Fit double logistic model to NDVI time series given parameters estimated with model_params.
model_ndvi(DT, observed = TRUE)Model parameter data.table appended with 'fitted' column of double logistic model of NDVI for a full year. Calculated at the daily scale with the following formula from Bischoff et al. (2012).
$$fitted = \frac{1}{1 + \exp{\frac{xmidS - t}{scalS}}} - \frac{1}{1 + \exp{\frac{xmidA - t}{scalA}}}$$
(See the "Getting started with irg vignette" for a better formatted formula.)
Other model:
model_params(),
model_start()
# 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 for xmidS and xmidA
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
## Two options: fit to full year or observed data
# Option 1 - returns = 'models'
# Double logistic model parameters
# given global starting parameters for scalS, scalA
# and output of model_start for xmidS, xmidA
mods <- model_params(
ndvi,
returns = 'models',
xmidS = 'xmidS_start',
xmidA = 'xmidA_start',
scalS = 0.05,
scalA = 0.01
)
# Fit to the whole year (requires assignment)
fit <- model_ndvi(mods, observed = FALSE)
# Option 2 - returns = 'columns'
model_params(
ndvi,
returns = 'columns',
xmidS = 'xmidS_start',
xmidA = 'xmidA_start',
scalS = 0.05,
scalA = 0.01
)
#> 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 xmidS xmidA scalS
#> <num> <num> <num> <num> <num> <num> <num>
#> 1: 0.1013699 NA 0.3808219 0.7808219 0.3731891 0.7588353 0.024809594
#> 2: 0.1013699 NA 0.3643836 0.7095890 0.3502720 0.7143040 0.045162901
#> 3: 0.1013699 NA 0.3643836 0.7095890 0.3449777 0.7123648 0.034784190
#> 4: 0.1013699 NA 0.3643836 0.7095890 0.3469861 0.7098906 0.038502148
#> 5: 0.1013699 NA 0.3643836 0.7095890 0.3502720 0.7143040 0.045162901
#> ---
#> 801: 0.6136986 1 0.4000000 0.7123288 0.3904855 0.7400015 0.009961817
#> 802: 0.6136986 1 0.3808219 0.7123288 0.3823665 0.7475907 0.009082290
#> 803: 0.6136986 1 0.3808219 0.7808219 0.3787929 0.7611913 0.025539421
#> 804: 0.6136986 1 0.4000000 0.7123288 0.3904855 0.7400015 0.009961817
#> 805: 0.6136986 1 0.3808219 0.7808219 0.3859633 0.7492422 0.012924676
#> scalA
#> <num>
#> 1: 0.03984095
#> 2: 0.03120381
#> 3: 0.03371281
#> 4: 0.01970562
#> 5: 0.03120381
#> ---
#> 801: 0.03408254
#> 802: 0.03335559
#> 803: 0.03799136
#> 804: 0.03408254
#> 805: 0.03646754
# Fit double logistic curve to NDVI time series for the observed days
model_ndvi(ndvi, observed = TRUE)
#> 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 xmidS xmidA scalS
#> <num> <num> <num> <num> <num> <num> <num>
#> 1: 0.1013699 NA 0.3808219 0.7808219 0.3731891 0.7588353 0.024809594
#> 2: 0.1013699 NA 0.3643836 0.7095890 0.3502720 0.7143040 0.045162901
#> 3: 0.1013699 NA 0.3643836 0.7095890 0.3449777 0.7123648 0.034784190
#> 4: 0.1013699 NA 0.3643836 0.7095890 0.3469861 0.7098906 0.038502148
#> 5: 0.1013699 NA 0.3643836 0.7095890 0.3502720 0.7143040 0.045162901
#> ---
#> 801: 0.6136986 1 0.4000000 0.7123288 0.3904855 0.7400015 0.009961817
#> 802: 0.6136986 1 0.3808219 0.7123288 0.3823665 0.7475907 0.009082290
#> 803: 0.6136986 1 0.3808219 0.7808219 0.3787929 0.7611913 0.025539421
#> 804: 0.6136986 1 0.4000000 0.7123288 0.3904855 0.7400015 0.009961817
#> 805: 0.6136986 1 0.3808219 0.7808219 0.3859633 0.7492422 0.012924676
#> scalA fitted
#> <num> <num>
#> 1: 0.03984095 1.738081e-05
#> 2: 0.03120381 4.024955e-03
#> 3: 0.03371281 9.079418e-04
#> 4: 0.01970562 1.693462e-03
#> 5: 0.03120381 4.024955e-03
#> ---
#> 801: 0.03408254 9.760091e-01
#> 802: 0.03335559 9.822608e-01
#> 803: 0.03799136 9.797107e-01
#> 804: 0.03408254 9.760091e-01
#> 805: 0.03646754 9.762660e-01