Light and growth. A leaf canopy of area index LAI (m² leaf per m² ground) intercepts the fraction 1 - e-k·LAI of the sunlight (Beer-Lambert law, k = 0.65). Dry matter is made at dB/dt = RUE · Q · (1 - e-k LAI) · fT · fw · fN (radiation-use efficiency RUE = 2 g per MJ of PAR, Q in MJ m-2 d-1), minus maintenance respiration m·B·2(T-20)/10 with m = 0.015 d-1. fT is a triangle: 0 at 5 C, 1 at 25 C, 0 at 38 C.
Water in the soil. Five 20 cm layers behave as tipping buckets: a layer holds water up to field capacity θfc, the surplus drains downward at rate kd per day (exponentially), and no root can pull water below the wilting point θwp. Evaporation takes some water from the top layer, shaded by the canopy.
Roots drink. The plant wants Tp = 1.1 · ET0 · (1 - e-k LAI), with a reference evaporation demand ET0 = 0.35 Q + 0.12 (T - 10) (a simple stand-in for Penman-Monteith). The demand is shared among layers in proportion to root length in that layer times a dryness factor, and limited by a hydraulic capacity proportional to total root length. The drawn root system is the same object that supplies the layer weights, so more roots in a layer really mean more uptake there. If the roots cannot deliver, fw = Tactual/Tp < 1 and photosynthesis falls proportionally (stomata close).
Nitrogen. Mineral N is one pool; uptake is Michaelis-Menten in the pool and proportional to root length, v·Lroot·N/(K+N), and cannot exceed what the new tissue needs (3.5 % N in new dry mass). Some N is mineralised from soil organic matter each day and some is leached with drainage water.
Where the sugar goes. When water or nitrogen is short, a larger share of new dry matter goes to roots (a "functional equilibrium": invest in the organ that captures the limiting resource); in low light a larger share goes to leaves. Leaf area is dry leaf mass times specific leaf area (0.03 m² g-1). Leaves yellow when nitrogen-starved and droop when water-stressed.
What is simplified. This is a "crop-model-style" toy: one plant type, constant weather, no night/day cycle, no roots in dry layers growing faster (no hydrotropism), no phosphorus or potassium, no disease, no stages of flowering. Root patterns are drawn in one plane for visibility, whereas real roots fill a volume. All constants (RUE, SLA, root hydraulic capacity, mineralisation, N needs, plant density 25 per m² for the single drawn plant) are typical magnitudes chosen for the demonstration, not calibrated to a species; treat the numbers as illustrative.
Checks on this page. (1) Water and nitrogen balance closes to rounding error in every preset. (2) With the canopy frozen and stresses off, growth must equal the closed-form line B0 + a·t. (3) With respiration on, it must follow a/m + (B0 - a/m)e-mt. (4) The Beer-Lambert closed form is compared with numerically stacking 2000 thin leaf layers. (5) Drainage of an over-full layer must decay as e-kd t.