How Universal Is the Relationship between Remotely Sensed Vegetation Indices and Crop Leaf Area Index? A Global Assessment

Leaf Area Index (LAI) is a key variable that bridges remote sensing observations to the quantification of agroecosystem processes. In this study, we assessed the universality of the relationships between crop LAI and remotely sensed Vegetation Indices (VIs). We first compiled a global dataset of 1459 in situ quality-controlled crop LAI measurements and collected Landsat satellite images to derive five different VIs including Simple Ratio (SR), Normalized Difference Vegetation Index (NDVI), two versions of the Enhanced Vegetation Index (EVI and EVI2), and Green Chlorophyll Index (CIGreen). Based on this dataset, we developed global LAI-VI relationships for each crop type and VI using symbolic regression and Theil-Sen (TS) robust estimator. Results suggest that the global LAI-VI relationships are statistically significant, crop-specific, and mostly non-linear. These relationships explain more than half of the total variance in ground LAI observations (R2 >0.5), and provide LAI estimates with RMSE below 1.2 m2/m2. Among the five VIs, EVI/EVI2 are the most effective, and the crop-specific LAI-EVI and LAI-EVI2 relationships constructed by TS, are robust when tested by three independent validation datasets of varied spatial scales. While the heterogeneity of agricultural landscapes leads to a diverse set of local LAI-VI relationships, the relationships provided here represent global universality on an average basis, allowing the generation of large-scale spatial-explicit LAI maps. This study contributes to the operationalization of large-area crop modeling and, by extension, has relevance to both fundamental and applied agroecosystem research.


Agro Site
The Agro site is a valuable data source which was designed for remote sensing product validation, and has been utilized in many satellite imagery oriented investigations [19,20]. However, we did not detect any statistically significant relationships between LAI and VI extracted from Landsat images when pooling data collected at different times, which violates a fundamental assumption of our study ( Figure S1). Moreover, we found nearly 1/3 of the maize LAI measures are greater than 8 m 2 /m 2 , which is beyond the prediction power of satellite derived VIs. Due to the lack of necessary metadata to resolve these issues and the large sample size at Agro (n = 290), we elected to eliminate the Agro site from the truncated dataset, but retain it in the full-range dataset. Figure S1. Scatterplot of surface reflectance derived NDVI versus LAI measurements of the Agro Site (colored by crop types).

SMEX02-WC Site
The SMEX02-WC site was excluded due to presence of unusually high value of the CIGreen calculated from surface reflectance. SMEX02-WC is located in Iowa, US. This site contains two types of crops: maize and soybean. Figure S2 shows the distribution of CIGreen (surface reflectance based) values for SMEX02-WC vs. the rest of the dataset. Over 50% of the SMEX02-WC CIGreen measurements were above 15, while the rest of the dataset as well as literature reported values for CIGreen range from 0.5 to 15 [21][22][23][24][25]. Thus, due to remotely sensed data quality concerns, we eliminated all data from this site in the establishment of the dataset, but used it to validate the refined LAI-EVI/EVI2 relationships.

SMAPEx2 Site
SMAPEx2 (Australia) contains 19 samples in pasture and 29 samples in cereals such as wheat and barley. It was eliminated as many of the measurements were taken during crop reproductive stage. Figure S3 shows a scatter plot of LAI versus EVI, colored by crop type. Although an overall relationship considering all crops is significant (R 2 = 0.18), there is no significant relationship for pasture and row crop data if treated separately (R 2 ≤ 0.02). In the figure, pasture LAI varies from 0-2 m 2 /m 2 . However, EVI stays around 0.18, and never rises above 0.21. The same behavior is also found in more than half of the row crop samples.
To explain the behavior of LAI in SMAPEx2, we investigated the photos taken for each record. Figure S4 shows two pasture fields at the time of measurement in SMAPEx2. Although plot YD_F606 has a much greater LAI (1.6 m 2 /m 2 ) than plot YA4_F14 (0.56 m 2 /m 2 ), the average EVI for both plots are almost the same. This is because the pasture in YD_F606 is mainly mature oats, with most leaves being yellow, which seem to be included in the measured LAI using an optical instrument such as LAI2000. The same issue also presents with cereals. Therefore, the definition of LAI used in SMAPEx2 might be different from the definition we used which contains only "green" leaves. We also found that the SMAPEx2 experiment was conducted in early December 2010. Hence most of the grains were at maturity and turned yellow ( Figure S5). The case for pasture is more complicated than grains, as it may contain a variety of plants, which mature at different time of the year. Without aids from photos taken in the field, it is difficult to determine or prove whether each LAI measures include yellow leaves or not. Therefore, we removed all data from SMAPEx2 as a precaution.      Table S4. Best-fit functions for the LAI-VI relationships ( = ( )) for major crops based on three levels of radiometric/atmospheric corrections. The last column gives the reasonable VI range that will produce LAI within [0,6] m 2 /m 2 and any value out of that range will result in either negative of excessive (greater than 6 m 2 /m 2 ) LAI.        Table S6. Best-fit functions for the LAI-VI relationships ( = ( )) for major crops based on surface reflectance using the dataset with a complete LAI data range.     Figure S8. LAI-EVI and LAI-EVI2 relationships based on Theil-Sen regression and the density distributions of the measured and predicted LAI for the full-range dataset. The first and third columns show scatter plots between LAI and EVI/EVI2 as well as the relationship (solid red line) and prediction interval (dashed red line) based on Theil-Sen regression. The second and fourth columns show density distributions of the measured (blue) and predicted (red) LAI based on EVI and EVI2 respectively.

Analysis of the Effect of Sun-Sensor Geometry on LAI-VI Relationships
We assessed the effect of Sun-sensor geometry on the global LAI-VI relationships. Since all the Landsat TM and ETM+ data we used are nadir viewing images, the bidirectional reflectance is only affected by the Sun illumination geometry, which eliminates the hot-spot in BRDF. In Figure S9, we plotted the Sun illumination angles of all the Landsat data we used in this study in a polar coordinate. The sun illumination angles do not have a large variation, as the zenith angle is mostly within 25° to 60°, and the azimuth angle is between 50° to 150°. Figure S10 shows the residuals from the global LAI-EVI relationship of all samples plotted over zenith and azimuth angles. For each angle, the distribution of residuals is centered at zero and spread equally towards positive and negative space, which confirms a normal distribution assumption of the regression and indicates that there is no significant effect of the sun illumination angles on the residuals and the LAI-VI relationships. Figure S9. Distribution of the sun illumination angles of all the Landsat data used in this study in a polar coordinate. Figure S10. The residuals from global LAI-EVI relationship plotted over sun azimuth and zenith angles.