CN103020444A - Day-scale primary productivity estimation method based on instantaneous photosynthetic rate integration - Google Patents

Abstract

The invention relates to a day-scale primary productivity estimation method based on instantaneous photosynthetic rate integration, and the method comprises the following steps of (1) calculation of instantaneous photosynthetic rate: establishing a cubic equation through a relationship formula among the coupled instantaneous photosynthetic rate, intercellular carbon dioxide (CO2) concentration and stomatal conductance, and calculating the instantaneous photosynthetic rate; (2) simulation of instantaneous weather data: simulating the instantaneous weather by utilizing a sinusoidal function through the characteristic that the temperature and radiation diurnal variation follows the sinusoidal variation principle; and (3) calculation of day-scale primary productivity integration: substituting the instantaneous photosynthetic rate solved in the step (1) in the simulated weather data to form a function adopting the time as a variable, utilizing a trapezoid or simpson formula to integrate the time, and acquiring the day-scale primary productivity. By utilizing the diurnal variation principle characteristics of the weather data and combining the instantaneous photosynthetic rate calculation formula, the measurement precision is high.

Description

A kind of based on instantaneous photosynthetic rate integration " my god " estimating and measuring method of yardstick primary productivity

Technical field

The present invention relates to the large field of global carbon parameter measurement and primary productivity time scale and change little field, particularly a kind of based on instantaneous photosynthetic rate numerical integration " my god " yardstick primary productivity estimating and measuring method.

Background technology

Primary productivity is the key factor of terrestrial ecosystems Carbon balance, also is that ecosystem carbon flux is originated at first.Ecosystem carbon flux shows as the different time scale feature, comprises " instantaneous ", " hour ", " my god ", " moon " and " year " etc.Although all be based upon on the instantaneous yardstick for most mechanism models, but since weather data mostly be greatly " my god " data of yardstick, according to weather data " my god " yardstick primary productivity estimation data are most popular in the usual research, therefore set up have " instantaneous " yardstick to " day " primary productivity of yardstick changes very necessary.Arrive for " instantaneous " at present " my god " in the research of yardstick conversion, do not consider the Diurnal Variation of meteorological element, do not introduce photosynthetic rate and stomatal conductance and concern that mechanism model calculates, calculate " day " primary productivity of yardstick produces the phenomenon of over-evaluating or underestimating easily, thereby limited global carbon deeply, study accurately.

Summary of the invention

Existing in order to solve " instantaneous " to " my god " yardstick primary productivity estimated value over-evaluated or underestimated problem, the invention provides a kind of weather data diurnal variation law feature of utilizing, and in conjunction with high " instantaneous " yardstick of instantaneous photosynthetic rate computing formula, measuring accuracy to " my god " yardstick primary productivity computing method.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of based on instantaneous photosynthetic rate integration " my god " estimating and measuring method of yardstick primary productivity, described measuring method may further comprise the steps:

1) calculating of instantaneous photosynthetic rate:

$A_{\mathrm{net},c}=V_{c\max }\frac{C_i-{\mathrm{\Γ}}^{*}}{C_i+K_c(1+[O_2/K_o\left]\right)}-R_d---\left(1a\right)$

With

$A_{\mathrm{net},j}=J\frac{C_i-{\mathrm{\Γ}}^{*}}{4(C_i-2{\mathrm{\Γ}}^{*})}-R_d---\left(1b\right)$

In the formula, A _{Net, c}And A _{Net, j}Represent respectively the lower and lower photosynthesis rate of light restriction of carboxylase (Rubisco) restriction, unit is μ mol m ^-2s ^-1V _CmaxThe maximal value of expression carboxylation rate, unit is μ mol m ^-2s ^-1J represents the Photosynthetic Electron transport, and unit is μ mol m ^-2s ^-1C _i[O ₂] expression iuntercellular CO ₂And oxygen concentration; Γ ^*CO when expression does not have dark respiration ₂Compensation point; K _cAnd K _oRepresent respectively CO ₂And O ₂The Michaelis-Menten constant; R _dBe the dark respiration amount of blade on daytime, pass through R _d=0.015V _Cmax.For convenient, with A _{Net, c}And A _{Net, j}It is as follows to be written as unified quantic:

$A_{\mathrm{net}}=\frac{a{C}_i-\mathrm{ad}}{e{C}_i+b}-R_d---\left(1c\right)$

In the formula, a, b, c, and d can be by obtaining with formula (1) and (2) contrast.

A _NetAnd C _iCan describe by following formula:

$C_i=C_s-\frac{A_{\mathrm{net}}}{g_s}---\left(2\right)$

$C_s=C_a-\frac{A_{\mathrm{net}}}{g_b}---\left(3\right)$

The relation of photosynthetic rate and stomatal conductance can be described by following formula:

$g_s=\frac{m{\mathrm{Ah}}_s}{C_s}+b^{\′}---\left(4\right)$

G in the formula _sBe stomatal conductance (mol m ^-2s ^-1), m is the experience factor relevant with vegetation and plant species, h _sThe relative humidity of atomsphere of blade surface, C _sThe CO of blade surface ₂Concentration, b ' is the empirical constant that the blade dark respiration causes.This formula is commonly called " Ball-Berry " model.Above-mentioned formula (1) ~ (4) have made up the cube formula of a photosynthetic rate, by finding the solution this formula, obtain three roots, wherein under field conditions (factors), the 3rd solution that root is corresponding correct, its form is as follows:

$A_{\mathrm{net}}=-2\sqrt{\frac{p^2-3q}{9}}\cos \left(\frac{a\cos (\frac{2p^3-9\mathrm{pq}+27r}{2\sqrt{{(p^2-3q)}^3}}+4\mathrm{\π})}{3}\right)-\frac{p}{3}---\left(5a\right)$

$p=\frac{\mathrm{e\β}+b{\mathrm{\θ}}^{\′}-\mathrm{a\α}+\mathrm{e\α}{R}_d}{\mathrm{e\α}}---\left(5b\right)$

$q=\frac{\mathrm{e\γ}+\frac{\mathrm{b\γ}}{C_a}-\mathrm{a\β}+\mathrm{ad}{\mathrm{\θ}}^{\′}+e{R}_d\mathrm{\β}+R_{d}b{\mathrm{\θ}}^{\′}}{\mathrm{e\α}}---\left(5c\right)$

$r=\frac{-\mathrm{a\γ}+\frac{\mathrm{ad\γ}}{C_a}+e{R}_d\mathrm{\γ}+\frac{R_d\mathrm{b\γ}}{C_a}}{\mathrm{e\α}}---\left(5d\right)$

In the formula β=C _a(g _bMh _s-2b '-g _b),

And θ '=g _bMh _s-b '. in formula (5a)-5 (d), meteorological element radiation, temperature, relative humidity are to calculate the final input variable of instantaneous photosynthetic rate;

2) based on the instantaneous simulation of climatic data of weather data diurnal variation law:

Because instantaneous weather data is difficult to obtain, the weather data that we obtain generally be " day " average data, therefore utilize the Diurnal Variation of meteorologic parameter to simulate the diurnal variation of weather data in the middle of a day.Generally speaking weather data (radiation, temperature, relative humidity) is all followed sinusoidal rule variation.Because relative humidity is less on the photosynthetic rate impact, the transient data of radiation and temperature is only simulated in this research, and the diurnal variation data of temperature are as follows

$T_t=T_{\min }+(T_{\max }-T_{\min })\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}}-a)}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]---\left(6a\right)$

T in the formula _tIt is t transient temperature constantly.T _MaxA day maximum temperature, T _MinIt is Daily minimum temperature.t _RiseBe at sunrise between t _SetBe that sunset time .a is the time lag of maximum temperature time of occurrence and local time at high noon, value is here, a=2*3600 (second), namely 2 hours.If time lag does not consider that formula (6a) can be expressed as:

$T_t=T_{\min }+(T_{\max }-T_{\min })\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}})}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]---\left(6b\right)$

For one day instantaneous radiation, can also represent by following formula:

$R_t=R_{\mathrm{noon}}\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}})}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]=\frac{\mathrm{\π}{R}_{\mathrm{daily}}}{2}\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}})}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]---\left(7\right)$

R in the formula _tT instantaneous radiation constantly, R _NoonRadiation constantly at noon, t _Set-t _RiseThat day is long, R _DailyIt is daily global radiation;

3) " my god " yardstick primary productivity integral and calculating:

With formula (6a) or (6b) and formula (7) with (5a) in conjunction with the function that obtains unique variable time t, then time t is carried out integration, formula is as follows:

${\mathrm{GPP}}_{\mathrm{daily}}={\∫}_{t_{\mathrm{rise}}}^{t_{\mathrm{set}}}{A}_{\mathrm{net}}\mathrm{dt}={\∫}_{t_{\mathrm{rise}}}^{t_{\mathrm{set}}}(-2\sqrt{\frac{p^2-3q}{9}}\cos (\frac{a\cos (\frac{2p^3-9\mathrm{pq}+27r}{2\sqrt{{(p^2-3q)}^3}}+4\mathrm{\π})}{3}-\frac{p}{3})\mathrm{dt}---\left(8\right)$

P in the formula, identical among the q, r and (5b)-(5d), use numerical integration method obtain " my god " numerical value of the primary productivity of yardstick.

Further, described measuring method is further comprising the steps of:

4) " my god " checking of yardstick primary productivity:

Utilize the CO2 flux data of flux observation tower observation to calculate " my god " primary productivity, the result who utilizes step 3) to obtain is verified.

Further again, in the described step 3), numerical integration method comprises trapezoid formula and Simpson (Simpson) formula.

Further, in the described step 4), except utilizing the measured data checking, also can utilize the model of hour step-length to carry out the primary productivity simulation of hour step-length, then whole day each hour analog result is added up, checking " my god " primary productivity of yardstick.

Technical conceive of the present invention is: photosynthesis rate mainly is subject to the impact of meteorological element.Meteorological element (radiation, temperature etc.) all has diurnal variation, and the relation between photosynthetic rate and the meteorological element shows as again nonlinear relationship simultaneously.Be difficult to method by simple average the photosynthetic rate of " instantaneous " yardstick is converted to " my god " primary productivity of yardstick.Because the diurnal variation law of this research and utilization meteorological element, and in conjunction with the photosynthetic rate mechanism model of " instantaneous " yardstick, by the method for being carried out integration the time calculate " my god " primary productivity of yardstick.The method can effectively avoid " my god " the yardstick primary productivity calculate over-evaluate or underestimate.

Beneficial effect of the present invention is mainly manifested in: (1), the full mechanism model of employing calculate instantaneous photosynthetic rate, to the effect that the models such as Farquhar model, intercellular CO2 concentration and photosynthetic rate relational model, Ball-Berry are coupled, have strengthened the mechanism of model; (2), because the Diurnal Variation of the meteorological element that model is considered, significantly reduced the meteorological element diurnal variation particularly radiation diurnal variation for " day " calculating of yardstick primary productivity over-evaluate problem, improved Primary Production calculation of force free height.(3), the method can not only be applicable to small scale (point), also is suitable for large scale (zone) Primary Production calculation of force.

Description of drawings

Fig. 1 be a kind of based on instantaneous photosynthetic rate integration " my god " process flow diagram of the estimating and measuring method of yardstick primary productivity.

Fig. 2 be utilize that trapezoidal numerical integration calculates " my god " synoptic diagram of yardstick primary productivity.

Fig. 3 be measured data to simulation " my god " the checking synoptic diagram of yardstick primary productivity.

Embodiment

The present invention is described further below in conjunction with accompanying drawing.

With reference to Fig. 1 ~ Fig. 3, a kind of based on instantaneous photosynthetic rate integration " my god " estimating and measuring method of yardstick primary productivity, described measuring method may further comprise the steps:

1) instantaneous photosynthetic rate is calculated: by Farquhar model, CO2 intercellular concentration and the models such as photosynthetic rate relational model and Ball-Berry are coupled, obtain the cubic equation of photosynthetic rate, by finding the solution this equation, obtain instantaneous photosynthetic rate;

2) based on the instantaneous weather data model of per day weather data: utilize the rule of weather data diurnal variation, with the Diurnal Variation of sine function simulation temperature, radiation data.

3) " my god " calculating of yardstick primary productivity: the instantaneous photosynthetic rate model of instantaneous weather data substitution that will simulate, the photosynthetic rate analogsimulation of generation take the time as unique independent variable, it is carried out from sun to sun integration, obtain " my god " primary productivity of yardstick.

4) result verification: utilize flux tower observation data and take " hour " as the data of the BEPS modeling of step-length to " my god " result of calculation of yardstick verifies, analyzes its error.

The below will be take a website BC-DF49 of Canadian flux observation grid as example, provide utilize the present invention calculate " my god " method of yardstick primary productivity.It is to be noted that given example is for the technical characterstic that the inventive method is described and functional characteristics, enabling being easier to understand the present invention, rather than limit usable range of the present invention.

Consult Fig. 1, it be implement a kind of based on instantaneous photosynthetic rate integration " my god " process flow diagram of the estimating and measuring method of yardstick primary productivity, concrete steps are as follows:

1) calculating of instantaneous photosynthetic rate:

In this example, calculating be Canadian carbon flux observational network BC-DF49 station data in 2008, the computing formula of instantaneous photosynthetic rate is:

$A_{\mathrm{net}}=-2\sqrt{\frac{p^2-3q}{9}}\cos \left(\frac{a\cos (\frac{2p^3-9\mathrm{pq}+27r}{2\sqrt{{(p^2-3q)}^3}}+4\mathrm{\π})}{3}\right)-\frac{p}{3}$

Variable reference in the formula, the technical scheme of this instructions.

2) based on the instantaneous weather data model of per day weather data: utilize per day digital simulation transient temperature to use formula to be:

$T_t=T_{\min }+(T_{\max }-T_{\min })\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}}-a)}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]---\left(6a\right)$

T in the formula _tIt is t transient temperature constantly.T _MaxA day maximum temperature, T _MinIt is Daily minimum temperature.t _RiseBe at sunrise between t _SetBe that sunset time .a is the time lag of maximum temperature time of occurrence and local time at high noon, value is here, a=2*3600 (second), namely 2 hours.To calculate since on January 1st, 2008 as first day, simulated 120,150,180,210 and 240 days temperature data, result such as table 1.

Table 2 is based on the temperature diurnal variation analogue value of sinusoidal variations

Utilize the instantaneous radiation formula of daily global radiation simulation to be:

$R_t=R_{\mathrm{noon}}\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}})}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]=\frac{\mathrm{\π}{R}_{\mathrm{daily}}}{2}\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}})}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]---\left(7\right)$

R in the formula _tT instantaneous radiation constantly, R _NoonRadiation constantly at noon, t _Set-t _RiseThat day is long, R _DailyIt is daily global radiation.The radiation data that calculates the 120th, 150,180,210 and 240 day is as shown in table 2.

Table 3 is based on the radiation diurnal variation analogue value of sinusoidal variations

3) " my god " the yardstick primary productivity calculates: utilize trapezoid formula that the photosynthetic rate of instantaneous yardstick is carried out from sun to sun integration, calculate " my god " primary productivity of yardstick.Result of calculation as shown in Figure 2.

4) modelling verification: utilize the value of actual measurement that analog result is verified, wherein the analogue value and measured value match R ²Be that 0.854, RMSE is 2.249g Cm ^-2Day ^-1Model result and measured result are very approaching as seen from Figure 3.

Claims (4)

1. One kind based on instantaneous photosynthetic rate integration " my god " estimating and measuring method of yardstick primary productivity,

   It is characterized in that: described measuring method may further comprise the steps:

   1) calculating of instantaneous photosynthetic rate:

   $A_{\mathrm{net},c}=V_{c\max }\frac{C_i-{\mathrm{\Γ}}^{*}}{C_i+K_c(1+[O_2/K_o\left]\right)}-R_d---\left(1a\right)$

   With

   $A_{\mathrm{net},j}=J\frac{C_i-{\mathrm{\Γ}}^{*}}{4(C_i-2{\mathrm{\Γ}}^{*})}-R_d---\left(1b\right)$

   In the formula, A _{Net, c}And A _{Net, j}Represent respectively the lower and lower photosynthesis rate of light restriction of carboxylase restriction, unit is μ mol m ^-2s ^-1V _CmaxThe maximal value of expression carboxylation rate, unit is μ mol m ^-2s ^-1J represents the Photosynthetic Electron transport, and unit is μ mol m ^-2s ^-1C _i[O ₂] expression iuntercellular CO ₂And oxygen concentration; Γ ^*CO when expression does not have dark respiration ₂Compensation point; K _cAnd K _oRepresent respectively CO ₂And O ₂The Michaelis-Menten constant; R _dBe the dark respiration amount of blade on daytime, pass through R _d=0.015V _Cmax, with A _{Net, c}And A _{Net, j}It is as follows to be written as unified quantic:

   $A_{\mathrm{net}}=\frac{a{C}_i-\mathrm{ad}}{e{C}_i+b}-R_d---\left(1c\right)$

   In the formula, a, b, c, and d is by obtaining with formula (1) and (2) contrast;

   A _NetAnd C _iDescribe by following formula:

   $C_i=C_s-\frac{A_{\mathrm{net}}}{g_s}---\left(2\right)$

   $C_s=C_a-\frac{A_{\mathrm{net}}}{g_b}---\left(3\right)$

   The relation of photosynthetic rate and stomatal conductance can be described by following formula:

   $g_s=\frac{m{\mathrm{Ah}}_s}{C_s}+b^{\′}---\left(4\right)$

   G in the formula _sBe stomatal conductance (mol m ^-2s ^-1), m is the experience factor relevant with vegetation and plant species, h _sThe relative humidity of atomsphere of blade surface, C _sThe CO of blade surface ₂Concentration, b ' is the empirical constant that the blade dark respiration causes;

   Above-mentioned formula (1a) ~ (4) have made up the cube formula of a photosynthetic rate, by finding the solution this formula, obtain three roots, wherein under field conditions (factors), the 3rd solution that root is corresponding correct, its form is as follows:

   $A_{\mathrm{net}}=-2\sqrt{\frac{p^2-3q}{9}}\cos \left(\frac{a\cos (\frac{2p^3-9\mathrm{pq}+27r}{2\sqrt{{(p^2-3q)}^3}}+4\mathrm{\π})}{3}\right)-\frac{p}{3}---\left(5a\right)$

   $p=\frac{\mathrm{e\β}+b{\mathrm{\θ}}^{\′}-\mathrm{a\α}+\mathrm{e\α}{R}_d}{\mathrm{e\α}}---\left(5b\right)$

   $q=\frac{\mathrm{e\γ}+\frac{\mathrm{b\γ}}{C_a}-\mathrm{a\β}+\mathrm{ad}{\mathrm{\θ}}^{\′}+e{R}_d\mathrm{\β}+R_{d}b{\mathrm{\θ}}^{\′}}{\mathrm{e\α}}---\left(5c\right)$

   $r=\frac{-\mathrm{a\γ}+\frac{\mathrm{ad\γ}}{C_a}+e{R}_d\mathrm{\γ}+\frac{R_d\mathrm{b\γ}}{C_a}}{\mathrm{e\α}}---\left(5d\right)$

   In the formula β=C _a(g _bMh _s-2b '-g _b), And θ '=g _bMh _s-b '. in formula (5a)-5 (d), meteorological element radiation, temperature, relative humidity are to calculate the final input variable of instantaneous photosynthetic rate;

   2) based on the instantaneous simulation of climatic data of weather data Diurnal Variation:

   The transient data of simulation radiation and temperature, the diurnal variation data of temperature are as follows

   $T_t=T_{\min }+(T_{\max }-T_{\min })\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}}-a)}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]---\left(6a\right)$

   T in the formula _tT transient temperature constantly, T _MaxA day maximum temperature, T _MinDaily minimum temperature, t _RiseBe at sunrise between t _SetBe sunset time, a is the time lag of maximum temperature time of occurrence and local time at high noon;

   Instantaneous radiation for one day represents by following formula:

   $R_t=R_{\mathrm{noon}}\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}})}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]=\frac{\mathrm{\π}{R}_{\mathrm{daily}}}{2}\sin \left[\frac{\mathrm{\π}(t-t_{\mathrm{rise}})}{t_{\mathrm{set}}-t_{\mathrm{rise}}}\right]---\left(7\right)$

   R in the formula _tT instantaneous radiation constantly, R _NoonRadiation constantly at noon, t _Set-t _RiseThat day is long, R _DailyIt is daily global radiation;

   3) " my god " yardstick primary productivity integral and calculating:

   With formula (6a) or (6b) and formula (7) with (5a) in conjunction with the function that obtains unique variable time t, then time t is carried out integration, formula is as follows:

   ${\mathrm{GPP}}_{\mathrm{daily}}={\∫}_{t_{\mathrm{rise}}}^{t_{\mathrm{set}}}{A}_{\mathrm{net}}\mathrm{dt}={\∫}_{t_{\mathrm{rise}}}^{t_{\mathrm{set}}}(-2\sqrt{\frac{p^2-3q}{9}}\cos (\frac{a\cos (\frac{2p^3-9\mathrm{pq}+27r}{2\sqrt{{(p^2-3q)}^3}}+4\mathrm{\π})}{3}-\frac{p}{3})\mathrm{dt}---\left(8\right)$

   P in the formula, identical among the q, r and (5b)-(5d), use numerical integration method obtain " my god " numerical value of the primary productivity of yardstick.
2. As claimed in claim 1 a kind of based on instantaneous photosynthetic rate integration " my god " estimating and measuring method of yardstick primary productivity, it is characterized in that: described measuring method also comprise " my god " checking of yardstick primary productivity:

   Utilize the CO2 flux data of flux observation tower observation to calculate " my god " primary productivity, the result who utilizes step 3) to obtain is verified.
3. As claimed in claim 1 a kind of based on instantaneous photosynthetic rate integration " my god " estimating and measuring method of yardstick primary productivity, it is characterized in that: in the described step 3), numerical integration method comprises trapezoid formula and Simpson (Simpson) formula.
4. As claimed in claim 2 a kind of based on instantaneous photosynthetic rate integration " my god " estimating and measuring method of yardstick primary productivity, it is characterized in that: in the described step 4), utilize the model of hour step-length to carry out the primary productivity simulation of hour step-length, then whole day each hour analog result is added up, checking " my god " primary productivity of yardstick.

Images