metadata/dimension_definitions.md

Dimension definitions

This document defines the dimensions and array orientations used in the released DERE dataset.

Temporal prediction setup

The complete ED target sequence spans 29 calendar years from 1992 to 2020.

The ED target values from December 1992 are used once as the initial state. Together with the monthly input features from the following 28 years, this initial state is used to predict the ED target variables for every month of the following 28 years.

The model performs prediction over 336 monthly time steps:

28 years × 12 months = 336 monthly prediction steps

The temporal relationship is:

Initial state:
    ed_simulation_y from the final month of the first year

Inputs:
    ed_simulation_x from every month of the following 28 years

Prediction targets:
    ed_simulation_y from every month of the following 28 years

Core dimensions

Dimension	Meaning
sample	A sampled global grid cell or an in-situ site matched to the corresponding simulation grid cell
full_year	Year axis of the complete ED target sequence, corresponding to 1992–2020; length 29
prediction_year	Year axis of the prediction period, corresponding to 1993–2020; length 28
month	Calendar month within a year; length 12
feature	Model-input variable; length 136
simulation_target	ED simulation output variable; length 10
observed_target	In-situ carbon-flux variable; length 3
age_class	Forest initial-age class used for age-specific ED simulation outputs, ED simulation PFT arrays, and LiDAR-derived age weights; length 18
network	In-situ dataset identifier: above (ABoVE), ameriflux (AmeriFlux), fluxnet (FLUXNET), icos-ww (ICOS-WW), or multiple (sites occurring in more than one network, separated to keep the network-specific subsets non-overlapping)
split	Dataset partition. The released data contain training and testing splits.

The 18 representative forest ages are:

[1, 10, 20, 30, 41, 50, 60, 70, 90,
 110, 140, 190, 240, 290, 340, 390, 440, 490]

GlobalMask arrays

The GlobalMask dataset is divided into two non-overlapping subsets:

• training split: 3373 global grid-cell samples used for model training.
• testing split: 852 held-out global grid-cell samples used for final model evaluation.

The two splits contain the same variables and use the same dimension definitions. They differ only in the number of samples.

ed_simulation_x

The array contains the monthly ED input features for the 28-year prediction period.

Dimensions:

[sample, prediction_year, month, feature]

Released shapes:

training split: [3373, 28, 12, 136]
testing split:  [852, 28, 12, 136]

ed_simulation_y

The array contains the complete 29-year age-specific ED simulation target sequence.

Dimensions:

[sample, age_class, full_year, month, simulation_target]

Released shapes:

training split: [3373, 18, 29, 12, 10]
testing split:  [852, 18, 29, 12, 10]

The initial target state is derived from the final month of the first year:

initial_y = ed_simulation_y[:, :, 0, -1, :]

Derived dimensions:

[sample, age_class, simulation_target]

The prediction target contains every month of the following 28 years:

target_y = ed_simulation_y[:, :, 1:, :, :]

Derived dimensions:

[sample, age_class, prediction_year, month, simulation_target]

The model relationship is:

initial_y from December 1992
+
ed_simulation_x from January 1993 through December 2020
→
target_y from January 1993 through December 2020

ed_simulation_pft_bl, ed_simulation_pft_nl, and ed_simulation_pft_gs

The arrays contain the annual age-specific ED simulation PFT fractions for broadleaf, needleleaf, and grass-and-shrub vegetation.

Dimensions:

[sample, age_class, full_year]

Released shapes:

training split: [3373, 18, 29]
testing split:  [852, 18, 29]

BL, NL, and GS are stored as separate arrays, so pft_type is not an explicit dimension.

lidar_age_weight_fraction

The array contains the LiDAR-derived fraction associated with each of the 18 forest age classes.

Dimensions:

[sample, age_class]

Released shapes:

training split: [3373, 18]
testing split:  [852, 18]

esa_cci_bl_fraction, esa_cci_nl_fraction, and esa_cci_gs_fraction

The arrays contain the annual ESA CCI broadleaf, needleleaf, and grass-and-shrub vegetation PFT fractions.

Dimensions:

[sample, full_year]

Released shapes:

training split: [3373, 29]
testing split:  [852, 29]

The three PFT groups are stored as separate arrays. There is no monthly dimension in these arrays.

InSituMatched arrays

The number of matched in-situ sites depends on the network subset and data split. Therefore, the symbolic sample dimension is used below instead of a fixed sample count.

ed_simulation_x

The array contains the same 28-year monthly ED input sequence used in the GlobalMask dataset, extracted at the matched in-situ locations.

Dimensions:

[sample, prediction_year, month, feature]

Shape:

[sample, 28, 12, 136]

ed_simulation_y

The array contains the complete 29-year age-specific ED simulation target sequence at the matched in-situ locations.

Dimensions:

[sample, age_class, full_year, month, simulation_target]

Shape:

[sample, 18, 29, 12, 10]

The initial state and prediction target are derived in the same way as for GlobalMask:

initial_y = ed_simulation_y[:, :, 0, -1, :]
target_y = ed_simulation_y[:, :, 1:, :, :]

Derived shapes:

initial_y:
    [sample, 18, 10]

target_y:
    [sample, 18, 28, 12, 10]

observed_y

The array contains the in-situ carbon-flux observations.

Dimensions:

[sample, full_year, month, observed_target]

Shape:

[sample, 29, 12, 3]

The three observed target variables are:

GPP
RECO
NEE

The first year is retained for temporal alignment with the complete ED target sequence. For model evaluation, predictions are compared with the available in-situ observations over the following 28-year prediction period. Missing observation time steps are excluded from evaluation.

lidar_age_weight_fraction

The array contains one LiDAR-derived fraction for each of the 18 age classes.

Dimensions:

[sample, age_class]

Shape:

[sample, 18]

esa_cci_bl_fraction, esa_cci_nl_fraction, and esa_cci_gs_fraction

The arrays contain the annual ESA CCI broadleaf, needleleaf, and grass-and-shrub vegetation PFT fractions at the matched in-situ locations.

Dimensions:

[sample, full_year]

Shape:

[sample, 29]

The three PFT groups are stored as separate arrays. There is no monthly dimension in these arrays.

Conceptual relationship to the paper

In the paper:

• x_(s,t) denotes physical and environmental conditions at location s and time t.
• c_k denotes an initial forest-age state.
• (y^P_(s,t))_k denotes the ED simulation output corresponding to initial age state c_k.
• y_(s,t) denotes the in-situ carbon-flux observation.
• z_(s,t) denotes the aggregated satellite PFT observation.
• alpha_k denotes the weight associated with an initial forest-age state.

In the released prediction setup, the first-year final-month ED target values provide the one-time initial target state. The monthly input features from the following 28 years are then used to predict the monthly ED target values over the same 28-year period.

Released-array summary

All released arrays use sample-first orientation whenever a sample dimension is present.

GlobalMask

ed_simulation_x:
    [sample, prediction_year, month, feature]

ed_simulation_y:
    [sample, age_class, full_year, month, simulation_target]

ed_simulation_pft_bl:
    [sample, age_class, full_year]

ed_simulation_pft_nl:
    [sample, age_class, full_year]

ed_simulation_pft_gs:
    [sample, age_class, full_year]

lidar_age_weight_fraction:
    [sample, age_class]

esa_cci_bl_fraction:
    [sample, full_year]

esa_cci_nl_fraction:
    [sample, full_year]

esa_cci_gs_fraction:
    [sample, full_year]

InSituMatched

ed_simulation_x:
    [sample, prediction_year, month, feature]

ed_simulation_y:
    [sample, age_class, full_year, month, simulation_target]

lidar_age_weight_fraction:
    [sample, age_class]

esa_cci_bl_fraction:
    [sample, full_year]

esa_cci_nl_fraction:
    [sample, full_year]

esa_cci_gs_fraction:
    [sample, full_year]

observed_y:
    [sample, full_year, month, observed_target]

The following arrays are derived from ed_simulation_y:

initial_y:
    [sample, age_class, simulation_target]

target_y:
    [sample, age_class, prediction_year, month, simulation_target]