Windtrap Density and the Vegetation Threshold of the Kynes Greening Plan: A Covert-Phase Trajectory Model of the Sietch-Country Planting Domain Driven by Collector Records of 10111–10190 AG

1. Introduction

The Fremen programme to green Arrakis began with the Imperial Planetologist Pardot Kynes, whose first surveys our sources place in the 10110s AG (Kynes, P., 10132 AG), and passed to his son Liet-Kynes, who directed it until his death in 10191 AG. Its instruments were windtraps, dew precipitators and poverty grass planted to fix dunes, all built and hidden by the Fremen. The elder Kynes reportedly projected three to five centuries for the transformation, a span never tested quantitatively.

Arrakis has no rainfall in this period, so water reaching a planting comes from a collector or from dew. Free water in the soil is also taken up by the sandtrout, the little makers, whose sequestration of water at depth keeps the planet dry; a companion study in this journal describes the membrane responsible and finds uptake well above what passive diffusion allows. Plantings compete with the sandtrout for every litre delivered, and the planners had to decide how quickly to build collectors to outrun that loss.

After the fall of the Harkonnen administration and Muad'Dib's accession, some two years after Liet-Kynes's death, cache water was released openly, a regime whose release volumes are not in our register. We therefore model the covert phase only: the recorded build-out of 10111–10190 AG and its counterfactual continuation. We argue that the timeline is set by the collector-years delivered before establishment: water withheld and never returned is a permanent delay, and timing matters chiefly through how much later build-out a shortfall postpones.

2. System Description

The system is the sietch-country planting domain, the sheltered basins near the cooperating sietches where the Fremen Planetological Survey recorded plantings. Its extent is our survey-derived estimate of 5,000 km² (range 4,000–6,500 km²). Cover, V, is the fraction of the domain under established vegetation, chiefly poverty grass and planted-dune shrubs.

Collectors enter the model as trap-equivalents (TE), each being one standard windtrap or a dew-precipitator field of equal yield. The Survey's collector register lists planting-domain collectors separately from sietch supply (Fremen Planetological Survey, 10111–10190 AG), and we used only the former. Liet-Kynes's ledgers give a yield of about 3.6 m³ per day per TE (range 2.7–4.5), or about 1,300 m³ per year, applied where it is collected (Kynes, L., 10190 AG). Sietch supply and the sealed greening cache form a separate store, modelled in an earlier study in these pages, on which the planting domain does not draw.

Reconstructed by decade, the register gives additions of 1, 2, 3, 4, 6, 8, 9 and 10 TE per 100 km² from 10111 to 10190 AG, reaching 43 TE per 100 km², or about 2,150 collectors. That density is uncertain by perhaps a fifth, since fields were abandoned and moved to evade detection.

At 43 TE per 100 km² the applied supply is 0.56 mm per year over the domain, and at the counterfactual plateau of 123 TE it is 1.6 mm, against a potential evaporation above 3,000 mm per year (Office of the Imperial Planetologist, Arrakis, 10150–10190 AG). Loss is therefore limited by the water available.

3. Model and Analysis

Root-zone water, M (mm), gains applied supply a and intercepted dew, and loses water to evaporation and sequestration: dM/dt = a + d·V − [e·g(V)·(1 − V) + s]·M. Paired trials on planted and bare dune plots give e = 1.6 per year and s = 2.4 per year (Oskarin, 10222 AG), so on bare ground the sandtrout take 60% of what is lost. The term s·M is an effective rate fitted to plot losses, standing in for an active uptake process whose moisture dependence we do not resolve. Dew interception is d = 6 mm per year per unit cover (Mardekh, 10219 AG).

Cover follows a logistic equation with moisture-dependent growth: dV/dt = r·[M²/(M² + K²)]·V·(1 − V/Vmax) − m·V, with r = 0.5 per year, K = 1 mm and a ceiling Vmax = 0.35 (Straka, 10231 AG). Net mortality m, which absorbs replanting, was fitted at 0.02 per year to the planting censuses of 10120–10140 AG. Growth balances mortality when root-zone water reaches about 0.2 mm, which on bare ground requires a supply of about 0.82 mm per year, or 63 TE per 100 km².

Shade and transpiration cool the surface by 20 K per unit cover from a planting-season mean of 325 K (Veyl, 10204 AG). Evaporation follows saturation vapour pressure through the Clausius–Clapeyron relation, g(V) = exp[−5,420 K × (1/T − 1/325 K)], a reduction of 16% at 17% cover. Vegetation also darkens pale sand, lowering albedo and offsetting part of this cooling. We neglect it; since cooling strength moves the threshold by under a year, the omission does not alter the results.

Self-sustainment is defined operationally: we ran the recorded schedule and switched every collector off once cover reached a set value. Switch-off at 16% cover or below led to collapse, whereas at 17% or above cover settled at 28.5% on dew and suppressed evaporation alone. The threshold, Vth, is therefore 0.17, below the 32.5% equilibrium reached with collectors running.

Initial cover, about 10 km² in 10111 AG, was back-extrapolated from the 10120–10140 AG censuses at the fitted mortality; the integration step was 0.01 years. After 10190 AG the final-decade rate is continued to year 160 (10270 AG), giving a plateau of 123 TE per 100 km². Shortfalls are measured in collector-years, one TE per 100 km² in service for a year. The early shortfall builds 25% fewer collectors in years 1–80, withholding about 290 collector-years. In one variant density is restored linearly by year 160 and nothing is returned, the catch-up withholding some 430 more; in the other, construction overshoots the recorded density until cumulative collector-years match by year 160. The later shortfall withholds the same 290 collector-years in years 81–120, then restores density by year 160 without returning them. We also halted deployment for single years, shifting every later addition, and varied each parameter by ±25%.

Under the recorded schedule, plantings contract from about 10 km² to 2.1 km² in year 100, when supply passes the establishment level. Cover then reaches 1% in year 196, 5% in year 224 and the threshold in year 242, near 10350 AG, settling at 32.5% within three further decades. Front-loading brings the threshold forward by 17–19 years. The early shortfall with density restored delays it by seven years, and the later shortfall by eight. When the withheld collector-years are returned, the early shortfall instead brings the threshold four years forward, the returned water arriving near establishment, when it does most good. A sustained 10% shortfall costs 35 years.

A single-year halt in year 10 or year 30 delays the threshold by 1.4 years, one in year 60 by 1.3 years, one in year 100 by 1.0 year and one in year 140 by 0.4 years. Each halt postpones every later addition, so an early one withholds far more water: about 120 collector-years for a halt in year 10, against about 20 in year 140. Per collector-year withheld, the late halt is the costlier; early deployment matters because it carries the whole later build-out forward.

Plateaus below about 63 TE per 100 km² never produce expansion. Holding the recorded schedule at 68 or 74 TE delays the threshold to roughly 1,100 and 650 years; reaching it within five centuries requires about 80. Near the establishment level these times are orders of magnitude only.

Sensitivity runs report the year cover first reaches 17%, with Vth held at its central value. Varying unit yield by ±25% moves that year from 242 to 195 or 381; sandtrout sequestration, to 203 or 295; bare-ground evaporation, to 216 or 274; maximum growth rate, to 210 or 307; mortality, to 220 or 268; dew interception, to 238 or 246; cooling strength, by under a year. Under the adverse settings of s, d, m and r, 17% cover is not self-sustaining and no threshold exists, and with evaporation raised by a quarter persistence requires about 20%. The largest schedule effect, 35 years, is smaller than five of these seven ranges.

4. Validation Against Field Data

Validation used the ledger's dune-fixation censuses for 10150–10190 AG, withheld from fitting (Kynes, L., 10190 AG). Each estimates hidden planted area from sample plots and traverses, with the ledger's own low and high figures. The modelled decline lies inside every census range (table below); mean absolute error is about 0.2 km² against ranges 1.5–2.5 km² wide, the model running low by 0.18 km² on average.

Such a validation is narrow. It tests only the contracting phase, when cover is below a thousandth of the domain; nothing in the covert record tests expansion, threshold or switch-off. Surveys after Muad'Dib's accession report rapid expansion under open cache release, as the model predicts, but we did not fit that period. The register also records construction better than abandonment.

5. Failure Modes

Sandtrout sequestration is the process best placed to defeat the plan. With s raised by a quarter, plantings expand while collectors run but collapse whenever supply stops; adverse dew, mortality or growth settings do the same. The switch-off result is fragile, and the model gives no warrant for stopping collectors once cover passes 17%. If dense plantings excluded sandtrout from the root zone, persistence would be more robust.

Collector yield is the second route to failure. Storms, sand burial and relocation all reduce it, and a sustained 25% loss delays 17% cover to year 381.

Structural simplification is a third: one soil layer, no atmospheric circulation, and one domain-wide cover value for scattered patches. The loss term treats active uptake as a first-order rate; if sandtrout keep drawing water at low moisture, losses are understated and the thresholds optimistic. Extrapolation to open erg or to the planet is not supported.

Stagnation is the failure planners could see. In every schedule, cover reaches 1% some 46–56 years before the threshold and 5% only 17–21 years before it, too late for correction. Earlier signals are supply density above about 63 TE per 100 km² and census cover that has stopped falling; cover still falling a decade later would place yield or loss outside our ranges.

6. Conclusion

Modelled as the Fremen built it, the Kynes greening is governed by the water delivered before establishment. Plantings shrink until collector density passes the establishment level. A year of deployment lost in the first six decades costs 1.3–1.4 years at the threshold because it postpones the rest of the build-out, and a shortfall whose collector-years are never returned costs several years even once density is restored; returning the water removes the penalty. Under the recorded schedule continued covertly, the threshold falls about 242 years after deployment began, near 10350 AG, short of the elder Kynes's lower bound. Across the parameter ranges 17% cover is first reached between years 195 and 381, well into his span, and under several adverse settings it would not persist without collectors.

For the covert phase, the practical conclusions are to build early, to make good any shortfall in delivered water and not only in collector numbers, to watch supply density and the direction of census cover, and to keep collectors running past the threshold until the sandtrout loss rate is better constrained.