DAMMmodel

Estimates CO₂ efflux (e.g., soil respiration (R_s), [μmol m^-2 s^-1]) as a function of temperature (e.g., soil temperature (T_s), [°C]) and soil moisture (θ, [m³ m^-3]).

Installation

Install with the Julia package manager Pkg, just like any other registered Julia package:

julia> ]
pkg> add DAMMmodel

or

julia> using Pkg; Pkg.add("DAMMmodel")

Usage

This package models respiration (CO₂ efflux, e.g., soil respiration (R_s)) as a function of soil temperature (T_s) and soil moisture (θ), using the Dual Arrhenius and Michaelis-Menten kinetics model (2012).

The package contains six functions: DAMMviz, DAMMfdata, DAMM, DAMMfit, DAMMmat, and DAMMplot.

Examples

DAMMviz

DAMMviz()

Interactive plot of the DAMM model

julia> DAMMviz()

DAMMfdata

DAMMfdata(n)

Generates a DataFrame of n fake data Tₛ, θ and Rₛ

julia> DAMMfdata(5)
5×3 DataFrame
 Row │ Tₛ       θ        Rₛ      
     │ Float64  Float64  Float64 
─────┼───────────────────────────
   1 │    10.8      0.3  2.04327
   2 │    31.5      0.1  7.8925
   3 │    38.7      0.7  1.6
   4 │    35.7      0.3  7.38025
   5 │    21.9      0.2  3.0012

DAMM

DAMM(x::VecOrMat{<: Real}, p::NTuple{7, Float64})

Calculate respiration as a function of soil temperature (Tₛ) and moisture (θ).

julia> df = DAMMfdata(100) # generates a fake dataset
100×3 DataFrame
 Row │ Tₛ       θ        Rₛ        
     │ Float64  Float64  Float64   
─────┼─────────────────────────────
   1 │    15.5      0.3   1.72216
   2 │    22.3      0.6   1.8213
  ⋮  │    ⋮        ⋮         ⋮
  99 │     9.5      0.2   0.223677
 100 │     6.6      0.6   0.730627
julia> fp # parameters: αₛₓ, Eaₛₓ, kMₛₓ, kMₒ₂, Sxₜₒₜ, Q10kM
(1.0e9, 64.0, 3.46e-8, 0.002, 0.7, 0.02, 1.0)
julia> DAMM(hcat(df.Tₛ, df.θ), fp) # μmolCO₂ m⁻² s⁻¹
100-element Vector{Float64}:
 6.023429035220588
 0.9298933641647085
 ⋮
 0.8444248717855868
 3.805243237387702

DAMMfit

DAMMfit(x::VecOrMat{<: Real}, Rₛ::Vector{Float64}, poro_val::Float64)

fit the DAMM model parameters to data.

julia> df = DAMMfdata(100) # generates a fake dataset
100×3 DataFrame
 Row │ Tₛ       θ        Rₛ        
     │ Float64  Float64  Float64   
─────┼─────────────────────────────
   1 │    27.1      0.3   4.345
   2 │    38.7      0.6  12.0106
  ⋮  │    ⋮        ⋮         ⋮
  99 │    18.6      0.5   0.894257
 100 │    19.4      0.4   3.79532
julia> p = DAMMfit(hcat(df.Tₛ, df.θ), df.Rₛ, 0.7) 
(2.034002955272664e10, 71.65411256289629, 9.903541279858033e-8, 0.003688664956456453, 0.7, 0.02, 1.0)
julia> DAMM(hcat(df.Tₛ, df.θ), p)
100-element Vector{Float64}:
  4.233540174412755
 10.41149919818871
  ⋮
  1.746141124513421
  1.9599317903590014

DAMMmat

DAMMmat(Tₛ::Array{Float64, 1}, θ::Array{Float64, 1}, R::Array{Float64, 1}, r::Int64)

Generates a matrix of DAMM output for gridded inputs x and y Inputs: soil temperature (Tₛ), soil moisture (θ), respiration (R), resolution (r)

julia> Tₛ = collect(15.0:2.5:40.0)
julia> θ = collect(0.2:0.05:0.7)
julia> R = [1.0, 1.2, 1.5, 2.0, 2.7, 3.8, 4.9, 6.7, 4.1, 2.0, 0.4]
julia> r = 10
julia> poro_val, params, x, y, DAMM_Matrix = DAMMmat(Tₛ, θ, R, r)

DAMMmat(Tₛ::Array{Float64, 1}, θ::Array{Float64, 1}, R::Array{Float64, 1}, r::Int64, n::Int64)

Bin data by n quantiles

julia> n = 4
julia> poro_val, Tmed, θmed, Rmed, params, x, y, DAMM_Matrix = DAMMmat(Tₛ, θ, R, r, n)

DAMMplot

DAMMplot(Tₛ::Array{Float64, 1}, θ::Array{Float64, 1}, R::Array{Float64, 1}, r::Int64)

Plot scatter of data and fitted DAMM surface

julia> df = DAMMfdata(100)
100×3 DataFrame
 Row │ Tₛ       θ        Rₛ       
     │ Float64  Float64  Float64  
─────┼────────────────────────────
   1 │    31.8      0.3  6.54735
   2 │    14.6      0.3  3.49235
  ⋮  │    ⋮        ⋮        ⋮
  99 │    17.2      0.4  0.880441
 100 │     5.2      0.2  0.0
julia> r = 50
julia> fig = DAMMplot(df.Tₛ, df.θ, df.Rₛ, r)

qbins

qbins(x, y, z, n)

Bins x into n quantiles, each xbin into n quantiles of y, return z quantile

julia> df = DataFrame(x=1:20, y=6:25, z=11:30)
julia> xmed, ymed, zmed = qbins(df.T, df.M, df.R, 3)
  xmed = [9, 9, 9, 15, 15, 15, 21, 21, 21]
  ymed = [12, 14, 16, 19, 20.5, 22, 25, 27, 29]
  zmed = [2, 4, 6, 8.5, 10.5, 15, 17, 19]

Contributing

Issues and pull requests are welcome!