Evaluation of average leaf inclination angle quantified by indirect optical instruments in crop fields

Average leaf inclination angle (${\overline{\theta }}_{\text{L}}$) is an important canopy structure variable that influences light regime, photosynthesis, and evapotranspiration of plants. ${\overline{\theta }}_{\text{L}}$ can be measured through direct methods (e.g., protractor), which are labor-intensive and time-consuming, or through indirect optical instruments, which are more efficient than the direct methods. However, uncertainties of different indirect optical instruments for quantifying ${\overline{\theta }}_{\text{L}}$ remain largely unquantified. In this study, we evaluated and compared the performances of three major indirect optical instruments: (1) LAI-2200, (2) 30°-tilted camera, and (3) digital hemispherical photography (DHP), in different crop fields over a growing season, benchmarked with direct measurements. LAI-2200 and 30°-tilted camera showed higher agreement with direct $\overline{\theta }$ measurements (R² = 0.54, RMSE = 7.37°; R² = 0.58, RMSE = 8.08°) than DHP (R² = 0.14, RMSE = 13.96°). Different performances of indirect optical instruments could be attributed to the accuracy of gap fraction measurement and the performance of the ${\overline{\theta }}_{\text{L}}$ quantification algorithms. When using the LAI-2200 algorithm, larger gap fraction gradients over view zenith angles led to larger ${\overline{\theta }}_{\text{L}}$ values, and smaller gap fraction gradients led to smaller ${\overline{\theta }}_{\text{L}}$ values. Such error propagation was larger in sparse canopy than in dense canopy. The Wilson G function of the LAI-2200 algorithm performed better in estimating ${\overline{\theta }}_{\text{L}}$ than the G function based on the ellipsoidal LAD function used by the CAN_EYE algorithm. We also proposed a modification of the LAI-2200 algorithm, which further improved the performance of LAI-2200 and 30°-tilted cameras in estimating ${\overline{\theta }}_{\text{L}}$. We envision that the low-cost 30°-tilted cameras provide a promising sensor solution to continuously monitor canopy structure for various ecosystems.