CN110083954B - Greenhouse crop water demand calculation method based on boundary layer resistance measurement technology - Google Patents
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Abstract
The invention relates to the research field of greenhouse crops, in particular to a greenhouse crop water demand calculation method based on a boundary layer resistance measurement technology.
Description
Technical Field
The invention relates to the technical field of greenhouse crop water demand research, in particular to a greenhouse crop water demand calculation method based on a boundary layer resistance measurement technology.
Background
At present, the greenhouse vegetable planting mode is rapidly developed in China, but research on water demand of greenhouse crops is scattered. The Penman-Monteith formula is based on an energy balance and water vapor diffusion theory, not only considers the physiological characteristics of crops, but also considers the change of aerodynamic parameters, has a more sufficient theoretical basis, and is the most common and reasonable method for calculating the field water demand of the crops at present. However, the planting environment of the greenhouse is relatively closed, the average internal wind speed is almost zero, the Peneman correction formula recommended by the Food and Agriculture Organization (FAO) of the United nations is mainly used for field crops, and many scholars at home and abroad study the applicability of the greenhouse in the greenhouse mainly by using a correction method. Therefore, the invention introduces the boundary layer resistance measurement technology into the Peneman formula to obtain a new method for calculating the water demand of the greenhouse crops.
Disclosure of Invention
Aiming at the defects and problems in the prior art, the invention provides a greenhouse crop water demand calculation method based on a boundary layer resistance measurement technology.
The technical scheme adopted by the invention for solving the technical problems is as follows: a greenhouse crop water demand calculation method based on a boundary layer resistance measurement technology comprises the following steps:
the first step is as follows: according to the Penman-Monteith equation, the water demand of the greenhouse crops is calculated by the following formula:
in the formula (I), the compound is shown in the specification,
ET-transpiration evaporation rate on the surface of a dry crop;
λ — latent heat of vaporization of water;
delta is the tangent slope of the temperature-saturated water vapor pressure relation curve;
R n -net radiation to the surface;
g-is the soil heat flux;
c p -specific heat at atmospheric pressure of the drying air;
ρ a -the density of the air;
e a -saturated water vapour pressure at a leaf surface air temperature of Ta;
e d -the actual water vapour pressure of the outside air;
r a -aerodynamic drag;
gamma-modified humidity constant;
γ — hygrometer constant;
r c -canopy pore diffusion resistance;
the second step is that: determination of the diffusion resistance r of the gas pores of the canopy c ：
According to the heat transfer principle, the sensible heat exchange flux between the blades and the surrounding air is:
in the formula (I), the compound is shown in the specification,
T l -crop leaf temperature;
T a -the temperature of the air surrounding the crop;
the latent heat exchange flux between the blade and its surrounding air is:
in the formula (I), the compound is shown in the specification,
e 0 -saturated water vapour pressure in the blade pores;
according to e 0 -e a ＝Δ(T l -T a ) Can lead out
e 0 -e d ＝Δ(T l -T a )+(r a -r d ) (5)
Substituting the three formulas of the formulas (3), (4) and (5) into an energy balance equation: r n H + λ E + G, from which r can be deduced c The calculation formula of (a) is as follows:
or
In the formula (I), the compound is shown in the specification,
LATD-represents the difference between the temperature of the crop leaves and the temperature of the air;
LATD＝T l -T a (8)
VPD-represents the saturated vapor pressure differential of air;
VPD＝e a -e d (9)
R' n -representing the total net radiation obtained by the crop canopy;
R' n ＝R n -G (10)
the third step: determination of the aerodynamic resistance r a ；
r a ＝r b +r g
In the formula (I), the compound is shown in the specification,
r b -representing blade laminar boundary layer resistance;
r g -representing turbulent boundary layer resistance above the canopy;
wherein, the boundary layer resistance r of the blade laminar flow b Measuring and calculating by a boundary layer diffusion resistance sensor;
the heat transfer coefficient of the metal wafer on the sensor is defined as:
in the formula (I), the compound is shown in the specification,
α -heat transfer coefficient of the metal wafer;
q-constant electric power to heat the wafer;
s-surface area of metal wafer;
Δ T-temperature difference between heated and unheated reference wafers;
heat transfer coefficient alpha and boundary layer resistance r b There is a strong correlation between them, which can be expressed by the following implicit function of air temperature:
α×r b ＝f(T i ) (12)
according to the heat balance principle, no water evaporation exists on the metal sheets, and only the change of sensible heat exists, so that the energy balance equations on the two metal sheets are respectively expressed as follows:
for the heated wafer:
for unheated wafers, Q =0, then:
in the formula (I), the compound is shown in the specification,
R nw ，R nn the radiation obtained from the heated and unheated wafers, respectively, can be considered to be the same in terms of the amount of radiation they obtain, since they are on the same horizontal plane, i.e. R nw ＝R nn ；
c p -the specific heat at constant pressure of air;
ρ a air density, which is a function of air temperature, can be represented by the following equation:
ρ a ＝1.2837-0.0039T a (15)
r bw ，r bn boundary layer resistances for the heated and unheated disks, respectively, where r is assumed bw ＝r bn ＝r b ；
T w ，T n ，T a -the heated wafer, the unheated wafer and the room air temperature, respectively;
subtracting the formulas (13) and (14), and obtaining a calculation formula of the boundary layer resistance after arrangement as follows:
turbulent boundary layer resistance r g Calculated by using the Thom and Oliver formulas:
in the formula (I), the compound is shown in the specification,
z-calculated height;
u z -wind speed at height z;
d-zero plane offset height;
z 0 -crown roughness;
wherein the crown roughness z 0 Represents an efficiency scale for the canopy to absorb momentum from the gas stream; the zero plane displacement height d represents the effective height when the whole canopy is reduced to a large blade layer, and can be determined by the following formula respectively:
d＝0.64h (19)
z 0 ＝0.13h (20)
h-crop height;
combining the formulas (18), (19) and (20) to obtain a calculation formula of the resistance of the turbulent layer above the crop canopy, wherein the calculation formula comprises the following steps:
finally, the boundary layer resistance (r) of the blade laminar flow is adjusted b ) And turbulent boundary layer resistance (r) above the canopy g ) Adding to calculate the aerodynamic resistance r a Then drag the aerodynamics to r a R can be obtained by substituting the formula (6) or (7) c And obtaining the water demand of the greenhouse crops through a Penman-Monteith equation.
The invention has the beneficial effects that: the greenhouse crop water demand calculation method based on the boundary layer resistance measurement technology introduces the boundary layer resistance measurement technology into a Peneman formula to obtain a new calculation method for calculating the greenhouse crop water demand.
Drawings
FIG. 1 is a schematic diagram of a BDR-02 sensor structure.
Fig. 2 is an aerodynamic profile.
Fig. 3 is a result of water demand calculation for greenhouse eggplant.
FIG. 4 is a correlation analysis between the calculated value and the measured value of the model.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Example 1: a method for calculating the water requirement of greenhouse crops based on boundary layer resistance measurement technique features that the water requirement of the crops is calculated by the following Penman-Monteith equation
In the formula (I), the compound is shown in the specification,
ET-transpiration evaporation rate of dry crop surface, kg/m 2 /s；
Lambda-latent heat of vaporization of water, J/kg;
delta is the slope of the tangent line on the temperature-saturated water vapor pressure relation curve, kPa/DEG C;
R n -net spokes for the earth's surfaceMiao, MJ/m 2 /d；
G-is the soil heat flux, MJ/m 2 /d；
c p The specific heat of the dry air at atmospheric pressure, can be taken out of c p ＝1012.0，J/kg/K；
ρ a Air density, kg/m 3 ；
e a -saturated steam pressure, kPa, at a leaf surface air temperature of Ta;
e d -actual water vapour pressure of the outside air, kPa;
r a -aerodynamic drag, s/m;
gamma-corrected humidity constant, kPa/deg.C,
γ -hygrometer constant, kPa/. Degree.C.;
r c -canopy pore diffusion resistance, s/m.
Canopy pore diffusion resistance r c Reflects the comprehensive physiological condition of crops, is a comprehensive function of factors such as solar radiation, water-vapor pressure difference, soil humidity of crops and the like, and researches show that r is c The relation with environmental factors is very complex, the variability is very large along with the differences of regional climate and soil characteristics, the measurement precision has very high requirements on instruments and operation, and therefore indirect methods are commonly used in practical research to obtain: (1) According to Peneman principle, deriving crown layer air hole resistance r c With aerodynamic resistance r a And the relation r between the transpiration evaporation capacity of crops c ＝f(r a ET). Wherein ET is obtained by measuring through a test method and a water balance principle; (2) R is deduced by referring to the steps of deriving Penman's formula according to the equation of energy balance, aerodynamics and thermodynamic principles c Is calculated by the expression r c ＝f(r a ) This method only requires the determination of r a The value of (c). The second method is adopted in the present embodiment.
Firstly, according to the heat transfer principle, the sensible heat exchange flux between the blade and the surrounding air is:
in the formula (I), the compound is shown in the specification,
T l -crop leaf temperature, deg.c;
T a the temperature of the air surrounding the crop, DEG C, other symbols have the same meaning as above.
The latent heat exchange flux between the blade and its surrounding air is:
in the formula (I), the compound is shown in the specification,
e 0 -saturated water vapour pressure, kPa, in the blade pores;
according to e 0 -e a ＝Δ(T l -T a ) Can lead out
e 0 -e d ＝Δ(T l -T a )+(r a -r d ) (5)
Substituting the three formulas of the formulas (3), (4) and (5) into an energy balance equation: r n H + λ E + G, from which r can be deduced c The calculation formula of (a) is as follows:
or
In the formula (I), the compound is shown in the specification,
LATD-represents the difference between the temperature of the crop leaves and the temperature of the air, deg.C;
LATD＝T l -T a (8)
VPD-represents the saturated vapor pressure differential of air, KPa;
VPD＝e a -e d (9)
R' n representing the total net radiation acquired by the crop canopy, MJ/m 2 /d；
R' n ＝R n -G (10)
In the calculation model of air pore resistance, R n 、LATD、VPD、ρ a c p The measurement and calculation of the parameters such as delta, gamma and the like are relatively easy, if the aerodynamic resistance r can be determined a R can be calculated according to the above formula c The value of (c). The DeBruin (1982) study showed that imprecise r a Can directly cause great deviation of air hole resistance and the diffusion resistance r of the air holes of the canopy c Whether the calculation result is accurate or not is crucial to how to correctly obtain the aerodynamic resistance r a 。
By aerodynamic drag is meant the drag experienced by the water vapor as it leaves the blade and evaporates into the air, as measured by the blade laminar boundary layer drag (r) b ) And turbulent boundary layer resistance (r) above the canopy g ) Two parts are formed.
(1) Laminar boundary layer resistance r b
The boundary layer is generally a relatively smooth air layer (laminar flow) around the surface of the blade or the canopy, and the high resistance of the boundary layer affects the evaporation and carbon dioxide exchange of the blade, which also indicates the state difference between the blade surface and the surrounding environment. In this embodiment, laminar boundary layer resistance (r) b ) Measured by the boundary layer diffusion resistance sensor BDR-02. The measurement principle is as follows:
the probe of the BDR-02 sensor shown in fig. 1 is composed of two optically responsive metal wafers, both of which are made of a low thermal conductivity material and are connected by a non-thermal conductivity material. A heating resistance wire is embedded in one of the metal wafers, and a continuous current with the power of Q is conducted to continuously raise the temperature of the wafer; and the other wafer is not heated as a reference, so that a temperature difference is generated between the heating plate and the unheated reference plate. Because of the existence of heat transfer, heat exchange is continuously carried out between the two metal wafers and the ambient air, so that the temperature difference between the two wafers changes at any time, and the larger the temperature difference is, the slower the air around the wafers flows, the less heat diffused from the wafers to the ambient air is, and the larger the thermal conductivity resistance is; conversely, the less resistance will be.
According to the above principle, if the temperature difference Δ T and r can be determined b The quantitative relationship between the two wafers can be calculated by measuring the temperature difference between the two wafers b The value is obtained. In fact, the output of the BDR-02 sensor is exactly the temperature difference Δ T between the two wafers, and not r b The temperature difference is measured by a pair of thermocouples on the wafer.
The heat transfer coefficient of the metal wafer on the sensor is defined as:
in the formula (I), the compound is shown in the specification,
alpha-heat transfer coefficient of metal disk, W/m 2 /K；
Q-constant electric power to heat the wafer, W;
s-surface area of Metal wafer, m 2 ；
Δ T-temperature difference between heated and unheated reference wafers, K;
heat transfer coefficient alpha and boundary layer resistance r b There is a strong correlation between them, which can be expressed by the following implicit function of air temperature:
α×r b ＝f(T i ) (12)
then, by measuring the temperature difference Δ T between the two wafers, and combining the heating power Q and the known parameters such as the surface area S of the wafers, α can be determined and r can be derived b The calculation formula of (2).
According to the heat balance principle, there is no water evaporation (its latent heat is 0) on the metal sheets, and there is only a change in sensible heat, so the energy balance equations on the two metal sheets are respectively expressed as:
for the heated wafer:
for unheated wafers, Q =0, then:
in the formula (I), the compound is shown in the specification,
R nw ，R nn -the radiation obtained on the heated and unheated wafers, W/m, respectively 2 Since they are on the same horizontal plane, they can be considered to receive the same amount of radiation, i.e. R nw ＝R nn ；
c p -specific heat at constant pressure of air, 1012.0 (J/kg/K);
ρ a air density, kg/m 3 Is a function of air temperature and can be represented by the following equation:
ρ a ＝1.2837-0.0039T a (15)
r bw ，r bn boundary layer resistances, s/m, for the heated and unheated discs, respectively, where r is assumed bw ＝r bn ＝r b ；
T w ，T n ，T a -the heated wafer, the unheated wafer and the room air temperature, K, respectively;
subtracting the formulas (13) and (14), and obtaining a calculation formula of the boundary layer resistance after arrangement as follows:
the constant electric power Q =40mW used in the test, and the surface area S =5cm of the metal wafer 2 Then, the boundary layer resistance calculation null formula can be written as:
r b ＝12.65×(1.2837-0.0039T a )×ΔT (17)
by the formula, the laminar flow edge of the greenhouse crops in the growth period is calculatedBoundary layer resistance r b The daily change rule of the weather is stable, and r is stable under different weather conditions b During the night period, it is relatively steady, while at 8:00 to 18:00 slightly fluctuating between and below their nighttime periods. r is b The daily maximum value of (A) is generally present at night and is kept around 100s/m, and the average daily value in the growth period is 87s/m and r b The change with time is not obvious in the growth process of the greenhouse crops.
(2) Turbulent boundary layer resistance r g
As shown in the aerodynamic profile of FIG. 3, the turbulent boundary layer resistance above the canopy is mainly influenced by the wind speed, considering that the air flow in the greenhouse is slower, to avoid r when the wind speed is 0 g In the infinite case, the inventor adopts Thom and Oliver formulas suitable for the case that the wind speed in the greenhouse is small:
in the formula (I), the compound is shown in the specification,
z-calculated height, m;
u z -wind speed at height z, m/s;
d-zero plane offset height, m;
z 0 -crown roughness, m;
wherein the crown roughness z 0 Represents an efficiency scale for the canopy to absorb momentum from the gas stream; the zero plane displacement height d represents the effective height when the whole canopy is reduced to a large blade layer, and can be respectively determined by the following formulas:
d＝0.64h (19)
z 0 ＝0.13h (20)
h-crop height, cm.
Combining the formulas (18), (19) and (20) to obtain a calculation formula of the resistance of the turbulent layer above the crop canopy, wherein the calculation formula comprises the following steps:
during the test period, the calculated height z =2m (the average height of a ventilation opening of a side window of a greenhouse) is taken, the heights of the test crops are controlled within 2m artificially, the average wind speed in the room in the daytime is not more than 0.5m/s, and then r g Less than 10s/m, with a value of between 7.6s/m and 9.6s/m, and approximately r b 1/10-1, consistent with the actual situation.
The boundary layer resistance (r) of the laminar flow of the blade b ) And turbulent boundary layer resistance (r) above the canopy g ) Adding up, the expression of the aerodynamic drag can be obtained as follows:
the specific calculation method of other parameters involved in the Penman formula can be directly referred to the existing data, and is not described in any way in the space.
Evaluating and analyzing test calculation results of greenhouse crop water demand model
The invention adopts the Penmann formula to calculate the water demand of eggplants in the Hubei province water-saving irrigation test base in 2006-2007 years in the whole growth period, and finally, the average variation value of the water demand in ten days is obtained, as shown in figure 3.
As can be seen from fig. 3, there are a number of large fluctuations in the water demand of a greenhouse eggplant throughout the growth period, which are related to changes in the external weather and the characteristics of the crop itself. Because the test crops belong to an infinite growth type, and the process of flowering and fruiting is repeated from planting to death, the water consumption of the test crops is also changed continuously. In addition, the simulation result of the greenhouse eggplant in 2006-2007 whole growth period by adopting the two models is consistent with the change rule of the actually measured data, and the change rule of the crop water demand calculated by the Peneman formula based on the boundary layer resistance measurement technology is basically consistent with the change condition of the crop water demand actually measured.
In order to further test the effectiveness of the crop water demand calculation model, the invention respectively performs correlation regression analysis on the fitting result and the measured value of the two models, and the result is shown in fig. 4.
Through analysis, the correlation coefficient between the water demand and the measured value calculated by the method reaches 0.9061, and the average relative misinsertion RE is 0.09. The method has the advantages that when a complex dynamic system of the greenhouse microclimate is processed, the Peneman formula based on the boundary layer resistance measurement technology is adopted to calculate the greenhouse crop water demand, the precision is high, and the model fitting result is reliable.
Claims (1)
1. A greenhouse crop water demand calculation method based on a boundary layer resistance measurement technology is characterized by comprising the following steps:
the first step is as follows: according to the Penman-Monteith equation, the water demand of the greenhouse crops is calculated by the following formula:
in the formula (I), the compound is shown in the specification,
ET-transpiration evaporation rate on the surface of a dry crop;
λ — latent heat of vaporization of water;
delta is the tangent slope of the temperature-saturated water vapor pressure relation curve;
R n -net radiation to the surface;
g-is the soil heat flux;
c p -specific heat at atmospheric pressure of the drying air;
ρ a -the air density;
e a -saturated water vapour pressure at a leaf surface air temperature of Ta;
e d -the actual water vapour pressure of the outside air;
r a -aerodynamic drag;
gamma-modified humidity constant;
γ — hygrometer constant;
r c -canopy pore diffusion resistance;
the second step is that: determination of the diffusion resistance r of the gas pores of the canopy c ：
According to the heat transfer principle, the sensible heat exchange flux between the blades and the surrounding air is:
in the formula (I), the compound is shown in the specification,
T l -crop leaf temperature;
T a -the temperature of the air surrounding the crop;
the latent heat exchange flux between the blade and its surrounding air is:
in the formula (I), the compound is shown in the specification,
e 0 -saturated water vapour pressure in the blade pores;
according to e 0 -e a ＝Δ(T l -T a ) Can lead out
e 0 -e d ＝Δ(T l -T a )+(r a -r d ) (5)
Substituting the three formulas of the formulas (3), (4) and (5) into an energy balance equation: r n H + λ E + G, from which r can be deduced c The calculation formula of (a) is as follows:
or
In the formula (I), the compound is shown in the specification,
LATD-represents the difference between the temperature of the crop leaves and the temperature of the air;
LATD＝T l -T a (8)
VPD-represents the saturated vapor pressure differential of air;
VPD＝e a -e d (9)
R' n -representing the total net radiation obtained by the crop canopy;
R' n ＝R n -G (10)
the third step: determination of the aerodynamic resistance r a ；
r a ＝r b +r g
In the formula (I), the compound is shown in the specification,
r b -representing blade laminar boundary layer drag;
r g -representing turbulent boundary layer resistance above the canopy;
wherein, the boundary layer resistance r of the blade laminar flow b Measuring and calculating by a boundary layer diffusion resistance sensor;
the heat transfer coefficient of the metal wafer on the sensor is defined as:
in the formula (I), the compound is shown in the specification,
α -heat transfer coefficient of the metal wafer;
q-constant electric power to heat the wafer;
s-surface area of metal wafer;
Δ T-temperature difference between heated and unheated reference wafers;
heat transfer coefficient alpha and boundary layer resistance r b There is a strong correlation between them, which can be expressed by the following implicit function of air temperature:
α×r b ＝f(T i ) (12)
according to the heat balance principle, no water evaporation exists on the metal sheets, and only the change of sensible heat exists, so that the energy balance equations on the two metal sheets are respectively expressed as follows:
for the heated wafer:
for unheated wafers, Q =0, then:
in the formula (I), the compound is shown in the specification,
R nw ，R nn the radiation obtained from the heated and unheated wafers, respectively, can be considered to be the same in terms of the amount of radiation they obtain, since they are on the same horizontal plane, i.e. R nw ＝R nn ；
c p -the specific heat at constant pressure of air;
ρ a air density, which is a function of air temperature, can be represented by the following equation:
ρ a ＝1.2837-0.0039T a (15)
r bw ，r bn boundary layer resistances for the heated and unheated disks, respectively, where r is assumed bw ＝r bn ＝r b ；
T w ，T n ，T a -the temperature of the heated wafer, the unheated wafer and the room air, respectively;
subtracting the formulas (13) and (14), and finishing to obtain a calculation formula of the boundary layer resistance, wherein the calculation formula is as follows:
turbulent boundary layer resistance r g Calculated by using the Thom and Oliver formulas:
in the formula (I), the compound is shown in the specification,
z-calculated height;
u z -wind speed at height z;
d-zero plane offset height;
z 0 -crown roughness;
wherein the crown roughness z 0 Represents an efficiency scale for the canopy to absorb momentum from the gas stream; the zero plane displacement height d represents the effective height when the whole canopy is reduced to a large blade layer, and can be determined by the following formula respectively:
d＝0.64h (19)
z 0 ＝0.13h (20)
h-crop height;
combining the formulas (18), (19) and (20) to obtain a calculation formula of the resistance of the turbulent layer above the crop canopy, wherein the calculation formula comprises the following steps:
finally, the boundary layer resistance (r) of the blade laminar flow is adjusted b ) And turbulent boundary layer resistance (r) above the canopy g ) Adding to calculate the aerodynamic resistance r a Then drag the aerodynamics to r a By substituting into formula (6) or (7), r can be obtained c And obtaining the water demand of the greenhouse crops through a Penman-Monteith equation.
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