CN110068299B - Calculation method of leaf area index of greenhouse crop - Google Patents

Calculation method of leaf area index of greenhouse crop Download PDF

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CN110068299B
CN110068299B CN201910367568.XA CN201910367568A CN110068299B CN 110068299 B CN110068299 B CN 110068299B CN 201910367568 A CN201910367568 A CN 201910367568A CN 110068299 B CN110068299 B CN 110068299B
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blade
leaf
layer
maximum
leaf area
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葛建坤
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North China University of Water Resources and Electric Power
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/28—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring areas
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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Abstract

The invention relates to the field of greenhouse crops, in particular to a method for calculating a leaf area index of a greenhouse crop, which divides each crop into a top layer, a middle layer and a bottom layer from top to bottom according to the height, and respectively records the total number of leaves of each layer during each measurement; selecting the largest blade and the smallest blade in each layer to measure the characteristic length respectively, calculating the blade area of the largest blade and the smallest blade in each layer respectively to obtain the average value of the blade areas, and taking the average value of the blade areas as the representative blade area of the blade characteristics of the layer; the product value of the representative leaf area of each layer and the total number of the leaves of the layer is accumulated to obtain the total leaf area of the single plant, namely the leaf area index of the plant can be obtained.

Description

Calculation method of leaf area index of greenhouse crop
Technical Field
The invention relates to the technical field of greenhouse crop research, in particular to a method for calculating a leaf area index of a greenhouse crop.
Background
The leaf area index is also known as the leaf area coefficient. Is the ratio of the total area of the plant leaves to the area of the land. It is related to the density and structure (single layer or multiple layers) of vegetation, the biological characteristics (branch angle, leaf growing angle, shade resistance, etc.) of trees and environmental conditions (illumination, moisture, soil nutrition status), and is a comprehensive index representing the light energy utilization status and the canopy structure of vegetation. However, due to the diversity of crops, the leaves of many crops grow rapidly in the growth period, the workload required for directly measuring the leaf area is very large, and the requirements on measuring instruments and methods are high. In order to find a method for calculating the leaf area index more simply and effectively, the inventor researches a method for calculating the leaf area index of a main crop in a greenhouse through experimental research.
The specific method comprises the following steps: selecting a plurality of representative plants in a test cell of a greenhouse, and measuring the growth and development conditions of the plants at regular intervals on average, wherein the measurement contents comprise: crop height, number of leaves, characteristic length of leaves, leaf area, etc. However, during the growth and development of crops, the difficulty and the workload of measuring the leaf area are increased along with the gradual increase of the number of leaves, so that the cost of required input instruments and labor cost are too high, and the measuring process is too complicated.
Disclosure of Invention
Aiming at the defects and problems in the prior art, the invention provides the method for calculating the leaf area index of the greenhouse crop.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for calculating the leaf area index of greenhouse crops comprises the following steps of firstly, dividing each crop into 3 levels from top to bottom according to the height: the top layer, the middle layer and the bottom layer are used for respectively recording the total number of the blades of each layer during each measurement; then, selecting the maximum blade and the minimum blade in each layer to measure the characteristic length, respectively calculating the blade area of the maximum blade and the blade area of the minimum blade in each layer, thereby obtaining the average value of the blade areas, and taking the average value of the blade areas as the representative blade area of the blade characteristics of the layer; finally, the product value of the representative leaf area of each layer and the total number of the leaves of the layer is accumulated to obtain the total leaf area of the single crop; that is, the leaf area index of a crop can be calculated by the following formula:
Figure BDA0002048711170000021
in the formula:
LAI-leaf area index of crop;
So-the area of the cell in which the plant under test is located;
Figure BDA0002048711170000024
-the individual mean leaf area of a representative crop;
m is the total number of plants in the cell;
wherein the content of the first and second substances,
Figure BDA0002048711170000022
that is to say that the first and second electrodes,
Figure BDA0002048711170000023
in the formula:
j-number of representative crop sequences;
i-the number of the tested crop hierarchical sequences; wherein, i ═ 1 represents the top layer, i ═ 2 represents the middle layer, and i ═ 3 represents the bottom layer;
ni-total number of leaves on the ith layer of the crop;
Smax,ij-maximum leaf area on the ith layer of the jth crop;
Smin,ijminimum leaf area on the ith layer of the jth crop.
In the method for calculating the leaf area index of the greenhouse crop, the characteristic length of the leaf comprises the maximum radial length of the leaf and the maximum transverse width of the leaf.
The method for calculating the leaf area index of the greenhouse crop comprises the following steps: firstly, randomly picking 20-50 leaves in the development and maturation period of greenhouse crops, measuring the radial maximum length and the transverse maximum width of each leaf, and measuring the actual leaf area of each leaf by using a scanning type leaf area meter; then, establishing a correlation equation between the actual leaf area and the maximum radial length and the maximum transverse width of the leaf; finally, calculating the blade area of the maximum blade and the minimum blade in each layer through the solved correlation equation; the product of the maximum radial length of the leaf and the maximum transverse width of the leaf is used as an independent variable to establish a single-factor regression model, namely:
S＝k·ab+c
in the formula:
s-actual leaf area per leaf;
a-maximum radial length of the blade;
b-maximum width of leaf in the transverse direction;
and analyzing the numerical values of the actual leaf area, the radial maximum length and the transverse maximum width of 20-50 leaves extracted at random by using mathematical statistic software to obtain a constant k and a constant c and obtain a leaf area calculation equation.
According to the method for calculating the leaf area index of the greenhouse crop, a binary linear regression model can be established by taking the product of the maximum radial length of the leaves and the maximum transverse width of the leaves as an independent variable, namely:
S＝k1·a+k2·b+k3
in the formula:
s-actual leaf area per leaf;
a-maximum radial length of the blade;
b-maximum width of leaf in the transverse direction;
using the numerical values of the actual leaf area, the radial maximum length and the transverse maximum width of 20-50 leaves picked at random to analyze by using mathematical statistic software to obtain a constant k1Constant k2And constant k3And obtaining a leaf area calculation equation.
The invention has the beneficial effects that: the invention relates to a method for calculating the leaf area index of greenhouse crops, which comprises the steps of sampling plants in a layered mode, establishing an equation between the characteristic length of leaves and the leaf area, calculating the leaf area index of the crops through a correlation equation formula, reducing the workload required by leaf area calculation as much as possible on the premise of using a high-precision measuring instrument as little as possible, effectively reducing the using times of the measuring instrument, simplifying the experimental process, facilitating the research on greenhouse test crops in different regions, and having the advantages of simple calculation method, reliable fitting data, high correlation degree of the fitting result of the calculated data and the actual measured data and high accuracy.
Drawings
FIG. 1 is a correlation analysis of the fitting results in case one employs a binary linear regression model.
FIG. 2 is a correlation analysis of the fitting results using the single-factor regression model in scheme two.
Fig. 3 is an analysis of the fit of the actual leaf area of the tomatoes to the calculated leaf area in protocol two.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Example 1: a method for calculating the leaf area index of greenhouse crops comprises the following specific steps:
selecting 3 representative plants in a test cell of a greenhouse, measuring the growth and development conditions of the plants on average every 10 days, wherein the measuring time is 1, 11 and 21 of each month respectively, and the measuring contents comprise: crop height, number of leaves, characteristic length of leaves, leaf area, etc. Considering that the measurement difficulty and workload of the leaf area are increased along with the gradual increase of the number of leaves in the growth and development period of crops, the following method is adopted to measure the leaf area by combining the actual situation of the self test:
firstly, each crop is divided into 3 levels according to the height from top to bottom: top layer, middle layer, bottom layer. The total number of leaves of each layer is recorded during each measurement, the maximum leaves and the minimum leaves in each layer are simultaneously selected for measuring the characteristic length respectively, then the average value of the leaf areas of the maximum leaves and the minimum leaves in each layer is used as the representative leaf area of the leaf characteristics of the layer, and finally the product of the representative leaf area of each layer and the total number of the leaves is accumulated to obtain the total leaf area of the single crop.
The leaf area index of a crop can then be calculated from the following formula:
Figure BDA0002048711170000051
in the formula (I), the compound is shown in the specification,
LAI-leaf area index of crop;
Soarea of the cell in which the plant to be tested is located, mm2；
Figure BDA0002048711170000054
Average leaf area per plant, mm for representative crops2；
m is the total number of plants in the plot.
Wherein the content of the first and second substances,
Figure BDA0002048711170000052
that is to say that the first and second electrodes,
Figure BDA0002048711170000053
in the formula (I), the compound is shown in the specification,
j-number of representative crop sequences;
i-the number of the tested crop layer sequences (i ═ 1 represents the top layer, i ═ 2 represents the middle layer, and i ═ 3 represents the bottom layer);
ni-total number of leaves on the ith layer of the crop;
Smax,ijmaximum leaf area on the ith layer of the jth crop, mm2；
Smin,ijMinimum leaf area on the ith layer of the jth crop, mm2；
From the above equation, the correctness of the calculation of LAI depends mainly on the measurement of the leaf area. Taking greenhouse tomatoes as an example, 30 leaves are picked at random in the tomato development and maturation period, the characteristic length (including the maximum radial length of the leaves and the maximum transverse width of the leaves, hereinafter referred to as length and width) is measured, and the leaf area is measured by a scanning type leaf area meter. And then, selecting 20 groups of data, analyzing by using mathematical statistic software, establishing a correlation equation between the actual leaf area and the characteristic length of the leaf, and using the correlation equation to calculate the actual leaf area of the tomato plant. In order to ensure the accuracy of the fitting values and the measured values, the fitting results were analyzed in the experiment with the remaining 10 sets of data as test samples.
Two protocols were used for regression analysis and the results were compared:
the first scheme is as follows: establishing a binary linear regression model by taking the maximum radial length and the maximum transverse width of the leaf as independent influence factors:
S＝k1·a+k2·b+k3
scheme II: taking the product of the maximum radial length of the leaf and the maximum transverse width of the leaf as an independent variable to establish a single-factor regression model:
S＝k·ab+c
both schemes are completed by using the regression of the internal function of matlab, and the results obtained after the first scheme fitting are shown in figure 1, and the results obtained after the second scheme fitting are shown in figure 2.
Through regression analysis of 20 groups of measured data, the square of the correlation coefficient of the regression equation of the first scheme is R20.9072, the average value of relative error is RE 0.1167; the square of the correlation coefficient of the regression equation of the second scheme is R2The average relative error value RE was 0.0965, as shown in table 1.
TABLE 1 comparison of tomato leaf area fitting equation results
Figure BDA0002048711170000061
As can be seen from the above chart, the correlation of the fitting results of the two schemes is high.
However, considering that the relative error of the second solution is smaller, the present embodiment finally uses the fitting equation obtained by the second solution to calculate the tomato leaf area.
The other 10 sets of data were substituted into the regression equation for solution two for testing, and the fitting results are shown in FIG. 3:
through inspection, the relative error between the fitting value and the measured value is obtained as RE being 4.54%, and the fitting precision is EAThe fitting accuracy of solution two is high at 94.20%, as shown in table 2:
TABLE 2 tomato leaf area fitting results
Figure BDA0002048711170000071
Wherein, the fitting precision is as follows:
Figure BDA0002048711170000072
in the formula: eATo estimate the precision; rmse is the total mean square error;
Figure BDA0002048711170000073
is the mean of the test spot data.
By adopting the same comparison method, the final leaf area fitting formulas of the greenhouse tomatoes, the cucumbers and the eggplants are respectively as follows:
greenhouse tomato:
S＝0.809·(ab)+892.17 (5)
greenhouse cucumber:
S＝0.6739·(ab)-601.34 (6)
greenhouse eggplant:
S＝1.1055·(ab)-2135.9 (7)
the leaf area index calculation formulas of the greenhouse tomatoes, the cucumbers and the eggplants are respectively obtained by substituting the formulas (5) to (7) into the formula (3):
greenhouse tomato:
Figure BDA0002048711170000081
greenhouse cucumber:
Figure BDA0002048711170000082
greenhouse eggplant:
Figure BDA0002048711170000083
calculating to obtain the tomato leaf area index in the seedling stage of 0.98, the flowering and fruit setting stage of 3.25 and the average value of the fruit mature stage of 4.81 in the test period; the leaf area index of the greenhouse eggplant is 0.81 in the seedling stage, the flowering and fruit setting stage is 1.86, and the average value of the fruit mature stage is 2.36; the seedling stage of the greenhouse cucumber is 0.46, the flowering and fruit setting stage is 1.74, and the average value of the fruit maturity stage is 2.11.

Claims (2)

1. A method for calculating the leaf area index of greenhouse crops is characterized by comprising the following steps: firstly, each crop is divided into 3 levels according to the height from top to bottom: the top layer, the middle layer and the bottom layer are used for respectively recording the total number of the blades of each layer during each measurement; then, selecting the maximum blade and the minimum blade in each layer to measure the characteristic length, respectively calculating the blade area of the maximum blade and the blade area of the minimum blade in each layer, thereby obtaining the average value of the blade areas, and taking the average value of the blade areas as the representative blade area of the blade characteristics of the layer; the calculation method of the blade area of the maximum blade and the minimum blade in each layer comprises the following steps: firstly, randomly picking 20-50 leaves in the development and maturation period of greenhouse crops, measuring the radial maximum length and the transverse maximum width of each leaf, and measuring the actual leaf area of each leaf by using a scanning type leaf area meter; then, establishing a correlation equation between the actual leaf area and the maximum radial length and the maximum transverse width of the leaf; finally, calculating the blade area of the maximum blade and the minimum blade in each layer through the obtained correlation equation; the product of the maximum radial length of the leaf and the maximum transverse width of the leaf is used as an independent variable to establish a single-factor regression model, namely:
S＝k·ab+c
in the formula:
s-actual leaf area per leaf;
a-maximum radial length of the blade;
b-maximum width of leaf in the transverse direction;
analyzing the numerical values of the actual leaf area, the radial maximum length and the transverse maximum width of 20-50 leaves extracted randomly by using mathematical statistic software to obtain a constant k and a constant c and obtain a leaf area calculation equation;
finally, the product value of the representative leaf area of each layer and the total number of the leaves of the layer is accumulated to obtain the total leaf area of the single crop; that is, the leaf area index of a crop can be calculated by the following formula:
Figure FDA0002579567420000011
in the formula:
LAI-leaf area index of crop;
So-the area of the cell in which the plant under test is located;
Figure FDA0002579567420000021
-the individual mean leaf area of a representative crop;
m is the total number of plants in the cell;
wherein the content of the first and second substances,
Figure FDA0002579567420000022
that is to say that the first and second electrodes,
Figure FDA0002579567420000023
in the formula:
j-number of representative crop sequences;
i-the number of the tested crop hierarchical sequences; wherein, i ═ 1 represents the top layer, i ═ 2 represents the middle layer, and i ═ 3 represents the bottom layer;
ni-total number of leaves on the ith layer of the crop;
Smax,ij-maximum leaf area on the ith layer of the jth crop;
Smin,ijminimum leaf area on the ith layer of the jth crop.
2. The method for calculating the leaf area index of the greenhouse crop as claimed in claim 1, wherein: a binary linear regression model can be established by taking the product of the maximum radial length of the leaf and the maximum transverse width of the leaf as an independent variable, namely:
S＝k1·a+k2·b+k3
in the formula:
s-actual leaf area per leaf;
a-maximum radial length of the blade;
b-maximum width of leaf in the transverse direction;
using the numerical values of the actual leaf area, the radial maximum length and the transverse maximum width of 20-50 leaves picked at random to analyze by using mathematical statistic software to obtain a constant k1Constant k2And constant k3And obtaining a leaf area calculation equation.
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CN112857266B (en) * 2020-12-30 2022-12-02 华东师范大学 Method for carrying out inversion estimation on total leaf area of whole plant in full leaf period
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