FOCUS on Contamination: Hydrology-Informed Noise-Aware Learning for Geospatial PFAS Mapping

The paper introduces FOCUS, a geospatial deep learning framework that leverages hydrological connectivity and environmental context to map PFAS contamination from sparse data, outperforming traditional methods and enabling scalable risk screening for prioritizing future sampling efforts.

The Gist

Imagine you are trying to find hidden treasure (PFAS contamination) in a massive, sprawling kingdom (the United States). The treasure is dangerous, but it's invisible to the naked eye. To find it, you need to send out explorers with expensive, high-tech metal detectors (scientific sampling).

The Problem:
Sending out explorers is incredibly expensive and slow. Right now, we only have a few hundred explorers scattered across the entire country. They've found some treasure, but there are huge gaps in the map. We don't know where the rest of the treasure is hiding.

Old methods tried to guess the missing spots by drawing straight lines between the explorers (like connecting dots) or by trying to simulate how the treasure moves using complex physics equations. But these methods often fail because the "treasure" doesn't move in straight lines; it follows rivers, gets stuck in soil, and spreads from factories in messy, unpredictable ways. Plus, with so few explorers, the guesses are often wrong.

The Solution: FOCUS
The authors of this paper built a new tool called FOCUS. Think of FOCUS as a super-smart detective who doesn't just look at where the explorers found treasure, but studies the entire landscape to figure out where the treasure must be.

Here is how FOCUS works, using some everyday analogies:

1. The "Context" Clues

Instead of just looking at the specific spot where an explorer found PFAS, FOCUS looks at the whole neighborhood. It uses free, high-resolution satellite data to see:

• The Roads (Hydrology): Where do the rivers flow? If a factory dumps poison upstream, FOCUS knows the poison will flow downstream, even if no explorer has checked that specific river bend yet.
• The Neighborhood (Land Cover): Is the area a busy industrial zone or a quiet forest? Factories are more likely to have the "treasure" (contamination) than a pine forest.
• The Source (Distance): How far is this spot from a known polluter?

2. The "Trust Score" (Noise-Aware Learning)

This is the most clever part. Because we have so few explorers, the data is "noisy."

• The Analogy: Imagine a game of "Telephone." If you tell a secret to one person, and they tell the next, the message gets distorted. In our case, we take a single measurement from one spot and try to guess what the whole surrounding area looks like. This creates "fake" labels that might be wrong.
• The Fix: FOCUS doesn't blindly trust every single data point. It assigns a "Trust Score" to every pixel on the map.
  • If a spot is right next to a known factory and right in the path of a river, FOCUS says, "I'm 90% sure this is contaminated."
  • If a spot is far away from factories and the river flow is weird, FOCUS says, "I'm not sure. This data point might be a fluke."
  • The Result: The AI learns to focus its energy on the "high trust" areas and ignores the "low trust" noise, preventing it from getting confused by bad data.

3. The "Heat Map"

Once trained, FOCUS doesn't just give you a list of numbers. It paints a Heat Map of the entire country.

• Red areas: "High risk! Send an explorer here immediately."
• Green areas: "Likely safe."
• Yellow areas: "Maybe, let's check."

Why This Matters

Before FOCUS, if you wanted to know if your local river was safe, you had to wait for a government agency to send a boat to test it, which could take years.

With FOCUS:

• It's Fast: It can scan the whole US in hours, not years.
• It's Smart: It uses the laws of physics (how water flows) and common sense (factories pollute) to make educated guesses.
• It Saves Money: Instead of testing every single river, officials can use the map to pick the most likely dangerous spots to test first.

The "Web Map"

The team even built a public website (like Google Maps for pollution) where anyone can zoom in on their town and see the predicted risk. It's like having a crystal ball that helps communities ask the right questions: "Hey, our town is in a red zone on the map, but we haven't tested it yet. Can we get a real test?"

In a nutshell:
FOCUS is a smart AI detective that fills in the blanks of a broken puzzle. It uses the few pieces we have, combined with knowledge of how rivers and factories work, to draw a complete picture of where dangerous chemicals are hiding, helping us protect our health before it's too late.

Technical Summary

1. Problem Statement

Per- and polyfluoroalkyl substances (PFAS) are persistent "forever chemicals" with severe public health impacts. However, mapping their contamination is hindered by:

• Data Scarcity: Field sampling is expensive and logistically difficult, resulting in sparse, unevenly distributed ground-truth data (e.g., only ~290 surface water points nationally in 2019).
• Limitations of Existing Models:
  • Physical Models (e.g., SWAT, MODFLOW): Require extensive data and are computationally expensive at large scales.
  • Geostatistical Methods (e.g., Kriging): Rely on assumptions of spatial stationarity that often fail for complex, source-driven contaminants like PFAS.
  • Traditional ML (e.g., Random Forests): Typically aggregate features around sparse points, discarding spatial structure and requiring manual feature engineering.
• Label Noise: Expanding sparse point measurements to pixel-level supervision for deep learning introduces structured, asymmetric noise (e.g., a point measurement may not represent the entire surrounding area, or detection limits may hide contamination).

2. Methodology: The FOCUS Framework

The authors propose FOCUS, a geospatial deep learning framework designed to learn from sparse, noisy labels by integrating hydrological and environmental priors.

A. Data Representation

• Input: Instead of aggregating features around points, FOCUS processes multi-channel raster images (patches) centered on sample points.
• Channels: Includes land cover (NLCD), hydrological flow direction (D8 algorithm), distance to industrial dischargers (EPA ECHO data), and distance to sampling points.
• Labels: Point-level measurements are expanded to surface water pixels within the patch. Pixels are labeled 1 (above health threshold) or 0 (below), with non-water pixels masked.

B. The Noise-Aware Objective (FOCUS Loss)

The core innovation is a Hydrology-Informed Noise-Aware Loss that addresses the "point-to-pixel" label noise.

1. Latent Noise Model: The authors assume an asymmetric flip noise model where the observed label $y_i$ differs from the latent true state $z_i$ with a pixel-specific probability $\eta_i$. Unlike standard noisy-label learning, $\eta_i$ is driven by physical processes (e.g., distance from a source, flow direction) rather than random annotation error.
2. Pixel Confidence ($M_i$): A correctness score is derived for each pixel based on environmental priors:
   • $p_{discharger}$: Decay with distance to PFAS facilities.
   • $p_{landcover}$: Industrial vs. natural land types.
   • $p_{sample}$: Decay from monitoring points.
   • $p_{downstream}$: Increase along hydrological flow.
   • Weights: Determined via grid search and domain expert validation (e.g., 40% dischargers, 30% flow, 20% land cover, 10% sample distance).
3. Loss Function: The FOCUS loss scales the standard Focal Loss by the confidence weight $M_i$:
   $$\mathcal{L}_{FOCUS} = \frac{1}{N} \sum_{i=1}^{N} M_i (1 - p_i)^\gamma [-y_i \log p_i - (1-y_i) \log(1-p_i)]$$
   • Mechanism: $M_i$ down-weights uncertain pixels (noise-robust), while the Focal term $(1-p_i)^\gamma$ up-weights hard examples.
   • Theoretical Guarantee: The authors prove that minimizing this loss serves as a valid surrogate objective that upper-bounds the noisy negative log-likelihood, effectively learning from the underlying clean labels despite the noise.

C. Model Architecture

• Backbone: Inspired by Prithvi (a geospatial foundation model), FOCUS uses a Masked Autoencoder (MAE) architecture.
• Pretraining: Instead of using raw satellite imagery pretraining, the model is pretrained on derived geospatial products (land cover, distance rasters) to better capture environmental nuances relevant to PFAS.
• Fine-tuning: The model is fine-tuned on the sparse PFAS data using the FOCUS loss.

3. Key Contributions

1. FOCUS Framework: A principled geospatial deep learning framework that integrates sparse observations with large-scale environmental context.
2. Noise-Aware Learning: Formalization of PFAS mapping as learning under structured, spatially dependent label noise, with a theoretical derivation showing the proposed loss is a valid surrogate.
3. Hydrology-Informed Priors: Derivation of pixel-wise confidence weights ($M_i$) that link physical processes (flow, industry proximity) to learning robustness.
4. Scalable Performance: Demonstration of superior scalability compared to traditional ML (feature aggregation) and physical simulations.
5. Real-World Deployment: Development of an interactive web map interface for policymakers and stakeholders to visualize risk.

4. Results and Evaluation

The framework was evaluated on US-wide data (2008, 2019, 2022) and validated with independent field samples.

• Performance vs. Baselines: FOCUS consistently outperformed:
  • Kriging: Better handling of non-stationary contamination patterns.
  • Pollutant Transport Simulations: More accurate and scalable.
  • Random Forests: Superior spatial coherence and F-scores (e.g., 79% F-score vs. 53% for RF in 2022).
  • Standard Focal Loss: The noise-aware variant significantly improved metrics (e.g., IoU increased from 36% to 67% in 2022).
• Real-World Validation:
  • Successfully identified 8 newly collected surface water samples in Ann Arbor, MI (2025) as highly contaminated, despite these locations being outside the training distribution.
  • Validated on independent MPART fish tissue data with high accuracy (85%).
• Efficiency: Feature extraction for a 44,000 km² region (Northern Michigan) took 3.2 hours with FOCUS (DL) compared to 2 days with Random Forests (ML), due to the elimination of per-point buffer aggregation.
• Robustness: High spatial consistency (>93% agreement) across overlapping patches and strong generalization in cross-state validation (out-of-distribution testing).
• Calibration: Low Expected Calibration Error (ECE ≤ 0.1), indicating reliable probability estimates.

5. Significance and Impact

• Scientific Advancement: Bridges the gap between sparse monitoring and large-scale risk assessment, providing a "screening-level" tool to prioritize follow-up sampling.
• Interdisciplinary Co-Design: Developed in close collaboration with environmental scientists and regulators (e.g., Environmental Working Group, Huron River Watershed Council) to ensure the model reflects scientific uncertainty and regulatory priorities.
• Policy Application: The web interface allows non-technical users to explore contamination risks, identify "unexplained" hotspots (high risk with no known nearby sources), and guide resource allocation for remediation.
• Ethical Considerations: The authors explicitly address the risks of public-facing risk maps (property values, environmental justice) by incorporating uncertainty visualization and engaging an advisory group to ensure responsible communication.

In summary, FOCUS demonstrates how AI can overcome data scarcity in environmental science by embedding domain knowledge (hydrology, industrial sources) directly into the learning objective, enabling robust, scalable, and actionable contamination mapping.