# 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:

```text
28 years × 12 months = 336 monthly prediction steps
```

The temporal relationship is:

```text
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:

```text
[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:

```text
[sample, prediction_year, month, feature]
```

Released shapes:

```text
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:

```text
[sample, age_class, full_year, month, simulation_target]
```

Released shapes:

```text
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:

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

Derived dimensions:

```text
[sample, age_class, simulation_target]
```

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

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

Derived dimensions:

```text
[sample, age_class, prediction_year, month, simulation_target]
```

The model relationship is:

```text
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:

```text
[sample, age_class, full_year]
```

Released shapes:

```text
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:

```text
[sample, age_class]
```

Released shapes:

```text
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:

```text
[sample, full_year]
```

Released shapes:

```text
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:

```text
[sample, prediction_year, month, feature]
```

Shape:

```text
[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:

```text
[sample, age_class, full_year, month, simulation_target]
```

Shape:

```text
[sample, 18, 29, 12, 10]
```

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

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

Derived shapes:

```text
initial_y:
    [sample, 18, 10]

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

### `observed_y`

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

Dimensions:

```text
[sample, full_year, month, observed_target]
```

Shape:

```text
[sample, 29, 12, 3]
```

The three observed target variables are:

```text
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:

```text
[sample, age_class]
```

Shape:

```text
[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:

```text
[sample, full_year]
```

Shape:

```text
[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

```text
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

```text
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`:

```text
initial_y:
    [sample, age_class, simulation_target]

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