# Retrieving yearly forest growth from satellite data: A deep learning based approach

Martin Schwartz, Philippe Ciais, Ewan Sean, Aurélien de Truchis, Cédric Vega, Nikola Besic, Ibrahim Fayad, Jean-Pierre Wigneron, Sarah Brood, Agnès Pelissier-Tanon, et al.

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## To cite this version:

Martin Schwartz, Philippe Ciais, Ewan Sean, Aurélien de Truchis, Cédric Vega, et al. Retrieving yearly forest growth from satellite data: A deep learning based approach. Remote Sensing of Environment, 2025, 330, pp.114959. 10.1016/j.rse.2025.114959. hal-05528811

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# Retrieving yearly forest growth from satellite data: A deep learning based approach

Martin Schwartz<sup>a, D, *</sup>, Philippe Ciais<sup>a, D</sup>, Ewan Sean<sup>b</sup>, Aurélien de Truchis<sup>b</sup>, Cédric Vega<sup>c</sup>, Nikola Besic<sup>c, D</sup>, Ibrahim Fayad<sup>a, b</sup>, Jean-Pierre Wigneron<sup>d</sup>, Sarah Brood<sup>e, D</sup>, Agnès Pelissier-Tanon<sup>a, D</sup>, Jan Pauls<sup>f, D</sup>, Gabriel Belouze<sup>a</sup>, Yidi Xu<sup>a</sup>

<figure><img src="image_4.png" /></figure>

## ARTICLE INFO

Edited by Marie Weiss

Dataset link: https://zenodo.org/records/15489231

**Keywords:**

- Deep learning

- Forest height

- Forest biomass

- Time series

- Forest growth

- GEDI

## ABSTRACT

High-resolution mapping of forest attributes is crucial for ecosystem monitoring and carbon budget assessments. Recent advancements have leveraged satellite imagery and deep learning algorithms to generate high-resolution forest height maps. While these maps provide valuable snapshots of forest conditions, they lack the temporal resolution to estimate forest-related carbon fluxes or track annual changes. Few studies have produced annual forest height, volume, or biomass change maps validated at the forest stand level. To address this limitation, we developed a deep learning framework, coupling data from Sentinel-1 (S1), Sentinel-2 (S2) and from the Global Ecosystem Dynamics Investigation (GEDI) mission, to generate a time series of forest height, growing stock volume, and aboveground biomass at 10 to 30-m spatial resolution that we refer to as FORMS-T (FORest Multiple Satellite Time series). Unlike previous studies, we train our model on individual S2 scenes, rather than on growing season composites, to account for acquisition variability and improve generalization across years. We produced these maps for France over seven years (2018–2024) for height at 10 m resolution and further converted them to 30 m maps of growing stock volume and aboveground biomass using leaf type-specific allometric equations. Evaluation against the French National Forest Inventory (NFI) showed an average mean absolute error of 3.07 m for height ($r^2 = 0.68$) across all years, 86 m³ ha⁻¹ for volume and 65.1 Mg ha⁻¹ for biomass. We further evaluated FORMS-T capacity to capture growth on a site where two successive airborne laser scanning (ALS) campaigns were available, showing a good agreement with ALS data when aggregating at coarser spatial resolution ($r^2 = 0.60$, MAE = 0.27 m for the 2020–2022 growth of trees between 10 and 15 m in 5 km pixels). Additionally, we compared our results to the NFI-based wood volume production at regional level and obtained a good agreement with a MAE of 1.45 m³ ha⁻¹ yr⁻¹ and $r^2$ of 0.59. We then leveraged our height change maps to derive species-specific growth curves and compared them to ground-based measurements, highlighting distinct growth dynamics and regional variations in forest management practices. Further development of such maps could contribute to the assessment of forest-related carbon stocks and fluxes, contributing to the formulation of a comprehensive carbon budget at the country scale, and supporting global efforts to mitigate climate change.

## 1. Introduction

Monitoring forest carbon stocks and fluxes is imperative for the effective implementation of forest-based climate actions, including re-forestation initiatives, sustainable forest management, and countries

commitment to maintain or increase forest carbon storage. Forest carbon resources can be estimated at the country scale with national forest inventories, which consist of systematic measurements of forest characteristics such as tree height, tree species and diameter at breast height (DBH) to estimate biomass, sometimes including revisits after

<footnote><sup>a</sup> Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL, CEA-CNRS-UVSQ, Université Paris Saclay, Gif-sur-Yvette, 91191, France</footnote>

<footnote><sup>b</sup> Kayros SAS, Paris, 75009, France</footnote>

<footnote><sup>c</sup> IGN, Laboratoire d'Inventaire Forestier, Nancy, 54000, France</footnote>

<footnote><sup>d</sup> ISPA, UMR 1391, INRA Nouvelle-Aquitaine, Bordeaux Villenave d'Ornon, France</footnote>

<footnote><sup>e</sup> Inria, Departement d'Informatique de l'Ecole Normale Supérieure, PSL Research University, Paris, France</footnote>

<footnote><sup>f</sup> University of Munster, Munster, 48149, Germany</footnote>

<footnote>* Corresponding author.
E-mail address: martin.schwartz@lsce.ipsl.fr (M. Schwartz).</footnote>
several years, in a representative sample of forest plots. However, these methods are based on statistical aggregation that perform well at regional and national level but cannot be used to monitor forests at finer scales. Additionally, inventory methods are labor-intensive and thus cannot provide a high temporal revisit of forest measurements. The use of remote sensing (RS) data has emerged as a promising approach to enhance the precision of these estimations, particularly through the concept of the multi-source forest inventories (Tomppo et al., 2008). RS imagery facilitates the acquisition of spatially continuous information at fine resolutions, with more frequent revisit intervals than field measurements. Nevertheless, as no satellite can directly measure biomass, mapping forest carbon stocks from remote sensing data requires the use of proxies and models to associate biomass values to a set of predicting variables such as forest height, climatic conditions, productivity indices, tree species, etc. Saatchi et al. (2011), Liu et al. (2023), Schwartz et al. (2023) and Lefsky et al. (2005). In recent years, there has been a significant increase in the production of high-resolution forest height maps, primarily due to the advancements in satellite technology, the development of advanced measuring instruments, and the introduction of novel deep learning (DL) based data fusion techniques. For instance, Pauls et al. (2024), Lang et al. (2023) and Weber et al. (2024) have mapped forest height on a global scale at a resolution of 10 m using Sentinel-1 (S1) and Sentinel-2 (S2) imagery, as well as deep learning models trained on height values measured by NASA's Global Ecosystem Dynamics Investigation (GEDI) mission. Liu et al. (2023) have produced a 3 m resolution map of tree height in Europe based on private data from Planet Labs imagery and trained with airborne laser scanning (ALS) height measurements. Tolan et al. (2024) have released a 1 m Al-based global canopy height map from private data from Maxar imagery. Most of these height maps provide a snapshot of the forest's state at a given year but do not account for temporal dynamics that could be used to monitor yearly forest height change, and variations in aboveground biomass (AGB) stocks. While some forest change maps are currently available, they predominantly concentrate on forest disturbances (Hansen et al., 2013; Reiche et al., 2021; Mermoz et al., 2024), with an emphasis on vegetation loss rather than growth. Recent studies have begun to address this gap in knowledge with the release of time series data on forest height such as Kacic et al. (2023) in Germany, Turubanova et al. (2023) in Europe, Dixon et al. (2025) and Favrichon et al. (2025) in California. However, the height change analysis of these studies is performed at regional level and none of them have captured a yearly increase in height at the pixel level, validated with ancillary reference data. Indeed, the mean absolute error (MAE) of these maps, when compared to field measurements, is typically close to 3 m, while the rate at which trees grow does not exceed 1 m yr⁻¹, even for fast-growing species. This level of error poses a challenge in detecting small growth signals.

The present study aims to address this shortcoming by following these three objectives: (i) Evaluating whether current satellite Earth Observation data coupled with deep learning can detect forest growth signals at meaningful spatial and temporal scales (ii) developing time series of forest structural variables that supports not only disturbance detection but also forest growth monitoring, and (iii) providing a scalable methodology that enables consistent forest mapping across years, which can inform forest management, biodiversity monitoring, and carbon accounting efforts. To follow these objectives, we developed a methodology to produce a time series of forest attribute maps (FORMS-T: FORest Multiple Source Time series) that aims to capture yearly forest growth signals, not only at regional and national scales, but also at finer scales close to pixel-level. The first application of FORMS-T was made over France, encompassing various climates, forest ecosystems, and terrain conditions. To produce the above-mentioned maps, we first train a deep learning model taking as input S1 composite and, unlike earlier approaches relying on static composites, individual S2 scenes from multiple conditions of acquisition, with GEDI RH₉₅ heights as training data, to obtain a seven-year annual time series map

(2018–2024) of canopy height. We further convert our time series to growing stock volume (GSV) and aboveground biomass (AGB) maps based on allometric relationships as these variables are key to forest management and carbon budget calculation. We then proceed to a thorough evaluation of the maps, especially of the yearly height increments, with the support of successive ALS campaigns. Finally, we derive species-specific growth curves from FORMS-T, coupled with a nationwide species map that we compare with field samples to evaluate the reliability of our time series.

## 2. Material and methods

### 2.1. Training data

The complete preprocessing workflow applied to GEDI, Sentinel-1 (S1), and Sentinel-2 (S2) data is visually detailed in Fig. 1 and more thoroughly explained in the following sections.

#### 2.1.1. GEDI

GEDI is a NASA spaceborne mission aboard the International Space Station (ISS) that collects information on the vertical structure of the world's forests using full-waveform LiDAR imagery. We used the GEDI L2 A v2 (Dubayah et al., 2020) product, which provides relative height metrics, including RH₉₅, which we used as a proxy for canopy dominant height. We downloaded all footprints covering France between April 2019 and January 2022 (234,747,773 footprints), which we filtered based on the metrics provided by the L2 A product (quality_flag = 1, nummodes > 0, RH₉₅ < 60 m) to improve the quality of the dataset while retaining a large amount of data (Fig. 1). Additional filtering based on an existing forest height product (Schwartz et al., 2023) is detailed in Appendix A, resulting in a final number of 67,355,565 GEDI RH₉₅ values used in this study.

#### 2.1.2. Sentinel-1

Sentinel-1 is a C-band Synthetic Aperture Radar (SAR) mission operated by the European Space Agency (ESA) that provides SAR backscattering images at a 10 m resolution globally since 2014, with a revisit interval of 6 days (12 days since the failure of Sentinel-1B in December 2021). We worked with the S1 original coordinate system, the Universal Transverse Mercator (UTM), to prevent information loss during data reprojection. France is in the 30N, 31N, and 32N UTM zones, which we subdivided into a custom grid of 20 km × 20 km tiles (See Appendix B) that we chose to balance between individual file size and number of total files. For each tile and each year from 2018 to 2024, we used all S1 Ground Range Detected (GRD) images between May and September, which correspond to the leaf-on season, acquired in ascending orbits with vertical-vertical (VV) and vertical-horizontal (VH) polarization bands. The years prior to 2018 were not included in this study to match the availability period of S2 images. To mitigate the effects of the terrain, we applied the Radiometric Terrain Correction (RTC) developed by Small (2011). Then, to reduce the effect of speckle noise, we finally relied on the computed yearly pixel-wise mean of all images within each S1 orbit (Fig. 1).

#### 2.1.3. Sentinel 2 (S2)

The Sentinel-2 mission is part of the ESA's Copernicus program, delivering Earth surface reflectance images since 2015 through its MultiSpectral Instrument (MSI). These images are sourced from two satellites, Sentinel 2A and 2B, which provide revisit frequencies of about 5 days at the equator and 2–3 days in mid-latitudes. The S2 MSI captures images across visible and infrared bands, from 10 m to 60 m resolution. Here, we used the L2A product which provides earth surface reflectances. Contrary to S1, S2 images are much less stable as they encompass various sun reflectance angles and atmospheric states, which makes the image composite look very different from one year
<figure><img src="image_5.png" /><figcaption>Fig. 1. Data pre-processing workflow.</figcaption></figure>

to another. A model trained on a composite image from a given year, as done in previous studies (Schwartz et al., 2023; Morin et al., 2023; Pauls et al., 2024; Lang et al., 2023), cannot obtain correct predictions on a composite image from another year. To tackle this issue, we rather used individual S2 scenes, thus creating a dataset of satellite imagery under diverse acquisition conditions caused by sun angles, atmospheric corrections, phenology, droughts, etc. This variability will be integrated in the model during the training process and contribute to the creation of a “year-agnostic” model, capable of predicting forest canopy height for years out of its training period (See Section 4.1). Since S2 images are also delivered in the UTM coordinate system, we employed the same three grids for each UTM zone used for S1 to partition France into 20 km × 20 km tiles B. For each tile and each year between 2018 and 2024, we used the least cloudy S2 image for of each month between May 1st and September 30th (leaf-on season), using the Scene Classification Layer (SCL) from the Level-2 A product (orthorectified surface reflectances) as a cloud mask (Fig. 1). Since S2 L2 A images from before 2018 were unavailable in the Amazon Web Services (AWS) storage used for our pipeline, we restricted this study to the 2018–2024 period. We kept only the four 10-m resolution reflectance bands (B02: Blue, B03: Green, B04: Red, B08: Near Infrared) that showed better results in previous studies (Schwartz et al., 2024) and the remaining clouds were masked based on SCL band by removing the pixels flagged as cloud medium or high probability or cloud shadows.

### 2.1.4. Additional datasets

French National Forest Inventory (NFI). Every year, the French institute responsible for the inventory (Institut national de l'information géographique et forestière, IGN) measures dendrometric attributes of more than 5000 new forest plots (30 m diameter) evenly distributed on France's mainland territory (IGN, 2024b). We used this dataset to validate the height maps produced by comparing the dominant height of the trees to the mean values of the FORMS-T pixels within each plot area. Dominant height is calculated by the French NFI as the mean height of the 7 trees with the larger diameter at breast height (DBH) in a plot, which would correspond to the mean height of the 100 larger trees in 1 ha. Plot AGB and GSV are calculated by the IGN based on allometric equations using DBH, species and heights. The GSV data only includes marketable wood volume defined as the main stem's volume of up to 7 cm diameter, only for trees with a DBH > 7.5 cm (IGN, 2024b). Additionally, tree core samples are collected as described in IGN (2024c): Among the main tree populations of the plot, the six largest trees are selected, and only dominant individuals with access to full light are retained. If a single species is clearly dominant in the plot, the two individuals of that species, chosen among these selected trees and closest to the center of the plot, are cored. Otherwise, one individual from each of the two main species (those closest to the plot center belonging to the selected trees) is sampled. These core samplings thus provide the age of the larger trees within this database and allowed us to derive height-age relationships that we further compared
to our data. The French NFI also provides regional inferences based on weighted plots data aggregation (https://ocre-gp.ign.fr/ocregp). In Section 3.4, we compare our results to their estimation of gross wood volume production (m³ ha⁻¹ yr⁻¹), from re-measures of plots after 5 years across the 2014–2022 period. This production is based on diameter growth of standing trees, but also includes an estimation of growth for the trees harvested in the 5 years period before the plot revisit.

**BD Forêt V2.** This dataset is a forest-type map of France (IGN, 2018a) that includes dominant species/genus/leaf type, forest types such as closed or open forests, and other vegetation categorizations. We used this dataset to analyze tree growth per species in Section 3.5. BD Forêt V2 is based on photo interpretation of aerial images from 2007 to 2018, which is before the period covered by FORMS-T (2018–2024). Therefore, young forest stands might not be detected and classified properly in some regions. We applied a negative buffer of 50 m on this dataset to avoid edge effects when selecting pixels belonging to a given tree species.

**IGN forest mask.** This dataset, produced with photo-interpretation and AI methods (IGN, 2024a) is a beta version of a forest mask that partly fits the definition of the Food and Agriculture Organization (FAO) characterizing forests as lands spanning more than 0.5 ha, trees able to reach a height above 5 m and tree cover higher than 10% (FAO, 2000). We used this dataset to filter out non-forest pixels in addition to the BD Forêt V2 as this mask is more up-to-date.

**Dominant leaf type 2018 map (DLT map).** This product maps the forest dominant leaf types (broadleaf or coniferous) all over Europe at 10 m resolution in 2018 using S2 images time series with a Random Forest classifier algorithm (European Environment Agency, 2020). We used this dataset to convert the height maps to growing stock volume and biomass maps with leaf types-specific allometric equations.

**Sylvoécorégions (SERs).** The French territory is divided into 91 eco-regions based on forest ecosystems and management practices (IGN, 2013). Among them, 86 are non-alluvial and were used in this study to carry out regional analyses that are more relevant, from a forestry perspective, than the administrative boundaries of departments.

**Grandes régions écologiques (GRECOs).** As defined by the French NFI, GRECOs (large ecological regions) are twelve broad bioclimatic-topographic zones (A–L) that group together the 91 SERs of metropolitan France. GRECOs serve to organize forest ecosystems at a scale intermediate between national-level divisions and finer-scale SERs, capturing major variations in climate, geology, elevation, and vegetation structure.

**Airborne Laser Scanning (ALS) in the Vosges region.** The ALS technology uses laser pulses emitted from an aircraft to measure distances and create highly accurate 3D models of the Earth's surface. To obtain forest growth data, we compared two ALS campaigns carried out in 2020 and 2022, over more than 300,000 ha, in the Vosges mountainous forested region in north-eastern France (See Appendix C for the exact site location). It will be referred to as the “Vosges site” in the following. The 2020 data comes from an ALS campaign carried out by IGN in February and March 2020 (Description in Ramirez Parra et al. (2024) and internal IGN sources). The 2022 data comes from the “Lidar HD” campaign, from the National Geographic Institute (IGN, 2025), which aims to scan the whole territory with high-resolution (>10 pts m⁻²) ALS data. It was acquired between January and April 2022 (https://macarte.ign.fr/carte/322ea69dab4c7e5afabc6ec7043b5994/acquisitionslidarhd). From these datasets, we derived two canopy height models (CHMs) for 2020 and 2022 at 1 m resolution that we resampled at 10 m by taking the maximum height values to facilitate the comparison with our maps.

## 2.2. Model

### 2.2.1. Deep learning approach with the U-Net model

The sensitivity of SAR and optical sensors to forest height and biomass has often shown saturation effects at different biomass levels, depending on the properties of the sensor and the forest (Joshi et al., 2017). Coupling hand-crafted texture indices with machine learning (ML) algorithms (Morin et al., 2019; Mutanga et al., 2023; Wang et al., 2022) can often partly overcome this limitation and achieve better predictions. In this study, we adopted a Deep Learning (DL) approach based on a U-Net model that showed promising results in recent studies (Dalagnol et al., 2022; Favrichon et al., 2025; Carter et al., 2024; Schwartz et al., 2024; Pauls et al., 2024; Wagner et al., 2024). The U-Net model (Ronneberger et al., 2015) belongs to the Convolutional Neural Networks (CNN) family and relies on a combination of convolution operations, a linear mathematical operation that combines nearby pixels in an image, and non-linear activation functions. During the training process of a CNN, the model modifies its weights, also called parameters, of its convolutions to extract the relevant features from the input image. The model uses these learned parameters to perform predictions on new input data. Specifically, the U-Net model has a “U” shape, consisting of both a contracting and an expanding path, enabling convolutions at various scales of an image with low computation costs. Here, we adapted the model to perform a pixel-wise regression, taking S1 and S2 images as input and producing a height map as output. Our U-Net has approximately 18 M of parameters and the same architecture as that described in a previous study (Schwartz et al., 2024) but with six input channels instead of fourteen due to the different input data (See Appendix D).

### 2.2.2. Training

To train the model, we divided the 20 km × 20 km tiles from the three UTM zones described in the preprocessing steps into the train, validation, and test sets. The overlapping tiles between nearby UTM zones were all included in the train set. We used the validation tiles to monitor the model performances during the training phase and the test tiles to carry out a final assessment of the model performance. The training procedure for the U-Net model followed the operations outlined in Fig. 2 and detailed here. We first randomly select (1) a train tile from one of the three UTM zones; (2) a year from 2019 to 2022 to fit the temporal extent of our GEDI database; (3) a S1 ascending orbit (May-Sep mean value) available within the selected tile and year; (4) a month between May and September in which we select the least cloudy S2 image. (5) The corresponding GEDI data are then filtered according to the S2 acquisition date (±180 days). (6) We take a random 512 × 512 pixel patch in the tile following specific conditions: At least 10% of the RH₉₅ values from GEDI must be above 10 m to ensure an adequate representation of forested areas in the training images and less than 10% of the S2 image patch should be covered by clouds. (7) The S1 and S2 images are combined into a single image with six bands (VV and VH from S1 and RGB + NIR from S2). (8) Steps 1 to 7 are repeated 8 times to create batches of input S1/S2 patches and thousands of GEDI labels. (9) The batches pass through the network, producing a batch of 8 prediction patches with a single output band per patch. (10) We calculate the mean absolute error (MAE) between the predictions and the GEDI RH₉₅ height data for the pixels corresponding to the center of a GEDI footprint following the method developed in previous studies (Lang et al., 2023; Fayad et al., 2023; Schwartz et al., 2023; Pauls et al., 2024). (11) The weights of the U-Net model are adjusted using backpropagation of the loss gradient. We used the PyTorch implementation of the Adam optimizer (Kingma and Ba, 2014) with a learning rate value of 0.001. (12) The previous operations are repeated ~10⁵ steps to train the model. For every 640 steps, we computed the MAE on the validation tiles by following the same operations without the backpropagation pass. After 90,560 steps (~2 days and 8 h on Amazon AWS cloud platform using a NVIDIA Tesla
<figure><img src="image_6.png" /><figcaption>Fig. 2. Model training workflow.</figcaption></figure>

T4 GPU of 16 GB), the validation MAE stopped decreasing, and we reduced the learning rate to 0.0001. After ~8000 additional steps with the same configuration (~5 h), the validation MAE was stable, and we stopped the model training.

We trained the model only on the years corresponding to the GEDI dataset time extent (2019–2022) to keep consistency between labels and images. Besides, we assumed that there were enough different acquisition conditions in this time period to represent all types of S2 images accurately. In line with previous research findings (Morin et al., 2023; Fayad et al., 2023), we encountered an underestimation of tall heights in the training and validation dataset. To reduce the mean absolute error (MAE) for higher heights while accepting a slight MAE increase for lower heights, we retrained our final model using a specific loss function for approximately 20 steps. This adapted loss function sums the MAE for three distinct height ranges: 0 to 5 m (representing ground level), 5 to 25 m (encompassing the majority of forest heights), and heights above 25 m (corresponding to tall trees). Each height class is weighted equally, in contrast to the previous MAE function, which was influenced by the training data distribution. Consequently, while there was a slight increase in MAE for lower heights, we observed a

decrease in MAE for higher heights in the validation dataset compared to previous studies (Schwartz et al., 2023). This weighting trade-off enabled us to maintain a relatively low MAE across all the height categories.

### 2.2.3. Height, biomass, and volume maps production

We applied the trained U-Net on S1 and S2 images from 2018 to 2024 and obtained one forest canopy RH<sub>95</sub> height map per year. To improve the reliability of the final products, we systematically carried out nine distinct predictions from the nine least cloudy images of the leaf-on season and computed their median value. We fully detailed the height map production process in Appendix E. Due to the SCL cloud mask and the RTC applied to S1 images, the final maps may not have data for small areas corresponding to buildings, lakes, or very steep terrain that we filled using bilinear inpainting. We converted the height maps to aboveground biomass (AGB) and growing stock volume (GSV) maps with empirical allometric power-law equations obtained using the French NFI data from 2018 to 2022. Half of the plot data was used for the calibration of these equations and the other half was used to evaluate the accuracy of the maps in the result section. We fitted one
height-AGB and one height-GSV power-law function per dominant leaf type (needleleaf/broadleaf) using a Huber regressor on the log values, which is less sensitive to outliers than a L2-based linear regression. These fits are illustrated in Appendix F. We obtained the following equations: $AGB_C = 1.27 \cdot H_C^{1.55}$, $AGB_B = 2.38 \cdot H_B^{1.39}$, $GSV_C = 0.99 \cdot H_C^{1.82}$, and $GSV_B = 1.36 \cdot H_B^{1.62}$, with B and C meaning broadleaf and coniferous. Then, we applied these equations to the height maps, using the Copernicus DLT map to separate coniferous and broadleaf forests. As the NFI plots have a 30 m diameter, and to avoid caveats related to too high resolution in biomass mapping (Duncanson et al., 2025), we produced the AGB and GSV maps at 30 m resolution by averaging the values obtained at 10 m resolution.

## 2.3. Additional definitions

**Disturbed pixels.** We define a disturbed pixel as a decrease in height of more than 5 m in a pixel time series that is persistent for at least two years. This decrease could be related to forest management practices such as clear-cuts, selective logging or natural events like pest attacks, fires, and storms. In the following results, disturbed pixels were removed from the calculation of aggregated growth metrics to avoid interfering with a potential height increase signal.

**Forest pixel.** For the whole study, we considered only pixels detected as forest by the IGN forest mask, to avoid working on other land cover types such as buildings.

**Metrics.** To assess the performance of the model compared to validation data, we used the widely accepted definition of the mean absolute error (MAE), and the determination coefficient ($r^2$) that measures the linear correlation between two datasets.

## 2.4. Time series post-processing

Although our training method was designed to be “year-agnostic”, some year-to-year variability persists in the generated forest height maps. We applied a post-processing procedure at the pixel level to address this issue and stabilize the resulting time series. This process was tailored based on whether or not a monotonic trend could be identified in the data. We used the Mann–Kendall statistical test (Kendall, 1948), which assesses the presence of consistent trends over time. Specifically, we computed the Mann–Kendall sum ($M_k = \sum_{i<j} \text{sign}(h_j - h_i)$) for each 7-year pixel-level time series spanning 2018–2024 across France. This approach allowed us to classify pixels into two categories: those exhibiting a significant monotonic trend ($|M_k| \ge 13$, $p < 0.05$) and those without a clear trend ($|M_k| \le 13$, $p < 0.05$). The corresponding p-values for the Mann–Kendall sum over a short time series were derived from the test statistic using a reference table (Table A18 in Gilbert (1987)). For the post-processing, we applied a three-year simple moving average (SMA) to pixels identified as having a monotonic trend and a five-year SMA to those without a significant trend. To manage the beginning and end of the time series (2018 and 2024) in the SMA, we first derived the 2017 and 2025 values based on the median slope given by the Theil–Sen estimator (Theil, 1950; Sen, 1968) and then applied the three-year SMA. Additionally, for disturbed pixels, we implemented a three-year SMA both preceding and following the disturbance year.

## 2.5. Growth curves

To derive species-specific growth curves presented in Section 3.5, we first computed the average growth per one-meter height class for all undisturbed pixels classified as a given category in the BD Forêt V2 dataset for all years relative to 2018 (Fig. 10 of the result section of this paper). This average growth per height class corresponds to the time derivative of the growth curve at a given height. By integrating the inverse of this quantity, we obtained growth curves per species (See Appendix G for additional details).

<caption>**Table 1**</caption>

FORMS-T error metrics when compared to the French NFI data for the 2018–2023 time period. The measurements from the 2024 NFI campaign were not yet available and could not be integrated into this table. The plots used to fit AGB and GSV equations were removed from the calculation. The last column shows the average metrics for all years.

<table><thead><tr><th>Metric</th><th>2018</th><th>2019</th><th>2020</th><th>2021</th><th>2022</th><th>2023</th><th>Average</th></tr></thead><tbody><tr><td>Height MAE (m)</td><td>3.11</td><td>3.01</td><td>3.01</td><td>3.04</td><td>3.07</td><td>3.18</td><td>3.07</td></tr><tr><td>Height r<sup>2</sup></td><td>0.67</td><td>0.69</td><td>0.69</td><td>0.68</td><td>0.69</td><td>0.67</td><td>0.68</td></tr><tr><td>GSV MAE (m<sup>3</sup> ha<sup>-1</sup>)</td><td>91.67</td><td>81.62</td><td>84.02</td><td>84.03</td><td>85.09</td><td>86.23</td><td>86.02</td></tr><tr><td>GSV r<sup>2</sup></td><td>0.39</td><td>0.41</td><td>0.42</td><td>0.41</td><td>0.40</td><td>0.38</td><td>0.40</td></tr><tr><td>AGB MAE (Mg ha<sup>-1</sup>)</td><td>67.20</td><td>61.72</td><td>63.59</td><td>64.27</td><td>65.26</td><td>66.21</td><td>65.11</td></tr><tr><td>AGB r<sup>2</sup></td><td>0.27</td><td>0.31</td><td>0.30</td><td>0.28</td><td>0.29</td><td>0.27</td><td>0.29</td></tr></tbody></table>

# 3. Results

## 3.1. Visual illustration

In Fig. 3, we illustrate the FORMS-T height predictions for 2018, 2021, and 2024 in four distinct forests distributed across the French territory. These include a maritime pine plantation in the Landes forest (Fig. 3.a), a Poplar plantation in Picardie (Fig. 3.b), a Larch forest in the Alps (Fig. 3.c) and a deciduous oak forest in Brittany (Fig. 3.d). The 2024–2018 column highlights the capability of our model to detect strong height losses in red, but also small height increases represented by blue areas. The height profiles drawn in the last column correspond to the segments visible on the map. They illustrate how our height time series behave following a spatial gradient across different nearby forest parcels. They highlight the difference in growth regimes between slow (larch, deciduous oaks) and fast-growing species (Poplar, maritime pines).

## 3.2. Validation with the French NFI dataset

For each year from 2018 to 2023, we compared our height estimates over France with NFI heights from ground measurements for the same year. This dataset was not used in the training process and therefore represents a completely independent source of validation data. As the 2024 French NFI campaign was not yet available, the validation for this year cannot be presented in this study. Results show stable performance metrics for the whole time series (Table 1). For dominant heights in the NFI, the average MAE for all years is 3.07 m, and the average $r^2$ value is 0.68, similar to previous studies focused on one year only for the same territory (Schwartz et al., 2023). The comparison with the GSV gives an MAE of 86 m$^3$ ha$^{-1}$ (43% of the mean NFI value), a $r^2$ of 0.40, and an average MAE of 65.1 Mg ha$^{-1}$ (42% of the mean NFI value), a $r^2$ of 0.29 for AGB, highlighting the difficulty of deriving accurate volume and biomass metrics from height and leaf type (Fig. 4).

## 3.3. Forest growth at pixel level

Forest height growth is a weak signal that is rarely above 50 cm per year, which makes it challenging to validate. We relied on two successive ALS campaigns in 2020 and 2022 covering more than 300,000 ha of forests in the Vosges site resampled at 10 m (by taking the maximum height) to have a correct growth estimation at this resolution. Fig. 5 shows a visual comparison of the maximum height difference between the two ALS campaigns, and the difference given by our time series. The height losses (corresponding to the red areas), likely due to forest clearcut for wood exploitation or sanitary reasons (e.g. bark beetle infestation), match the patterns observed in the ALS data. Even though the forest growth was evaluated over a short interval of 2 years, we found that the growth region (blue areas) matches quite well the ALS-derived growth areas. However, there is a tendency to overestimate the magnitude of the growth in our map compared to the ALS data.
<figure><img src="image_7.png" /><figcaption>**Fig. 3.** FORMS-T Forest height in 2018, 2021, and 2024; Google Maps © images; and the difference between 2024 and 2018. The last column shows the height profiles of the segment drawn on the maps. The four lines correspond to different tree species: (a) Maritime pines (44.54°N, -1.03°E) (b) Poplar plantation (49.72°N, 3.86°E) (c) Larches (44.98°N, 6.47°E) (d) Deciduous oaks (48.30°N, -3.61°E). Red pixels correspond to disturbance areas.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 4.** Height (a), GSV (b) and AGB (c) comparison between our maps and NFI plot measurements for the same years. For GSV and AGB, the plots used to fit the allometric equations were removed. The dashed line represents the 1:1 axis. Brighter colors indicate a higher density of points.</figcaption></figure>

**Fig. 6** illustrates the aggregated growth per height class given by our time series and by the ALS data in the Vosges site. For most height classes (10 m to 40 m), the median growth matches the ALS-derived growth. As observed previously (Fig. 5), compared to the ALS data, there is a slight tendency to overestimate the magnitude of the growth, except for the two lower height classes (0–5 m, 5–10 m).

To understand at which spatial scale our time series of annual dominant height is reliable to capture a clear growth signal, we compared this signal to the ALS-derived growth at several resolutions spanning from 10 m to 10 km in the Vosges region for trees in the 10–15 m height class (Fig. 7). We found the MAE of height change between 2020 and 2022 decreased from 0.82 m at 10 m resolution to 0.25 m at 10 km. The
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Comparison of height predictions and height differences for ALS data and FORMS-T in the Vosges site (48.54°N, 7.07°E). (a) Aerial image (2018) from the BD ortho dataset (IGN, 2018b), (b) ALS 2020 resampled at 10 m resolution by taking the maximum height within each pixel. (c) FORMS-T for 2020 (d) Difference between the 2022 and the 2020 ALS acquisition at 10 m resolution (e) Difference between the FORMS-T 2022 and 2020 predictions at 10 m resolution. Height gains and losses are shown in blue and red respectively.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Tree growth per height class in the Vosges site for ALS data and for our predictions. The median growth value is represented by a black line, while the lower and upper quartiles are represented by the lower and upper edges of the boxes, respectively. The whiskers symbolize the 5th and 95th percentiles. Disturbed pixels, corresponding to a height loss of more than 5 m were excluded from this calculation. The area covered by each class is represented by gray bars.</figcaption></figure>

ME, indicating the bias in the growth prediction, is stable through the aggregation process (0.19 m on average). There is almost no correlation at 10 to 100 m ($r^2$ < 0.1), while for coarser resolutions, the correlation increases up to a $r^2$ of 0.60 for aggregation at 5 km. The overestimation of some growth areas, visible in Fig. 5, are clearly outlined here in the shape of the scatter plots corresponding to a pixel size of 500 m and 1 km, where the ALS growth of about 1 m is overestimated for a large group of pixels.

### 3.4. Wood volume production at a regional scale

Mainland France encompasses various forests with complex structures, ages, different terrain conditions, and mixed species. Our GSV time series could help understand better the distribution of forest biological production in France. To evaluate this potential, we computed the mean wood volume production (WVP) for each SER (See Section 2.1.4), derived from the median slope of the time series (Theil-Sen
<figure><img src="image_11.png" /><figcaption>**Fig. 7.** Comparison of the tree height growth (Vosges site), between 2020 and 2022 in our time series and ALS at different resolutions (10 m to 10 km). Only pixels corresponding to trees in the 10–15 m class of height (according to the 2020 ALS measures) were taken into account here. For ALS, the 10 m resolution growth corresponds to the difference between the maximum height of 2020 and 2022 within a 10 m pixel. For coarser resolutions, the growth corresponds to the average of these 10 m growths within larger pixels. Brighter colors indicate higher density of points. The dashed black lines represent the 1:1 axis.</figcaption></figure>

estimator) and compared it to the gross wood volume production (See Section 2.1.4) given by NFI aggregated statistics (Fig. 8). Overall, aggregating FORMS-T map at regional level leads to a MAE of 1.45 m³ ha⁻¹ yr⁻¹ (r² = 0.59) when it comes to estimating the annual wood volume production. We observe an underestimation of the production in the north-western part of the country (Fig. 8.b), while mountainous regions and the south-western part of France as well as the Mediterranean basin are rather well estimated.

### 3.5. Growth curves

We propose here to aggregate our height time series at regional and national scales to highlight the different growth dynamics of French tree species. First, we used the FORMS-T map to analyze the height growth between 2018 and 2024 for 10⁶ forest pixels in the Landes forest, a 1 M ha maritime pine plantation in Southwestern France (Fig. 9.a). Except for disturbed pixels, we observe that most 2024 values are higher than their corresponding 2018 values, highlighting a growth signal at pixel level. For each 1-m height class and for each year we then computed the median of this height difference relative to 2018 (Fig. 9.b). Up to 25 m, these curves are well-ordered, indicating a consistency in the growth signal retrieved by FORMS-T maps.

We applied this aggregation process to large regions called “Grandes régions écologiques” (GRECOs, see Section 2.1.4) in Fig. 10, filtering pixels by tree species or groups of species as classified in the “BD Forêt V2” database (See Section 2.1.4). We observe large differences from one species to another, in terms of growth rate and growth pattern. Some species can grow more than 50 cm per year for lower height classes, such as Black locust, Poplar, or Maritime Pines, corresponding

to standard growth rates for these trees. For instance Burgess et al. (2005), found various growth rates for different Poplar hybrids and sites in England with a typical yearly growth value slightly above 1 m, which is consistent with the high growth rates observed for lower Poplar heights in Fig. 10. On the contrary, slow-growing species like Evergreen Oaks (in the Mediterranean area) do not show any signal of height increase for any height class. In addition to that, this figure highlights the different growing strategies of tree species that could be related to their different biological properties, or specific forest management practices. While species like Larch seem to have similar growth at any height above 10 m (0.18 m yr⁻¹ at 10 m and 0.22 m yr⁻¹ at 20 m), other species like Black Locust grow much faster when they are smaller with an average growth rate of 0.25 m yr⁻¹ at 10 m, and only 0.05 m yr⁻¹ at 20 m.

By integrating the data shown in Fig. 10, we derived height-age growth curves per species (See Appendix F). These FORMS-T growth curves correspond to the growth curves derived from the median yearly growth of our FORMS-T time series. Such height-age relationships provide insights in forest growth dynamics (Véga and St-Onge, 2009; Pellissier-Tanon et al., 2024). In Fig. 11, we show these curves and compare them to the height-age curves derived from NFI data. There is a good general agreement between the FORMS-T and the NFI data but with an underestimation of FORMS-T values. However, the curves derived from the 75th percentile growth match relatively well the NFI-derived growth curves for most species such as deciduous oak, Douglas fir and maritime pine. Other species with lower growth rates that are located in mountainous areas, such as larch, Austrian pine and evergreen oak, do not show good agreement with the NFI data.
<figure><img src="image_12.png" /><figcaption>**Fig. 8.** (a) Wood volume production per forest ecological regions from NFI official statistics (2018–2023) compared to the aggregated wood volume production from our maps (TheilSen slope of the GSV time series. Only positive values are taken into account as we compare it to the gross volume production). Gray segments represent the uncertainties associated with NFI values. Blue and red colors represent the estimation error. The total wood volume of the SER given by NFI statistics is reflected in dot sizes. (b) Visualization of the volume production error between our estimation and official NFI statistics, for each SER.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** (a) Comparison of the 2024 forest height values of 10⁶ pixels of the Landes forest with their values in 2018. Brighter colors indicate a higher density of points. The black line represents the median 2024 height value for each 1 m-height class of the x-axis. Only pixels with a height value higher than 3 m were considered here to avoid taking into account non-forest pixels. The red dots represent the pixels where a disturbance occurred in the time series and were excluded from the median calculation. (b) Median growth of all forest pixels per height class relative to 2018. The disturbed pixels (See Section 2.3) were excluded from the median calculation. The gray histogram shows the area covered per each height class.</figcaption></figure>

# 4. Discussion

## 4.1. A real year-agnostic model?

To retrieve forest height annual changes, one of this study's goals was to design a “year-agnostic” model. We mean here a model capable of predicting canopy height for any year with S1 and S2 images, independent of the period it was trained on. For this, we designed a deep learning training framework that takes individual S2 scenes as input, rather than the composite images used in most previous studies (Lang et al., 2023; Fayad et al., 2023; Pauls et al., 2024; Schwartz et al., 2024), with the underlying idea that the model will be

able to differentiate between real canopy height changes and artifacts caused by variability in reflectance due to S2 data variability as input. This is made possible by the large volume of training data, which captures a wide range of conditions related to phenology and short-term drought anomalies. These variations are implicitly filtered by the model as “noise”, allowing it to focus on extracting consistent annual height changes and enabling stable yearly predictions. The integration of radar (S1), optical (S2), and spaceborne LiDAR (GEDI) data allows us to exploit complementary information on forest structure, enhancing the reliability of forest attribute estimates across time. Despite this novel framework, we had to perform several actions to further stabilize the maps, like taking the median of nine predictions,
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Median growth per height class relative to 2018 of all forest pixels within a given region categorized per species (14 species or species group were selected here based on the classification provided in BD Forêt V2). Green and blue text indicate broadleaved and coniferous species, respectively. The letters after the species names correspond to the chosen region on the map in the bottom right.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Forest growth curves derived from the growth values obtained in Fig. 10. The dashed black lines represent NFI-derived growth curves. The letter after the species name corresponds to the region used to build the growth curve. The 75th growth derived from FORMS-T is highlighted with a blue line to show its correspondence to NFI-derived growth.</figcaption></figure>
from 9 different S1/S2 combinations, to get the map of a given year. Additionally, to enhance the coherence of the time series, we applied post-processing based on temporal moving averages that significantly improved the MAE from 3.41 m to 3.07 m, in comparison to NFI dominant heights across all years. This value can be considered as the uncertainty in the model prediction. Even though a deeper analysis of the propagation of uncertainties through the estimation process could be valuable, it falls beyond the scope of this study as it requires a complex methodology, especially for deep learning architectures. This reduction of the uncertainty with post-processing shows that FORMS-T is still partly influenced by the inherent variability of satellite images. A single image might not contain enough information to reliably retrieve height, suggesting that aggregating several acquisitions is the only way to obtain more accurate predictions. Previous studies on canopy height time series (Turubanova et al., 2023) had to apply similar post-processing rules to obtain consistent height time series. The aggregation process we used – taking the median prediction from the nine least cloudy images between May and September of a given year – has the advantage of providing a reliable snapshot of forest height for that year. However, as this method depends on the distribution of cloud-free days, the equivalent date of the resulting composite image may differ from one year to the next, and from one region to another. An alternative would be to restrict the time window in which the images are chosen, but there is a risk of not having enough images to create a cloud-free composite. Future improvement regarding forest time series mapping could be based on spatiotemporal deep learning models taking a time series as input to predict a consistent time series of canopy height. Some recent studies worked with spatiotemporal deep learning, like Dixon et al. (2025), who used Planet time series as input but only to predict a single canopy height map, or Ge et al. (2022) who used S1 time series to predict canopy height in boreal regions in Finland. However, to our current knowledge, no studies have designed a model capable of predicting a consistent time series from a time series of satellite images.

## 4.2. Retrieving forest growth from satellite images

Many recent studies aiming at forest height and biomass mapping with new RS data (GEDI, S1, S2, Planet, etc.) allowed an insight into the forest state for a given year (Lang et al., 2023; Pauls et al., 2024; Liu et al., 2023; Morin et al., 2023; Sothe et al., 2022; Tolan et al., 2024). Some other studies produced time series but mostly focused on applications related to height or biomass loss (Kacic et al., 2023; Hansen et al., 2013; Turubanova et al., 2023). However, simultaneously evaluating forest carbon losses and gains remains crucial to obtaining exhaustive forest carbon fluxes. The validation data for such assessments is difficult to obtain, especially because yearly forest height growth is a very weak signal (typically less than 1 m yr⁻¹). Visual observation of several sites (Fig. 3) clearly shows FORMS-T's capabilities to retrieve height growth, especially for fast-growing monospecific plantations like Poplar or Maritime Pines, which suggests that our product is capable of retrieving height growth at forest stand level. To obtain a quantitative validation, we used two successive ALS campaigns on the Vosges site (See Section 2.1.4). Even if ALS is a very precise tool, the two acquisitions were made with different devices, potentially leading to small differences in maximum height estimations. Here, we showed that our model was able to capture a consistent growth signal for aggregated areas (5 km), but not at the pixel level (Fig. 7). Aggregating the growth by height classes (Fig. 6) shows a consistent median growth compared to ALS data, except for lower height which could be related to training data used in FORMS-T, as GEDI-derived height is less reliable for low forest heights (Dubayah et al., 2020). A potential limitation arises from the fact that the ALS campaigns (2020: February–March, 2022: January–April) and the FORMS-T maps (based on May–September imagery) do not perfectly overlap in time. The FORMS-T growth estimate likely reflects mid-growing-season conditions, whereas the ALS data spans early-season measurements. As a result, both datasets approximately

cover two full growing seasons, but with temporal offsets that may introduce discrepancies in growth comparisons. To further assess the ability to capture a consistent growth signal, we used a species/groups of species database, the “BD Forêt V2”, and examined the median growth per height class (Fig. 10). We observed different growth patterns from one species to another, consistent with typical growth rate values. For instance, the high reduction of growth rate for Black locust between 10 m and 20 m observed in Fig. 10 is highlighted in Rédei et al. (2014) for Hungarian Black Locust stands, but with higher growth rates in general : ~0.7 m yr⁻¹ for 10 m trees and ~0.1 m yr⁻¹ for 20 m trees, with a high variability from one site to another. The aggregations performed here give a clue on a median growth rate that actually encompasses several underlying factors such as climate variability, intra-specific variability, forest management practices, or soil composition. Further analysis including these factors could contribute to better understanding forest growth regimes. Comparing the growth from FORMS-T GSV maps to the gross volume production from NFI data at the regional level revealed a slight underestimation of the productivity for most regions (Fig. 8), but a generally good agreement between satellite-based and field-based data at SER scale (r² = 0.59). As shown previously in Fig. 4, our maps tend to underestimate higher height, biomass, and volume values, which makes changes more easily detectable in the low end of the height distribution, thus explaining this underestimation. Furthermore, in older forests with a stable canopy height, the wood volume production mainly comes from the increment in tree diameter, which is not captured in our GSV time series as they were directly derived from height-based allometric equations. Additionally, forest inventory includes the recruitment of young lower trees that are not seen with satellites, especially in heterogeneous forests with mixed ages. This could explain the underestimations shown in Fig. 8. Conversely, we also observe overestimation in specific SERs located in mountainous areas. This could be due to terrain effects leading to higher height predictions and, consequently, overestimation of wood volume increments. This comparison is somehow limited as the gross production is not directly accessible from our maps, and we took only the positive growth values to obtain an indicator reasonably close to this definition.

While our results demonstrate the potential to detect forest height growth from satellite imagery after spatial aggregation, they also highlight ongoing limitations. The overall model accuracy (MAE = 3.07 m) remains higher than the magnitude of typical interannual height increments in temperate forests. As such, distinguishing small, real growth signals from noise is inherently challenging, especially at the pixel scale and in structurally complex stands. This reinforces the idea that while satellite-based growth monitoring is feasible, it still requires careful interpretation and some level of spatial or temporal aggregation to yield reliable results.

## 4.3. Species-specific growth curves

Understanding and analyzing forest growth curves is fundamental in forestry science, providing critical insights into tree development, forest dynamics, and ecosystem management. These curves, which depict the relationship between tree height and age are often modeled using well-established Sigmoid or asymptotic models like Chapman-Richards (Chapman, 1961; Richards, 1959), von Bertalanffy (von Bertalanffy, 1938), or Schumacher (Schumacher, 1939) as well as process-based models like the 3-PG model (Landsberg and Waring, 1997). The parameters of these growth curves strongly depend on environmental factors and can be very different from one site to another (Rédei et al., 2014). In Fig. 11, we derived growth curves from satellite data only, without using one of these models, by integrating the growth per height class as explained in Appendix G. Thus, our growth curves encompass a wide variety of sites for a given species/group of species in a given region which is reflected by the large difference between the 25th and the 75th percentile growth curve. Based on tree core samples of the
dominant trees of NFI plots, we could also reconstruct NFI height-age relationships and compare them to our growth curves. Interestingly, FORMS-T median growth curves largely underestimate the NFI-based ones, but the 75th percentile of our maps shows a strong agreement with NFI data. We presume that one of the reasons for this is that NFI height-age curves are derived from dominant trees of NFI plots while our curves are based on a median of all the pixels, thus not representing the same group of trees.

## 4.4. Toward satellite-based monitoring of biomass fluxes at high-resolution?

To mitigate anthropogenic CO₂ emissions, many countries' strategies rely on the capacity of their forest sinks. For instance, in France, the national strategy to reduce emissions relies on a yearly carbon absorption by forests of 116 MtCO₂eq yr⁻¹ in 2015 which accounts for 25% of the 457 MtCO₂eq emitted yearly (SNBC, 2020). However, recent studies relying on national forest inventory data showed a decline in European forest productivity in the past years (Hertzog et al., 2025; Tijerín-Triviño et al., 2025) partly in response to climate change. Coupled with increased mortality or stronger harvests, this could lead to forests becoming net carbon sources. The 7-year time series proposed in this study is particularly valuable for identifying trends in forest growth and could be used as a complementary data source to monitor forest carbon fluxes. Indeed, we showed that aggregating FORMS-T at a regional scale (Fig. 8) agrees well with NFI-based data in terms of wood volume production estimation. Satellite-based maps can be produced yearly and provide more up-to-date monitoring than NFI campaigns which need several years to obtain an estimation of forest biomass fluxes at selected locations. The ability to map forest growth, not only loss, is hence a critical step toward building a more comprehensive carbon budget. Additionally, we showed that aggregating FORMS-T at a lower resolution (5 km pixels, see Fig. 7) still brings a robust height growth signal, paving the way toward a possible evaluation of biomass fluxes at a much finer scale than countries or regions. However, many uncertainties remain, especially regarding the height to volume/biomass conversion, and further improvements are required to be confident about biomass flux estimation at a fine scale with satellite data. Indeed, we used allometric equations, based on power laws, to derive GSV and AGB from forest height (See Appendix F). The global MAE across all years when compared to NFI data represents 42% of the average value for AGB, and 43% for GSV, while it is only 16% for height, which highlights this lower reliability of our AGB and GSV maps. Even though the dominant tree height is a main driver of tree biomass, other key parameters are involved, such as diameter, stand structure, tree species, and wood density, which can vary a lot from one tree to another, even within the same species (Cuny et al., 2025).

Beyond their indispensable role in carbon monitoring, forest growth and biomass accumulation are also relevant indicators for biodiversity conservation. Studies have shown that forest structure and above-ground biomass are often positively associated with species richness and habitat quality (Singh et al., 2017; Dyola et al., 2022; Torresani et al., 2023). By enabling spatially and temporally explicit monitoring of these structural attributes, the FORMS-T product could support biodiversity assessments in protected areas such as the Natura 2000 network, where maintaining habitat complexity is a key management objective. Moreover, when combined with disturbance data, such as the European Forest Disturbance Atlas (Viana-Soto and Senf, 2025), repeated estimations of biomass or canopy height from FORMS-T can support the inference of ecological resilience (the capacity to recover) and resistance (the ability to withstand change) in response to perturbations. Thus, while primarily designed for forest dynamics and carbon flux monitoring, our approach also provides valuable data for assessing broader ecological properties.

## 4.5. Forest disturbances

This study mainly focused on the capacity of FORMS-T to capture forest growth. However, our product can also estimate forest losses after natural disturbances or forest cuts for wood exploitation. As an illustration, Fig. 12 shows the evolution of forest height in the old-growth forest of “La Teste de Buch”, which underwent a severe fire event in 2022 (Gil, 2022). The 2022 prediction shows the height before the fire. Interestingly, the 2023 and 2024 images are very different. Indeed, although the fire was over in 2023, some dead trees were still standing. On the contrary, in 2024, most of the forest disappeared due to salvage logging to minimize the loss of commercial timber.

More generally, knowing the precise location and time of a forest clearcut could help understand better forest's harvesting regimes (Su-vanto et al., 2025) and monitor forest management at the tree stand level. Existing studies already propose such disturbance maps, such as the Sufosat project in France (Mermoz et al., 2024), and FORMS-T maps could bring a supplementary source of information to these datasets.

## 4.6. Performance across diverse forest ecosystems and applicability to other regions

While FORMS-T was developed and evaluated only in France, it still covers a high level of ecological and structural forest diversity. France encompasses a wide range of climatic zones (oceanic, Mediterranean, continental, and alpine), forest types (broadleaf, coniferous, and mixed), and management practices. This diversity results in a wide variety of canopy structures, stand compositions, and successional stages. We assessed the model's performance across different forest ecosystems by analyzing the MAE per SER, as compared to NFI's height measurements over multiple years (Fig. 13). These SERs reflect ecologically and structurally distinct forest units. Results show that the model performs best in flat, homogeneous regions such as the Landes forest in southwestern France, which is dominated by monospecific maritime pine plantations. In contrast, error rates are higher in topographically varied regions that host more complex forests, such as the Alps, Pyrenees, and Massif Central. These findings are consistent with those of Besic et al. (2025), who observed increased prediction uncertainty in steep terrain.

Several studies support the view that France's forests are structurally comparable to many temperate ecosystems globally. For instance, Ehbrecht et al. (2021) evaluated forest structural complexity worldwide and found that France exhibits a comparable or higher degree of complexity to other temperate regions. Similarly, de Conto et al. (2024) introduced the Waveform Structural Complexity Index (WSCI), derived from GEDI LiDAR data, showing that French forests rank among the most structurally diverse in temperate biomes. These findings suggest that the methodology presented here is likely applicable to many forested regions beyond France, particularly in other temperate or boreal environments. Tropical forests, despite their major importance, are outside the scope of this study. Adapting the FORMS-T framework for these ecosystems would require further research, especially due to the high cloud coverage and a limited amount of GEDI data over these areas. Nevertheless, recent studies using deep learning and similar satellite data sources (Lang et al., 2023; Pauls et al., 2024) have shown promising results in canopy height mapping over these areas, which suggests that similar methods could eventually be extended to these biomes.

# 5. Conclusion

We developed a methodology using a deep learning model to produce FORMS-T: a consistent times series (2018–2024) of forest height (10 m), growing stock volume (30 m), and aboveground biomass (30 m) over France from satellite imagery (S1, S2) and spaceborne LiDAR data (GEDI). Contrary to previous studies, we focused our analysis on forest
<figure><img src="image_16.png" /><figcaption>Fig. 12. FORMS-T canopy height in the “La Teste de Buch” forest (44.57°N, -1.18°E) in 2022, 2023 and 2024. A huge fire occurred in this area in July 2022.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 13. Mean absolute error between FORMS-T canopy height predictions and NFI-measured heights for each Sylvoécorégion over the 2018–2024 period. The color scale is centered on the national average MAE of 3.07 m. Regions shown in green indicate better-than-average model performance, while those in purple indicate higher errors. The Landes forest (monospecific plantation of maritime pines) is highlighted with a black border.</figcaption></figure>

growth rather than forest losses, introducing a novel framework that includes individual S2 scenes training and trend-aware temporal post-processing. We showed visual examples suggesting FORMS-T can detect a yearly forest height growth signal at the 10 m pixel level, especially in monospecific plantations. However, quantitative validation using ALS data shows that the growth signal is more robust and reliable when aggregated at coarser resolution (~5 km), especially in structurally complex forests. We have demonstrated several applications of our maps, including the derivation of species-specific growth curves, the estimation of regional wood volume production, and the ability to detect biomass losses. Further development of such maps will open up the possibility of annual forest carbon budgets, taking into account both losses (disturbance, timber exploitation, natural mortality) and gains

(forest growth), and contribute to appropriate forest management to meet countries' emission reduction commitments.

### CRediT authorship contribution statement

**Martin Schwartz:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Philippe Ciais:** Writing – review & editing, Writing – original draft, Supervision, Methodology, Funding acquisition, Conceptualization. **Ewan Sean:** Writing – review & editing, Resources, Methodology, Data curation. **Aurélien de Truchis:** Writing – review & editing, Resources, Methodology, Data curation. **Cédric Vega:** Writing – review & editing, Validation. **Nikola Besic:** Writing – review & editing, Validation. **Ibrahim Fayad:** Writing – review & editing, Methodology. **Jean-Pierre Wigneron:** Writing – review & editing, Conceptualization. **Sarah Brood:** Writing – review & editing. **Agnès Pelissier-Tanon:** Writing – review & editing, Methodology. **Jan Pauls:** Writing – review & editing, Methodology. **Gabriel Belouze:** Writing – review & editing, Methodology. **Yidi Xu:** Writing – review & editing.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This work is supported by the PEPR FairCarboN which is funded by the French national agency for research. We are grateful to Jean Pierre Renaud (ONF) for providing us with the Vosges ALS data of 2020 and to Catherine Ottlé (LSCE) for her feedbacks at the early stage of this work.

## Appendix A. GEDI filters

Some studies suggest using several filters such as keeping only night acquisitions from full power beams to ensure high GEDI data quality (Li et al., 2024). Here, we tested a different approach that consists of filtering the waveforms based on their difference from the FORMS-H map (Schwartz et al., 2023), a 10 m resolution height map in France obtained in a previous study. Although the FORMS-H
<figure><img src="image_18.png" /><figcaption>**Fig. A.14.** Comparison between FORMS-H height (m) and GEDI RH<sub>95</sub> height on a subset of 1 M footprints in France. The red footprints correspond to the waveforms that were filtered out from the GEDI dataset to improve the reliability of our training data.</figcaption></figure>

map cannot serve as a perfect reference height dataset, we considered
that a significant discrepancy between the generated map and a GEDI
measurement could be attributed to errors in the GEDI data or to a
temporal difference between GEDI and the reference FORMS-H map.
Therefore, we chose to apply the two following filters: The absolute
difference between the GEDI RH<sub>95</sub> height and the FORMS-H height
should be less than 15 m (|RH<sub>95</sub> - FORMS - H| < 15 m). A cus-
tomized version of the normalized difference should be less than 4,
as given by $\frac{|RH_{95}-FORMS-H|}{\min(RH_{95},FORMS-H)-1.5} < 4$. This condition reinforces the
filtering constraints for lower heights and enables the removal of most
outliers related to clearcut or geolocation errors. These conditions were
based on visual interpretations of the GEDI-FORMS-H scatterplot (Fig.
A.14). The objective was to remove obvious outliers and enhance the
reliability of the dataset. After applying all the filters mentioned above,
we obtained a dataset of 67,355,565 footprints, which accounts for 29%
of all the raw downloaded waveforms.

**Appendix B. UTM zones and tiles used in the study**

See Fig. B.15.

**Appendix C. Vosges ALS site**

See Fig. C.16.

**Appendix D. Model architecture**

See Fig. D.17.

**Appendix E. Height maps production**

We detail below and in Fig. E.18 the production process of FORMS-T
height maps: 1. We divided France into a finer grid of 10 km × 10 km,
which offered the advantage of having less cloudy S2 images. We intro-
duced an 8-pixel overlap between the tiles, resulting in tiles measuring
1016 × 1016 pixels rather than 1000 × 1000 pixels. During the final
merging process, this overlap will be used to create a smooth transition
between tiles and mitigate the edge effect inherent to CNN models that
come from the convolution operation. We then followed steps 2 to 5 for
each year and each individual tile: 2. Random selection of one available

<figure><img src="image_19.png" /><figcaption>**Fig. B.15.** France UTM zones 32630 (blue), 32631 (white), 32632 (red), and 20 × 20 km tiles used to download the data used in this study.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. C.16.** Location of the ALS Vosges site (red). The background layer represents ground elevation (SRTM30 Colored Hillshade, Terrestris GmbH).</figcaption></figure>

S1 orbit and computation of the mean of all available images from the
Ground Range Detected (GRD) product between May and September
after applying the Radiometric Terrain Correction (RTC), similar to
the training dataset. 3. Selection of the nine least cloudy S2 images
(based on the SCL band) from the L2 A product between May and
September. 4. Generation of nine height predictions with our trained
U-Net model based on these nine images combined with the S1 mean
image. 5. Calculation of the median of the nine height predictions to
reduce the variability. 6. Merging of the tiles for each UTM zone by
taking a weighted mean of the overlapping pixels, with the weights
decreasing linearly as they approached the tile's border. Reprojection
of the products to the French coordinate system (Lambert 93, EPSG:
2154) using the bicubic interpolation algorithm implemented in the
gdal library (GDAL/OGR contributors, 2025) and final merge between
the three UTM zones with a weighted mean for overlapping pixels.

**Appendix F. Height-GSV and height-AGB allometric equations**

See Fig. F.19.
<figure><img src="image_21.png" /><figcaption>Fig. D.17. U-Net model architecture similar to the one used in a previous study (Schwartz et al., 2024) but with six input channels instead of fourteen.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>Fig. E.18. Workflow showing the production of the final maps. The numbers with a black background correspond to the steps described in the text.</figcaption></figure>

## Appendix G. Growth curves computation

Classical forestry science models height-age relationships using parametric functions such as the Chapman-Richards (Chapman, 1961; Richards, 1959), Schumacher (Schumacher, 1939), or von Bertalanffy (von Bertalanffy, 1938) models, which describe growth patterns based

on physiological assumptions. In contrast, our method is fully data-driven: we compute the mean annual height increment per height class from FORMS-T and numerically integrate the inverse to reconstruct height-age growth curves. While our approach does not rely on predefined parametric models, it follows a similar logic in that the derived growth curve reflects the progressive development of forest height over time.
<figure><img src="image_23.png" /><figcaption>Fig. F.19. Height-GSV and height-AGB allometric equations (red) fitted with a Huber regressor for deciduous (left) and coniferous (right) NFI plots (2018–2022) compared to our FORMS-T height for the same years. Only the 50% of NFI plots used to obtain the allometric relationships are represented.</figcaption></figure>

If g is the growth curve function for a specific species or group of species:

$$g(a) = h \qquad (G.1)$$

with a being age, and h height, then its inverse function $g^{-1}$ is the function that returns the age, given the height. The mean growth per height class obtained with FORMS-T maps is a function that returns the height growth in one year, given the height, and that could be written as $g'og^{-1}$ with ◦ being the composition operator that operate such as $g'og^{-1}(h) = g'(g^{-1})(h)$.

The following steps details how we can retrieve g by knowing $g'og^{-1}$:

Because g and $g^{-1}$ are inverse functions, their composition is the identity function and their derivative is 1:

$$(gog^{-1})' = 1 \qquad (G.2)$$

After applying the chain rule (the derivative of the composition of two differentiable functions), we obtain:

$$g'og^{-1} \cdot g^{-1}' = 1 \qquad (G.3)$$

and then:

$$g^{-1}' = \frac{1}{g'og^{-1}} \qquad (G.4)$$

By integrating the inverse of the growth per height class obtained with FORMS-T maps $g'og^{-1}$, we thus obtained $g^{-1}$ and therefore g, the growth curve function for each species or group of species.

$$g^{-1}(h) = \int_{0}^{h} \frac{1}{(g'og^{-1})(x)} dx \qquad (G.5)$$

because $g^{-1}(0) = 0$ as trees with a height of 0 have an age of 0.

## Data availability

The FORMS-T canopy height, AGB, and GSV time series (2018–2024) at 10 and 30 m resolution in France are freely available under the CC BY 4.0 license via Zenodo: https://zenodo.org/records/15489231. GEDI L2a data used in this study were downloaded from the NASA earthdata search website (https://search.earthdata.nasa.gov/search). Sentinel-1 and Sentinel-2 images were accessed from AWS registry of open data https://registry.opendataAWS/sentinel-1 and https://registry.opendataAWS/sentinel-2L2a-cogs/. The French NFI aggregated statistics were obtained from the official computation service (OCRE, https://ocreg-gp.ign.fr/ocregp/), while map validation was performed at plot level by the authors.

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