A photosynthetic light-response (PLR) curve is a mathematical description of a single biochemical process and has been widely applied in many eco-physiological models. To date, many PLR measurement designs have been suggested, although their differences have rarely been explored, and the most effective design has not been determined. In this study, we measured three types of PLR curves (High, Middle and Low) from planted Larix olgensis trees by setting 31 photosynthetically active radiation (PAR) gradients. More than 530 million designs with different combinations of PAR gradients from 5 to 30 measured points were conducted to fit each of the three types of PLR curves. The influence of different PLR measurement designs on the goodness of fit of the PLR curves and the accuracy of the estimated photosynthetic indicators were analysed, and the optimal design was determined. The results showed that the measurement designs with fewer PAR gradients generally resulted in worse predicted accuracy for the photosynthetic indicators. However, the accuracy increased and remained stable when more than 10 measurement points were used for the PAR gradients. The mean percent error (M%E) of the estimated maximum net photosynthetic rate (P_max) and dark respiratory rate (R_d) for the designs with less than 10 measurement points were, on average, 16.4 times and 20.1 times greater than those for the designs with more than 10 measurement points. For a single tree, a unique PLR curve design generally reduced the accuracy of the predicted photosynthetic indicators. Thus, three optimal measurement designs were provided for the three PLR curve types, in which the root mean square error (RMSE) values reduced by an average of 8.3% and the coefficient of determination (R²) values increased by 0.3%. The optimal design for the High PLR curve type should shift more towards high-intensity PAR values, which is in contrast to the optimal design for the Low PLR curve type, which should shift more towards low-intensity PAR values

2.1. Site description

The experiments were conducted in 2017 at the experimental forest farm of Northeast Forestry University in Maoershan (45°23′21″N, 127°37′56″E). The site is characterized by a midlatitude monsoon climate, with warm, wet summers and cold, dry winters. The average temperature throughout the growing season at the site is 17.0 °C (with a range from -1.3 °C to 39.4 °C), the average precipitation throughout the growing season is 944 mm. The type of soil is typic Eutroboralfs, and the total forest coverage is approximately 83.3%, including 14.7% plantation.

2.2. PLR measurements

In this study, three sample plots (20 m × 30 m) were established within 18-year-old pure L. olgensis plantations of the same habitat. The diameter at breast height (DBH) and tree height (H) were measured for each tree whose DBH was greater than 5 cm in each plot, and the quadratic mean diameters (Dg) for three plots were calculated independently. Then, three sample trees with DBH values respectively similar to the Dg of the three plots were selected to represent the average state of each plot. According to previous research, the upper limit of the PLR curves was significantly different within different crown whorls in the vertical direction. Thus, we divided the crowns of three sample trees respectively into three equal divisions based on the crown depth (Figure 1). Three types of PLR curves, which were tagged as High, Middle and Low (Figure 2), were measured in each division (Upper, Middle and Lower) for a sample tree. The measurements were conducted using a portable photosynthesis system (LI-6400XT, LI-COR, Inc., Lincoln, Nebraska, USA) coupled with a standard light-emitting diode (LED) light source (Li-6400-02B) at 31 PAR levels (2000, 1900, 1800, 1700, 1600, 1500, 1400, 1300, 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 150, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10 and 0 μmol m^-2 s^-1). As needle clusters generally overlapped each other, those covered needles could not receive light; therefore, they only have respiration but no photosynthesis. If we do not remove these needles, then they will be calculated into the sample leaf area and consequently reduce the value of the PLR curves. Therefore, the covered needles were removed before measuring to avoid incorrect PLR curve measurements. The reserved sample needles were acclimated for 20 min at a CO₂ concentration of 370 μmol m^-2 s^-1 and a PAR value of 1400 μmol m^-2 s^-1. Then, the sample needles were allowed to equilibrate for a minimum of 2 min at each PAR gradient before the data were logged during the measurement of the PLR curves. The PLR curves were measured from 8:00 to 17:00 from the 25^th of August to the 27^th of August in 2018. The temperature (T) and relative humidity (RH) were approximately 28 ℃~30 ℃ and 30%~40% during the measurement, which would not cause stomatal closure. Once the measurements of the PLR curves were performed, the sample needles were scanned and surveyed with Image-Pro Plus 6.0 software (Media Cybernetics, Bethesda, MD, USA) in the laboratory, resulting in a projected leaf area. These methods expand upon those given in previous publications