CN110162830B - Variable irrigation node prediction method based on blade tension on-line monitoring - Google Patents
Variable irrigation node prediction method based on blade tension on-line monitoring Download PDFInfo
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Abstract
The invention discloses a variable irrigation node prediction method based on blade tension on-line monitoring, and belongs to the field of water-saving irrigation. Establishing a leaf area and biomass estimation model, and establishing a biomass and leaf tension relation model by using a rectangular hyperbolic equation. Biomass is monitored on line based on nondestructive measurement of maximum leaf length, leaf width and plant height. And fitting the biomass growth curve along with time by using a Logistic equation, deriving the fitted equation and calculating the biomass growth rate. And calculating the growth time corresponding to the biomass growth rate at different drought levels as a certain fixed proportion of the reference value by taking the biomass growth rate at the control level as a reference, namely the irrigation node. And calculating the value of the corresponding blade tension according to a Logistic equation and a relation model of biomass and blade tension, thereby predicting the variable irrigation node through online monitoring of the blade tension. The method overcomes the defect that the prior art can not predict the physiological water demand nodes of the plants in time, and provides a basis for variable irrigation.
Description
Technical Field
The invention relates to a variable irrigation node prediction method based on-line monitoring of blade tensity, and belongs to the technical field of crop information detection and water-saving irrigation.
Background
Traditionally, information such as crop water demand critical period and critical period, farmland soil water consumption or canopy temperature and the like is generally used as a basis for setting irrigation time and irrigation quantity. However, these methods are easily limited by environmental and geographical factors, or depend on experience, and cannot fully consider the water utilization condition of crops, which easily results in excessive irrigation or insufficient water supply. Plants do not always require sufficient water during growth and drought does not always reduce yield. Water-saving irrigation is to obtain the highest economic benefit by using the minimum water consumption on the basis of ensuring the crop yield. The research on the application of the physiological response information of the crops to the drought in the accurate irrigation gradually draws attention, and the smooth implementation of the accurate irrigation lies in the real-time monitoring of the water-needed nodes of the plants under the drought. However, the prior art still cannot realize the online prediction of the irrigation nodes based on the plant physiological response.
The crop yield and the biomass are in positive correlation, the research on the biomass has an important role in predicting the crop yield, and the online estimation of the biomass and the analysis of the change rule of the biomass are beneficial to the prediction of the plant irrigation node in advance. In most researches, the measurement of biomass is established on the basis that local or whole plants are damaged, the direct acquisition of the plant biomass is difficult, and the expression and estimation of the biomass by adopting some direct and easy-to-measure indexes are urgently needed to establish a non-destructive online measurement method of the biomass.
In addition, the direct and rapid measurement of the moisture condition of the leaves and the establishment of the relation between the moisture condition of the leaves and the biomass can provide powerful guarantee for the online prediction of the water irrigation nodes. In the case of drought stress on crops, the carbonic anhydrase in the body is stimulated to increase the activity and catalyze intracellular HCO 3 - Conversion to H 2 And O, changing the cell moisture condition and the change trend of photosynthesis, and delaying the urgent need of crops for moisture. This moisture regulation and control process can change the change law of indexes such as blade water potential or gas pocket conductance to a certain extent, and the effect of this process has postponing nature, is difficult to be monitored out by the instrument instant time, influences people according to traditional indexes such as blade water potential, gas pocket conductance to the accurate analysis and the judgement of crop water deficit situation. The leaf tensity can represent the change of the cell sap concentration and the cell volume, can better and more directly reflect the moisture condition of the plant, and the construction of the direct relation between the leaf tensity and the biomass is helpful to establish the timely implementation of irrigation on the online monitoring of the leaf tensity.
Disclosure of Invention
The invention aims to solve the technical problem of providing a variable irrigation node prediction method based on leaf tension on-line monitoring, which can realize the timely prediction of plant variable irrigation nodes by on-line monitoring of electrophysiological parameters and biomass and combining a biomass estimation model and a relation model between the biomass and the leaf tension, is simple, convenient and quick, has high accuracy and provides scientific support for plant physiological information detection and water-saving irrigation technologies.
A variable irrigation node prediction method based on blade tension on-line monitoring comprises the following steps:
firstly, culturing model plant seedlings in a laboratory, and selecting model plants of inspected plants;
setting different drought stress levels to culture the model plants;
step three, carrying out index measurement on the model plant;
fitting the product of the leaf area and the maximum leaf length and the maximum leaf width by using a leaf area regression equation to obtain an estimation model of the leaf area; fitting the relationship between the biomass, the plant height and the leaf area by using a biomass model to obtain an estimation model of the biomass; constructing a relation model of biomass and leaf tension by using a rectangular hyperbolic equation;
selecting the plants to be inspected under different drought levels, and measuring the maximum leaf length, the maximum leaf width and the plant height of the plants to be inspected at the same time interval and in the same time period in the step three;
step six, calculating a biomass growth curve along with time by utilizing a leaf area estimation model and a biomass estimation model according to the maximum leaf length, the maximum leaf width and the plant height;
step seven, fitting the biomass growth curve along with time, then obtaining a derivative of a fitting equation, and calculating the biomass growth rate under different drought levels;
step eight, calculating the growth time corresponding to the biomass growth rate at different drought levels as the reference value P% by taking the biomass growth rate at the reference level as a reference, namely the irrigation node;
and step nine, calculating a value corresponding to the tension of the leaves according to the fitted equation and the biomass and leaf tension relation model and the irrigation nodes, thereby predicting the variable irrigation nodes through online monitoring.
Further, the regression equation of the leaf area in the four steps is A = u X (X) 1 ×X 2 ) v Wherein u, v are constants, X 1 Denotes the maximum leaf length, X 2 Denotes the maximum leaf width and a denotes the leaf area.
Further, the biomass model in step four is logDW = r + qXlog (A) 2 xH), wherein DW is biomass, A is leaf area, H is plant height, and r and q are constants.
Further, the rectangular hyperbolic equation in the four centers of the steps is
Where DW is biomass, T d M is the leaf tension, n is a constant, where m represents DW when the biomass is the maximum biomass max Half a hour T d The value is obtained.
Further, the fitting equation in the ninth step adopts a 4-parameter Logistic equation:
wherein Y is 0 The initial amount of logarithmic growth phase, a is the upper limit of the growth amount of the growth indicator in the whole growth process, X 0 The time required to achieve 50% of the maximum growth of the log growth phase, X is the number of days treated, Y is the dry weight biomass, b is the fitting coefficient.
Further, 4-parameter Logistic equation is derived to obtain the biomass growth rate
Further, the calculation method of the water filling node in the step eight is as follows: biomass growth rate GR at control level f For reference, the biomass growth rate GR at each drought level was calculated e The growth time corresponding to the reference value P% is defined as a water filling node; i.e. GR e ＝Y e '＝P％×Y f '＝P％×GR f Wherein Y is e ' is the derivative of the biomass growth curve at each drought level, Y f ' is a biomass growth curve under controlDerivative, P is an integer.
The invention has the advantages that:
1) The method is based on nondestructive measurement of maximum leaf length, maximum leaf width and plant height, can realize online nondestructive monitoring of biomass according to a leaf area and biomass estimation model, and is simple, convenient and quick.
2) The method analyzes the growth rate based on the online monitoring of the biomass, and judges the irrigation nodes according to the growth rate, so that the water utilization efficiency can be improved, and the economic benefit maximization is realized.
3) According to the method, the prediction of variable irrigation nodes is realized by monitoring the tension of the leaves according to a 4-parameter Logistic equation and a relation model of biomass and the tension of the leaves, plant physiological response information is applied to water-saving irrigation, and the result accuracy is high.
Drawings
FIG. 1 is a graph of the linear relationship between the product of the blade area and the maximum blade length and the maximum blade width of the blade;
FIG. 2 is a graph of log-log linear relationship of dry weight biomass to leaf area and plant height;
FIG. 3 is a graph of leaf blade tension fitted to dry weight biomass;
FIG. 4 is a graph of biomass as a function of time at different drought levels.
Detailed Description
The embodiments of the present invention will be further described with reference to the accompanying drawings.
The basic principle of the invention is as follows:
the Michaelis equation, which represents the relationship between the initial rate of the enzymatic reaction and the substrate concentration, is:
in the formula: i is the absorption rate of the plant to the nutrient; i is max The maximum absorption rate of the plant body to the nutrients; k m Is the Michaelis constant, i.e. when the absorption rate is the maximum absorption rate I max The external nutrient concentration for half a time; c is the concentration of external nutrients.
The same applies toThe Mie's equation can also be used to describe net photosynthetic rate and photosynthetically active radiation intensity or CO 2 They can also be expressed by a rectangular hyperbolic equation, such as equation (2):
in the formula: p N Is the net photosynthetic rate; i is photosynthetically active radiation intensity or intercellular CO 2 Concentration; p N max Is saturated light intensity or CO 2 Net photosynthetic rate at saturation, i.e. maximum net photosynthetic rate; r is the respiratory rate; k is the Michaelis constant.
The total reaction formula of photosynthesis is CO 2 +H 2 O＝(CH 2 O)+O 2 Wherein (CH) 2 O) represents a saccharide. CO 2 2 And H 2 O is the reaction substrate of photosynthesis and the reaction proportion is 1:1, namely net CO in the process of photosynthesis 2 Assimilation rate equivalent to net H 2 O rate of assimilation. The plant leaf is composed of a large number of cells, the water condition of the plant leaf can be accurately reflected by the change of the concentration and the volume of the cell sap, and the change of the concentration and the volume of the cell sap can be reflected by the tension of the leaf. Biomass is mainly determined by the magnitude of the net photosynthetic rate of the plant leaves. Therefore, photosynthesis is responsible for light intensity or CO 2 The response rectangular hyperbolic model can also be used for curve fitting of biomass to leaf tone response, as in equation (3):
in the formula: DW is biomass; t is d The degree of tension of the leaves; m and n are constants, wherein m represents DW when the biomass is the maximum biomass max Half a hour T d The value is obtained.
In addition, the 4 parameter Logistic equation is:
in the formula: y is 0 Is the initial amount of logarithmic growth phase; a is the upper limit of the growth amount of the growth index in the whole growth process; x 0 The time (days) required to reach 50% of the maximal increase in logarithmic growth phase; x is the treatment days; y is biomass; and b is a fitting coefficient.
The rate of biomass growth can be derived from equation (4), as shown in equation (5):
wherein GR represents the growth rate of the biomass, and the growth time corresponding to the growth rate of the biomass at each drought level as a reference value P% is calculated by taking the growth rate of the biomass at the control level as a reference, and is defined as a watering node; the rate of biomass growth at various drought levels is calculated as follows:
GR e ＝Y e '＝P％×Y f '＝P％×GR f (6)
wherein, GR f Representing the rate of increase of biomass at a control level, GR e Denotes the rate of biomass growth, Y, at each drought level e ' is the derivative of the biomass growth curve at each drought level, Y f ' is the derivative of the biomass growth curve at the control level, and P is an integer with a value between 0 and 100.
And substituting the time (corresponding to X) corresponding to the irrigation node under each drought level into the equation (4) to obtain the corresponding biomass, and further calculating the blade tension value corresponding to each irrigation node through the equation (3). Based on the monitoring of the tension of the plant leaves under drought, irrigation can be carried out when the tension of the plant leaves is reduced to the tension value of the leaves corresponding to the irrigation nodes, and therefore variable irrigation nodes are mastered in advance through the online monitoring of the tension of the leaves, and prediction is achieved.
The specific implementation process of the invention is as follows:
step one, germinating plant seeds by using plug trays with the same specification in a laboratory, preparing a culture solution to culture model plant seedlings until the leaf stage is more than 3, and selecting plants with more consistent growth as model plants of inspected plants;
setting different drought stress levels to culture the model plants;
step three, when the model plant is cultured for about 1 week, index determination is carried out by taking the first unfolded leaf as an investigation object in the same time period; random selection of plants to determine maximum leaf length X 1 Maximum leaf width X 2 And the leaf area A; randomly selecting other plants to measure the leaf area, the plant height H and the biomass DW; randomly selecting plants under different drought levels, measuring water potential W and physiological capacitance CP of leaves, and calculating tensity T of leaves d Simultaneously measuring the corresponding biomass;
the blade tension is calculated by the formula:
wherein: t is d Is the tension of the blade, CP is the physiological capacitance, W is the water potential of the blade, i is the dissociation coefficient, R is the gas constant, T is the thermodynamic temperature, epsilon 0 In terms of the dielectric constant in vacuum, a is the relative dielectric constant of cytosolic solutes, and M is the relative molecular mass of cytosolic solutes.
Fitting the product of the leaf area, the maximum leaf length and the maximum leaf width by using a leaf area regression equation to obtain an estimation model of the leaf area; fitting the relationship between the biomass, the plant height and the leaf area by using a biomass model to obtain an estimation model of the biomass; constructing a relation model of biomass and leaf tension by using a rectangular hyperbolic equation;
the estimation model of the leaf area is:
A＝u×(X 1 ×X 2 ) v (8)
wherein: u and v are constants, X 1 Denotes the maximum leaf length, X 2 Represents the maximum leaf width, a represents the leaf area;
the estimation model of biomass is:
logDW＝r+q×log(A 2 ×H) (9)
wherein: DW is biomass, H is plant height, and r and q are constants;
the relationship model of biomass and leaf tension is as follows:
wherein: m and n are constants, wherein m represents DW when the biomass is the maximum biomass max Half a hour T d A value;
selecting the inspected plant to be tested which grows under different drought levels, taking the first expanded leaf as an inspected object, processing the inspected plant from the 1 st day of different drought levels, measuring the maximum leaf length, the maximum leaf width and the plant height of the inspected plant at the same time interval in the third step every 2 days, and continuously measuring for more than 2 weeks;
step six, calculating a biomass growth curve along with time by utilizing a leaf area estimation model and a biomass estimation model according to the maximum leaf length, the maximum leaf width and the plant height;
step seven, fitting the growth curve of the biomass along with the time by utilizing a 4-parameter Logistic equation to obtain a fitting equation
Wherein: y is 0 The initial amount of logarithmic growth phase, a is the upper limit of the growth amount of the growth indicator in the whole growth process, X 0 The time (days) required to achieve 50% of the maximum increase in logarithmic growth phase, X is the number of days of treatment, Y is the dry weight biomass, b is the fitting coefficient
And then, the derivative of the fitting equation is obtained:
wherein the biomass growth rate GR = Y', calculating the biomass growth rate under different drought levels;
step eight, calculating the growth time corresponding to the biomass growth rate at different drought levels as the reference value P% by taking the biomass growth rate at the reference level as a reference, namely the irrigation node; the irrigation node calculation method comprises the following steps: biomass growth Rate under control (GR) f ) For reference, the biomass Growth Rate (GR) was calculated at each drought level e Wherein e is drought level) is P% of the reference value, and defined as a watering node; i.e. GR e ＝Y e '＝P％×Y f '＝P％×GR f Wherein Y is e ' is the derivative of the biomass growth curve at each drought level, Y f ' is the derivative of the biomass growth curve under control, P is an integer, and the value is between 0 and 100;
and step nine, calculating a value corresponding to the tension of the blades according to the irrigation nodes in the step eight according to a 4-parameter Logistic equation and a relation model (equations (3) and (4)) of biomass and the tension of the blades, and predicting the variable irrigation nodes through online monitoring of the tension of the blades.
Based on the monitoring of the tension of the plant leaves under drought, irrigation can be carried out when the tension of the plant leaves is reduced to the tension value of the leaves corresponding to the irrigation nodes, and therefore variable irrigation nodes are mastered in advance through the online monitoring of the tension of the leaves, and prediction is achieved.
Example (b):
germinating Orychophragmus violaceus seeds with the same specification in a plug tray in a laboratory, preparing a culture solution to culture model plant seedlings, selecting Orychophragmus violaceus plants with more consistent growth as model plants of inspected plants when the leaf period is more than 3, and simulating different drought stress levels (0, 10, 20, 40, 80 g.L) by adding polyethylene glycol 6000 -1 At 0 g.L -1 Control) was performed on the model plants. When the model plants were cultured for about 1 week, the index measurement was performed with the first developed leaf as an object to be examined during 9 to 11 am. Randomly selecting 15 plants to determine the maximum leaf length, the maximum leaf width and the leaf area (see table 1), randomly selecting 5 plants to determine the leaf area, the plant height and the biomass (see table 2), randomly selecting 15 plants at different drought levels (selecting 3 plants at each level) to measureLeaf water potential and physiological capacitance, leaf tone was calculated and the corresponding biomass was measured (see table 3).
TABLE 1 Orychophragmus violaceus model plant maximum leaf Length, maximum leaf Width and leaf area
TABLE 2 leaf area, plant height and biomass of orychophragmus violaceus model plants
TABLE 3 model plant leaf water potential, physiological capacity, leaf tensity and biomass of orychophragmus violaceus at different drought levels
Fitting the product of the leaf area and the maximum leaf length and the maximum leaf width by using a leaf area regression equation, wherein a fitted curve is shown in figure 1, and the obtained leaf area estimation model is A = 0.93X (X) 1 ×X 2 ) 1.03 Wherein R is 2 ＝0.973，P<0.0001,n =15. The biomass model is utilized to fit the relationship between the biomass, the plant height and the leaf area, the fitting curve is shown as figure 2, and the estimated model of the biomass is logDW = -2.75+0.86 × log (A) 2 X H), wherein R 2 ＝0.985，P<0.001,n =5. Fitting the relationship between biomass and leaf tension by using a rectangular hyperbolic equation, wherein the fitted curve is shown in FIG. 3, and the fitted equation is obtained
Wherein R is 2 ＝0.809，P<0.0001，n＝15。
Selecting detected orychophragmus violaceus growing under different drought levels, taking the first unfolded leaf as a detection object, detecting the maximum leaf length, the maximum leaf width and the plant height of the detected orychophragmus violaceus every 2 days in the 9-00 am period from 1 day of treatment of the orychophragmus violaceus under different drought levels, and continuously detecting for more than 2 weeks. According to the maximum leaf length, the maximum leaf width and the plant height, a leaf area estimation model A =0.93 × (X) 1 ×X 2 ) 1.03 And biomass estimation model logDW = -2.75+0.86 × log (A) 2 Xh), the growth curve of biomass over time at each drought level was calculated (see fig. 4). Using a 4 parameter Logistic equation
And (3) fitting the biomass growth curves along with time under different drought levels to obtain corresponding fitting equations, and then performing derivation on the fitting equations, wherein the results are shown in a table 4, namely the biomass growth rates under different drought levels.
Table 4 estimation of biomass at different drought levels of Orychophragmus violaceus by using 4-parameter Logistic equation and derivation by fitting equation
And calculating the growth time corresponding to the biomass growth rate at different drought levels as the reference value P% by taking the biomass growth rate at the control level as a reference, namely the irrigation node. Taking P =70 and 50 as examples, the corresponding irrigation nodes are calculated as shown in table 5. Meanwhile, according to a 4-parameter Logistic equation and a biomass and blade tension relation model, calculating a value corresponding to the blade tension according to the irrigation nodes.
TABLE 5 irrigation nodes of orychophragmus violaceus at different drought levels
* Number of days of ineffectiveness and T d The value is obtained.
X in Table 4 0 The rate of biomass growth was X for the number of days required to achieve 50% of the maximum growth in the logarithmic growth phase 0 Highest in the day and gradually decreasing thereafter. Thus, the biomass growth rate at each stress level was at each corresponding X 0 Finally decreases to 0,X after days 0 The rate of biomass growth before the day can better represent the plant growth condition. This example shows X at various stress levels 0 The biomass growth rate before day was 10, 20, 40 and 80 g.L compared to the control -1 X at level 0 The values were 6.28, 1.47, 3.53 and 3.85, respectively, and thus, 20 g.L -1 At the level, 1.77 days, 40 g.L -1 20.10 and 15.60 days at level and 80 g.L -1 Both 8.08 and 7.06 days at level are invalid values.
The lack of proper water can reduce the growth rate of plants and affect the yield, but also can promote the proper improvement of the yield and quality and improve the water utilization efficiency. As shown in Table 5, 10 g.L for controlling the growth rate of orychophragmus violaceus was 70% or 50% of the control -1 The irrigation node of orychophragmus violaceus at PEG level should be 4.90 or 2.66 days at 20 g.L -1 The irrigation node of orychophragmus violaceus at PEG level should be 1.41 days. 10 g.L -1 T corresponding to irrigation node of orychophragmus violaceus under PEG level d The values are 0.99 or 0.48, 20 g.L respectively -1 T corresponding to irrigation node of orychophragmus violaceus under PEG level d The value was 0.69. For 10 g.L -1 The orychophragmus violaceus with PEG level can be used for establishing a variable irrigation scheme, irrigation is carried out when the growth rate of the orychophragmus violaceus in 4 th to 5 th days is reduced to 70% of the contrast, and then irrigation is carried out again when the growth rate of the orychophragmus violaceus in 2 nd to 3 th days after irrigation is reduced to 50% of the contrast. And by the online monitoring of the tension of the blades, the irrigation can be implemented when the tension of the blades is reduced to the corresponding value. Therefore, the prediction of the variable irrigation node based on the blade tension on-line monitoring is realized.
The above results also show that 10 g.L -1 Radix Brassicae Rapae with PEG level and 20 g.L -1 Longer duration stress, 40, 80 g.L, was tolerated by plants at PEG levels -1 The growth of orychophragmus violaceus was severely inhibited at PEG levels.
The above description is only a preferred embodiment of the present invention, and the present invention is not limited to the above embodiment, and it should be noted that any equivalent substitution, obvious modification made by those skilled in the art under the teaching of the present specification are within the spirit scope of the present specification, and the present invention should be protected.
Claims (7)
1. A variable irrigation node prediction method based on blade tension on-line monitoring is characterized by comprising the following steps:
firstly, culturing model plant seedlings in a laboratory, and selecting model plants of inspected plants;
setting different drought stress levels to culture the model plants;
step three, carrying out index measurement on the model plant;
fitting the product of the leaf area and the maximum leaf length and the maximum leaf width by using a leaf area regression equation to obtain an estimation model of the leaf area; fitting the relationship between the biomass, the plant height and the leaf area by using a biomass model to obtain an estimation model of the biomass; constructing a relation model of biomass and leaf tension by using a rectangular hyperbolic equation;
fifthly, selecting the inspected plants under different drought levels, and measuring the maximum leaf length, the maximum leaf width and the plant height of the inspected plants at the same time interval in the same time period in the third step;
step six, calculating a biomass growth curve along with time by utilizing a leaf area estimation model and a biomass estimation model according to the maximum leaf length, the maximum leaf width and the plant height;
step seven, fitting the biomass growth curve along with time, then obtaining a derivative of a fitting equation, and calculating the biomass growth rate under different drought levels;
step eight, calculating the growth time corresponding to the biomass growth rate at different drought levels as the reference value P% by taking the biomass growth rate at the reference level as a reference, namely the irrigation node;
wherein P is an integer having a value between 0 and 100;
and step nine, calculating a value corresponding to the tension of the leaves according to the fitted equation and the relation model of the biomass and the tension of the leaves and the irrigation nodes, thereby predicting the variable irrigation nodes through online monitoring of the tension of the leaves.
2. The method for predicting variable irrigation nodes based on online monitoring of blade tension as claimed in claim 1, wherein the regression equation of the area of the blade in the four steps is A = u X (X) 1 ×X 2 ) v Wherein u and v are constants, X 1 Denotes the maximum leaf length, X 2 Denotes the maximum leaf width and a denotes the leaf area.
3. The variable irrigation node prediction method based on blade tension on-line monitoring as claimed in claim 1, wherein the biomass model in the fourth step is logDW = r + qxlog (A) 2 xH), wherein DW is biomass, A is leaf area, H is plant height, and r and q are constants.
4. The variable irrigation node prediction method based on-line monitoring of blade tension as claimed in claim 1, characterized in that the rectangular hyperbolic equation in the four directions of the steps is
Where DW is biomass, T d M is the leaf tension, n is a constant, where m represents DW when the biomass is the maximum biomass max Half a hour T d The value is obtained.
5. The variable irrigation node prediction method based on blade tension on-line monitoring according to claim 1, characterized in that the fitting equation in the ninth step adopts a 4-parameter Logistic equation:
wherein Y is 0 The initial amount of logarithmic growth phase, a is the upper limit of the growth amount of the growth indicator in the whole growth process, X 0 The time required to achieve 50% of the maximum growth of the log growth phase, X is the number of days treated, Y is the dry weight biomass, b is the fitting coefficient.
6. The variable irrigation node prediction method based on blade tension on-line monitoring as claimed in claim 5, wherein 4-parameter Logistic equation is derived to obtain biomass growth rate
7. The variable irrigation node prediction method based on blade tension on-line monitoring according to claim 1, characterized in that the irrigation node calculation method in the eighth step is as follows: biomass growth rate GR at control level f For reference, the biomass growth rate GR at each drought level was calculated e The growth time corresponding to the reference value P% is defined as a water filling node; i.e. GR e ＝Y e '＝P％×Y f '＝P％×GR f Wherein Y is e ' is the derivative of the biomass growth curve at each drought level, Y f ' is the derivative of the biomass growth curve at the control level.
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