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Agricultural Catchment Model

The Agricultural Catchment Model is Landuse Analyst’s core spatial solver. It calculates the land area required to sustain a human settlement based on caloric demand, crop productivity, soil fertility, slope penalties, and travel-time constraints.

Given a settlement centroid and demographic parameters, the engine propagates outward across the underlying terrain — constructing Von Thünen land-use rings (intensive arable cultivation, pastoral grazing, and firewood collection) and evaluating whether the site achieves caloric self-sufficiency.

Access: The Catchment Model is open to all visitors at /model.

When to use it

Anatomy of the interface

The Catchment Model interface pairs a scrolling Control Sidebar on the left with a full-viewport Map Canvas on the right.

Catchment Model workspace interface with reference tags A1 to A7
Figure 1 — The Agricultural Catchment Model workspace.
TagControlWhat it does
A1Site Selection AccordionSelect pre-configured archaeological benchmark sites (e.g. Tell esh-Shuna N., Jericho, Khirbet ez-Zeraqon) or enter custom lat/lon coordinates.
A2Population & DemographicsSet settlement population count ($P$), daily per-capita caloric requirement (default $2,100 \text{ kcal/person/day}$), and demographic distribution.
A3Crop Mix & Yield AllocationConfigure crop proportions (wheat/barley vs pulses vs olives), baseline yields ($\text{kg/ha}$), and biennial fallow practices.
A4Friction & Propagation SettingsSelect octagonal grid vs radial propagation, slope penalty function (Minetti equation), and maximum walking time cutoff.
A5Compute ButtonSubmits the scenario to the spatial engine and renders the resulting catchment rings on the map canvas.
A6Catchment Centroid MarkerMap pin marking the settlement center. Drag to reposition the settlement over new terrain.
A7Results Summary OverlayHUD panel reporting total arable hectares, caloric self-sufficiency percentage, annual surplus/deficit, and total labor hours.

Input parameters & calibration levers

Doing it this way allowed me to decouple demographic demand from physical land capability, ensuring that every variable — from caloric density to slope-induced energy expenditure — carries a transparent receipt.

Model input controls and calibration levers with reference tags B1 to B6
Figure 2 — Input parameter sliders and calibration accordions.
TagParameter ControlRange / OptionsDefaultComputational Effect
B1Settlement Population50 – 50,000 persons1,200Directly scales total annual caloric requirement: $E_{\text{total}} = P \times E_{\text{daily}} \times 365$.
B2Per-Capita Daily Demand1,500 – 3,500 kcal/day2,100Standard caloric intake baseline adjusted for age/gender distribution.
B3Cereal Crop Fraction0% – 100%65%Land fraction dedicated to wheat and barley (yield $\approx 1,200 \text{ kg/ha}$; $3,300 \text{ kcal/kg}$).
B4Pulse Crop Fraction0% – 100%20%Land fraction dedicated to legumes (lentil, chickpea; yield $\approx 800 \text{ kg/ha}$; $3,400 \text{ kcal/kg}$).
B5Grid Propagation Modeloctagonal / radialoctagonalOctagonal 8-neighbor cost-grid propagation eliminates Manhattan diagonal distortion ($d$ orthogonal, $\sqrt{2}d$ diagonal).
B6Slope Penalty Modelminetti / tobler / flatminettiApplies metabolic cost curve vs terrain incline: $C_w(i) = 280.5 i^5 - 58.7 i^4 + 33.2 i^3 + 1.8 i^2 + 7.8 i + 2.5$.

Walkthrough: Running a Catchment Simulation

Follow these steps to analyze an agricultural site:

1. Select a Benchmark Site

  1. Expand the Site Selection accordion (A1).
  2. Pick Tell esh-Shuna N. from the dropdown. The map automatically pans to the Northern Jordan Valley ($32.61^\circ\text{N}, 35.61^\circ\text{E}$).

2. Set Demographics & Crop Requirements

  1. In Population & Demographics (A2), set the population slider (B1) to 1,200 persons.
  2. Keep the daily caloric baseline (B2) at 2,100 kcal/day.
  3. In Crop Mix (A3), verify the 65% cereal / 20% pulse / 15% olive split with biennial fallow enabled ($\beta = 2.0$).

3. Configure Propagation Geometry

  1. In Friction & Slope (A4), ensure Octagonal Propagation (B5) and Minetti Slope Penalty (B6) are selected.
  2. Set the maximum walking radius cutoff to 60 minutes (1-hour walk limit).

4. Execute and Read Results

  1. Click COMPUTE CATCHMENT (A5).
  2. Inspect the map canvas (A6):
    • Blue Inner Zone: Intensive arable cultivation ring.
    • Amber Outer Ring: Pastoral grazing and firewood collection zone.
  3. Review the Results Summary HUD (A7):
    • Total Arable Area: $412.5\text{ ha}$
    • Caloric Self-Sufficiency: $108.4%$
    • Annual Surplus: $+77.2 \times 10^6\text{ kcal/yr}$

How it works

The question, then, is how to model catchment expansion without falling into the trap of isotropic circular buffers. Real agriculturalists do not walk in perfect circles — they follow paths of least resistance across slope contours and river crossings.

The Catchment Model uses an 8-neighbor octagonal cost-propagation algorithm across a $30\text{ m}$ digital elevation grid.