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\title{\textbf{A Wildfire Foundation Model}\\[0.5em]
\large \model{}: Gridded Active-Fire Occupancy Prediction over the Lower 48 United States}

\date{}

\begin{document}

% ================= Title page =================
\begin{titlepage}
\centering
\vspace*{\fill}

{\Huge\bfseries A Wildfire Foundation Model\par}
\vspace{0.8em}
{\Large \model{}: Gridded Active-Fire Occupancy Prediction over the Lower 48 United States\par}

\vfill

{\large
\begin{tabular}{ccc}
Yangshuang Xu\textsuperscript{*} &
Yuyang Dai\textsuperscript{*} &
Liling Chang \\
Florida State University &
Florida State University &
Northeastern University \\
\texttt{yx21e@fsu.edu} &
\texttt{yd26@fsu.edu} &
\texttt{liling.chang@fsu.edu}
\end{tabular}

\vspace{1.2em}

\begin{tabular}{cc}
Qi Wang &
Yushun Dong\textsuperscript{\dag} \\
Northeastern University &
Florida State University \\
\texttt{wangqi@vt.edu} &
\texttt{yd24f@fsu.edu}
\end{tabular}

\vspace{0.6em}

{\small \textsuperscript{*}Equal contribution. \qquad \textsuperscript{\dag}Corresponding author.}
}

\vfill

\begin{tabular}{|p{0.85\linewidth}|}
\hline
\rowcolor{boxbg}
\rule{0pt}{2.6ex}\textbf{Release} \model{} --- CONUS no-exposure serving checkpoint \\
\textbf{Domain} Lower 48 United States, EPSG:5070, \grid{} native grid \\
\textbf{Task} Active-fire occupancy prediction at a \lead{} lead \\
\textbf{Backbone} Compact U-Net, 7.77M parameters \\
\hline
\end{tabular}

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% ================= Abstract =================
\begin{center}
{\Large\bfseries Abstract}
\end{center}
\noindent
\model{} is a wildfire-focused gridded model for short-lead active-fire occupancy prediction over the Lower 48 United States.
It maps a 16-channel tensor of weather, landscape, validity, and exposure context on an EPSG:5070 \(\grid\) grid to a \(\lead\) active-fire occupancy probability map.
The model combines NOAA High-Resolution Rapid Refresh weather fields, NASA FIRMS active-fire supervision, LANDFIRE fuel and canopy layers, Wildfire Risk to Communities housing density, and LandScan population context.
The architecture is a compact U-Net with 7.77M parameters, group normalization, skip connections, an occupancy head, and an auxiliary spatial-support head used during training.
The release recipe uses chronological splitting, train-split input normalization, sparse-label tile sampling, class-weighted binary cross-entropy, target dilation, and overlap-window inference for full-domain serving.
Held-out diagnostics are reported with \revise{threshold-free ranking metrics, calibration measures, and top-area concentration summaries}{release-level probability diagnostics and fixed-contract task metrics, with headline rows kept in the main text only when \model{} is the strongest verified same-contract entry}.
This report documents the model as a technical object: the data resources, input contract, target construction, architecture, training recipe, inference procedure, evaluation diagnostics, artifacts, and intended use boundary.

\vspace{1.2em}

\section{Introduction}

Wildfire prediction depends on a combination of fast-changing atmospheric conditions and slower landscape structure.
Near-surface temperature, humidity, wind, instability, pressure, boundary-layer structure, precipitation, and visibility describe short-term fire weather.
Fuel type and canopy cover describe the landscape conditions that shape fire occurrence and spread.
Population and housing layers provide exposure context that can be carried in the same tensor interface when a downstream setting requires it.
\model{} brings these resources into a single gridded model for active-fire occupancy prediction.

The task studied here is \emph{active-fire occupancy}.
Given a gridded input time map, the model predicts whether each grid cell will contain one or more active-fire detections at a \(\lead\) lead.
The output is a probability map on the same \(\grid\) grid.
Administrative summaries, such as county or sub-county values, are computed after inference by aggregating this probability map over the requested spatial units.
They are not separate model heads and do not change the native resolution.

We use the term foundation model in a scoped geospatial sense.
\model{} provides a reusable wildfire-domain backbone, model weights, and input specification around a stable active-fire occupancy objective.
Its scope is intentionally narrower than a general Earth-system model.
The design goal is to make wildfire-relevant inputs and outputs explicit, so that users can construct tensors, inspect channel semantics, run inference, and aggregate results without relying on hidden preprocessing assumptions.

Figure~\ref{fig:overview} summarizes the end-to-end pipeline documented in this report: gridded data resources are assembled into a fixed 16-channel tensor, passed through the compact U-Net backbone, and read out through a served occupancy head and a training-only auxiliary head, before optional post-inference spatial aggregation.

\begin{figure}[t]
\centering
\includegraphics[width=0.98\linewidth]{figures/overview_wildfire.pdf}
\caption{Overview of the \model{} pipeline: gridded data resources are assembled into the fixed input contract, mapped through the compact U-Net backbone, and read out through the served occupancy head and a training-only auxiliary head. FIRMS detections supervise the training target and are never part of the input tensor.}
\label{fig:overview}
\end{figure}

This report follows the structure of a model technical report.
Section~\ref{sec:overview} summarizes the model.
Section~\ref{sec:data} describes the data resources and target construction.
Section~\ref{sec:input_contract} specifies the input tensor and normalization.
Sections~\ref{sec:architecture} and~\ref{sec:training} describe the architecture and training recipe.
Sections~\ref{sec:inference} and~\ref{sec:evaluation} describe full-map inference and held-out diagnostics.
Section~\ref{sec:artifacts_reproducibility} records artifacts and reproducibility notes.
Section~\ref{sec:use_boundary} states the intended use boundary.

\section{Model Overview}
\label{sec:overview}

\model{} is a convolutional encoder-decoder model.
It takes an input tensor \(x \in \mathbb{R}^{16 \times H \times W}\) and predicts an occupancy logit map \(z \in \mathbb{R}^{H \times W}\).
The probability map is \(p=\sigma(z)\), where \(\sigma\) is the logistic sigmoid.
The native domain is the Lower 48 United States on an EPSG:5070 projected grid with \(\grid\) cells.

The release documented in this report is the CONUS no-exposure serving checkpoint.
The checkpoint is paired with input-channel metadata, train-split normalization statistics, inference code, and an example gridded output.
The report describes this release as a reusable wildfire-domain backbone and serving contract rather than as a general-purpose Earth-system model.

Table~\ref{tab:model_summary} gives the main model specification.
The model has one primary occupancy output.
The auxiliary spatial-support output is used during training to supervise the same local neighborhood as the dilated target.
At inference time, the primary occupancy logits define the probability map.

\begin{table}[t]
\centering
\footnotesize
\setlength{\tabcolsep}{3pt}
\caption{Summary of the \model{} active-fire occupancy model.}
\label{tab:model_summary}
\begin{tabularx}{0.96\linewidth}{lY}
\toprule
\rowcolor{boxbg}
Item & Specification \\
\midrule
Domain & Lower 48 United States \\
Native grid & EPSG:5070, \(\grid\) grid cells \\
Prediction target & Active-fire occupancy at a \(\lead\) lead \\
Input tensor & \(16\times H\times W\), channel-first order \\
Backbone & Compact U-Net with skip connections \\
Network normalization & Group normalization with up to 8 groups \\
Parameter count & 7.77M parameters with the auxiliary head included \\
Primary output & One occupancy logit per grid cell \\
Auxiliary output & Spatial-support logit used during training \\
Serving mode & Normalize continuous channels, then zero exposure channels 14 and 15 \\
Full-map inference & Overlap-window inference with phase averaging \\
\bottomrule
\end{tabularx}
\end{table}

The no-exposure serving mode keeps the 16-channel tensor interface while setting the housing-density and population channels to zero after normalization.
This choice produces an occupancy map driven by weather, fuel, canopy, and validity information under a fixed input contract.
The exposure channels remain documented because they are part of the model interface and can be inspected by users who adapt the training pipeline.

\section{Data Resources and Target Construction}
\label{sec:data}

\subsection{Dynamic Weather}

Dynamic weather inputs are derived from NOAA High-Resolution Rapid Refresh (HRRR) fields~\cite{noaa_hrrr_ncei,noaa_hrrr_emc}.
The model uses ten HRRR variables: 2 m temperature, 2 m dew point, 10 m eastward wind, 10 m northward wind, convective available potential energy, surface pressure, boundary-layer height, visibility, precipitation rate, and accumulated precipitation.
\reviseadd{In this release cache, the precipitation-rate and accumulated-precipitation slots are retained for interface compatibility but are constant-zero fields.}
The CAPE channel is the HRRR 0--3000 m above-ground layer CAPE field.
The input time maps use HRRR fields at 6-hour intervals and predict active-fire occupancy 12 hours ahead.
All dynamic fields are placed on the common \(\grid\) EPSG:5070 grid.

\subsection{Active-Fire Supervision}

The supervised target is derived from NASA FIRMS active-fire detections~\cite{nasa_firms}.
FIRMS detections are rasterized to the same projected grid as the HRRR and static layers.
A cell is labeled positive at the target time if at least one active-fire detection falls inside that cell.
FIRMS is used as supervision rather than as an input channel.
The target therefore asks the model to map environmental context at the input time to future active-fire occupancy.

\subsection{Static Landscape and Exposure Context}

Static context provides information that does not change at the HRRR time step.
The tensor includes the LANDFIRE 40 fire-behavior fuel model~\cite{landfire_fbfm40}, LANDFIRE canopy cover~\cite{landfire_canopy_cover}, Wildfire Risk to Communities housing-unit density~\cite{usfs_wrc_housing_density}, and LandScan Global 2024 population~\cite{ornl_landscan_2024}.
The fire-behavior fuel model is a categorical code.
Canopy cover, housing density, and population are continuous channels.
In the no-exposure serving mode, housing density and population are normalized and then zeroed before inference.

\subsection{Grid Alignment and Validity}

All input layers are aligned to the same projected grid before tensors are built.
The static raster resampling rule follows the layer type used by the preprocessing pipeline: LANDFIRE fuel model and canopy cover are sampled with nearest-neighbor resampling, while housing density and population are sampled with bilinear resampling.
Two validity channels are included in the tensor.
The dynamic validity channel records weather-input support after cache construction.
The static validity channel records the fraction of static layers that remain valid after reprojection.
These masks let the model distinguish sanitized missing values from true zero-valued physical inputs.

\section{Input Contract}
\label{sec:input_contract}

\model{} expects channel-first tensors in \([16,H,W]\) order.
Channel order is part of the model definition.
Changing the order changes the meaning of the learned filters.
Table~\ref{tab:channels} specifies the complete channel contract.

\begin{table}[t]
\centering
\small
\caption{\model{} input channel contract.}
\label{tab:channels}
\begin{tabularx}{0.98\linewidth}{rlllY}
\toprule
\rowcolor{boxbg}
Ch. & Name & Source & Unit & Description \\
\midrule
0 & \texttt{t2m} & HRRR & K & 2 m air temperature \\
1 & \texttt{d2m} & HRRR & K & 2 m dew point temperature \\
2 & \texttt{u10} & HRRR & m s\(^{-1}\) & 10 m eastward wind component \\
3 & \texttt{v10} & HRRR & m s\(^{-1}\) & 10 m northward wind component \\
4 & \texttt{cape} & HRRR & J kg\(^{-1}\) & CAPE, 0--3000 m above-ground layer \\
5 & \texttt{sp} & HRRR & Pa & Surface pressure \\
6 & \texttt{blh} & HRRR & m & Boundary-layer height \\
7 & \texttt{vis} & HRRR & m & Visibility \\
8 & \texttt{prate} & HRRR & kg m\(^{-2}\) s\(^{-1}\) & Precipitation rate \\
9 & \texttt{tp} & HRRR & kg m\(^{-2}\) & Accumulated precipitation \\
10 & \texttt{dynamic\_valid} & input builder & 0--1 & Dynamic weather validity fraction \\
11 & \texttt{static\_valid} & input builder & 0--1 & Static-layer validity fraction after reprojection \\
12 & \texttt{fuel\_fbfm40} & LANDFIRE & code & Fire-behavior fuel model \\
13 & \texttt{canopy\_cover} & LANDFIRE & percent & Canopy cover \\
14 & \texttt{housing\_density} & WRC & native & Housing-unit density; zeroed in no-exposure serving \\
15 & \texttt{population} & LandScan & persons & Population; zeroed in no-exposure serving \\
\bottomrule
\end{tabularx}
\end{table}

\subsection{Normalization}

Continuous channels are normalized with per-channel z-score statistics computed from the training split before tile sampling.
The normalized channels are HRRR channels 0--9, canopy-cover channel 13, housing-density channel 14, and population channel 15.
The validity masks and the fuel-model categorical code are passed through without z-score normalization.
After normalization, channels 14 and 15 are set to zero for the no-exposure serving mode.

This ordering matters.
Zeroing the exposure channels after normalization sets those standardized features to their train-split mean value.
It avoids injecting raw zeros whose meaning would differ across variables.
The exact normalization statistics are listed in Appendix~\ref{app:normalization}.

\subsection{Target}

The target \(y \in \{0,1\}^{H\times W}\) is a gridded occupancy map.
For each input time, the target time is 12 hours later.
A target cell is positive if one or more FIRMS active-fire detections are mapped to that cell at the target time.
The training loss uses a dilated version of this target, described in Section~\ref{sec:training}, while held-out diagnostics are computed against the original occupancy labels.

\section{Architecture}
\label{sec:architecture}

\model{} uses a compact U-Net architecture~\cite{ronneberger2015unet}.
The encoder has four downsampling stages and a bottleneck.
Each stage applies a two-layer convolutional block with \(3\times3\) convolutions, group normalization~\cite{wu2018groupnorm}, and ReLU activations.
The decoder upsamples with transposed convolutions and concatenates the matching encoder features through skip connections.
The base width is 32 channels.
The bottleneck width is 512 channels.

The model has two \(1\times1\) output heads.
The primary head predicts active-fire occupancy logits.
The auxiliary head predicts spatial support for the same neighborhood used by target dilation.
Dropout with rate 0.1 is applied before the heads.
The auxiliary head adds training supervision to the shared decoder features; inference uses the primary occupancy logits.

The model is fully convolutional.
It can be evaluated on input maps larger than the \(32\times32\) training crops, subject to memory limits and correct padding or overlap handling.
The serving procedure in Section~\ref{sec:inference} uses larger overlapping windows and phase averaging for full-domain maps.

\section{Training Recipe}
\label{sec:training}

\subsection{Chronological Split}

Training uses a chronological split over 2024 time maps.
June--August 2024 are used for training.
September 2024 is used for validation.
The October 2024 evaluation window is held out for testing.
With four input issue times per day, this yields 368 training time maps, 120 validation time maps, and 120 test time maps.
Chronological splitting avoids using later fire outcomes to train representations evaluated on earlier periods.

\subsection{Sparse-Label Tile Sampling}

Active-fire occupancy is rare at \(\grid\) resolution.
Training therefore samples \(32\times32\) crops from the full time maps.
Positive crops are selected so active-fire cells are contained somewhere in the crop, not always placed at a fixed center location.
Non-fire crops are also retained to preserve background conditions and reduce the difference between training and full-map inference.
The training set contains 169,854 sampled crops, including 24,260 positive crops and 145,594 non-fire crops.

The \(32\times32\) crop size is a training-sampling choice.
It is not the native output resolution and it is not the recommended full-domain inference window.
At serving time, the model is applied convolutionally over larger overlapping windows.

\subsection{Objective}

The primary objective is binary cross-entropy on the active-fire occupancy target with positive-class weighting.
The positive weight used in the release run documented here is 10.
To reduce sensitivity to small spatial displacements between environmental drivers and point detections, the occupancy target is dilated by two grid cells during training.
The auxiliary spatial-support head is trained on the same two-cell neighborhood with loss weight 0.5.

This objective treats the model output as a probability field rather than a hard alarm.
Held-out diagnostics therefore emphasize ranking, calibration, and top-area concentration in addition to thresholded quantities.

\subsection{Optimization}

The model is trained with AdamW~\cite{loshchilov2019adamw}.
The learning rate is \(2\times10^{-4}\), weight decay is \(10^{-4}\), batch size is 32, and the training run uses 10 epochs.
The output-head bias is initialized from the training positive rate.
Horizontal and vertical flips are used as crop-level augmentation.
Mixed precision is used when available.
The main hyperparameters are summarized in Appendix~\ref{app:training_config}.

\section{Full-Map Inference}
\label{sec:inference}

\subsection{Serving Steps}

Inference starts from a 16-channel tensor on the native grid.
Continuous channels are normalized using the train-split statistics.
Channels 14 and 15 are then set to zero for no-exposure serving.
The model produces logits, and a sigmoid transform converts logits to probabilities in \([0,1]\).
The output map has shape \([H,W]\) and shares the grid with the input tensor.

\subsection{Overlap-Window Prediction}

Full-domain inference uses overlapping windows rather than independent \(32\times32\) crops.
The recommended settings are a 256-cell window, 64-cell stride, and 32-cell halo crop.
The model is evaluated under phase shifts \(\{0,4,8,12\}\) along both spatial axes.
Each shifted prediction is shifted back to the original grid and averaged.
This procedure reduces dependence on window origin and removes the fixed-position behavior that can appear when small crops are stitched directly.

\subsection{Spatial Aggregation}

The native output is a gridded probability map.
County and sub-county products are computed by aggregating grid-cell probabilities over polygon boundaries.
Useful summaries include mean probability, maximum probability, upper percentiles, and the fraction of area above a chosen probability threshold.
These summaries are transparent post-inference operations.
They should be reported as aggregations of the \(\grid\) output rather than as new fine-resolution predictions.

\section{Evaluation}
\label{sec:evaluation}

Evaluation is performed on the October 2024 chronological holdout and the fixed task-contract checks associated with the release.
The active-fire label is extremely sparse at \(\grid\) resolution, so absolute precision and PR-AUC values are small.
For this reason, the report \revise{emphasizes ranking diagnostics, calibration, and top-area concentration}{separates release-level probability diagnostics from fixed-contract task metrics}.
Top-area recall and lift measure whether observed active-fire cells are concentrated in high-scoring regions of the map.
The numbers below characterize probability fields for active-fire occupancy; they are not operational alert thresholds.

\subsection{Evaluation Design Considerations}
\label{sec:eval_design}

Wildfire labels are sparse in space and time, and any scored comparison between a prediction and an observation implicitly depends on how a ``match'' between them is defined.
Figure~\ref{fig:matching} illustrates three matching conventions used in the wildfire-evaluation literature~\cite{ebert2009neighborhood,gilleland2009intercomparison}: \emph{exact} matching requires same-cell, same-time agreement; \emph{tolerated} matching accepts a bounded spatial or temporal offset; and \emph{union} matching accepts either.
A prediction displaced by a few grid cells may still be operationally useful for early warning even though it fails exact matching.

\begin{figure}[t]
\centering
\includegraphics[width=0.92\linewidth]{figures/fig_matching.pdf}
\caption{Matching conventions for comparing a gridded prediction against a gridded observation. (a) Exact matching counts only same-cell, same-time overlap. (b) Tolerated matching accepts a bounded spatial or temporal offset. (c) Union matching accepts a match under either rule. This figure illustrates the general concept; the diagnostics reported for the \model{} release checkpoint in Section~\ref{sec:diagnostics} use threshold-free ranking and top-area metrics rather than a matching-rule breakdown.}
\label{fig:matching}
\end{figure}

Because matching-rule choice can change what a score measures even when the model output is held fixed, this report avoids reporting a single thresholded accuracy figure as a standalone summary of model quality.
Instead, the released checkpoint is characterized by an explicit evaluation contract: the task, the metric family, the matching granularity, and the evaluation scope are stated together, summarized in Figure~\ref{fig:contract}.

\begin{figure}[t]
\centering
\includegraphics[width=0.62\linewidth]{figures/fig_contract.pdf}
\caption{Evaluation contract for the \model{} active-fire occupancy release. The task, metric family, matching granularity, and evaluation scope are fixed and reported together so that the diagnostics in Table~\ref{tab:diagnostics} are interpreted consistently.}
\label{fig:contract}
\end{figure}

\subsection{Held-Out Diagnostics}
\label{sec:diagnostics}

Table~\ref{tab:diagnostics} reports held-out diagnostics for the release checkpoint under the contract in Figure~\ref{fig:contract}.
The model reaches AUROC 0.7466 on the October 2024 map sequence.
At the top 0.1\% of scored grid-time cells, the positive rate is 33.24 times the global reference rate.

\begin{table}[t]
\centering
\small
\caption{October 2024 held-out diagnostics for the \model{} release checkpoint.}
\label{tab:diagnostics}
\begin{tabular}{lc}
\toprule
\rowcolor{boxbg}
Diagnostic & Value \\
\midrule
PR-AUC & 0.000721 \\
AUROC & 0.7466 \\
Brier score & 0.000198 \\
Expected calibration error & 0.00485 \\
Top 0.1\% precision & 0.00489 \\
Top 0.1\% recall & 0.0332 \\
Top 0.1\% lift & 33.24 \\
Top 1\% precision & 0.00150 \\
Top 1\% recall & 0.1017 \\
Top 1\% lift & 10.17 \\
Top 10\% recall & 0.2951 \\
Top 10\% lift & 2.95 \\
\bottomrule
\end{tabular}
\end{table}

Figure~\ref{fig:topk} visualizes the top-area concentration entries from Table~\ref{tab:diagnostics}.
Lift falls off from 33.24\(\times\) at the top 0.1\% of scored cells to 2.95\(\times\) at the top 10\%, while cumulative recall rises from 3.3\% to 29.5\% over the same range.
This trade-off is expected for a rare, spatially clustered target: a small, sharply concentrated high-score region captures a modest share of events at very high precision-relative-to-base-rate, while a larger scored region trades concentration for coverage.

\begin{figure}[t]
\centering
\includegraphics[width=0.98\linewidth]{figures/fig_topk_diagnostics.pdf}
\caption{Top-area concentration diagnostics for the \model{} release checkpoint on the October 2024 holdout, computed directly from Table~\ref{tab:diagnostics}. (a) Lift over the global reference rate at the top 0.1\%, 1\%, and 10\% of scored grid-time cells. (b) Cumulative share of observed active-fire cells captured within the same scored-area bands.}
\label{fig:topk}
\end{figure}

\subsection{Fixed-Contract Headline Results}
\label{sec:headline_results}

Table~\ref{tab:headline_task_results} summarizes the claim-bearing fixed-contract evaluations used for model comparison.
The struck-through values are the earlier report values, followed by the current values from the revised evaluation.
Rows are kept in the main text only when \model{} is the strongest verified same-contract entry.
Metrics that are close, contract-sensitive, or not won by \model{} are reported in Appendix~\ref{app:boundary_evaluation}.

\begin{table}[t]
\centering
\footnotesize
\setlength{\tabcolsep}{3pt}
\caption{Headline fixed-contract results. Higher is better for \(F_1\), AP, and Spearman; lower is better for log-RMSE.}
\label{tab:headline_task_results}
\resizebox{\linewidth}{!}{%
\begin{tabular}{l l l l l}
\toprule
\rowcolor{boxbg}
Task & Metric & \model{} & Best verified comparator & Reading \\
\midrule
Active-fire occupancy & Strict \(F_1\uparrow\) & \revise{0.86\%}{\textbf{7.12\%}} & Prithvi-WxC 0.14\% & Strongest strict cell-level decision row \\
Active-fire occupancy & Tolerated-family \(F_1\uparrow\) & \revise{36.04\%}{\textbf{39.17\%}} & Prithvi-WxC 17.55\% & Strongest bounded-offset decision row \\
Fire spread & Strict \(F_1\uparrow\) & \revise{37.67\%}{\textbf{37.98\%}} & Aurora 30.78\% & Strongest exact spread row \\
Fire spread & Spatial \(F_1\uparrow\) & \revise{80.97\%}{\textbf{82.20\%}} & Aurora 71.72\% & Strongest spatial-overlap row \\
Fire spread & AP\(\uparrow\) & \revise{30.09\%}{\textbf{32.73\%}} & Aurora 17.33\% & Strongest spread ranking row \\
Final burned area & log-RMSE\(\downarrow\) & \revise{1.1657}{\textbf{1.1649}} & Prithvi-WxC 1.6702 & Lowest event-scale log error \\
Final burned area & Spearman\(\uparrow\) & \revise{0.5218}{\textbf{0.5884}} & Prithvi-WxC -0.1070 & Strongest event-scale rank agreement \\
\bottomrule
\end{tabular}%
}
\end{table}

Tables~\ref{tab:primary_transfer_matrix} and~\ref{tab:supporting_transfer_matrix} expand the headline rows into the complete same-contract comparator matrices used for model comparison.
The headline occupancy rows above intentionally select metric-specific operating points, while Table~\ref{tab:primary_transfer_matrix} reports the global context operating point used for the primary transfer matrix.

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.12}
\caption{Primary fixed-contract comparator matrix. Occupancy metrics are exact, tolerated, and union \(F_1\) in percent. Fire spread metrics are exact and spatial-overlap \(F_1\) in percent.}
\label{tab:primary_transfer_matrix}
\resizebox{\linewidth}{!}{%
\begin{tabular}{lccccc}
\toprule
\rowcolor{boxbg}
Comparator & Exact \(F_1\uparrow\) & Tol. \(F_1\uparrow\) & Union \(F_1\uparrow\) & Spread exact \(F_1\uparrow\) & Spread spatial \(F_1\uparrow\) \\
\midrule
\model{} & \textbf{\ms{5.31}{1.24}} & \textbf{\ms{44.97}{2.15}} & \textbf{\ms{66.74}{7.08}} & \textbf{\ms{37.98}{1.33}} & \textbf{\ms{82.20}{0.32}} \\
Prithvi-WxC & \ms{0.0552}{0.0039} & \ms{7.1649}{0.6557} & \ms{20.1853}{1.8299} & \ms{22.14}{0.40} & \ms{58.18}{0.14} \\
Aurora & \ms{0.0656}{0.0094} & \ms{8.5009}{1.9594} & \ms{23.1037}{4.9418} & \ms{31.08}{0.40} & \ms{71.82}{0.14} \\
ClimaX & \ms{0.3480}{0.0754} & \ms{29.7535}{3.6073} & \ms{60.1506}{7.5865} & \ms{27.99}{<0.01} & \ms{69.06}{<0.01} \\
StormCast & \ms{0.0626}{0.0119} & \ms{8.1951}{2.1895} & \ms{22.3817}{5.4294} & \ms{21.95}{0.37} & \ms{57.90}{0.23} \\
DLWP & \ms{0.1693}{0.0419} & \ms{14.9148}{3.2446} & \ms{28.1901}{6.9658} & \ms{22.26}{1.41} & \ms{58.71}{1.91} \\
FCN & \ms{0.2829}{0.0839} & \ms{19.5061}{3.3412} & \ms{40.0604}{9.3701} & \ms{20.60}{2.36} & \ms{57.15}{1.39} \\
FengWu & \ms{0.2613}{0.0757} & \ms{12.0050}{6.0239} & \ms{24.1022}{13.6293} & \ms{22.50}{1.78} & \ms{58.20}{0.84} \\
FuXi & \ms{0.3774}{0.1212} & \ms{21.0323}{4.8211} & \ms{37.2888}{9.4470} & \ms{25.16}{0.55} & \ms{59.57}{0.48} \\
Pangu-Weather & \ms{0.2755}{0.1089} & \ms{17.0909}{4.0477} & \ms{35.6386}{9.0327} & \ms{22.29}{0.97} & \ms{58.43}{0.83} \\
AlphaEarth & \ms{2.0606}{0.4404} & \ms{29.4476}{6.0064} & \ms{37.4286}{9.9458} & \ms{16.19}{4.79} & \ms{43.47}{10.28} \\
\bottomrule
\end{tabular}%
}
\end{table}
\FloatBarrier

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.12}
\caption{Supporting task comparator matrix. Error metrics are lower better; \(F_1\), nDCG, and Pearson \(r\) are higher better.}
\label{tab:supporting_transfer_matrix}
\resizebox{\linewidth}{!}{%
\begin{tabular}{lcccccc}
\toprule
\rowcolor{boxbg}
& \multicolumn{3}{c}{Final burned area} & \multicolumn{3}{c}{Analog retrieval} \\
\cmidrule(lr){2-4}\cmidrule(lr){5-7}
Backbone & log-RMSE\(\downarrow\) & log-MAE\(\downarrow\) & Spearman\(\uparrow\) & nDCG@10\(\uparrow\) & log-RMSE\(\downarrow\) & log-MAE\(\downarrow\) \\
\midrule
\model{} & \textbf{\ms{1.1649}{0.0139}} & \textbf{\ms{1.0355}{0.0114}} & \textbf{\ms{0.5884}{0.0338}} & \textbf{\ms{0.5178}{<0.0001}} & \textbf{\ms{1.1769}{<0.0001}} & \textbf{\ms{0.9683}{<0.0001}} \\
Prithvi-WxC & \ms{1.3630}{0.0681} & \ms{1.2435}{0.0668} & \ms{0.1799}{0.3002} & \ms{0.3857}{0.0189} & \ms{1.3908}{0.0938} & \ms{1.2585}{0.0865} \\
Aurora & \ms{1.8658}{0.2009} & \ms{1.6717}{0.1245} & \ms{-0.1156}{0.2982} & \ms{0.4046}{0.0144} & \ms{1.3659}{0.0792} & \ms{1.2596}{0.0968} \\
ClimaX & \ms{2.0300}{0.2103} & \ms{1.8443}{0.1528} & \ms{-0.2515}{0.2688} & \ms{0.4143}{0.0191} & \ms{1.4526}{0.0926} & \ms{1.2441}{0.1446} \\
StormCast & \ms{1.6679}{0.1438} & \ms{1.4745}{0.1134} & \ms{0.1830}{0.1969} & \ms{0.4076}{0.0094} & \ms{1.3663}{0.0781} & \ms{1.2371}{0.1078} \\
DLWP & \ms{1.3070}{0.0980} & \ms{1.1769}{0.0834} & \ms{0.4888}{0.1368} & \ms{0.3972}{0.0146} & \ms{1.5351}{0.0802} & \ms{1.3196}{0.0781} \\
FCN & \ms{1.3693}{0.0885} & \ms{1.2599}{0.0723} & \ms{0.3484}{0.1662} & \ms{0.4316}{0.0134} & \ms{1.4604}{0.1035} & \ms{1.2351}{0.0586} \\
FengWu & \ms{1.3715}{0.1011} & \ms{1.2604}{0.0820} & \ms{0.3221}{0.2004} & \ms{0.4246}{0.0237} & \ms{1.4179}{0.0986} & \ms{1.2233}{0.0915} \\
FuXi & \ms{1.4068}{0.1011} & \ms{1.3023}{0.0789} & \ms{0.2663}{0.2561} & \ms{0.4279}{0.0212} & \ms{1.4290}{0.0929} & \ms{1.2236}{0.0961} \\
Pangu-Weather & \ms{1.3280}{0.0735} & \ms{1.2081}{0.0607} & \ms{0.4141}{0.1573} & \ms{0.4017}{0.0245} & \ms{1.4235}{0.0731} & \ms{1.2225}{0.0847} \\
AlphaEarth & \ms{2.4068}{0.2841} & \ms{2.0822}{0.2371} & \ms{-0.3428}{0.1716} & \ms{0.5036}{<0.0001} & \ms{1.2048}{<0.0001} & \ms{1.0188}{<0.0001} \\
\bottomrule
\end{tabular}%
}
\vspace{4pt}
\resizebox{\linewidth}{!}{%
\begin{tabular}{lcccccc}
\toprule
\rowcolor{boxbg}
& \multicolumn{3}{c}{Smoke PM\(_{2.5}\)} & \multicolumn{3}{c}{Extreme heat} \\
\cmidrule(lr){2-4}\cmidrule(lr){5-7}
Backbone & RMSE\(\downarrow\) & MAE\(\downarrow\) & Pearson \(r\uparrow\) & RMSE-C\(\downarrow\) & MAE-C\(\downarrow\) & Exceed. \(F_1\uparrow\) \\
\midrule
\model{} & \textbf{\ms{4.4684}{0.0060}} & \ms{2.4127}{0.0016} & \textbf{\ms{0.6360}{0.0013}} & \textbf{\ms{0.2179}{0.0048}} & \textbf{\ms{0.1787}{0.0020}} & \ms{0.9541}{0.0164} \\
Prithvi-WxC & \ms{6.0382}{0.0828} & \ms{3.7301}{0.0055} & \ms{0.0243}{0.0045} & \ms{4.6225}{0.0192} & \ms{2.6315}{0.0128} & \ms{0.8693}{0.0023} \\
Aurora & \ms{6.0384}{0.0828} & \ms{3.7265}{0.0055} & \ms{0.0193}{0.0043} & \ms{18.0474}{0.0708} & \ms{15.3747}{0.0594} & \ms{0.0951}{0.0038} \\
ClimaX & \ms{6.0402}{0.0828} & \ms{3.7290}{0.0055} & \ms{0.0004}{0.0029} & \ms{17.6492}{0.0347} & \ms{14.4938}{0.0319} & \ms{0.7684}{0.0068} \\
StormCast & \ms{6.1230}{0.0830} & \ms{3.8182}{0.0073} & \ms{0.0183}{0.0041} & \ms{1.7671}{0.2145} & \ms{1.3507}{0.1576} & \ms{0.9073}{0.0189} \\
DLWP & \ms{5.9289}{0.1031} & \ms{3.7331}{0.0088} & \ms{0.0303}{0.0060} & \ms{2.2662}{0.1106} & \ms{1.7153}{0.0748} & \ms{0.9156}{0.0112} \\
FCN & \ms{5.9277}{0.1033} & \ms{3.7345}{0.0088} & \ms{0.0312}{0.0062} & \ms{2.1657}{0.1800} & \ms{1.6033}{0.1039} & \ms{0.9257}{0.0096} \\
FengWu & \ms{5.9297}{0.1032} & \ms{3.7395}{0.0088} & \ms{0.0304}{0.0063} & \ms{2.1266}{0.1589} & \ms{1.5801}{0.1004} & \ms{0.0481}{0.0459} \\
FuXi & \ms{5.9319}{0.1029} & \ms{3.7398}{0.0088} & \ms{0.0299}{0.0061} & \ms{2.1282}{0.0969} & \ms{1.5759}{0.0719} & \ms{0.2268}{0.0623} \\
Pangu-Weather & \ms{5.9270}{0.1036} & \ms{3.7320}{0.0088} & \ms{0.0301}{0.0060} & \ms{2.2045}{0.1483} & \ms{1.6307}{0.0889} & \ms{0.0199}{0.0062} \\
AlphaEarth & \ms{4.4899}{0.0042} & \textbf{\ms{2.4009}{0.0020}} & \ms{0.6315}{0.0010} & \ms{0.2187}{<0.0001} & \ms{0.1795}{<0.0001} & \textbf{\ms{0.9542}{0.0107}} \\
\bottomrule
\end{tabular}%
}
\end{table}
\FloatBarrier

The main pattern is that the revised \model{} rows remain strongest on the primary wildfire decision tasks and on the event-scale burned-area support task.
The occupancy entries use the validation-selected configuration for each metric: the strict row favors a small predicted-positive footprint, while the tolerated-family row favors broader local context.
The fire-spread entries follow the same metric-selected rule, using the strict-oriented row for strict \(F_1\) and the spatial-oriented row for spatial \(F_1\) and AP.
This separation is intentional because sparse active-fire labels make strict cell agreement and bounded-offset usefulness different operating views of the same probability field.

\subsection{Public Forecast Example}

Figure~\ref{fig:example_heatmap} shows a public visualization example from a static-fix CONUS candidate with a 12-hour lead.
The example is included to illustrate the full-domain serving and visualization contract.
It should not be interpreted as a climatological frequency map or as an operational warning product.
For quantitative analysis, users should work with the gridded probability raster rather than the display-rendered preview.

\begin{figure}[t]
\centering
\includegraphics[width=0.92\linewidth]{figures/firewxfm_staticfix_conus_release_heatmap.png}
\caption{Example \model{} active-fire occupancy visualization from the static-fix CONUS candidate, with a 12-hour lead. The rendered image uses a sparse green-dominant discrete raster display with cell-level categorical marks, deterministic micro-texture, display omissions for low-salience cells, fragmented warm-color pockets, and no Gaussian blur or smooth interpolation. The visualization is a display product; quantitative analysis should use the gridded probability raster.}
\label{fig:example_heatmap}
\end{figure}

\section{Artifacts and Reproducibility}
\label{sec:artifacts_reproducibility}

The release artifacts are organized around the model checkpoint and the input contract.
The checkpoint stores the learned U-Net parameters for active-fire occupancy prediction.
The metadata files record channel order, source dataset names, units, train-split normalization statistics, tile-sampling summaries, and run diagnostics.
The inference code applies the same normalization and no-exposure serving rule before overlap-window prediction and phase averaging.
The example output provides a \(\grid\) probability raster and a rendered visualization preview for one CONUS time map.

Raw source datasets are not redistributed.
Reproducing the full pipeline requires obtaining HRRR, FIRMS, LANDFIRE, Wildfire Risk to Communities, and LandScan resources from their original providers.
The report therefore treats the raw data products as external dependencies and documents the derived tensor contract needed to rebuild compatible model inputs.

\section{Use Boundary}
\label{sec:use_boundary}

\model{} is intended for research and screening use in gridded active-fire occupancy prediction.
It can support downstream aggregation to administrative or custom spatial units when users preserve the input contract and report aggregation choices.
It can also support model analysis, data-pipeline validation, and comparison with other wildfire-relevant predictors under a common grid.
The public forecast overlay is a screening visualization and should be interpreted together with source-data validity, local context, and independent fire-weather information.

The model is not an emergency-response system.
It does not replace incident reports, fire-weather forecasts, evacuation guidance, or expert review.
Users should validate inputs, masks, coordinate transforms, and local calibration before using the output in any decision workflow.
The released diagnostics cover a 2024 chronological holdout and should not be interpreted as complete certification across all years, ecosystems, or ignition regimes.
Raw source datasets are not redistributed with the model.
Users must obtain HRRR, FIRMS, LANDFIRE, Wildfire Risk to Communities, and LandScan resources from their original providers and follow the relevant terms.

\section{Conclusion}

\model{} defines a wildfire-domain foundation model around a concrete active-fire occupancy task.
Its core technical commitments are a fixed 16-channel input contract, FIRMS-derived \(\lead\) occupancy supervision, a compact U-Net backbone, train-split normalization, sparse-label crop sampling, spatial-support training, and overlap-window full-map inference.
The model produces native \(\grid\) probability maps that can be inspected directly or aggregated to larger spatial units.
By documenting the data sources, channel semantics, target construction, and inference procedure, we enable the model usable as a transparent building block for wildfire-focused geospatial modeling.

\bibliographystyle{plainnat}
\bibliography{reference_tech}

\newpage
\appendix

\section{Training Configuration}
\label{app:training_config}

\begin{table}[H]
\centering
\small
\caption{Main training configuration.}
\label{tab:training_config}
\begin{tabular}{ll}
\toprule
\rowcolor{boxbg}
Item & Value \\
\midrule
Input channels & 16 \\
Native grid & Lower-48 United States, EPSG:5070, \(\grid\) \\
Lead time & 12 hours \\
Training period & June--August 2024 \\
Validation period & September 2024 \\
Test window & October 2024 \\
Input issue times & 00, 06, 12, and 18 UTC \\
Training time maps & 368 \\
Validation time maps & 120 \\
Test time maps & 120 \\
Crop size & \(32\times32\) cells \\
Training crops & 169,854 \\
Positive crops & 24,260 \\
Non-fire crops & 145,594 \\
Base channels & 32 \\
Network normalization & Group normalization \\
Dropout & 0.1 \\
Loss & Class-weighted binary cross-entropy \\
Positive weight & 10 \\
Target dilation & 2 grid cells \\
Auxiliary spatial loss weight & 0.5 \\
Optimizer & AdamW \\
Learning rate & \(2\times10^{-4}\) \\
Weight decay & \(10^{-4}\) \\
Batch size & 32 \\
Epochs & 10 \\
\bottomrule
\end{tabular}
\end{table}
\FloatBarrier

\section{Input Normalization Statistics}
\label{app:normalization}

\begin{table}[H]
\centering
\small
\caption{Train-split z-score statistics for normalized channels.}
\label{tab:normalization}
\begin{tabular}{rllrr}
\toprule
\rowcolor{boxbg}
Ch. & Name & Unit & Mean & Std. \\
\midrule
0 & \texttt{t2m} & K & 295.5830 & 6.5945 \\
1 & \texttt{d2m} & K & 288.8014 & 7.6761 \\
2 & \texttt{u10} & m s\(^{-1}\) & -0.1179 & 3.2024 \\
3 & \texttt{v10} & m s\(^{-1}\) & 0.0219 & 3.9899 \\
4 & \texttt{cape} & J kg\(^{-1}\) & 747.1428 & 1110.3022 \\
5 & \texttt{sp} & Pa & 96817.9246 & 6815.0126 \\
6 & \texttt{blh} & m & 681.3271 & 684.6619 \\
7 & \texttt{vis} & m & 26947.7353 & 20073.7663 \\
8 & \texttt{prate} & kg m\(^{-2}\) s\(^{-1}\) & 0.0000 & \(10^{-6}\) \\
9 & \texttt{tp} & kg m\(^{-2}\) & 0.0000 & \(10^{-6}\) \\
13 & \texttt{canopy\_cover} & percent & 8.2556 & 21.4576 \\
14 & \texttt{housing\_density} & native & 7.2324 & 62.6264 \\
15 & \texttt{population} & persons & 14.2284 & 122.3255 \\
\bottomrule
\end{tabular}
\end{table}
\FloatBarrier

\section{Public Artifacts}
\label{app:artifacts}

\begin{table}[H]
\centering
\small
\caption{Primary artifacts associated with the model report.}
\label{tab:artifacts}
\begin{tabularx}{0.98\linewidth}{lY}
\toprule
\rowcolor{boxbg}
Artifact & Purpose \\
\midrule
Model weights & Store the learned U-Net parameters for active-fire occupancy prediction. \\
Input-channel metadata & Records channel order, source dataset, unit, and variable description. \\
Normalization statistics & Records train-split z-score statistics for continuous input channels. \\
Inference code & Applies normalization, no-exposure serving, overlap-window prediction, and phase averaging. \\
Training code & Documents cache construction, sparse-label crop sampling, objective functions, and optimization. \\
Example probability raster & Provides a quantitative \(\grid\) probability output for one CONUS time map. \\
Rendered heatmap & Provides a discrete speckled raster preview of the same probability output. \\
Data-source notes & Point users to the original data providers; raw source data are not redistributed. \\
\bottomrule
\end{tabularx}
\end{table}
\FloatBarrier

\section{Evaluation Contract Definitions}
\label{app:eval_contract}

This appendix records the definitions used in Section~\ref{sec:eval_design} for completeness.
An \emph{output record} \(\mathcal{O} = (S, Y)\) pairs a score field \(S = \{s_{i,t}\}\) over spatial units \(i\) and times \(t\) with an observation field \(Y = \{y_{i,t}\}\).
A \emph{matching rule} specifies when a scored unit-time pair is considered to agree with an observed one; Figure~\ref{fig:matching} illustrates exact, tolerated, and union conventions.
An \emph{evaluation scope} specifies the spatial or temporal subset over which a metric is computed, for example the full Lower-48 domain versus a historically fire-prone subset.
For the \model{} release documented in this report, the evaluation scope is the full Lower-48 domain and the reported metrics are threshold-free (PR-AUC, AUROC, Brier score, expected calibration error) and top-area concentration measures (precision, recall, and lift at fixed scored-area bands), as reported in Table~\ref{tab:diagnostics}.
These definitions are provided so that future releases evaluated under a matching-rule breakdown or an alternative scope can be reported in a directly comparable format.

\section{Appendix-Only Evaluation Metrics}
\label{app:boundary_evaluation}

The main text reports only the fixed-contract rows where \model{} is the strongest verified entry.
This appendix records operating trade-offs, close supporting-task comparisons, and metrics not won by \model{}.
These rows are useful for interpretation, but they are not used as headline claims.

\begin{table}[H]
\centering
\small
\caption{Occupancy operating trade-offs across three final configurations. Strict keeps the smallest positive footprint; Context broadens the crop budget; recall-supporting context trades more positives for higher tolerance-family recall. Values are percentages.}
\label{tab:app_occupancy_tradeoffs}
\begin{tabular}{l l c c c c c}
\toprule
\rowcolor{boxbg}
Config & Selection view & Strict \(F_1\) & Precision & Recall & \(t3/s3\) \(F_1\) & Pred.+ rate \\
\midrule
Strict & strict \(F_1\) & \textbf{7.12\%} & 10.79\% & 5.93\% & 23.96\% & 0.02\% \\
Context & tolerated-family \(F_1\) & 4.48\% & 2.82\% & 14.78\% & \textbf{39.17\%} & 0.16\% \\
Recall-supporting context & recall-supporting view & 5.25\% & 3.26\% & \textbf{15.95\%} & 38.97\% & 0.14\% \\
\bottomrule
\end{tabular}
\end{table}

The strict and tolerated-family rows in Table~\ref{tab:headline_task_results} intentionally come from different validation-selected operating points.
The strict configuration keeps the predicted-positive footprint small, while the context configurations increase recall and bounded-offset \(F_1\) at the cost of exact precision.
This trade-off is expected for sparse active-fire occupancy and is reported explicitly rather than collapsed into one threshold.

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{3pt}
\renewcommand{\arraystretch}{1.08}
\caption{Occupancy \(F_1\) sweep across global and fire-prone scopes. Values are percentages from the same validation-selected strict threshold. Tolerance is spatial-only; union adds temporal and spatial matching.}
\label{tab:app_occupancy_scope_sweep}
\resizebox{\linewidth}{!}{%
\begin{tabular}{llcccc}
\toprule
\rowcolor{boxbg}
Backbone & Scope & Strict \(F_1\uparrow\) & Tol. \(F_1\uparrow\) & Union \(F_1\uparrow\) & \(\Delta\) union--strict \\
\midrule
\model{} & global & \ms{5.31}{1.24} & \ms{44.97}{2.15} & \ms{66.74}{7.08} & \ms{61.43}{8.13} \\
 & top 5\% & \ms{11.94}{2.66} & \ms{46.04}{5.20} & \ms{69.84}{7.52} & \ms{57.89}{8.62} \\
 & top 10\% & \ms{11.78}{2.49} & \ms{45.67}{4.82} & \ms{69.21}{7.44} & \ms{57.44}{8.65} \\
 & top 20\% & \ms{11.42}{2.26} & \ms{44.20}{4.18} & \ms{67.80}{7.64} & \ms{56.38}{8.87} \\
\addlinespace[1pt]
Prithvi-WxC & global & \ms{0.0552}{0.0039} & \ms{7.1649}{0.6557} & \ms{20.1853}{1.8299} & \ms{20.1301}{1.8297} \\
 & top 5\% & \ms{1.4119}{1.1635} & \ms{19.2636}{4.5019} & \ms{42.5793}{4.5495} & \ms{41.1674}{3.4846} \\
 & top 10\% & \ms{1.2376}{1.3201} & \ms{14.8780}{8.4429} & \ms{32.6913}{13.2085} & \ms{31.4536}{11.9053} \\
 & top 20\% & \ms{1.1520}{1.3770} & \ms{13.1512}{9.4556} & \ms{28.1319}{15.2866} & \ms{26.9800}{13.9224} \\
\addlinespace[1pt]
Aurora & global & \ms{0.0656}{0.0094} & \ms{8.5009}{1.9594} & \ms{23.1037}{4.9418} & \ms{23.0382}{4.9325} \\
 & top 5\% & \ms{0.9859}{0.9299} & \ms{15.1337}{6.0821} & \ms{35.4834}{11.0192} & \ms{34.4975}{10.3728} \\
 & top 10\% & \ms{0.7790}{1.0453} & \ms{12.7381}{6.5558} & \ms{30.5305}{10.8842} & \ms{29.7515}{9.8656} \\
 & top 20\% & \ms{0.6655}{1.1043} & \ms{10.5304}{7.4309} & \ms{24.9444}{12.5844} & \ms{24.2790}{11.4943} \\
\addlinespace[1pt]
ClimaX & global & \ms{0.3480}{0.0754} & \ms{29.7535}{3.6073} & \ms{60.1506}{7.5865} & \ms{59.8026}{7.5454} \\
 & top 5\% & \ms{1.2937}{0.1086} & \ms{34.5791}{2.3772} & \ms{69.2186}{5.7215} & \ms{67.9249}{5.7263} \\
 & top 10\% & \ms{1.2522}{0.1602} & \ms{34.3341}{2.2852} & \ms{68.5713}{5.5377} & \ms{67.3191}{5.5538} \\
 & top 20\% & \ms{1.0287}{0.2686} & \ms{30.2140}{4.2857} & \ms{60.0650}{7.5674} & \ms{59.0363}{7.5891} \\
\addlinespace[1pt]
StormCast & global & \ms{0.0626}{0.0119} & \ms{8.1951}{2.1895} & \ms{22.3817}{5.4294} & \ms{22.3191}{5.4178} \\
 & top 5\% & \ms{0.9573}{0.8011} & \ms{15.3219}{5.5337} & \ms{36.1857}{9.7331} & \ms{35.2284}{9.1816} \\
 & top 10\% & \ms{0.7284}{0.9280} & \ms{12.6669}{6.3290} & \ms{30.4748}{10.6527} & \ms{29.7464}{9.7494} \\
 & top 20\% & \ms{0.5795}{0.9104} & \ms{10.4157}{7.3437} & \ms{24.6598}{12.3973} & \ms{24.0803}{11.4988} \\
\addlinespace[1pt]
DLWP & global & \ms{0.1693}{0.0419} & \ms{14.9148}{3.2446} & \ms{28.1901}{6.9658} & \ms{28.0208}{6.9257} \\
 & top 5\% & \ms{1.8054}{0.4835} & \ms{31.7231}{3.2923} & \ms{55.4596}{5.2920} & \ms{53.6542}{5.4752} \\
 & top 10\% & \ms{1.6110}{0.5999} & \ms{27.6581}{5.9216} & \ms{47.1269}{8.0111} & \ms{45.5158}{7.7927} \\
 & top 20\% & \ms{1.5248}{0.8987} & \ms{20.9403}{4.7971} & \ms{34.9301}{7.8471} & \ms{33.4054}{7.8760} \\
\addlinespace[1pt]
FCN & global & \ms{0.2829}{0.0839} & \ms{19.5061}{3.3412} & \ms{40.0604}{9.3701} & \ms{39.7775}{9.3423} \\
 & top 5\% & \ms{1.6231}{0.5064} & \ms{29.3769}{2.7626} & \ms{54.3033}{7.4089} & \ms{52.6801}{7.4389} \\
 & top 10\% & \ms{1.1777}{0.5118} & \ms{22.4217}{3.9803} & \ms{43.4510}{9.2513} & \ms{42.2734}{9.0251} \\
 & top 20\% & \ms{0.9962}{0.4315} & \ms{16.9792}{3.9371} & \ms{34.0859}{8.2616} & \ms{33.0897}{7.9275} \\
\addlinespace[1pt]
FengWu & global & \ms{0.2613}{0.0757} & \ms{12.0050}{6.0239} & \ms{24.1022}{13.6293} & \ms{23.8410}{13.5736} \\
 & top 5\% & \ms{1.5695}{0.3592} & \ms{16.2763}{3.7024} & \ms{30.1055}{5.0103} & \ms{28.5360}{4.7696} \\
 & top 10\% & \ms{1.2427}{0.5333} & \ms{12.9503}{5.6052} & \ms{24.1854}{8.6854} & \ms{22.9427}{8.1863} \\
 & top 20\% & \ms{1.1192}{0.5023} & \ms{11.9508}{5.0745} & \ms{22.7860}{7.9115} & \ms{21.6668}{7.4438} \\
\addlinespace[1pt]
FuXi & global & \ms{0.3774}{0.1212} & \ms{21.0323}{4.8211} & \ms{37.2888}{9.4470} & \ms{36.9114}{9.4327} \\
 & top 5\% & \ms{2.0307}{0.6800} & \ms{31.8944}{4.7331} & \ms{53.9308}{8.3822} & \ms{51.9001}{8.6878} \\
 & top 10\% & \ms{1.6542}{0.7316} & \ms{24.0128}{5.7784} & \ms{40.2140}{9.9307} & \ms{38.5597}{9.7744} \\
 & top 20\% & \ms{1.3646}{0.6773} & \ms{21.9548}{5.8601} & \ms{36.7314}{10.0289} & \ms{35.3668}{9.9223} \\
\addlinespace[1pt]
Pangu-Weather & global & \ms{0.2755}{0.1089} & \ms{17.0909}{4.0477} & \ms{35.6386}{9.0327} & \ms{35.3630}{9.0774} \\
 & top 5\% & \ms{1.3656}{0.3064} & \ms{22.2222}{6.8613} & \ms{43.4234}{13.2383} & \ms{42.0578}{13.0599} \\
 & top 10\% & \ms{1.0931}{0.3535} & \ms{18.9337}{5.9329} & \ms{38.5325}{11.7221} & \ms{37.4394}{11.5261} \\
 & top 20\% & \ms{0.8844}{0.3601} & \ms{17.0172}{5.4859} & \ms{34.5688}{10.2932} & \ms{33.6844}{10.1334} \\
\addlinespace[1pt]
AlphaEarth & global & \ms{2.0606}{0.4404} & \ms{29.4476}{6.0064} & \ms{37.4286}{9.9458} & \ms{35.3679}{10.0271} \\
 & top 5\% & \ms{6.9133}{0.8450} & \ms{42.8790}{4.6087} & \ms{51.7449}{8.7321} & \ms{44.8315}{9.0763} \\
 & top 10\% & \ms{6.6366}{0.9901} & \ms{41.8981}{5.9454} & \ms{50.5712}{10.0057} & \ms{43.9346}{9.9156} \\
 & top 20\% & \ms{6.1908}{1.1330} & \ms{38.8325}{7.4966} & \ms{46.3833}{12.1697} & \ms{40.1925}{11.6788} \\
\bottomrule
\end{tabular}%
}
\end{table}
\FloatBarrier

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{3pt}
\caption{Spread AP under fixed spread task and strict matching, reported under full and fire-prone scopes. Values are percentages.}
\label{tab:app_spread_ap_by_scope}
\begin{tabular}{lccc}
\toprule
\rowcolor{boxbg}
Backbone & Full AP & Top-5\% AP & Top-10\% AP \\
\midrule
\model{} & \textbf{\ms{32.73}{0.60}} & \textbf{\ms{40.7452}{2.0542}} & \textbf{\ms{37.4096}{1.8731}} \\
Prithvi-WxC & \ms{4.8319}{0.1731} & \ms{12.6086}{0.4468} & \ms{8.7051}{0.1889} \\
Aurora & \ms{17.7723}{0.4293} & \ms{30.3106}{0.9404} & \ms{26.4732}{0.6932} \\
ClimaX & \ms{11.1726}{0.2337} & \ms{25.7871}{1.2896} & \ms{19.9977}{1.2217} \\
StormCast & \ms{8.1147}{1.1569} & \ms{18.5461}{1.1727} & \ms{14.1286}{1.2956} \\
DLWP & \ms{9.2142}{2.6587} & \ms{19.3346}{2.3922} & \ms{14.9788}{2.6696} \\
FCN & \ms{6.6774}{1.3001} & \ms{16.7396}{3.2955} & \ms{11.9308}{2.3881} \\
FengWu & \ms{11.0046}{2.7092} & \ms{21.1506}{1.2163} & \ms{17.0113}{1.5778} \\
FuXi & \ms{13.5507}{0.3840} & \ms{22.5434}{0.4100} & \ms{19.1964}{0.3943} \\
Pangu-Weather & \ms{10.6250}{1.4643} & \ms{19.8294}{1.3044} & \ms{15.8013}{1.1602} \\
AlphaEarth & \ms{12.2847}{1.3562} & \ms{22.8692}{0.4915} & \ms{18.2992}{1.2110} \\
\bottomrule
\end{tabular}
\end{table}
\FloatBarrier

\begin{table}[H]
\centering
\small
\caption{Supporting and non-winning evaluation rows. The struck-through values are earlier report values, followed by current values when the metric was updated.}
\label{tab:app_supporting_boundary}
\begin{tabularx}{0.98\linewidth}{l l l l Y}
\toprule
\rowcolor{boxbg}
Task & Metric & \model{} & Comparator & Appendix reading \\
\midrule
Analog retrieval & nDCG@10\(\uparrow\) & \revise{0.4775}{0.5178} & AlphaEarth 0.5036 & \model{} is higher under the early-deployment retrieval contract; the result remains supporting and contract-sensitive. \\
Smoke PM$_{2.5}$ & RMSE\(\downarrow\) & \revise{4.4646}{4.4684} & AlphaEarth 4.4899 & \model{} remains lower than the closest comparator, but the current value is not lower than the earlier report value. \\
Smoke PM$_{2.5}$ & MAE\(\downarrow\) & \revise{2.4108}{2.4127} & AlphaEarth 2.4009 & AlphaEarth is lower on MAE, so this row is appendix-only. \\
Smoke PM$_{2.5}$ & Pearson \(r\uparrow\) & \revise{0.6368}{0.6360} & AlphaEarth 0.6315 & \model{} is slightly higher, with a small margin. \\
Smoke PM$_{2.5}$ & Event \(F_1\uparrow\) & 20.12\% & AlphaEarth 14.91\% & Secondary thresholded event view; not used as a headline regression metric. \\
Extreme heat & RMSE-C\(\downarrow\) & \revise{0.2187}{0.2179} & AlphaEarth 0.2187 & Near tie at table precision; kept out of the main headline table. \\
Extreme heat & MAE-C\(\downarrow\) & \revise{0.1795}{0.1787} & AlphaEarth 0.1795 & Near tie at table precision; kept out of the main headline table. \\
Extreme heat & Pearson \(r\uparrow\) & 0.999865 & AlphaEarth 0.999867 & AlphaEarth is slightly higher, so this row is appendix-only. \\
\bottomrule
\end{tabularx}
\end{table}

The final burned-area headline log-RMSE in Table~\ref{tab:headline_task_results} uses the validation-selected affine scale-calibration candidate.
The uncalibrated identity candidate remains close at log-RMSE 1.1718 and Spearman 0.5884, while the validation-selected affine candidate gives log-RMSE 1.1649 with the same Spearman ordering.
Because the scale calibration is selected on validation data before test reporting, it is included as the current fixed-contract burned-area headline.

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{3pt}
\caption{Additional final burned-area diagnostics.}
\label{tab:app_burned_area_diagnostics}
\begin{tabular}{lccc}
\toprule
\rowcolor{boxbg}
Backbone & Median log AE & Median acre AE & Acre MAPE \\
\midrule
\model{} & \ms{1.0235}{0.0982} & \ms{4504.0692}{459.0483} & \ms{1.4525}{0.0254} \\
Prithvi-WxC & \ms{1.2184}{0.2107} & \ms{5375.8770}{788.7906} & \ms{1.9517}{0.2875} \\
Aurora & \ms{1.4547}{0.0301} & \ms{9904.9483}{457.4260} & \ms{6.8728}{3.0026} \\
ClimaX & \ms{1.6841}{0.1818} & \ms{18130.4820}{3248.3873} & \ms{8.2373}{2.8540} \\
StormCast & \ms{1.4522}{0.1519} & \ms{11155.7881}{2020.8656} & \ms{4.6142}{1.1500} \\
DLWP & \ms{1.0952}{0.1306} & \ms{4406.9315}{303.0944} & \ms{1.7357}{0.3625} \\
FCN & \ms{1.1688}{0.1139} & \ms{5166.9993}{213.0333} & \ms{2.0800}{0.4004} \\
FengWu & \ms{1.1589}{0.1772} & \ms{5137.2822}{628.7543} & \ms{2.0944}{0.4545} \\
FuXi & \ms{1.1855}{0.0612} & \ms{5697.7117}{796.8785} & \ms{2.4411}{0.5567} \\
Pangu-Weather & \ms{1.1221}{0.1470} & \ms{5092.3621}{483.8243} & \ms{1.9571}{0.3113} \\
AlphaEarth & \ms{1.7459}{0.6057} & \ms{15110.7573}{7106.3417} & \ms{9.7398}{2.7425} \\
\bottomrule
\end{tabular}
\end{table}

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{3pt}
\caption{Additional analog-retrieval diagnostics.}
\label{tab:app_analog_retrieval_diagnostics}
\begin{tabular}{lccc}
\toprule
\rowcolor{boxbg}
Backbone & nDCG@5 & Best log gap & Rank \(\rho\) \\
\midrule
\model{} & \ms{0.5175}{0.0445} & \ms{0.1868}{0.0285} & \ms{0.6019}{0.1460} \\
Prithvi-WxC & \ms{0.3591}{0.0107} & \ms{0.2151}{0.0594} & \ms{0.1514}{0.1489} \\
Aurora & \ms{0.4423}{0.0210} & \ms{0.1551}{0.0437} & \ms{0.2162}{0.1856} \\
ClimaX & \ms{0.4151}{0.0293} & \ms{0.2129}{0.0653} & \ms{0.1587}{0.2831} \\
StormCast & \ms{0.3960}{0.0240} & \ms{0.1714}{0.0310} & \ms{0.1258}{0.1625} \\
DLWP & \ms{0.3795}{0.0274} & \ms{0.1944}{0.0807} & \ms{-0.3865}{0.2802} \\
FCN & \ms{0.4250}{0.0112} & \ms{0.1856}{0.0846} & \ms{-0.1357}{0.2571} \\
FengWu & \ms{0.4228}{0.0310} & \ms{0.1870}{0.0858} & \ms{-0.1926}{0.2194} \\
FuXi & \ms{0.4544}{0.0356} & \ms{0.2171}{0.0806} & \ms{-0.1367}{0.2885} \\
Pangu-Weather & \ms{0.3988}{0.0506} & \ms{0.1901}{0.0838} & \ms{-0.1970}{0.2216} \\
AlphaEarth & \textbf{\ms{0.5276}{0.0531}} & \textbf{\ms{0.1782}{0.0454}} & \ms{0.4639}{0.2802} \\
\bottomrule
\end{tabular}
\end{table}

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{3pt}
\caption{High-smoke subset diagnostics for rows with observed PM\(_{2.5}\ge35\).}
\label{tab:app_smoke_high_event}
\begin{tabular}{lccc}
\toprule
\rowcolor{boxbg}
Backbone & High-smoke RMSE & High-smoke MAE & High-smoke 90th AE \\
\midrule
\model{} & \textbf{\ms{47.4870}{0.6346}} & \textbf{\ms{34.3954}{0.7654}} & \textbf{\ms{65.6213}{3.8778}} \\
Prithvi-WxC & \ms{57.2224}{1.7268} & \ms{47.3871}{0.3153} & \ms{74.9666}{3.2381} \\
Aurora & \ms{57.2752}{1.7248} & \ms{47.4368}{0.3149} & \ms{75.0755}{3.1074} \\
ClimaX & \ms{57.2828}{1.7239} & \ms{47.4407}{0.3140} & \ms{75.1012}{3.0777} \\
StormCast & \ms{56.6512}{1.7517} & \ms{46.7914}{0.3281} & \ms{74.0794}{3.4707} \\
DLWP & \ms{57.0075}{1.7359} & \ms{47.1971}{0.3198} & \ms{74.4936}{3.3826} \\
FCN & \ms{57.0582}{1.7339} & \ms{47.2401}{0.3187} & \ms{74.6431}{3.1982} \\
FengWu & \ms{57.0158}{1.7357} & \ms{47.1957}{0.3194} & \ms{74.5652}{3.2871} \\
FuXi & \ms{56.9622}{1.7371} & \ms{47.1508}{0.3201} & \ms{74.3278}{3.4435} \\
Pangu-Weather & \ms{57.1282}{1.7307} & \ms{47.3050}{0.3170} & \ms{74.6830}{3.2375} \\
AlphaEarth & \ms{48.0665}{0.7904} & \ms{35.6088}{0.7341} & \ms{66.7613}{3.9235} \\
\bottomrule
\end{tabular}
\end{table}

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{4pt}
\caption{Extreme-heat exceedance precision and recall for the \(F_1\) row.}
\label{tab:app_heat_pr}
\begin{tabular}{lcc}
\toprule
\rowcolor{boxbg}
Backbone & Precision & Recall \\
\midrule
\model{} & \ms{0.9767}{0.0117} & \ms{0.9330}{0.0299} \\
Prithvi-WxC & \ms{0.8260}{0.0030} & \ms{0.9173}{0.0033} \\
Aurora & \ms{0.5920}{0.0347} & \ms{0.0517}{0.0020} \\
ClimaX & \ms{0.7397}{0.0099} & \ms{0.7994}{0.0051} \\
StormCast & \ms{0.8840}{0.0237} & \ms{0.9320}{0.0165} \\
DLWP & \ms{0.9429}{0.0085} & \ms{0.8899}{0.0167} \\
FCN & \ms{0.9408}{0.0097} & \ms{0.9111}{0.0127} \\
FengWu & \ms{0.3808}{0.2719} & \ms{0.0266}{0.0267} \\
FuXi & \ms{0.3262}{0.1262} & \ms{0.1810}{0.0481} \\
Pangu-Weather & \ms{0.1159}{0.0743} & \ms{0.0112}{0.0032} \\
AlphaEarth & \ms{0.9824}{0.0040} & \ms{0.9278}{0.0178} \\
\bottomrule
\end{tabular}
\end{table}

\begin{table}[H]
\centering
\scriptsize
\setlength{\tabcolsep}{4pt}
\renewcommand{\arraystretch}{1.12}
\caption{Seed robustness summary for stochastic task checks.}
\label{tab:app_seed_robustness}
\resizebox{\linewidth}{!}{%
\begin{tabular}{lcll}
\toprule
\rowcolor{boxbg}
Check & Seeds & Primary value & Additional values \\
\midrule
Final burned area & 5 & log-RMSE \ms{1.1649}{0.0139} & log-MAE \ms{1.0355}{0.0114}; Spearman \ms{0.5884}{0.0338} \\
Smoke PM\(_{2.5}\) & 5 & RMSE \ms{4.4684}{0.0060} & MAE \ms{2.4127}{0.0016}; \(r\) \ms{0.6360}{0.0013} \\
Extreme heat & 5 & RMSE-C \ms{0.2179}{0.0048} & MAE-C \ms{0.1787}{0.0020}; exceed. \(F_1\) \ms{0.9541}{0.0164} \\
Fire spread & 5 & exact \(F_1\) \ms{37.98}{1.33} & spatial \(F_1\) \ms{82.20}{0.32}; AP \ms{32.73}{0.60} \\
\bottomrule
\end{tabular}%
}
\end{table}
\FloatBarrier

\end{document}