How we tested passage through the valley.

The source is the georeferenced 2016 USGS lidar-derived 1 metre bare-earth digital terrain model. The analysis domain is 5,800 by 5,700 metres with a 100 metre source halo. Coordinates use EPSG:32613, with bounds of easting 376,000 to 381,800 metres and northing 4,362,500 to 4,368,200 metres.

• Each 2 metre routing elevation is the arithmetic mean of its four underlying 1 metre cells.
• The 10 metre comparison surface uses 10 by 10 cell means aligned with the earlier terrain model.
• The original upstream and downstream gate footprints, east-west separator, and A through D pool polygons remain fixed across comparisons.
• Side restrictions apply only through the north-south reach of the combined modeled pools. Unrestricted connectors join the gates outside that reach.

Modeled pools and existing ponds are barriers. Their polygons are expanded by half a routing-cell diagonal before cell centers are tested. Existing mapped streams remain traversable under the crossing and fording assumption used in the earlier analysis.

The main route model excludes broad hillsides steeper than 35 degrees. That broad slope is calculated from the mean 10 metre terrain with a 20 metre central-difference span, then interpolated to the 2 metre routing grid.

A 1 metre cell is classified as a candidate steep face only when it meets both tests:

1. Slope of at least 60 degrees, calculated from elevations 2 metres apart in each horizontal direction.
2. At least 5 metres of elevation difference within an 11 by 11 cell neighborhood, spanning 10 metres between the outer cell centers.

A 2 metre route cell is blocked when any of its four underlying 1 metre cells meets both tests. The classifier adds no gap closing, dilation, component pruning, or modeled rockfall runout.

Each traversable cell connects to as many as eight neighbors. A diagonal move is allowed only when both adjoining orthogonal cells are also open, preventing a route from cutting between two blocked corners.

Each directed edge costs its 3D length multiplied by the normalized anisotropic routing cost from Berti et al. (2022):

θ is the signed grade of movement in degrees, so uphill and downhill travel receive different costs. Results are relative terrain-effort units rather than calories or a species-specific probability of passage.

An implicit C++ A* solver calculates neighbors as needed. Its lower-bound heuristic uses the global minimum cost multiplier, reached at a 7.5 degree descent, multiplied by straight-line horizontal distance to the destination gate. Independent tests compare A*, full Dijkstra, and reverse-edge distances against a separately built SciPy graph.

Read the Berti et al. terrain-energy method

The opportunity envelopes answer a different question from the single easiest route: how much terrain remains available if a route may cost slightly more than today's minimum?

Full Dijkstra accumulation calculates the minimum cost from the upstream gate to every cell. A reversed-edge calculation does the same from every cell to the downstream gate. Adding those two values gives the minimum possible gate-to-gate cost of a route that passes through each cell.

Every alternative is then tested against the same current-valley minimum multiplied by 1.05, 1.10, and 1.20. The reported between-gate area includes cells within northings 4,363,455 to 4,367,455 metres that remain inside each shared cost budget.

Writing the rule explicitly: C(v) = d(upstream, v) + d(v, downstream). A cell is eligible when C(v) ≤ (1 + b) × C₀, where C₀ is the current-valley minimum and b is 0.05, 0.10, or 0.20. For example, the current minimum of 5,325.3486 relative-cost units gives a +5% ceiling of 5,591.6160 units. Eligible 2 by 2 metre cells inside the between-gate band contribute 4 square metres each; the reported loss is 100 × (A₀ − Aₛ) / A₀, using the same budget for the current and reservoir scenarios.

effort_change_pct

Change from the matching baseline with the same scenario, side, and direction.

added_cliff_effort_pct

Isolated change from adding the candidate-face mask while shoreline, access, and broad-slope rules remain unchanged.

ascent_native_m

Cumulative ascent sampled on the native 2 metre route surface.

ascent_smooth_10_m

Cumulative ascent sampled on the standardized mean 10 metre surface along the same route.

access_within_100_m / 250_m

Length of route within the named distance of the current mapped road and trail alignment.

newly_excluded_cliff_cells_before_side

Candidate cells blocked after water and broad-slope screening but before east-west side restrictions.

Opportunity-envelope area is a computational measure of route choice within a common terrain-cost budget. It is distinct from occupied habitat acreage or a measured biological corridor width.

1. Compile the solver: g++ -O3 -std=c++17 scripts/implicit_astar.cpp -o scripts/implicit_astar.
2. Run python3 scripts/run_lidar.py to recreate all 200 route records.
3. Run python3 scripts/compute_envelopes.py to recreate the 5%, 10%, and 20% route-opportunity summaries.
4. Run the solver, algorithm, route, and envelope QA scripts preserved with the analysis package.

The independent review reconstructed all 200 exported paths, checked 375,693 vertices and 256,431 diagonal edges against the saved constraints, recalculated route metrics, and found no numerical defect in the reviewed implementation or final outputs.

Required Python packages are NumPy, SciPy, Shapely, PyProj, and Rasterio. The saved package retains the source terrain, masks, routes, results, scripts, environment record, and checksums needed to reproduce the analysis without new data retrieval.