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Journal of Arid Land  2020, Vol. 12 Issue (6): 1083-1092    DOI: 10.1007/s40333-020-0081-y
Research article     
Spectral parameter-based models for leaf potassium concentration estimation in Ping'ou hybrid hazelnut
ZHAO Shanchao, PAN Cunde*()
College of Forestry and Horticulture, Xinjiang Agricultural University, Urumqi 830052, China
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Ping′ou hybrid hazelnut is produced by cross cultivation and is widely cultivated in northern China with good development prospects. Based on a field experiment of fertilizer efficiency, the leaf spectral reflectance and leaf potassium (K) concentration were measured with different quantities of K fertilizer applied at four fruit growth stages (fruit setting stage, fruit rapid growth stage, fruit fat-change stage, and fruit near-maturity stage) of Ping′ou hybrid hazelnut in 2019. Spectral parameters that were significantly correlated with leaf K concentration were selected using Pearson correlation analysis, and spectral parameter estimation models of leaf K concentration were established by employing six different modelling methods (exponential function, power function, logarithmic function, linear function, quadratic function, and cubic function). The results indicated that at the fruit setting period, leaf K concentration was significantly correlated with Dy (spectra slope of yellow edge), Rg (reflectance of the green peak position), λo (red valley position), SDb (blue edge area), SDr/SDb (where SDr represents red edge area), and (SDr-SDb)/(SDr+SDb) (P<0.01). There were significant correlations of leaf K concentration with Dy, Rg, SDb, Rg/Ro (where Ro is the reflectance of the red valley position), and (Rg-Ro)/(Rg+Ro) at the fruit rapid growth stage (P<0.01). Further, significant correlations of leaf K concentration with Rg, Ro, RNIR/Green, and RNIR/Blue were obtained at the fruit fat-change period (P<0.01). Finally, leaf K concentration showed significant correlations with Dr, Rg, Ro, SDy (yellow edge area), and SDr at the fruit near-maturity stage (P<0.01). Through a cubic function analysis, regression estimation model of leaf K concentration with highest fitting degree (R2) values at the four fruit growth stages was established. The findings in this study demonstrated that it is feasible to estimate leaf K concentration of Ping′ou hybrid hazelnut at the various phenological stages of fruit development by establishing regression models between leaf K concentration and spectral parameters.

Key wordsleaf K concentration      spectrum      cubic function      regression models      fruit growth stages      Ping'ou hybrid hazelnut     
Received: 17 August 2020      Published: 10 November 2020
Corresponding Authors: Cunde PAN     E-mail:
About author: *PAN Cunde (E-mail:
Cite this article:

ZHAO Shanchao, PAN Cunde. Spectral parameter-based models for leaf potassium concentration estimation in Ping'ou hybrid hazelnut. Journal of Arid Land, 2020, 12(6): 1083-1092.

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Parameter based on spectral index Parameter based on spectral position Parameter based on spectral area
RNIR/Green Db (spectra slope of blue edge) SDb (blue edge area)
RNIR/Red λb (blue edge position) SDy (yellow edge area)
RNIR/Blue Dr (spectra slope of red edge) SDr (red edge area)
SDr/SDb λr (red edge position)
SDr/SDy Dy (spectra slope of yellow edge)
Rg/Ro λy (yellow edge position)
(NIR-Green)/(NIR+Green) Rg (reflectance of the green peak position)
(NIR-Red)/(NIR+Red) λg (green peak position)
(NIR-Blue)/(NIR+Blue) Ro (reflectance of the red valley position)
(SDr-SDb)/(SDr+SDb) λo (red valley position)
Table 1 Types of spectral parameters
Spectral parameter r Spectral parameter r
Db 0.6941* RNIR/Green -0.3152
λb -0.3491 RNIR/Red -0.2781
Dr 0.5121 NIR/Blue 0.4457
λr -0.4801 SDr/SDb -0.6628**
Dy 0.9422** SDr/SDy -0.0497
λy -0.0041 Rg/Ro 0.1331
Rg 0.7891** (NIR-Green)/(NIR+Green) -0.3015
λg 0.6501* (NIR-Red)/(NIR+Red) -0.2914
Ro 0.6561* (NIR-Blue)/(NIR+Blue) 0.4291
λo 0.6752** (SDr-SDb)/(SDr+SDb) -0.6948**
SDb 0.7471** (SDr-SDy)/(SDr+SDy) -0.5062
SDy 0.0901 (Rg-Ro)/(Rg+Ro) 0.1231
SDr 0.4292
Table 2 Pearson correlation coefficients between leaf K concentration and spectral parameters of Ping'ou hybrid hazelnut at the fruit setting stage
Spectral parameter r Spectral parameter r
Db 0.6581* RNIR/Green -0.0291
λb -0.0211 RNIR/Red 0.3091
Dr 0.4782 NIR/Blue 0.4352
λr 0.1152 SDr/SDb -0.4373
Dy 0.9461** SDr/SDy 0.1973
λy -0.1451 Rg/Ro 0.6831**
Rg 0.7652** (NIR-Green)/(NIR+Green) -0.0161
λg 0.3031 (NIR-Red)/(NIR+Red) 0.3211
Ro 0.0672 (NIR-Blue)/(NIR+Blue) 0.4272
λo 0.5222 (SDr-SDb)/(SDr+SDb) -0.4942
SDb 0.7281** (SDr-SDy)/(SDr+SDy) 0.1532
SDy -0.5441* (Rg-Ro)/(Rg+Ro) 0.6821**
SDr 0.5811*
Table 3 Pearson correlation coefficients between leaf K concentration and spectral parameters of Ping'ou hybrid hazelnut at the fruit rapid growth stage
Spectral parameter r Spectral parameter r
Db 0.3831 RNIR/Green -0.7312**
λb -0.0762 RNIR/Red -0.5532*
Dr 0.4623 NIR/Blue 0.6662**
λr 0.4601 SDr/SDb -0.2692
Dy 0.3781 SDr/SDy 0.2122
λy -0.2322 Rg/Ro 0.3461
Rg 0.8262** (NIR-Green)/(NIR+Green) -0.7341**
λg -0.2171 (NIR-Red)/(NIR+Red) -0.5581*
Ro 0.8591** (NIR-Blue)/(NIR+Blue) 0.6641*
λo 0.3101 (SDr-SDb)/(SDr+SDb) 0.2321
SDb 0.3772 (SDr-SDy)/(SDr+SDy) 0.3165
SDy 0.3712 (Rg-Ro)/(Rg+Ro) 0.3341
SDr 0.3912
Table 4 Pearson correlation coefficients between leaf K concentration and spectral parameters of Ping'ou hybrid hazelnut at the fruit fat-change stage
Spectral parameter r Spectral parameter r
Db 0.4951 RNIR/Green 0.0042
λb 0.3011 RNIR/Red 0.0641
Dr 0.7982** NIR/Blue 0.4553
λr -0.4791 SDr/SDb -0.2691
Dy 0.6011* SDr/SDy 0.5212
λy -0.4225 Rg/Ro 0.4761
Rg 0.9201** (NIR-Green)/(NIR+Green) 0.0209
λg 0.0011 (NIR-Red)/(NIR+Red) 0.0712
Ro 0.9101** (NIR-Blue)/(NIR+Blue) 0.4481
λo 0.0012 (SDr-SDb)/(SDr+SDb) -0.2461
SDb 0.6681* (SDr-SDy)/(SDr+SDy) 0.4392
SDy 0.6871** (Rg-Ro)/(Rg+Ro) 0.4701
SDr 0.7912**
Table 5 Pearson correlation coefficients between leaf K concentration and spectral parameters of Ping'ou hybrid hazelnut at the fruit near-maturity stage
Growth stage Spectral
Fitting degree R2
Power function Exponential function Logarithmic function Linear function Quadratic function Cubic
Fruit setting stage λo 0.4523 0.4525 0.4551 0.4551 0.4558 0.4571
Rg 0.5869 0.5891 0.6167 0.6225 0.6235 0.6247
Dy 0.9201 0.8643 0.9253 0.8881 0.9091 0.9436
SDb 0.4923 0.5245 0.5221 0.5571 0.5678 0.5691
SDr/SDb 0.4489 0.4151 0.4737 0.4385 0.4935 0.4977
(SDr-SDb)/(SDr+SDb) 0.4541 0.4563 0.4793 0.4821 0.4821 0.5166
Fruit rapid growth stage Dy 0.9291 0.8845 0.9341 0.8941 0.9498 0.9511
Rg 0.5659 0.5691 0.5817 0.5855 0.5865 0.6037
SDb 0.4781 0.5163 0.4893 0.5301 0.5391 0.5596
Rg/Ro 0.4605 0.4608 0.4653 0.4661 0.4662 0.5217
(Rg-Ro)/(Rg+Ro) 0.4561 0.4609 0.4581 0.4641 0.4651 0.5091
Fruit fat-change stage Rg 0.7091 0.6818 0.7031 0.6817 0.7021 0.7098
Ro 0.7512 0.7411 0.7421 0.7371 0.7491 0. 8028
RNIR/Green 0.5591 0.5541 0.5397 0.5335 0.5415 0.5637
RNIR/Blue 0.4341 0.4333 0.4413 0.4431 0.4432 0.4641
Fruit near-maturity stage Dr 0.6332 0.6151 0.6521 0.6361 0.6541 0.7028
Rg 0.8501 0.8311 0.8647 0.8465 0.8865 0.9247
Ro 0.8191 0.8203 0.8253 0.8271 0.8282 0.8401
SDr 0.4908 0.4801 0.4822 0.4719 0.5094 0.7791
SDy 0.6201 0.6059 0.6396 0.6257 0.6398 0.6821
Table 6 Fittings of regression models using spectral parameters associated with leaf K concentration of Ping'ou hybrid hazelnut at different fruit growth stages
Fruit setting
Fruit rapid growth
Fruit fat-change
Fruit near-maturity
R2 0.9436 0.9511 0.8028 0.9247
n 42 42 42 42
P value 0.0001 0.0001 0.00075 0.0001
${{\hat{\sigma }}^{2}}$ 0.11492 0.11242 0.40462 0.11492
Normal distribution
chi-square test of residuals
e~N(0, 0.68522)
e~N(0, 0.34152)
e~N(0, 0.42062)
e~N(0, 0.52172)
First-order autocorrelation
test of residuals
$\in $[1.468, 2.532]
$\in $[1.468, 2.532]
$\in $[1.468, 2.532]
$\in $[1.468, 2.532]
Test for homogeneity
of variance
W=0.3573<F0.05(13, 28)=2.09 W=0.4229<F0.05(13, 28)=2.09 W=0.0582<F0.05(13, 28)=2.09 W=0.3573<F0.05(13, 28)=2.09
Table 7 Residual inspection of the regression relationship between leaf K concentration and the most effective spectral parameters established by the cubic regression equation at different fruit growth stages
Fig. 1 Relationships between estimated and measured values for leaf K concentration of Ping'ou hybrid hazelnut at different fruit growth stages
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