The study area is located in Qixia County, Yantai City, Shandong Province (37˚0'05"N - 37˚032"N, 12˚00'33"E - 12˚10'15"E). The city is located in the hinterland of Jiaodong Peninsula, with a total area of 2017 km². Its terrain is mountain hills. The city’s climate is warm temperate monsoon semi-humid climate. It’s average annual temperature is 11.3˚C and the average annual rainfall is 754 mm, frost-free period of each year is 207 d. The total length of cultivation in this area is 2690 h, the total area of Qixia apple orchard is 4.4 × 105 hm², the annual output is 1.45 × 107 t. The time of collecting leaf samples is new shoots period of apple trees (5.20.2014). At the time of collection, 24 orchards were randomly selected. Four apple trees were randomly selected from each orchard. So a total of 96 trees were selected. Then, 8 pieces of similar size and healthy leaves were collected in the middle of the growth branches of each apple tree. Finally, put the sample into the preservation bag, number, and then put it into the preservation box back to the laboratory.

Spectral measurements were performed using ASDFieldSpec4 with a band of 350 nm - 2500 nm. The spectral resolution is 3 nm and the sampling interval is 1.4 nm in the range of 350 nm - 1000 nm. The spectral resolution is 8 nm and the sampling interval is 2 nm in the range of 1000 nm - 2500 nm. The whole measurement process is carried out in a dark room which can control the illumination condition. At the time of determination, the leaf samples should be measured on the black rubber mat (the reflectivity is approximately 0). The angle of the spectrometer is 25˚, The probe is vertically aligned with the middle of the blade, and at 0.10 m from the sample surface. The light source is spectrometer’s own 50 W halogen lamp, the distance from the sample center is 0.50 m. Each sample was observed in 10 spectra and averaged as the spectral reflectance value of the sample. Make whiteboard correction in time when measuring.

After the spectral data collection was completed, the leaves were placed in an oven at 80˚C, sterilized for 20 min, then cooled to 60˚C and dried to constant weight. The potassium content was determined by flame photometric method.

Using ViewSpec software to convert the leaf DN value into spectral reflectance, and using software EXCEL, SPSS to achieve further processing and analysis. In order to reduce the difference of light intensity, the unevenness of the sample and the influence of the instrument noise on the spectral characteristics of the target. In addition, in order to extract the spectral information fully, reflect the difference of plant growth status better and study the relationship between plant biochemical composition and hyperspectral, ratio vegetation index (RVI), difference vegetation index (DVI) and normalized vegetation index (NDVI) is constructed, which can be calculated as

where R_λ1 and R_λ2 represent spectral reflectance at wavelengths λ1 and λ2, respectively.

Correlation analysis between the three vegetation indices which constructed by the spectral reflectance of 96 apple leaves and potassium contents, and then use the stepwise regression analysis method to select the sensitive wavelength or wavelength combination. Using the selected spectral parameters as independent variables, 72 samples were randomly selected to establish a RF regression model, and the remaining 24 were used for the model test. The effect of the fitting between the estimated and the measured values is evaluated by using the coefficient of determination (R²), root mean square error (RMSE) and relative error (RE%) to test the stability and applicability of the model. The larger the R², the smaller RMSE and RE%, the better the prediction effect of the model. Their equations can be calculated as

where is the measured potassium content value, is the estimated value, is the average value of, and the number of samples is n.

The level of potassium content has an important effect on the spectral reflectance of leaves [18] , showing obvious regularity in the observed wavelength range. 96 samples were sorted according to the potassium content from less to more, and were divided into 4 groups according to the order. The average of the spectral data and the potassium content was calculated for each group (Table 1). The hyperspectral curves of four different potassium levels with wavelength were obtained, which were K1, K2, K3 and K4, respectively. It is show on in Figure 1.

As we can see from Figure 1, the overall spectral reflectance also increased with the increase in the level of potassium nutrition. In the visible light 350 nm - 680 nm, near infrared 800 nm - 1300 nm, 1400 nm - 1850 nm, 1900 nm - 2500 nm reflectivity increased significantly, the remaining bands are smaller.

Combine any two wavelengths in the band range (350 nm - 2500 nm), put them into Equations (1)-(3) respectively to obtain different vegetation indices, and

then use software Matlab to analyze their correlation with the potassium content. The contour map shows in Figures 2-4.

The horizontal and vertical coordinates of the contour map are wavelengths, and the color difference in the middle of the map indicates the level of correlation. Since the wavelengths of the vegetation index are random, any two wavelengths are combined twice, the contour map is symmetrically distributed along the diagonal. From Figures 2-4, it is clear that which wavelengths or bands of the different vegetation indices are better correlated.

Random Forest (RF) is a natural non-linear modeling tool proposed by Breiman and Cutler in 2001 [21] , which is a new model replacing traditional machine learning methods such as neural networks. It has excellent performance in the face of a large number of data. RF does not need to worry about the multicollinearity problems faced by general regression analysis and is not be used as a variable choice which can be used to invert the potassium content of apple leaves in hyperspectral data. A large number of theoretical and practical studies have proved that RF regression analysis has a high prediction accuracy, and its number of regression numbers selected depends mainly on two important parameters: Ntree and Mtry, where Ntree is the number of decision trees, Mtry is the number of sample predictors at each split node [22] [23] . The random forest regression analysis was performed in data processing software DPS. The RVI, DVI and NDVI in the Tables 2-4 were taken as independent variables. The parameters Ntress = 300 and Mtry = 3. The proportion of forest training samples was 50%, and the evaluation model of potassium content in apple leaves was established respectively.

The measured values of the 72 training samples were fitted and the random forest estimates were fitted. The data obtained from the three vegetation indices were created a scatter plot as shown in Figure 5.

The determination coefficient of DVI in the three vegetation indices was the highest, reaching 0.8995, R² of RVI and NDVI were 0.8875 and 0.8817, respectively. The RMSE and RE% of DVI are the smallest, respectively reaching 0.0791 and 0.0617, the RMSE of RVI and NDVI were 0.1126 and 0.1154, RE% were 0.0858 and 0.0875. As we can see that the random forest model of potassium content in apple leaves established by difference vegetation index is better.

In order to test the adaptability and accuracy of the random forest regression model, the scatter plot of measured value and estimated values of 24 independent test samples were established, as shown in Figure 6.

The R² of three vegetation indices are all above 0.77 and their RMSE are all below 0.13. However, the results of the model established by DVI are better than the other two vegetation indices. The maximum coefficient of determination is

0.8205, the mean square error is 0.1071, and the relative error is 0.0756. The results of the verification are very satisfactory. It can be seen that the random forest regression model has good adaptability for complex data, and the model is stable.