第 4 章气孔导度模型的拟合

气孔导度模型的拟合是通过 fitBB 来实现的，可以拟合三个 Ball-Berry 类型的气孔导度模型，共有下面几个参数：

气孔导度 (gs),
光合 (A),
外界 CO₂ 浓度 (Ca)
水气压亏缺 (VPD).

其三个模型的简介如下：

4.1 BallBerry 模型

Ball, Woodrow, and Berry (1987) 发表的文章中的模型：

\[\begin{equation} g_s = g0 + g1(\frac{A h_r}{C_a}) \tag{4.1} \end{equation}\]

其中 A 为净光合速率，g₀ 和 g₁ 为拟合参数，h_r 为叶片表面的相对湿度，C_a 为叶片处CO₂浓度。

4.2 BBLeuning 模型

Leuning (1995) 发表的文章中的模型：

\[\begin{equation} g_s = g_0 + g_1(\frac{A}{(C_a - \Gamma)(1 + \frac{D}{D_0})}) \tag{4.2} \end{equation}\]

其中 \(\Gamma\) 为 CO₂ 补偿点，g₀、g₁ 和 D₀ 为拟合参数。

4.3 BBOptiFull 模型

Belinda E. Medlyn et al. (2011) 发表的文章中的模型：

\[\begin{equation} g_s^* \approx g_0 + g_1(1 + \frac{g_1}{D}) \frac{A}{C_a} \tag{4.3} \end{equation}\]

额外的参数 g_k 来自于 Remko A. Duursma et al. (2013) \[\begin{equation} g_s = g_0 + 1.6(1 + \frac{g_1}{D}(1-g_k)) \frac{A}{C_a} \tag{4.4} \end{equation}\]

4.4 `fitBB` 函数

fitBB(data, varnames = list(
  ALEAF = "A", GS = "gsw", VPD = "VPDleaf",
  Ca ="CO2_s", RH = "RHcham"), 
  gsmodel = c("BBOpti", "BBLeuning", "BallBerry",
              "BBOptiFull"), fitg0 = FALSE)

参数的意义:

data：待分析的数据文件。
varnames：注意，函数默认数据为 6400 格式，因此 6800 的数据文件要安装上文的参数修改。相对湿度只有在使用 BallBerry 时才需要输入。
gsmodel：上述三个模型之一。
fitg0：默认不计算g0，若需要，改为TRUE。

代码示例：

library(plantecophys)

aci <- read.csv("./data/aci.csv")
aci <- subset(aci, Obs > 0)
fitBB(aci, varnames = list(ALEAF = "Photo", GS = "Cond", VPD = "VpdL",
  Ca = "CO2S", RH = "RH_S"), gsmodel = "BBOpti", fitg0 = TRUE)

## Result of fitBB.
## Model :  BBOpti 
## Both g0 and g1 were estimated.
## 
## Coefficients:
## g0  g1
## 0.326 -0.992 
## 
## For more details of the fit, look at summary(myfit$fit)
## To return coefficients, do coef(myfit).
## (where myfit is the name of the object returned by fitBB)

4.5 `fitBBs` 函数

如果我们有多个物种的数据，那么使用 fitBBs 则可以快速拟合多条曲线的数据。我们先整合两次的数据，然后再查看运行结果：

aci01 <- read.csv("./data/aci01.csv")
aci01 <- subset(aci01, Obs > 0)
multiBB <- data.frame(
  A = c(aci$Photo, aci01$Photo),
  GS = c(aci$Cond, aci01$Cond),
  CO2S = c(aci$CO2S, aci01$CO2S),
  VPD = c(aci$VpdL, aci01$VpdL),
  RH = c(aci$RH_S, aci01$RH_S),
  species = c(rep("species1", length(aci$Photo)),
  rep("species2", length(aci01$Photo)))
)

mod2 <- fitBBs(multiBB, group = "species",  
               varnames = list(
               ALEAF = "A", GS = "GS", VPD = "VPD",
               Ca ="CO2S", RH = "RH"), 
               gsmodel = "BallBerry", fitg0 = TRUE)

## RH provided in % converted to relative units.
## RH provided in % converted to relative units.

coef(mod2)

##      group         g0         g1
## 1 species1 0.32638852 -0.1734554
## 2 species2 0.05158725 -0.0218842

参考文献

Ball, J. Timothy, Ian E. Woodrow, and Joseph A. Berry. 1987. A Model Predicting Stomatal Conductance and Its Contribution to the Control of Photosynthesis Under Different Environmental Conditions. Springer Netherlands.

Duursma, Remko A., Paxton Payton, Michael P. Bange, Katrina J. Broughton, Renee A. Smith, Belinda E. Medlyn, and David T. Tissue. 2013. “Near-Optimal Response of Instantaneous Transpiration Efficiency to Vapour Pressure Deficit, Temperature and CO\(_2\) in Cotton (Gossypium Hirsutum l.).” Agricultural & Forest Meteorology 168 (1): 168–76.

Leuning, R. 1995. “A Critical Appraisal of a Combined Stomatal‐photosynthesis Model for C3 Plants.” Plant Cell and Environment 18 (4): 339–55.

Medlyn, Belinda E., Remko A. Duursma, Derek Eamus, David S. Ellsworth, I. Colin Prentice, Craig V. M. Barton, Kristine Y. Crous, Paolo De Angelis, Michael Freeman, and Lisa Wingate. 2011. “Reconciling the Optimal and Empirical Approaches to Modelling Stomatal Conductance.” Global Change Biology 17 (6): 2134–44.

第 4 章 气孔导度模型的拟合