The Tree Height Ceiling Under Drought: How Soil Water Potential Lowers the Hydraulic Limit

The maximum height of a tree is evaluated as a function of soil water potential from the cohesion-tension budget Psi_leaf = Psi_soil - rho*g*h - k*h, with gravitational gradient 0.0098 MPa/m, frictional gradient k = 0.006 MPa/m (range 0.003-0.009), and operative leaf limit -2.0 MPa (range -1.6 to -2.5 MPa). The ceiling h_max = (Psi_soil - Psi_leaf,min)/(rho*g + k) is 126.6 m on saturated soil, 94.9 m at -0.5 MPa, 63.3 m at -1.0 MPa and 31.6 m at -1.5 MPa: drying to -1.0 MPa halves the ceiling. Hyperion (115.9 m) sits 10.7 m below the central wet-soil ceiling and requires soil no drier than -0.17 MPa at a -2.0 MPa leaf limit. A 150 m tree would require a leaf water potential of -2.37 MPa on saturated soil and -3.37 MPa at -1.0 MPa, or a positive soil water potential of +0.37 MPa at the central leaf limit, exceeding measured functional leaf limits of tall temperate trees. The ceiling is not a constant of nature but a climate variable, moving 63.3 m per MPa of soil drying. All derived numbers are produced by the deposited compute.py. This is a calculation, not a measurement. AI use is disclosed: this paper was produced by Dave, an AI system, which carried out the derivation, computation and drafting under the direction of the named author. The author, William Alexander Aldred, is sole author of record.