Calculate the instantaneous rate of green-up.
calc_irg(DT, id = "id", year = "yr", scaled = TRUE)Extended data.table 'irg' column of instantaneous rate of green-up calculated for each day of the year, for each individual and year.
The DT argument expects a data.table of model estimated parameters for double logistic function of NDVI for each year and individual. Since it is the rate of green-up, model parameters required are only xmidS and scalS.
The scaled argument is used to optionally rescale the IRG result to 0-1, for each year and individual.
The id argument is used to split between sampling units. This may be a point id, polygon id, pixel id, etc. depending on your analysis. This should match the id provided to filtering functions. The formula used is described in Bischoff et al. (2012):
$$IRG = (exp((t + xmidS) / scalS)) / (2 * scalS * (exp(1) ^ ((t + xmidS) / scalS)) + (scalS * (exp(1) ^ ((2 * t) / scalS))) + (scalS * exp(1) ^ ((2 * xmidS) / scalS)))$$
(See the "Getting started with irg vignette" for a better formatted formula.)
Other irg:
irg()
# Load data.table
library(data.table)
# Read in example data
ndvi <- fread(system.file("extdata", "sampled-ndvi-MODIS-MOD13Q1.csv", package = "irg"))
# Filter and scale NDVI time series
filter_ndvi(ndvi)
#> id NDVI SummaryQA DayOfYear yr filtered winter rolled
#> <int> <num> <num> <int> <num> <num> <num> <num>
#> 1: 0 0.1864 3 11 2015 0.3076500 0.3076500 0.3076500
#> 2: 1 0.0541 2 3 2015 0.3163400 0.3163400 0.3163400
#> 3: 2 0.1781 3 11 2015 0.2649875 0.2649875 0.2649875
#> 4: 3 0.1024 2 5 2015 0.2301750 0.2301750 0.2301750
#> 5: 4 0.0898 2 3 2015 0.2177150 0.2177150 0.2177150
#> ---
#> 801: 2 0.1179 2 364 2019 0.2649875 0.2649875 0.2649875
#> 802: 3 0.0789 2 364 2019 0.2301750 0.2301750 0.2301750
#> 803: 4 0.1572 2 364 2019 0.2177150 0.2177150 0.2177150
#> 804: 5 0.0763 2 364 2019 0.3163400 0.3163400 0.3163400
#> 805: 6 0.1197 2 362 2019 0.3149325 0.3149325 0.3149325
#> top
#> <num>
#> 1: 0.8735000
#> 2: 0.8632175
#> 3: 0.8707500
#> 4: 0.8635525
#> 5: 0.8476000
#> ---
#> 801: 0.8707500
#> 802: 0.8635525
#> 803: 0.8476000
#> 804: 0.8632175
#> 805: 0.8632000
scale_doy(ndvi)
#> id NDVI SummaryQA DayOfYear yr filtered winter rolled
#> <int> <num> <num> <int> <num> <num> <num> <num>
#> 1: 0 0.1864 3 11 2015 0.3076500 0.3076500 0.3076500
#> 2: 1 0.0541 2 3 2015 0.3163400 0.3163400 0.3163400
#> 3: 2 0.1781 3 11 2015 0.2649875 0.2649875 0.2649875
#> 4: 3 0.1024 2 5 2015 0.2301750 0.2301750 0.2301750
#> 5: 4 0.0898 2 3 2015 0.2177150 0.2177150 0.2177150
#> ---
#> 801: 2 0.1179 2 364 2019 0.2649875 0.2649875 0.2649875
#> 802: 3 0.0789 2 364 2019 0.2301750 0.2301750 0.2301750
#> 803: 4 0.1572 2 364 2019 0.2177150 0.2177150 0.2177150
#> 804: 5 0.0763 2 364 2019 0.3163400 0.3163400 0.3163400
#> 805: 6 0.1197 2 362 2019 0.3149325 0.3149325 0.3149325
#> top t
#> <num> <num>
#> 1: 0.8735000 0.027397260
#> 2: 0.8632175 0.005479452
#> 3: 0.8707500 0.027397260
#> 4: 0.8635525 0.010958904
#> 5: 0.8476000 0.005479452
#> ---
#> 801: 0.8707500 0.994520548
#> 802: 0.8635525 0.994520548
#> 803: 0.8476000 0.994520548
#> 804: 0.8632175 0.994520548
#> 805: 0.8632000 0.989041096
scale_ndvi(ndvi)
#> id NDVI SummaryQA DayOfYear yr filtered winter rolled
#> <int> <num> <num> <int> <num> <num> <num> <num>
#> 1: 0 0.1864 3 11 2015 0.3076500 0.3076500 0.3076500
#> 2: 1 0.0541 2 3 2015 0.3163400 0.3163400 0.3163400
#> 3: 2 0.1781 3 11 2015 0.2649875 0.2649875 0.2649875
#> 4: 3 0.1024 2 5 2015 0.2301750 0.2301750 0.2301750
#> 5: 4 0.0898 2 3 2015 0.2177150 0.2177150 0.2177150
#> ---
#> 801: 2 0.1179 2 364 2019 0.2649875 0.2649875 0.2649875
#> 802: 3 0.0789 2 364 2019 0.2301750 0.2301750 0.2301750
#> 803: 4 0.1572 2 364 2019 0.2177150 0.2177150 0.2177150
#> 804: 5 0.0763 2 364 2019 0.3163400 0.3163400 0.3163400
#> 805: 6 0.1197 2 362 2019 0.3149325 0.3149325 0.3149325
#> top t scaled
#> <num> <num> <num>
#> 1: 0.8735000 0.027397260 0
#> 2: 0.8632175 0.005479452 0
#> 3: 0.8707500 0.027397260 0
#> 4: 0.8635525 0.010958904 0
#> 5: 0.8476000 0.005479452 0
#> ---
#> 801: 0.8707500 0.994520548 0
#> 802: 0.8635525 0.994520548 0
#> 803: 0.8476000 0.994520548 0
#> 804: 0.8632175 0.994520548 0
#> 805: 0.8632000 0.989041096 0
# Guess starting parameters
model_start(ndvi)
#> Key: <scaled>
#> id NDVI SummaryQA DayOfYear yr filtered winter rolled top
#> <int> <num> <num> <int> <num> <num> <num> <num> <num>
#> 1: 4 0.1262 3 38 2015 0.217715 0.2177150 NA 0.8476000
#> 2: 1 0.0599 2 38 2016 0.316340 0.3163400 NA 0.8632175
#> 3: 3 0.0714 2 38 2016 0.230175 0.2301750 NA 0.8635525
#> 4: 4 0.0433 2 38 2016 0.217715 0.2177150 NA 0.8476000
#> 5: 5 0.0599 2 38 2016 0.316340 0.3163400 NA 0.8632175
#> ---
#> 801: 1 0.8755 1 225 2015 0.875500 0.3163400 0.8671 0.8632175
#> 802: 2 0.8740 1 225 2015 0.874000 0.2649875 0.8732 0.8707500
#> 803: 3 0.8643 1 225 2015 0.864300 0.2301750 0.8643 0.8635525
#> 804: 5 0.8755 1 225 2015 0.875500 0.3163400 0.8671 0.8632175
#> 805: 6 0.8729 1 225 2015 0.872900 0.3149325 0.8688 0.8632000
#> t scaled xmidS_start xmidA_start
#> <num> <num> <num> <num>
#> 1: 0.1013699 NA 0.3808219 0.7808219
#> 2: 0.1013699 NA 0.3643836 0.7095890
#> 3: 0.1013699 NA 0.3643836 0.7095890
#> 4: 0.1013699 NA 0.3643836 0.7095890
#> 5: 0.1013699 NA 0.3643836 0.7095890
#> ---
#> 801: 0.6136986 1 0.4000000 0.7123288
#> 802: 0.6136986 1 0.3808219 0.7123288
#> 803: 0.6136986 1 0.3808219 0.7808219
#> 804: 0.6136986 1 0.4000000 0.7123288
#> 805: 0.6136986 1 0.3808219 0.7808219
# Double logistic model parameters given starting parameters for nls
mods <- model_params(
ndvi,
return = 'models',
xmidS = 'xmidS_start',
xmidA = 'xmidA_start',
scalS = 0.05,
scalA = 0.01
)
# Fit double logistic curve to NDVI time series
fit <- model_ndvi(mods, observed = FALSE)
# Calculate IRG for each day of the year
calc_irg(fit)
#> id yr xmidS xmidA scalS scalA t
#> <int> <num> <num> <num> <num> <num> <num>
#> 1: 4 2015 0.3731891 0.7588353 0.02480959 0.03984095 0.000000000
#> 2: 4 2015 0.3731891 0.7588353 0.02480959 0.03984095 0.002739726
#> 3: 4 2015 0.3731891 0.7588353 0.02480959 0.03984095 0.005479452
#> 4: 4 2015 0.3731891 0.7588353 0.02480959 0.03984095 0.008219178
#> 5: 4 2015 0.3731891 0.7588353 0.02480959 0.03984095 0.010958904
#> ---
#> 12806: 4 2019 0.3820566 0.7359233 0.02430961 0.05110263 0.989041096
#> 12807: 4 2019 0.3820566 0.7359233 0.02430961 0.05110263 0.991780822
#> 12808: 4 2019 0.3820566 0.7359233 0.02430961 0.05110263 0.994520548
#> 12809: 4 2019 0.3820566 0.7359233 0.02430961 0.05110263 0.997260274
#> 12810: 4 2019 0.3820566 0.7359233 0.02430961 0.05110263 1.000000000
#> fitted irg
#> <num> <num>
#> 1: 2.879348e-07 1.173251e-06
#> 2: 3.217973e-07 1.310242e-06
#> 3: 3.596309e-07 1.463229e-06
#> 4: 4.019004e-07 1.634078e-06
#> 5: 4.491251e-07 1.824875e-06
#> ---
#> 12806: 7.011788e-03 2.080883e-11
#> 12807: 6.648203e-03 1.469710e-11
#> 12808: 6.303351e-03 9.236763e-12
#> 12809: 5.976280e-03 4.358408e-12
#> 12810: 5.666083e-03 0.000000e+00