Trapezoid temperature function (TPF)

Trapezoid temperature function with four cardinal temperatures reflecting a range of optimum temperatures for photosynthesis¹.

\(\ f(T_{ab}) = ( T_{day} - T_{min}) / ( T_{optmin} - T_{min})\)

$ f(T_{cd}) = ( T_{max} - T_{day}) / ( T_{max} - T_{optmax}) $

Where:

\(\ f(T) = 0; T_{day} <= T_{min}\) or $ T_{day} >= T_{max} $

$ f(T) = 1; T_{optmin} <= T_{day} <= T_{optmax} $

Code for TPF:

PythonR

# ----------------------------------------------
# Trapezoidal Temperature Function (TPF) 
# ----------------------------------------------
def calculate_TPF(Tday, Tmin, Toptmin, Toptmax, Tmax):
    tpf = 0
    if (Toptmin > Toptmax):
        print("Min Optimum Temperature greater than Max Opt. Temperature")
        tpf = np.nan
    elif (Toptmax > Tmax):
        print("Max Optimum Temperature greater than Maximum Temperature")
        tpf = np.nan
    else:
        if ((Tday < Tmin) or (Tday > Tmax)):
            tpf = 0
        elif ((Tday >= Toptmin) and (Tday <= Toptmax)):
            tpf = 1
        elif (Tday < Toptmin):
            gradient, intercept, r_value, p_value, std_err = stats.linregress([Tmin,Toptmin],[0,1])
            tpf = Tday * gradient
        elif (Tday > Toptmax):
            gradient, intercept, r_value, p_value, std_err = stats.linregress([Toptmax, Tmax],[1,0])
            tpf = 1-((Tday-Toptmax)*abs(gradient))
    #
    return tpf

# Trapezoidal Temperature Function
calculateTPF <- function(Tday, Tmin, Toptmin, Toptmax, Tmax){
    tpf <- 0
    if (Toptmin > Toptmax){
        warning("Min Optimum Temperature greater than Maximum Opt. Temperature")
        tpf <- NA
    } else if (Toptmax > Tmax){
        warning("Max Optimum Temperature greater than Maximum Temperature")
        tpf <- NA
    } else {
        if ((Tday <= Tmin) | (Tday >= Tmax)){
        tpf <- 0
        } else if ((Tday >= Tmin) & (Tday < Toptmin)){
        interceptLeft <- lsfit(x=c(Tmin,Toptmin), y=c(0,1))$coefficients[1]
        slopeLeft <- lsfit(x=c(Tmin,Toptmin), y=c(0,1))$coefficients[2]
        tpf <- Tday * slopeLeft + interceptLeft
        } else if ((Tday > Toptmax) & (Tday <= Tmax)){
        interceptRight <- lsfit(x=c(Toptmax, Tmax), y=c(1,0))$coefficients[1]
        slopeRight <- lsfit(x=c(Toptmax, Tmax), y=c(1,0))$coefficients[2]
        tpf <- Tday * slopeRight + interceptRight
        } else if ((Tday >= Toptmin) & (Tday <= Toptmax)) { 
        tpf <- 1
        }
    }
    return(tpf)
}
calculateTPF_wrap <- function( Tday, Tmin, Toptmin, Toptmax, Tmax) {
    y <- vector("numeric", length (Tday)) 
    for (i in 1:length(Tday)) {
        y[[i]] <- calculateTPF( Tday=Tday[[i]], Tmin, Toptmin, Toptmax, Tmax) 
    }
    return(y)
}

The whole R code can be found in the Github repository at Rcode folder.

---

1. four parameters ↩