  % �� allows [H] placement
\newcommand{\uniformtablesize}{
  \small
  \renewcommand{\arraystretch}{1.15}
  \setlength{\tabcolsep}{5pt}
}

\section{Results and Discussion}
\paragraph{Pretrained Models.}
We use four modality-specific encoders, each pretrained independently to capture domain-relevant spatial and spectral features: 
(i) Sentinel-2 (S2) optical imagery for vegetation and land-cover representation; 
(ii) Sentinel-1 (S1) radar backscatter for surface roughness and soil moisture estimation; 
(iii) Climate gridded meteorological variables for long-term environmental context; and 
(iv) PlanetScope (P) high-resolution imagery for fine-scale texture details. 
All encoders are trained using self-supervised objectives on their respective datasets and later used for downstream evaluation. 
S2 and P correspond to Spectral-MAE models, S1 to the BYOL-Denoise model, and Climate to the Climate-MAE. 
Pretraining performance for all encoders is summarized in Table~\ref{tab:pretrain_metrics_combined}.


\begin{table}[h]
\centering
\caption{Validation reconstruction metrics across modalities and embedding dimensions (32, 64, 128). 
Metrics are computed on held-out validation data for each modality.}
\label{tab:pretrain_metrics_combined}
\resizebox{\linewidth}{!}{
\begin{tabular}{lcccccc}
\toprule
\textbf{Model} & \textbf{Dim} & \textbf{Bands} & \textbf{R$^2$} $\uparrow$ & \textbf{F1} $\uparrow$ & \textbf{MSE} $\downarrow$ & \textbf{MAE} $\downarrow$ \\
\midrule
\multirow{3}{*}{S2} 
 & \textbf{32}  & 10 & 0.9671 & 0.9764 & 0.00080 & 0.0128 \\
 & 64  & 10 & 0.9237 & 0.9455 & 0.0022  & 0.0245 \\
 & 128 & 10 & 0.9215 & 0.9475 & 0.0022  & 0.0250 \\
\cmidrule(lr){1-7}
\multirow{3}{*}{S1} 
 & \textbf{32}  & 2  & 0.9245 & 0.9444 & 0.0305 & 0.0291 \\
 & 64  & 2  & 0.9199 & 0.9389 & 0.0196 & 0.0213 \\
 & 128 & 2  & 0.9267 & 0.9290 & 0.0240 & 0.0242 \\
\cmidrule(lr){1-7}
\multirow{3}{*}{P} 
 & \textbf{32} & 8  & 0.9616 & 0.9500 & 0.00057 & 0.0101 \\
 & 64  & 8  & 0.9289 & 0.9436 & 0.0010  & 0.0151 \\
 & 128 & 8  & 0.9389 & 0.9398 & 0.0009  & 0.0147 \\
\cmidrule(lr){1-7}
\multirow{3}{*}{Climate} 
 & \textbf{32}  & 4  & 0.9201 & 0.9799 & 0.0137  & 0.0354 \\
 & 64  & 4  & 0.8275 & 0.9650 & 0.0263  & 0.0713 \\
 & 128 & 4  & 0.7521 & 0.9669 & 0.0371  & 0.0894 \\
\bottomrule
\end{tabular}}
\end{table}

\noindent
The 32-dimensional embeddings deliver consistently strong performance across all modalities. Consequently, all experiments adopt 32-dimensional embeddings for efficiency. For spectral modalities (S2 and P), incorporating band metadata, central wavelength and FWHM into the spectral meta-embedding is empirically beneficial rather than heuristic: for S2, R$^2$ improves from 0.8682 to 0.9671, and for P from 0.9349 to 0.9616. Unlike unified multimodal models with shared attention, our modular pretraining independently optimizes each modality for domain-specific spectral and spatial features, producing compact, well-aligned representations without higher-dimensional overhead.  Table~\ref{tab:param_counts} reports trainable parameters and FLOPs per forward pass for this configuration, highlighting the lightweight yet expressive design of all encoders, with Spectral-MAEs remaining below 6.5M FLOPs.
\vspace{8pt}
\begin{table}[h]
\centering
\scriptsize
\caption{Computational and architectural complexity of modality-specific encoders.  
Reported for the final pretrained models used in multimodal fusion experiments.  
The notation 6E–3D indicates a Transformer architecture with 6 encoder layers and 3 decoder layers.}
\label{tab:param_counts}
\setlength{\tabcolsep}{9pt}
\renewcommand{\arraystretch}{1.15}
\begin{tabular}{lccc}
\toprule
\textbf{Model} & 
\shortstack{\textbf{Architecture}\\\textbf{Type}} & 
\shortstack{\textbf{Trainable}\\\textbf{Parameters}} & 
\shortstack{\textbf{FLOPs}\\\textbf{(In millions)}} \\
\midrule
S2 & Transformer (6E–3D) & 1,277,473 & 6.481 \\
P & Transformer (6E–3D) & 1,277,473 & 5.263 \\
Climate  & Transformer (6E–3D) & 1,673,345 & 3.944 \\
S1 & ViT + MLP Denoiser  &   116,226 & 0.299 \\
\bottomrule
\end{tabular}
\end{table}
\vspace{2pt}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%  Udaiveer   %%%%%%%%%%%%%%%%
% \subsection{Finetuning with MLP Head}
% To evaluate the discriminative capability of multimodal representations, we fine-tune a lightweight classifier on frozen encoder embeddings extracted from pretrained models. For every configuration, the \textbf{best-performing checkpoint weights} are loaded, the encoder is instantiated, and its output embeddings are extracted to serve as fixed input features to the classifier. The classifier is trained using \textbf{AdamW} (learning rate $3{\times}10^{-4}$, weight decay $5{\times}10^{-4}$) with a label-smoothed cross-entropy loss (smoothing $=0.05$), dropout $=0.1$, and $100$ training epochs. The batch size $=128$ is kept identical across all runs, and evaluation is performed on a held-out test split to ensure consistent comparison across model variants.

% \paragraph{Balanced sampling and modality control.}
% Each experimental setting uses class-balanced sampling to remove bias across categories. For the 50,000-sample dataset, we allocate a \textbf{minimum of 5,000 samples per class}, ensuring that all classes are equally represented. Moreover, all comparisons between models are conducted under \emph{modality-matched conditions}. For example, if a baseline model uses S1, S2, and E modalities, the same combination is used for our Fusion model.

% \subsubsection{Concatenative Modality Fusion}
% Concatenation fusion provides a strong baseline, with clear performance scaling as additional modalities are introduced. Models trained with all available modalities consistently outperform those using fewer inputs, validating the complementary nature of radar, optical, climate, and topographic features. However, the linear fusion scheme lacks explicit inter-modality interaction, motivating attention-based alternatives.  
% Table~\ref{tab:fusion_results} summarizes the fine-tuning performance across different modality subsets using 50,000 samples.

% \subsubsection{Cross Attention-Based Modality Fusion}
% To model dependencies between sensing modalities, we extend the fusion layer with cross-attention, allowing each modality’s embedding to query and aggregate information from others. Cross-attention yields consistent improvements, particularly in the presence of CLS tokens, showing its ability to compensate for weaker modality-specific supervision as presented in table 3. For the largest setup (50k samples with all modalities), accuracy reaches \textbf{86.28\%} (CLS) and \textbf{83.51\%} (w/o CLS).

% % \begin{table}[H]
% % \centering
% % \small
% % \caption{Evaluation with missing modalities. Accuracy is reported when individual modalities (Sentinel-2, Sentinel-1, PlanetScope, or Climate) are removed at test time. The model maintains stable performance due to the learned zero-slot tokens and binary presence masking used in the fusion transformer.}

% % \label{tab:fusion_results}
% % \resizebox{\linewidth}{!}{
% % \begin{tabular}{lccccc}
% % \toprule
% % \textbf{Model} & \textbf{Modalities} & \textbf{Samples} & \textbf{Fusion Method} & \shortstack{\textbf{Accuracy (\%)}\\\textbf{with CLS}} & 
% % \shortstack{\textbf{Accuracy (\%)}\\\textbf{without CLS}} \\
% % \midrule
% % Spear & S2 & 50000 & Concatenation & 67.77 & 75.84 \\
% % Spear & S2 & 50000 & Cross-Attention & \textbf{67.92} & \textbf{78.15} \\
% % Spear & S1, S2 & 50000 & Concatenation & 75.60 & 73.67 \\
% % Spear & S1, S2 & 50000 & Cross-Attention & \textbf{79.73} & \textbf{79.68} \\
% % Spear & S1, S2, Climate & 50000 & Concatenation & 85.76 & 79.85 \\
% % Spear & S1, S2,  Climate & 50000 & Cross-Attention & \textbf{86.00} & \textbf{83.66} \\
% % Spear & S1, S2, P, Climate & 50000 & Concatenation & 86.16 & 82.02 \\
% % Spear & S1, S2, P, Climate & 50000 & Cross-Attention & \textbf{86.28} & \textbf{83.51} \\
% % \bottomrule
% % \end{tabular}}
% % \vspace{0mm}
% % \end{table}

% The cross-attention fusion consistently outperforms both concatenation and unimodal baselines under identical input conditions. Gains are most evident when additional non-optical modalities (e.g., radar, climate, and elevation) are present, confirming the model’s ability to exploit complementary spectral and geophysical cues. Balanced sampling ensures that improvements are not driven by class imbalance but by genuinely stronger feature generalization. These results demonstrate that the proposed Fusion framework, especially when equipped with cross-attention, serves as a robust and scalable backbone for multimodal understanding in remote sensing.



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% \subsection{Finetuning with Random Forest Head}
% % Anjali

% The Random Forest (RF) classifier was employed as the downstream head to evaluate the discriminative quality of the learned feature embeddings.  
% They are particularly effective for heterogeneous feature spaces, making them suitable for fused multi-modal embeddings.  
% For this experiment, we used the following hyperparameters: \texttt{N\_ESTIMATORS = 500}, \texttt{MAX\_DEPTH = 35}, \texttt{MIN\_SAMPLES\_SPLIT = 2}, \texttt{MIN\_SAMPLES\_LEAF = 1}, \texttt{MAX\_FEATURES = 'sqrt'}, and \texttt{N\_JOBS = -1}.  
% These settings were chosen to ensure a balance between computational efficiency and classification accuracy across varying modality combinations.


% % \begin{table}[H]
% % \small
% % \centering
% % \caption{Ablation study of Random Forest downstream classification accuracy (\%) using different modality combinations and fusion strategies. The number of data points for each class (k).}
% % \label{tab:downstream_ablation}
% % \resizebox{\linewidth}{!}{
% % \begin{tabular}{lcccc}
% % \toprule
% % \textbf{Model Combination} & \textbf{Data Points (k)} & \textbf{Concatenation (\%)} & \textbf{Cross-Attention (\%)} \\
% % \midrule
% % S2 & 5000 & 82.00 & 82.38 \\
% % S2 + Climate & 5000 & 89.97 & 88.62 \\
% % S2 + S1 + Climate & 5000 & 90.13 & \textbf{88.82} \\
% % S2 + S1 + P + Climate  & 5000 & \textbf{90.23} & 84.40 \\
% % \bottomrule
% % \end{tabular}}
% % \end{table}

% \begin{table}[H]
% \centering
% \caption{Comparison of fusion strategies across model types (RF and MLP).}
% \label{tab:fusion_results_combined}
% \resizebox{\linewidth}{!}{
% \begin{tabular}{llccc}
% \toprule
% \textbf{Model Type} & \textbf{Model / Combination} & \textbf{Data Points (k)} & \textbf{Concatenation (\%)} & \textbf{Cross-Attention (\%)} \\
% \midrule
% \multirow{4}{*}{\textbf{MLP}} 
%  & S2 & 5000 & 75.84 & \textbf{78.15} \\
%  & S2 + Climate & 5000 & 73.67 & \textbf{79.68} \\
%  & S2 + S1 + Climate & 5000 & 79.85 & \textbf{83.66} \\
%  & S1 + S2 + P + Climate & 5000 & 82.02 & \textbf{83.51} \\
% \cmidrule(lr){1-5}
% \multirow{4}{*}{\textbf{RF}} 
%  & S2 & 5000 & 82.00 & 82.38 \\
%  & S2 + Climate & 5000 & 89.97 & 88.62 \\
%  & S2 + S1 + Climate & 5000 & 90.13 & \textbf{88.82} \\
%  & S2 + S1 + P + Climate & 5000 & \textbf{90.23} & 84.40 \\
% \bottomrule
% \end{tabular}}
% \end{table}



% \noindent
% \textbf{Summary.}  
% From Table~\ref{tab:downstream_ablation}, it can be observed that the concatenation-based fusion strategy achieves slightly higher accuracy than cross-attention across most modality combinations. The best performance of \textbf{90.23\%} was obtained when all four modalities (\textit{S2, S1, Climate, and Planet}) were fused, highlighting that even a lightweight Random Forest classifier can effectively leverage complementary spectral and radar information in a sample-efficient manner.
\subsection{Fusion-Based Classification}
We evaluate the discriminative capability of multimodal embeddings using two classifier heads a lightweight Multi-Layer Perceptron (MLP) and a Random Forest (RF) under both concatenation and cross-attention fusion strategies.

\subsubsection{Classification with MLP Head}
\label{subsec:mlp_head}
A lightweight MLP classifier is trained on top of frozen encoder embeddings from the best pretrained checkpoints. Training uses AdamW (learning rate $3{\times}10^{-4}$, weight decay $5{\times}10^{-4}$), label-smoothed cross-entropy loss ($\epsilon{=}0.05$), dropout $0.1$, batch size $128$, and runs for $100$ epochs with balanced class sampling. As shown in Table~\ref{tab:fusion_results_combined}, cross-attention consistently surpasses concatenation, confirming its ability to enhance inter-modality interactions even with a small classifier.

\subsubsection{Classification with Random Forest Head}
A Random Forest (RF) head evaluates the generality of the learned embeddings, leveraging its robustness to heterogeneous fused features. The results in Table~\ref{tab:fusion_results_combined} indicate that concatenation-based fusion slightly outperforms cross-attention for most modality combinations, with a peak accuracy of 90.23\% when all four modalities (\textit{S2, S1, Climate, Planet}) are fused. Overall, concatenation tends to suit non-parametric models like RF, whereas cross-attention is more effective with parametric heads such as the MLP.

\begin{table}[h]
\centering
\small
\caption{Comparison of fusion strategies across different classification heads (MLP and RF).
Each configuration uses balanced samples across eight classes. 
Accuracy values (\%) are reported for both concatenation and cross-attention strategies.}
\label{tab:fusion_results_combined}
\resizebox{\linewidth}{!}{
\begin{tabular}{llccc}
\toprule
\textbf{Head} & 
\textbf{Modalities} & 
\textbf{Samples} & 
\shortstack{\textbf{Accuracy (\%)}\\\textbf{with Concatenation}} & 
\shortstack{\textbf{Accuracy (\%)}\\\textbf{with Cross-Attention}} \\
\midrule
\multirow{4}{*}{\textbf{MLP}} 
 & S2 & 5000 & 75.84 & \textbf{78.15} \\
 & S2 + Climate & 5000 & 73.67 & \textbf{79.68} \\
 & S2 + S1 + Climate & 5000 & 79.85 & \textbf{83.66} \\
 & S1 + S2 + P + Climate & 5000 & 82.02 & \textbf{83.51} \\
\cmidrule(lr){1-5}
\multirow{4}{*}{\textbf{RF}} 
 & S2 & 5000 & \textbf{82.38} & 82.00 \\
 & S2 + Climate & 5000 & \textbf{89.97} & 88.62 \\
 & S2 + S1 + Climate & 5000 & \textbf{90.13} & 88.82 \\
 & S2 + S1 + P + Climate & 5000 & \textbf{90.23} & 84.40 \\
\bottomrule
\end{tabular}}
\end{table}

\vspace{6pt}
\noindent

\subsection{Comparison with Benchmark Models (MLP Head)}
To ensure a fair assessment, we further compare our multimodal fusion results against existing pretrained models that use identical modality inputs (Table~\ref{tab:modality_matched}).  
All models follow the same fine-tuning protocol described in
Section~\ref{subsec:mlp_head}, loading pretrained encoders,
freezing them, and training the same lightweight MLP
classification head on extracted embeddings.
 We compare our approach against four benchmark models - CNN baseline~\cite{o2015introduction}, SatMAE++~\cite{cong2022satmae}, ViT-S/16 (SSL4EO)~\cite{10261879}, and Presto~\cite{tseng2023lightweight}, with detailed descriptions provided in Section~\ref{subsubsec:benchmark_models}.

\begin{table}[h]
\centering
\small
\caption{Modality-matched comparison of fine-tuned performance at 50k samples.
Each model uses the same input modalities and balanced class distribution. Dimensions denote the size of the final feature representation used for classification.}
\label{tab:modality_matched}
\setlength{\tabcolsep}{5pt}
\renewcommand{\arraystretch}{1.15}
\resizebox{\linewidth}{!}{
\begin{tabular}{lccccc}
\toprule
\textbf{Model} & 
\textbf{Modalities} & 
\textbf{Samples} & 
\textbf{Dimension} & 
\shortstack{\textbf{Accuracy (\%)}\\\textbf{with CLS}} & 
\shortstack{\textbf{Accuracy (\%)}\\\textbf{without CLS}} \\
\midrule
SatMAE++ & S2 & 50,000 & 768 & – & 69.42 \\
SPEAR (Concat) & S2 & 50,000 & 260 & 67.77 & 75.84 \\
SPEAR (Cross) & S2 & 50,000 & 260 & \textbf{67.92} & \textbf{78.15} \\
\midrule
ViT-S/16 (SSL4EO) & S1, S2 & 50,000 & 768 & – & 74.76 \\
SPEAR (Concat) & S1, S2 & 50,000 & 260 & 75.60 & 73.67 \\
SPEAR (Cross) & S1, S2 & 50,000 & 260 & \textbf{79.73} & \textbf{79.68} \\
\midrule
CNN & S1, S2, Climate & 50,000 & 64 & – & 74.80 \\
SPEAR (Concat) & S1, S2, Climate & 50,000 & 260 & 85.76 & 79.85 \\
SPEAR (Cross) & S1, S2, Climate & 50,000 & 260 & \textbf{86.00} & \textbf{83.66} \\
\midrule
Presto & S1, S2, Climate & 50,000 & 128 & – & 61.66 \\
SPEAR (Concat) & S1, S2, Climate & 50,000 & 260 & 85.76 & 79.85 \\
SPEAR (Cross) & S1, S2, Climate & 50,000 & 260 & \textbf{86.00} & \textbf{83.66} \\
\bottomrule
\end{tabular}}
\vspace{-2mm}
\end{table}


\begin{table*}[h]
\centering
\small
\caption{Cross-dataset downstream classification performance.
Each model is evaluated across multiple benchmark datasets using class-balanced samples.
Metrics represent classification accuracy (\%). ``–'' indicates cases where fusion does not apply.}
\label{tab:cross_dataset_results}
\setlength{\tabcolsep}{7pt}
\renewcommand{\arraystretch}{1.15}
\vspace*{\floatsep}
\begin{tabular}{lcccccc}
\toprule
\textbf{Model} & \textbf{Dataset} & \textbf{Modalities} & \textbf{Samples} & \textbf{Classes} & \textbf{Fusion Method} & \textbf{Accuracy (\%)} \\
\midrule
RF & Sickle & S2 & 200 & 5 & – & 62.60 \\
ViT-S/16 (SSL4EO) & Sickle & S2 & 200 & 5 & – & 71.50 \\
SatMAE++ & Sickle & S2 & 200 & 5 & – & 71.25 \\
SPEAR (Ours) & Sickle & S2 & 200 & 5 & Concatenation & \textbf{73.5} \\
SPEAR (Ours) & Sickle & S2 & 200 & 5 & Cross-Attention & 71.0 \\
\midrule
RF & Sen1Floods11 & S2 & 1,000 & 2 & – & 88.87 \\
ViT-S/16 (SSL4EO) & Sen1Floods11 & S2 & 1,000 & 2 & – & 96.00 \\
SatMAE++ & Sen1Floods11 & S2 & 1,000 & 2 & – & 96.25 \\
SPEAR (Ours) & Sen1Floods11 & S2 & 1,000 & 2 & Concatenation & \textbf{97.50} \\
SPEAR (Ours) & Sen1Floods11 & S2 & 1,000 & 2 & Cross-Attention & 97.23 \\
\midrule
RF & VIIRS Fire & S2 & 5,100 & 2 & – & 91.22 \\
ViT-S/16 (SSL4EO) & VIIRS Fire & S2 & 5,100 & 2 & – & 98.91 \\
SatMAE++ & VIIRS Fire & S2 & 5,100 & 2 & – & 98.86 \\
SPEAR (Ours) & VIIRS Fire & S2 & 5,100 & 2 & Concatenation & \textbf{99.23} \\
SPEAR (Ours) & VIIRS Fire & S2 & 5,100 & 2 & Cross-Attention & 98.18 \\
RF & VIIRS Fire & S1+S2 & 5,100 & 2 & – & 90.21 \\
ViT-S/16 (SSL4EO) & VIIRS Fire & S1+S2 & 5,100 & 2 & – & 98.95 \\
SPEAR (Ours) & VIIRS Fire & S1+S2 & 5,100 & 2 & Concatenation & \textbf{99.64} \\
SPEAR (Ours) & VIIRS Fire & S1+S2 & 5,100 & 2 & Cross-Attention & 98.45 \\
\midrule
% RF & GFSAD1000 & S2 & 8,000 & 2 & – & 74.73 \\
% SatMAE++ & GFSAD1000 & S2 & 8,000 & 2 & – & 82.87 \\
% ViT-S/16 (SSL4EO) & GFSAD1000 & S2 & 8,000 & 2 & – & 83.34 \\
% SPEAR (Ours) & GFSAD1000 & S2 & 8,000 & 2 & Concatenation & \textbf{85.88} \\
% SPEAR (Ours) & GFSAD1000 & S2 & 8,000 & 2 & Cross-Attention & 83.56 \\
% RF & GFSAD1000 & S1+S2 & 8,000 & 2 & – & 77.94 \\
% ViT-S/16 (SSL4EO) & GFSAD1000 & S1+S2 & 8,000 & 2 & – & 84.00 \\
% SPEAR (Ours) & GFSAD1000 & S1+S2 & 8,000 & 2 & Concatenation & \textbf{85.97} \\
% SPEAR (Ours) & GFSAD1000 & S1+S2 & 8,000 & 2 & Cross-Attention & 83.94 \\
% \midrule
RF & Dynamic World Landcover & S1+S2+Climate & 5,000 & 9 & – & 80.67 \\
Presto & Dynamic World Landcover & S1+S2+Climate & 5,000 & 9 & – & 84.49 \\
SPEAR (Ours) & Dynamic World Landcover & S1+S2+Climate & 5,000 & 9 & Concatenation & \textbf{88.60} \\
SPEAR (Ours) & Dynamic World Landcover & S1+S2+Climate & 5,000 & 9 & Cross-Attention & 87.82 \\
\bottomrule
\end{tabular}
\end{table*}

\subsection{Downstream Dataset and Evaluation}
To assess the effectiveness of the pretrained multimodal representations, classification experiments conducted using a Random Forest (RF) classifier to evaluate feature transferability across diverse Earth observation (EO) domains.
\paragraph{Datasets and Evaluation.}
We evaluate on four benchmark datasets Sickle \cite{sani2024sickle}, Sen1Floods11~\cite{bonafilia2020sen1floods11}, VIIRS Active Fire~\cite{schroeder2014new}, and Dynamic World Landcover~\cite{brown2022dynamic} covering agricultural, flood, fire, and global land-cover classification tasks (see Section~\ref{subsubsec:downstream_dataset}). As summarized in Table~\ref{tab:cross_dataset_results}, SPEAR delivers consistently strong performance across diverse sensing conditions and tasks, while remaining robust to missing modalities. Its modular design enables operation with one to four modalities (optical, radar, climate, and PlanetScope) without retraining or performance degradation. Furthermore, the model is highly sample-efficient, leveraging self-supervised embeddings to deliver reliable results under limited labeled data. Overall, SPEAR is both modality-agnostic and data-efficient, achieving scalable and consistent performance across diverse EO benchmarks.


% \begin{itemize}
%     \item \textbf{Sickle\cite{sani2024sickle}:} Agricultural crop classification from Sentinel-2 imagery (200 samples, 5 classes).
%     \item \textbf{Sen1Floods11 \cite{bonafilia2020sen1floods11}:} Flood extent detection using Sentinel-2 imagery (1,000 samples, 2 classes).
%     \item \textbf{VIIRS Active Fire \cite{schroeder2014new}:} Burned area mapping combining Sentinel-1 radar and Sentinel-2 optical data (5,100 samples, 2 classes).
%     % \item \textbf{GFSAD1000} \cite{Thenkabail_GFSAD_2016}: Cropland extent mapping at 1 km resolution using Sentinel-1 and Sentinel-2 data (8,000 samples, 2 classes).
%     \item \textbf{Dynamic World Landcover} \cite{brown2022dynamic}: Global land cover classification from Sentinel-2, sentinel-1, climate and PlanetScope imagery with near real-time updates across 9 semantic classes (5000 samples, 9 classes).
% \end{itemize}


% \begin{table}[H]
% \centering
% \caption{Downstream Random Forest classification performance across datasets using different modality combinations and fusion strategies. Metrics represent classification accuracy (\%). S2 = Sentinel-2, S1 = Sentinel-1.}
% \label{tab:downstream_overall}
% \resizebox{\linewidth}{!}{
% \begin{tabular}{lccccc}
% \toprule
% \textbf{Model Combination} & \textbf{Dataset} & \textbf{Samples} & \textbf{Classes} & \textbf{Fusion Method} & \textbf{Accuracy (\%)} \\
% \midrule
% S2 & Sickle & 200 & 5 & Concatenation & \textbf{73.5} \\
% S2 & Sickle & 200 & 5 & Cross-Attention & 71.0 \\
% \midrule
% S2 & Sen1Floods11 & 1,000 & 2 & Concatenation & 96.0 \\
% S2 & Sen1Floods11 & 1,000 & 2 & Cross-Attention & \textbf{96.25} \\
% \midrule
% S2 & VIIRS Fire & 5,100 & 2 & Concatenation & 83.38 \\
% S1 & VIIRS Fire & 5,100 & 2 & Concatenation & 79.65 \\
% S1 + S2 & VIIRS Fire & 5,100 & 2 & Concatenation & \textbf{88.8} \\
% S2 & VIIRS Fire & 5,100 & 2 & Cross-Attention & 80.95 \\
% S1 & VIIRS Fire & 5,100 & 2 & Cross-Attention & 79.01 \\
% S1 + S2 & VIIRS Fire & 5,100 & 2 & Cross-Attention & 87.97 \\
% \midrule
% S2 & GFSAD1000 & 8,000 & 2 & Concatenation & 76.78 \\
% S1 & GFSAD1000 & 8,000 & 2 & Concatenation & 67.97 \\
% S1 + S2 & GFSAD1000 & 8,000 & 2 & Concatenation & \textbf{80.25} \\
% S2 & GFSAD1000 & 8,000 & 2 & Cross-Attention & 78.22 \\
% S1 & GFSAD1000 & 8,000 & 2 & Cross-Attention & 66.94 \\
% S1 + S2 & GFSAD1000 & 8,000 & 2 & Cross-Attention & 77.22 \\
% \midrule
% S2 + S1 + P + Clim & Dynamic World Landcover & 5,000 & 8 & Concatenation & \textbf{90.23} \\
% S2 + S1 + P + Clim & Dynamic World Landcover & 5,000 & 8 & Cross-Attention & 84.40 \\
% \bottomrule
% \end{tabular}}
% \end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Conclusion and Future Work}
We presented SPEAR, a self-supervised, pixel-level, multi-modal foundation framework that unifies optical, radar, and climate data through physics-aware pretraining. Unlike patch-based Earth observation models, SPEAR learns wavelength- and scale-conditioned embeddings directly at the pixel level, capturing fine spectral and geophysical structure while remaining robust to missing modalities. Three lightweight learners Spectral-MAE, BYOL-Denoise, and Climate-MAE produce compact 32-D embeddings that are fused via concatenation or cross-attention into a unified, sensor- and scale-aware representation. Despite its small size ($\sim$1M parameters), SPEAR achieves competitive accuracy with existing EO SSL models across diverse downstream tasks, including land-cover, flood, and wildfire classification, and operates flexibly with any subset of modalities.

Future work will explore temporal self-supervision and dynamic fusion using time-series data (e.g., Sentinel-2 and ERA5), expand pretraining to continental and global scales, and incorporate additional modalities such as LiDAR and hyperspectral data. These extensions aim toward a universal, physics-guided foundation model for scalable, multi-sensor Earth observation.

\section{Acknowledgement}
The authors acknowledge CNH Industrial for providing the collaboration and field resources essential to this research.