Crop growth analysis: LAI, CGR, RGR, NAR and LAD
The classical growth analysis indices, what each one means, how to calculate them from two harvests, and how leaf area links light capture to yield.
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How fast is a crop growing, and why? Growth analysis answers these questions with nothing more than a balance, a ruler or leaf-area meter, and a few formulas. By harvesting plants at intervals and measuring their dry weight and leaf area, it splits growth into the size of the crop's "solar panel" (leaf area) and how efficiently that panel works.
The method was developed in Britain in the early twentieth century, by V. H. Blackman, F. G. Gregory and D. J. Watson among others, and it remains a core part of crop physiology and agronomy courses and exams, mostly as calculations.
The growth curve
Plotted against time, the dry weight of an annual crop follows an S-shaped (sigmoid) curve:
- Lag phase: slow growth after emergence, while seedlings live on seed reserves and leaf area is small.
- Exponential (log) phase: growth proportional to the size already reached, because more leaves capture more light to make still more leaves.
- Linear phase: the canopy covers the ground, and the crop gains a roughly constant amount of dry matter per day.
- Senescence (plateau): leaves age and die, and growth slows and stops near maturity.
The indices
Growth analysis uses dry weight (W, usually per unit ground area for crops), leaf area (A), and the time interval between two harvests (t1 and t2).
Leaf area index (LAI)
LAI has no units. An LAI of 3 means three square metres of leaf above each square metre of ground. Crops usually need an LAI of about 3 to 5 to intercept around 90 to 95 per cent of the incoming light; the LAI at which this happens is called the critical LAI. Above it, lower leaves are shaded and add little. The idea of an optimum LAI, above which shaded leaves respire more than they gain, was popular in the mid-twentieth century; in most crops, net growth actually levels off rather than falling.
Crop growth rate (CGR)
CGR is the slope of the growth curve. It is low early, peaks during the linear phase, and declines with senescence. Typical peak values for healthy field crops are about 15 to 30 g/m2 per day, and higher for vigorous C4 crops such as maize and sugarcane.
Relative growth rate (RGR)
RGR is growth per unit of existing dry weight, the "compound interest rate" of growth, a concept introduced by Blackman in 1919. It is highest in young plants and falls steadily with age, because a growing proportion of the plant is stem, root and storage tissue that does not photosynthesise, and because leaves shade each other.
Net assimilation rate (NAR)
NAR, also called unit leaf rate, is the gain in dry weight per unit leaf area per day: a measure of how productive each square metre of leaf is. It falls as the canopy closes and leaves shade each other.
Leaf area duration (LAD)
LAD combines how much leaf there is and how long it lasts. Watson showed in the 1940s that differences in yield between seasons and varieties were often explained much better by LAD than by NAR: crops differ more in how much leaf they keep and for how long than in how efficient each leaf is. LAD after flowering is closely related to grain yield in cereals, which is why stay-green varieties, which keep green leaves longer, can yield more under late stress.
Other ratios
- Leaf area ratio (LAR) = leaf area ÷ total plant dry weight.
- Specific leaf area (SLA) = leaf area ÷ leaf dry weight; its inverse is specific leaf weight.
- Leaf weight ratio (LWR) = leaf dry weight ÷ total dry weight; LAR = SLA × LWR.
The indices fit together neatly:
- RGR = NAR × LAR: relative growth depends on leaf efficiency and on how much leaf the plant has per unit of weight.
- CGR = NAR × LAI: crop growth depends on leaf efficiency and on how much leaf covers the ground.
A worked example
Growth analysis from two harvests
A crop is sampled 30 and 50 days after sowing:
| Day 30 | Day 50 | |
|---|---|---|
| Dry weight (g/m2) | 50 | 250 |
| LAI | 0.8 | 3.0 |
- CGR = (250 − 50) ÷ 20 = 10 g/m2 per day.
- RGR = (ln 250 − ln 50) ÷ 20 = ln 5 ÷ 20 = 1.609 ÷ 20 = 0.080 g/g per day: the crop was adding about 8 per cent to its weight each day.
- NAR = 10 × (ln 3.0 − ln 0.8) ÷ (3.0 − 0.8) = 10 × 1.322 ÷ 2.2 ≈ 6.0 g/m2 of leaf per day. (LAI can be used in place of leaf area because both harvests are per square metre of ground.)
- LAD = (0.8 + 3.0) ÷ 2 × 20 = 38 days.
Check: CGR ≈ NAR × mean LAI, where the appropriate mean LAI over the interval is 2.2 ÷ 1.322 = 1.66; 6.0 × 1.66 ≈ 10. The figures agree.
Light, radiation use efficiency and yield
Growth analysis connects directly to the modern way of thinking about crop yield:
- Crop growth = light intercepted × radiation use efficiency (RUE, grams of dry matter per megajoule of intercepted radiation).
- Light intercepted depends on LAI and canopy architecture, following an approximately exponential relationship (fraction intercepted = 1 − e−kL, where k is the extinction coefficient and L the LAI). Erect-leaved canopies, with lower k, let light penetrate deeper and suit high LAI.
- Yield = total dry matter × harvest index.
Typical RUE values are about 1.2 to 1.5 g/MJ for C3 crops such as wheat and rice, and about 1.6 to 2.0 g/MJ for C4 crops such as maize and sorghum, measured on intercepted solar radiation.
Limits of classical growth analysis
- It needs destructive sampling, many plants, and careful sampling to reduce variation; differences between harvests can be swamped by plant-to-plant variability.
- Formulas such as NAR assume particular relationships between weight and leaf area between harvests.
- Roots are often left out, so "dry weight" usually means above-ground dry weight.
- Today, curve fitting (functional growth analysis), remote sensing of canopy cover and LAI, and crop simulation models build on the same concepts.
Key points
- Crop dry weight follows a sigmoid curve: lag, exponential, linear and senescence phases.
- LAI = leaf area ÷ ground area; about 3–5 gives near-full light interception (critical LAI).
- CGR = ΔW ÷ Δt; RGR = Δln W ÷ Δt; NAR = growth per unit leaf area; LAD = mean LAI × days.
- RGR = NAR × LAR and CGR = NAR × LAI.
- Yield differences are often explained more by leaf area duration than by NAR.
- Growth = intercepted light × RUE; yield = dry matter × harvest index.
What the exams ask
- School-leaving and entrance papers: definitions of LAI, CGR and RGR, and the phases of the growth curve.
- Degree and research-fellowship entrances: calculating CGR, RGR, NAR and LAD from data, relationships between indices, critical and optimum LAI, and radiation use efficiency.
- Professional and research examinations: interpreting growth analysis experiments, light interception and extinction coefficients, and linking growth to yield.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Why does RGR fall as the plant gets bigger?
A growing share of the plant is stem, root and storage tissue that does not photosynthesise, and as leaves multiply they shade each other, so each gram of plant supports less new growth.
What is a good LAI?
Enough to intercept most of the light, usually around 3 to 5 for field crops, maintained for as long as possible. Much higher LAI adds little and may increase lodging and disease.
Can I measure LAI without cutting plants?
Yes. Canopy analysers measure light below and above the canopy, and smartphone apps and satellite or drone images estimate canopy cover and LAI, though each needs calibration for the crop.
Sources
- Watson, D. J. "Comparative physiological studies on the growth of field crops. I. Variation in net assimilation rate and leaf area between species and varieties, and within and between years." Annals of Botany 11, 41–76 (1947).
- Blackman, V. H. "The compound interest law and plant growth." Annals of Botany 33, 353–360 (1919).
- Radford, P. J. "Growth analysis formulae: their use and abuse." Crop Science 7, 171–175 (1967).
- Hunt, R. Plant Growth Curves: The Functional Approach to Plant Growth Analysis. Edward Arnold, 1982.
- Monteith, J. L. "Climate and the efficiency of crop production in Britain." Philosophical Transactions of the Royal Society B 281, 277–294 (1977).
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