimental, Gardner or Russo are preferred for anything quantitative, and closure B (SIGMA), which integrates the real Richards flux and needs none of this, is preferred where the answer matters. The caveat is confined to closure A's recharge: the σ column and the ENSLAVED equilibrium use each law's retention and conductivity directly.

The benchmarks on the record. The explicit-kernel plan's G1/G2 track schedules, in order: step 4, the σ column against the Broadbridge–White exact Richards solution and a HYDRUS-1D single column with layer-count convergence at \(m \in \{4, 8, 16\}\) — the in-house reference for everything after it; step 7, dry-down under evaporative demand against the HYDRUS reference, both closures; step 13, the Brooks–Corey and van Genuchten closure-A laws behind the earlier draft's gates, of which the finite-volume plan states the acceptance — van Genuchten's \(q_0\) agreeing with HYDRUS-1D on a single column within 2 %, with the cost over Gardner measured; and step 18, the closure ladder, \(\alpha L \in \{0.5, 1, 3, 5, 10\}\) across closures A and B and the Russo and Gardner laws, a publishable crossover measurement that confirms or adjusts the AUTO thresholds and sets the C_GW and C_COL defaults. The finite-volume plan's acceptance for the ladder is recharge volume over the storm, peak groundwater outflow timing and magnitude, wall-clock per simulated day, and the \(L^2\) error against a one-dimensional Richards reference on a single prism.

Current state. None of them has run. No test under tests/ mentions HYDRUS or a closure ladder, and Broadbridge–White appears in the tree only as a comment. The kernel already seeds closure A and closure B from the same hydrostatic storage so that the ladder will compare trajectories rather than initial conditions — the harness is anticipated, not built.

What Implemented would require. For each of the three laws, the closure-A recharge trajectory on a single column — wetting, drainage and dry-down under ET — against closure B and a HYDRUS-1D reference across the ladder's \(\alpha L\) range, within a stated tolerance (the plan's 2 %), with the result recorded in the manual. Either that agreement licenses the rate as it stands, or a published closed form or a fitted rate constant replaces \(\bar K/\sigma(L)\) in (9-5) and the header's warning comes out. The ladder as drafted measures Russo and Gardner only, so Brooks–Corey and van Genuchten would have to be added to it; and since the ladder's purpose in the plan is the AUTO crossover, the per-law HYDRUS comparison is the promotion gate proper. Experimental

10.5 `MODE PER_SUBCATCH` for the mesh aquifer

[2D_AQUIFER_OPTIONS] MODE (Section: [2D_AQUIFER_OPTIONS]) accepts MESH, the default, and PER_SUBCATCH. The design of the second is one degenerate cell per subcatchment, no mesh sections, lateral flux zero and node exchange with the subcatchment's outlet node — the vehicle by which a pipe-only project with no mesh would get the Chapter 9 kernel (head-driven groundwater inflow and exfiltration through the outlet, the legacy [GWF] override winning where authored) and the vehicle the transport plan of §10.1 keys its migration on. Its gates were step 8 of the G1 track and, at step 22, an overhead under 1.2× the legacy solver of Chapter 5.

The code implements less. The token is parsed, written back and readable through the API; at initialisation it sets the lateral edge count to zero, so no Darcy faces are built and no lateral flux is booked. Everything else is the mesh path: the state is sized to the mesh's cell count — a deck with MODE PER_SUBCATCH and no mesh fails with "[2D_AQUIFER] authored but the mesh is empty" — and the cell-to-subcatchment and outlet-node mappings the vehicle needs, subcatch_outlet_node_ and cell_subcatch_, are declared in the solver and neither assigned nor read anywhere in the tree. (The surface router has a member of the same name, populated by centroid-in-polygon for the SUBCATCH_AQUIFER infiltration destination of Chapter 8 §8.4; it is not the solver's.) What PER_SUBCATCH means today is "the mesh kernel with lateral flow removed" (§9.1, §9.11): usable, and not what the design says. Experimental

10.6 Where the rest of the record is

ROADMAP.md carries three of these items. §2.3 is the groundwater advection–dispersion model, still listed as planned scope with no status line, which §10.1 details; §5.2 is the spatially explicit groundwater of Chapter 9, whose status line still reads "no implementation yet" — the roadmap has not caught up with the kernel, and the two Experimental items of §10.4 and §10.5 are what remains open in it; §6 is LID as storage nodes, §10.2 here and §10.8 of the hydraulics reference. LID detailed output has no roadmap entry and lives in its plan alone. For the modeller rather than the developer, the application manual's "What is coming" chapter lists the same items with their badges and the option keys that must not be mistaken for working ones.

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