Probabilistic NDVI Forecasting from Sparse Satellite Time Series and Weather Covariates

TL;DR

This work tackles short-term NDVI forecasting under sparse, irregular clear-sky satellite observations by introducing a transformer-based probabilistic framework with decoupled history and future encoders. It outputs multi-step NDVI quantiles up to $h=14$ days ahead and incorporates cumulative and extreme-weather covariates alongside robust data interpolation and horizon-aware loss weighting. Across European data, the method consistently outperforms statistical and deep-learning baselines on both point forecasts and uncertainty quantification, with ablations confirming the primacy of target history and benefits from multimodal covariates. The approach offers a practical, scalable tool for precision agriculture, delivering calibrated predictions and favorable compute-performance trade-offs, and sets the stage for climate-zone and crop-type conditioned generalization.

Abstract

Accurate short-term forecasting of vegetation dynamics is a key enabler for data-driven decision support in precision agriculture. Normalized Difference Vegetation Index (NDVI) forecasting from satellite observations, however, remains challenging due to sparse and irregular sampling caused by cloud coverage, as well as the heterogeneous climatic conditions under which crops evolve. In this work, we propose a probabilistic forecasting framework specifically designed for field-level NDVI prediction under clear-sky acquisition constraints. The method leverages a transformer-based architecture that explicitly separates the modeling of historical vegetation dynamics from future exogenous information, integrating historical NDVI observations with both historical and future meteorological covariates. To address irregular revisit patterns and horizon-dependent uncertainty, we introduce a temporal-distance weighted quantile loss that aligns the training objective with the effective forecasting horizon. In addition, we incorporate cumulative and extreme-weather feature engineering to better capture delayed meteorological effects relevant to vegetation response. Extensive experiments on European satellite data demonstrate that the proposed approach consistently outperforms a diverse set of statistical, deep learning, and recent time series baselines across both point-wise and probabilistic evaluation metrics. Ablation studies further highlight the central role of target history, while showing that meteorological covariates provide complementary gains when jointly exploited. The code is available at https://github.com/arco-group/ndvi-forecasting.

Figures (3)

• Figure 1: Overview of the proposed pipeline for probabilistic NDVI forecasting. (a) Sentinel-2 cubes are cloud-masked to derive clear-sky NDVI, combined with meteorological series and engineered features; future covariates are perturbed to model forecast uncertainty. (b) Transformer-based probabilistic forecasting architecture with decoupled history and future branches. Historical observations are encoded through a dedicated transformer encoder and aggregated via temporal average pooling. Future meteorological covariates are processed by a separate transformer encoder; due to irregular satellite revisit times, sparse temporal selection retains only embeddings corresponding to actual Sentinel-2 acquisition dates. The pooled history representation is concatenated with the selected future embeddings and passed to a quantile prediction head, which outputs multi-step NDVI quantiles at $q \in \{0.1, 0.5, 0.9\}$, providing both point forecasts and calibrated uncertainty estimates.
• Figure 2: Ground truth versus predicted NDVI by aggregated Köppen–Geiger climate group. The gray dashed line shows the 1:1 reference, and the red line shows the linear fit.
• Figure 3: Comparison of forecasting models in terms of RMSE (y-axis, lower is better) and parameter count in millions (x-axis, log scale; lower is better). Bubble size denotes inference cost (MFLOPs, batch size 1). The arrow highlights the desirable region (low RMSE with smaller models)