Establishment of leaf area estimation model for jujube trees

Abstract:【Objective】The study aims to establish a reliable and accurate leaf area (LA) estimation model based on leaf length (LL) and leaf width (LW) which can be measured non-destructively. Leaf ar- ea is usually determined by destructive methods, which are time-consuming and impossible to make successive measurements on the same leaf samples. Non-destructive portable leaf area laser scanners are expensive and complex. The model-based leaf area estimation overcomes the above defects. Howev- er, the optimal model needs to be selected from candidate models for jujube trees【. Methods】Eight ju- jube cultivars with significant differences in leaf morphology,including‘Junzao’‘Lizao’‘Qiyuexian’‘Suanzao’‘Zanhuangdazao’‘Fengmiguan’‘Gagazao’and‘Jinsixiaozao’, were used as the materi- als. Leaves were sampled and then scanned with a laser scanner to obtain digital images. Leaf morpho- logical parameters, such as LL, LW, LA and petiole length (PL), were extracted using ImageJ software. There were 17 candidate models established and compared. Each model was established and validated using pooled data from all cultivars and separately for each cultivar. A further validation was conducted for the general models constructed with pooled data to evaluated their applicability to different individu- al cultivars. The root mean square error (RMSE), determination coefficient (R2) and Akaike information criterion (AIC) were used to evaluate the accuracy of the established models for leaf area through the comparisons between predicted values and actually measured values of leaf area. Each dataset was sepa- rated randomly into training dataset (75% of the data) and testing dataset (25% of the data) to fit and validate models by using R software.【Results】3 287 leaves were sampled and significant differences were found among the cultivars in LL, LW, LA, PL, LL/LW ratio, PL/(PL+LL) ratio and roundness. The coefficient of variation (CV) in leaf area (LA) was the largest (64.44% ), and followed by PL (43.41%), LW (37.24%) and LL (32.20%). LL, LW and their integrated variables, such as LL+LW, LL× LW, LL2 and LW2 etc., could be used as the independent variables to predict the LA for all cultivars. By using all data together, the 17 models showed varied predictivity (71.66 ≤ R2 ≤ 99.52% , 0.51 ≤RMSE ≤ 3.09 cm2 and 3 769.08 ≤ AIC ≤ 16 947.72). Among those models, model 16 LA = a (LL × LW)b had the highest accuracy (R2=99.52%, RMSE=0.44 cm2, AIC=3 769.08), followed in descending order by model 5 LA = a (LL×LW) (R2=99.40%, RMSE=0.46 cm2, AIC=4 076.65), model 9 LA = a LL2 + b LW2 (R2=99.34% , RMSE=0.51 cm2, AIC=4 487.99), model 14 LA = a (LL + LW)b (R2=98.87% , RMSE=0.65 cm2, AIC=6 469.08), model 6 LA = a (LL+LW)2 (R2=98.84%, RMSE=0.64 cm2, AIC=6 563.66), and model 17 LA = (LL × LW)b (R2=98.72% , RMSE=0.70 cm2, AIC=6 627.65). Estimation with all the models for each cultivar showed that models 5, 6, 9 and 17 met the requirements of accura- cy to predict the leaf area for all the cultivars. The coefficient of models 5, 6 and 17, had smallest CVamong cultivars (2.71%, 2.91% and 3.41%, respectively) as compared to the other models. When the all-data models were validated by individual cultivars, models 5 and 6 still had a high accuracy of leaf area estimation, with the lowest R2 appearing in‘Suanzao’in model 6, which was 96.80%, and the larg- est decrease in RMSE appearing in‘Lizao’in the same model, which was 0.145 1 cm2. Yet, when com- pared the R2 between cultivar specified and all-data based model 17, the R2 in cultivar specified model 17 for‘Suanzao’and‘Jinsixiaozao’decreased from 97.27% and 94.22% to 84.16% and 83.51% in all- data model, respectively. The model coefficients for model 5 and 6 were 0.703 5 and 0.164 6, respec- tively. LA was estimated with a higher accuracy by employing LW alone compared to LL alone, irre- spective of cultivars. LA estimation was not always improved by employing both LL and LW as com- pared to employing single variable. LA can be estimated by employing LW alone with model LA = a LWb, but the model coefficients need to be ajusted acccording cultivar. The minimum number of leaves was 250 to estimate the model coefficients for models 5 and 6 with relative lower errors.【Conclusion】For a specific cultivar, models 5, 6, 9 and 17 can meet the requirements of accuracy to predict the leaf area without the use of any expensive instruments but need to be fitted to obtain specific model coeffi- cients for individual cultivars. Among the above 4 models, models 5 and 6 can be used to estimate leaf area accurately using the same model coefficients, irrespective of cultivar. The minimum sample size of 250 is required for models 5 and 6 to obtain reliable model coefficients. The accuracy leaf area model will be helpful to develop three-dimensional virtual jujube trees with accurate leaf dimensions.