Net Assimilation Rate (Gregory Formula)
Computes the net assimilation rate of a plant by the classic Gregory formula, the core of plant growth analysis. The rate is the dry matter gain per day multiplied by the ratio between the difference of the natural logarithms of the two leaf areas and the difference of the areas themselves: NAR = [(W2 − W1) ÷ interval] × [ln(A2) − ln(A1)] ÷ (A2 − A1). The result measures net photosynthetic efficiency per unit of leaf area, with respiration already discounted — typical values for annual crops in full growth lie between 5 and 15 grams per square metre of leaf per day, and a decline along the cycle indicates canopy self-shading. Gregory's (1926) logarithmic form was adopted rather than the approximation NAR = mass gain ÷ (mean leaf area × interval), because the former is exact when leaf area grows linearly with dry mass over the interval, which is the standard assumption of classic growth analysis. Enter the initial and final dry masses, the initial and final leaf areas and the interval between the two samplings.
Result
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NAR: how much dry matter each square metre of leaf makes
Growth analysis only reaches the net assimilation rate at the end of a lot of bench work: two destructive samplings, plants dried at 65 °C to constant mass, leaf area read blade by blade on an area meter. Dry weight gain across the two dates, on its own, answers little — a heavy plant may have bulked up merely by carrying a lot of leaf, rather than by photosynthesising well. NAR splits the two apart: it measures how much dry matter each square metre of leaf delivered per day, with respiration already netted out. That single figure tells an efficient cultivar from a merely large one, and it flags canopy self-shading when it falls through the second half of the cycle.
Gregory's formula reads NAR = [(W2 − W1) ÷ interval] × [ln(A2) − ln(A1)] ÷ (A2 − A1). W1 and W2 are total dry masses in grams, A1 and A2 the leaf areas in square metres, and the interval goes in days. With the on-screen defaults — 4.5 g and 12.8 g of mass, 0.032 m² and 0.078 m² of area, 14 days — the answer is 11.483 g/m²/day, ordinary for an annual crop in full growth, where the range usually sits between 5 and 15. The 1926 logarithmic form was kept instead of the mean-leaf-area shortcut, since the log version stays exact whenever leaf area grows in proportion to dry mass within the interval. The gap matters: those same figures through the arithmetic mean would give 10.779.
Linearity between area and mass bounds everything else. Intervals beyond three weeks, or harvests that catch the plant switching phase — flowering, the onset of grain filling — break the relationship and the value stops meaning anything physical. Equal initial and final areas get rejected, since the denominator collapses to zero; when the two areas sit very close together, the mathematical limit of the formula is mass gain divided by the area itself, and that case deserves a hand calculation. The usual unit slip is typing area in square centimetres: 320 and 780 cm² in place of 0.032 and 0.078 m² return 0.001148, ten thousand times smaller, with no warning on screen.
Frequently asked questions
Where does the default 11.483 g/m²/day come from?
Why must the initial and final leaf areas differ?
Can I enter leaf area in square centimetres?
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