The exceedance fan: seeing your probability of exceeding a limit over time

The Wind Agent's exceedance fan presents a time series of forecast wind conditions, typically mean speed or gust, against a user-specified operational limit. Each hour on the fan shows a range of possible outcomes, derived from an ensemble forecast, rather than a single deterministic prediction. This range is visualised as shaded bands, indicating the probability distribution of the wind metric at each forecast hour.

The horizontal axis represents time, extending from the present out to the forecast horizon (e.g., 5–10 days). The vertical axis shows the wind speed or gust in the chosen units (e.g., m/s, km/h, mph, knots). A horizontal line marks the user's operational limit. The key feature of the fan is how these bands widen with increasing lead time, directly illustrating the growing uncertainty inherent in longer-range forecasts. This allows users to quickly identify periods where the risk of exceeding their limit is low, moderate, or high.

For example, an operation with a gust limit of 20 m/s (approximately 39 knots) might see the fan indicating a low probability of exceedance for the next 24 hours, with the 90th percentile band remaining well below the limit. However, by 72 hours out, the 90th percentile band might cross the limit, suggesting a 10% chance of gusts reaching or surpassing 20 m/s. This visual summary aids in planning by highlighting periods of higher confidence and those requiring closer monitoring.

The shaded bands on the exceedance fan correspond to different percentiles of the ensemble forecast distribution. Typically, these might represent the 10th, 25th, 50th (median), 75th, and 90th percentiles. These are derived from the individual members of an ensemble forecast, which are multiple model runs initiated with slightly perturbed initial conditions to capture the range of possible atmospheric evolutions.

• The 50th percentile (median) represents the most likely outcome, with half of the ensemble members forecasting a lower value and half a higher value. This is often similar to a deterministic forecast.
• The 10th and 90th percentiles define a range within which 80% of the ensemble members fall. If the 90th percentile is below your limit, there is less than a 10% chance of exceeding that limit. Conversely, if the 10th percentile is above your limit, there is a greater than 90% chance of exceeding it.
• The 25th and 75th percentiles further refine this, indicating the interquartile range where the central 50% of forecasts lie.

Consider an example: if at a specific hour, the 10th percentile for mean wind speed is 5 m/s, the 50th percentile is 8 m/s, and the 90th percentile is 12 m/s, it means:

• 10% of ensemble members predict speeds of 5 m/s or less.
• 50% of ensemble members predict speeds of 8 m/s or less.
• 90% of ensemble members predict speeds of 12 m/s or less.

If your limit is 10 m/s, and the 90th percentile is 12 m/s, then 10% of the ensemble members are predicting speeds above 10 m/s. This allows for a quantitative assessment of risk.

Beyond showing percentile bands, the exceedance fan often includes a distinct shaded area or line that directly plots the probability of exceeding your specified limit. This is a direct output of the ensemble: for each forecast hour, the instrument counts how many ensemble members predict a wind speed or gust above your limit, and expresses this as a fraction or percentage.

For instance, if an ensemble has 50 members, and at a particular hour, 15 of those members predict a gust exceeding your 15 m/s limit, then the probability of exceedance shown on the fan for that hour would be 15/50 = 30%. This shaded line provides an immediate visual cue for risk assessment, complementing the percentile bands.

This direct probability line is particularly useful for rapid decision-making. If your operational procedure states that work must cease if the probability of exceedance for a certain metric (e.g., gust) rises above 20%, you can quickly scan the fan for where this line crosses the 20% threshold. This is more efficient than mentally calculating the risk from percentile bands alone.

It is important to remember that this probability is conditional on the ensemble's representation of reality. It reflects the model's internal uncertainty, not necessarily the absolute likelihood in the real world. However, it is a robust indicator of the forecast's confidence in staying below or going above a critical value.

A fundamental characteristic of numerical weather prediction is that forecast accuracy generally decreases with increasing lead time. This is due to the chaotic nature of the atmosphere and the propagation of initial condition and model uncertainties. The exceedance fan visually represents this by showing the percentile bands widening as the forecast extends further into the future.

For example, in the short term (e.g., 0–24 hours), the 10th and 90th percentile bands for wind speed might be relatively close, perhaps spanning only 2–3 m/s. This indicates a high degree of confidence in the forecast. However, by 72 hours out, these bands might spread to cover 8–10 m/s, signifying much greater uncertainty. This widening means that the range of plausible wind speeds or gusts becomes larger, and therefore, the probability of hitting a specific threshold becomes more diffuse.

This visual cue is critical for operational planning. It suggests that decisions requiring high confidence should ideally be made for periods within the narrower, more certain part of the fan. For longer lead times, the widening bands indicate that plans should be more flexible, incorporating contingency measures, or that a 'go/no-go' decision should be deferred until the forecast tightens up. The Wind Agent's Agreement Spine also provides a direct measure of how much different models agree, which often correlates with the width of the ensemble fan.

Traditional deterministic forecasts provide a single value for wind speed or gust at each forecast hour. While seemingly precise, this single line masks the inherent uncertainty in the prediction. It represents just one possible outcome from a vast array of atmospheric possibilities.

The exceedance fan, by contrast, offers a probabilistic view. Instead of stating 'the gust will be 15 m/s', it might show 'the median gust is 12 m/s, but there's a 20% chance of gusts exceeding 15 m/s'. This shift from a single point estimate to a distribution of probabilities provides a more complete and honest representation of the forecast.

Consider an operation with a gust limit of 15 m/s. A deterministic forecast might show 14 m/s, suggesting a safe window. However, the exceedance fan might reveal that while the median is 14 m/s, the 90th percentile is 18 m/s, indicating a significant risk (10% chance) of exceeding the limit. Relying solely on the deterministic forecast in such a scenario could lead to an underestimation of risk.

This distinction is particularly important for high-stakes operations where the cost of an exceedance is substantial. The fan encourages a risk-aware approach, moving away from binary 'yes/no' decisions based on a single number towards a nuanced understanding of probabilities. It empowers users to make more informed decisions by considering the full spectrum of plausible outcomes.

The primary application of the exceedance fan is to identify optimal operational windows where the probability of exceeding a specific limit is acceptably low. By setting your critical wind speed or gust limit, the fan immediately highlights periods of higher and lower risk.

Worked Example: Imagine you are planning a drone survey with a maximum operational gust limit of 10 m/s. You look at the exceedance fan for your location. For the next 24 hours, the shaded area showing the probability of exceeding 10 m/s remains below 5%. This indicates a low-risk window. However, from 24 to 48 hours, the probability rises to 25%, and beyond 48 hours, it consistently stays above 40%.

Your operational protocol states that drone flights are permitted when the probability of exceeding the gust limit is below 10%. Based on the fan:

• Next 24 hours: Probability < 5%. This is a suitable window for operations.
• 24–48 hours: Probability rises to 25%. This window is too risky under your protocol.
• Beyond 48 hours: Probability > 40%. Definitely unsuitable.

This direct visual assessment allows you to confidently schedule your drone survey within the next 24 hours, while understanding that later periods carry too much risk. The fan helps to programme a decision rule directly into your planning, rather than relying on subjective interpretation of numbers. It is a key component of the Grounded Agent's advice.

While powerful, the exceedance fan has limitations that users must understand to avoid misinterpretation:

1. Ensemble size and representativeness: The accuracy of the probability estimates depends on the number of ensemble members and how well they represent the true range of atmospheric possibilities. Smaller ensembles (e.g., 20 members) provide less robust statistics than larger ones (e.g., 50 members).
2. Model bias: Ensembles, like deterministic models, can exhibit biases. If the underlying model consistently over- or under-forecasts wind speeds, the entire fan may be shifted, affecting the perceived probabilities.
3. Resolution and local effects: Ensemble members are typically run at coarser resolutions than deterministic models. This means they may not capture highly localised phenomena (e.g., specific terrain effects, sea breezes in complex coastal areas) as accurately. The fan provides a regional probability, which may need to be adjusted with local knowledge.
4. Correlation between members: Ensemble members are not entirely independent; they share common model physics and initial conditions. This means the spread might not fully encompass all possible futures, especially for rare, high-impact events.

Users should interpret the fan in conjunction with other information, such as the Agreement Spine (which shows inter-model agreement), recent observations (via the evidence records), and local knowledge. For instance, if the fan shows a low probability of exceedance but the Agreement Spine indicates significant divergence between models, caution is warranted. The fan is a sophisticated tool, but not a replacement for meteorological expertise and critical thinking.

The exceedance fan and the exceedance curve are complementary visualisations of ensemble forecast data, each serving a distinct purpose. While the fan shows the probability of exceeding a limit over time, the exceedance curve provides a detailed probability distribution for a single forecast hour.

The exceedance curve plots the probability of a wind metric (speed or gust) being at or above any given value. For a specific hour on the fan, if you were to draw a vertical slice through the percentile bands, that slice would correspond to the cumulative distribution function, which is the basis for the exceedance curve. For example, if the fan shows a 20% chance of exceeding 15 m/s at 48 hours, the exceedance curve for that 48-hour point would show a 20% probability at the 15 m/s mark.

See it live: To understand the connection, select a specific hour on the exceedance fan. Then, navigate to the exceedance curve chart for that same hour. You will observe that the probability values on the curve directly correspond to the percentile ranges and exceedance probabilities shown on the fan for that moment in time. The fan gives you the overview across the forecast, while the curve allows you to drill down into the precise probabilities for all possible thresholds at a critical hour. Together, they provide a comprehensive picture of forecast uncertainty and risk.