### 2.11.2.3. Vegetation Water Potential[¶](#vegetation-water-potential "Permalink to this headline")

Both plant water supply and demand are functions of vegetation water potential. PHS explicitly models root, stem, shaded leaf, and sunlit leaf water potential at each timestep. PHS iterates to find the vegetation water potential \\(\\psi\\) (vector) that satisfies continuity between the non-linear vegetation water supply and demand (equations [(2.11.8)](#equation-11-103), [(2.11.9)](#equation-11-104), [(2.11.12)](#equation-11-107), [(2.11.14)](#equation-11-109), [(2.11.19)](#equation-11-201), [(2.11.20)](#equation-11-202)).

(2.11.23)[¶](#equation-11-301 "Permalink to this equation")\\\[\\psi=\\left\[\\psi\_{sunleaf},\\psi\_{shadeleaf},\\psi\_{stem},\\psi\_{root}\\right\]\\\]

(2.11.24)[¶](#equation-11-302 "Permalink to this equation")\\\[\\begin{split}\\begin{aligned} E\_{sun}&=q\_{1a}\\\\ E\_{shade}&=q\_{1b}\\\\ E\_{sun}+E\_{shade}&=q\_{1a}+q\_{1b}\\\\ &=q\_2\\\\ &=\\sum\_{i=1}^{nlevsoi}{q\_{3,i}} \\end{aligned}\\end{split}\\\]

PHS finds the water potentials that match supply and demand. In the plant water transport equations [(2.11.24)](#equation-11-302), the demand terms (left-hand side) are decreasing functions of absolute leaf water potential. As absolute leaf water potential becomes larger, water stress increases, causing a decrease in transpiration demand. The supply terms (right-hand side) are increasing functions of absolute leaf water potential. As absolute leaf water potential becomes larger, the gradients in water potential increase, causing an increase in vegetation water supply. PHS takes a Newton’s method approach to iteratively solve for the vegetation water potentials that satisfy continuity [(2.11.24)](#equation-11-302).

