How numerical weather prediction works

Numerical Weather Prediction (NWP) models are built upon a set of fundamental physical laws, known as the primitive equations. These equations describe the conservation of momentum (Newton's second law), mass, energy (first law of thermodynamics), and water vapour, alongside the ideal gas law. They are partial differential equations that relate changes in atmospheric variables (such as wind, temperature, pressure, and humidity) over time and space.

To solve these complex equations, the atmosphere is discretised into a three-dimensional grid of points or cells. Each cell represents a small volume of the atmosphere, and within it, the model calculates the average values of atmospheric variables. The horizontal resolution of these grids varies; global models might have grid cells tens of kilometres across, while regional models can resolve features down to a few kilometres. Vertically, models typically use dozens to over a hundred layers, extending from the surface up into the stratosphere.

The equations are then approximated for each grid cell, transforming continuous physical processes into discrete algebraic operations that can be solved computationally. This process is iterative: the model calculates the state of the atmosphere at a future time step based on its current state, then uses that new state to calculate the next, and so on. The accuracy of this approximation depends heavily on the grid resolution and the numerical schemes used.

For a forecast to be accurate, the model must start from the best possible representation of the current atmospheric state. This initial state is derived from a vast array of observations collected globally. These include surface weather stations, weather balloons (radiosondes), radar, commercial aircraft, and satellite data (e.g., cloud-top temperatures, atmospheric soundings, wind vectors from cloud motion). Billions of observations are assimilated into the model's initial state daily.

Data assimilation is the process of combining these disparate observations with a previous short-range forecast (the 'background' or 'first guess') to produce a statistically optimal estimate of the current atmospheric state. This is not simply averaging; it involves sophisticated mathematical techniques, such as 4D-Var (four-dimensional variational assimilation) or ensemble Kalman filters, which account for the uncertainties in both the observations and the model's background forecast.

Because observations are sparse and unevenly distributed, and each has its own error characteristics, the initial state is never perfect. Small errors in the initial conditions can grow significantly over time, a concept central to the predictability of the atmosphere. The quality of the initial conditions is a primary determinant of forecast skill, especially for shorter lead times.

Once the initial conditions are established, the NWP model advances the atmospheric state forward in time through a series of discrete steps. Each time step involves solving the primitive equations for every grid cell to calculate how the variables will change over a short period. This new state then becomes the starting point for the next time step. The length of a time step is typically very short, often on the order of minutes, to maintain numerical stability and accuracy. For example, a 72-hour forecast might involve thousands of time steps.

The atmosphere is a chaotic system, meaning that even tiny, unresolvable errors in the initial conditions or approximations in the model equations can lead to large divergences in the forecast over time. This phenomenon, often referred to as the 'butterfly effect', dictates that forecast skill inevitably decreases with increasing lead time. Beyond approximately 10–14 days, the atmosphere's inherent unpredictability makes deterministic forecasts largely unreliable.

Consider a model with a 10 km grid. A small, unobserved thunderstorm, perhaps 5 km across, might influence local wind patterns significantly. This thunderstorm is 'sub-grid scale' and not directly represented. Its absence or misrepresentation in the initial state can propagate errors that affect larger-scale features hours or days later. This exponential growth of error is why ensemble forecasting is critical.

Many important atmospheric processes occur at scales smaller than the model's grid resolution. These sub-grid scale processes cannot be explicitly resolved by the primitive equations at the grid cell level. Examples include cloud formation, precipitation, turbulence, and the interaction of the atmosphere with the land surface. To account for their effects, models use parameterisation schemes.

Parameterisation involves developing simplified physical or statistical relationships that represent the average effect of these small-scale processes on the larger-scale grid. For instance, a cloud parameterisation scheme might estimate the amount of precipitation within a grid cell based on its average temperature and humidity, even though the individual clouds within that cell are not resolved. Similarly, boundary layer schemes estimate the transfer of heat, moisture, and momentum between the surface and the lowest model layers.

These schemes are a major source of uncertainty and differences between models. Different parameterisations can lead to varying predictions for rainfall, temperature, and wind, particularly in complex terrain or during convective events. Improving parameterisation schemes is an active area of research in NWP.

While global models cover the entire Earth, regional models (also known as limited-area models or LAMs) focus on a smaller geographical domain, such as Europe or Ireland. They operate at a higher spatial resolution than global models, allowing them to represent local features like coastlines, mountains, and urban areas with greater detail. This improved resolution often leads to more accurate forecasts for specific locations.

However, regional models cannot exist in isolation. They need information about the atmospheric conditions at their boundaries to run. These boundary conditions are provided by a coarser-resolution global model. For example, a regional model covering Ireland would receive information about incoming weather systems, temperature, and pressure from a global model at its northern, southern, eastern, and western edges.

The quality of a regional model's forecast is therefore dependent on the accuracy of the global model providing its boundary conditions. If the global model makes a significant error in predicting a large-scale weather system, that error will propagate into the regional model's forecast. This dependency highlights the interconnectedness of NWP systems, from global to local scales.

Running NWP models requires immense computational power. Each grid cell needs to have its equations solved for each time step, and as resolution increases, the number of grid cells and the computational effort grow exponentially. Doubling the horizontal resolution (e.g., from 20 km to 10 km) quadruples the number of horizontal grid cells. If the time step also needs to be halved for stability (which is often the case), the total computational cost increases by a factor of eight.

For example, if a model with 20 km resolution and a 10-minute time step takes 1 hour to compute a 72-hour forecast, a 10 km resolution version might take 8 hours. This exponential scaling means that there are practical limits to how fine a resolution models can achieve, even with supercomputers. Meteorological centres continuously invest in faster hardware and more efficient algorithms to push these boundaries.

The balance between resolution, forecast lead time, and computational budget is a critical decision for every operational NWP centre. This constraint is a primary reason why different models have different resolutions and why global models typically have coarser grids than regional models.

The raw output from an NWP model consists of atmospheric variables on its native grid. However, most users require forecasts for specific geographical points, not for 10 km x 10 km grid cells. Post-processing is the crucial step of transforming this raw grid output into user-friendly point forecasts.

This involves several techniques:

1. Interpolation: Values for a specific location are estimated from the surrounding grid points. Simple methods include bilinear interpolation, while more complex methods account for terrain and local effects.
2. Statistical Correction (MOS - Model Output Statistics): Models often exhibit systematic biases (e.g., consistently forecasting temperatures too high or winds too low in certain conditions). MOS uses historical observations to statistically correct these biases, improving local accuracy.
3. Derived Products: Calculating quantities not directly output by the model, such as gust speeds (often derived from mean wind and turbulence kinetic energy), or converting wind speeds to Beaufort scale.

For example, a model might predict a mean wind speed of 10 m/s for a grid cell containing a coastal headland. Post-processing would then use local terrain data and MOS corrections to refine this to a more accurate value for the specific point on the headland, potentially higher due to local acceleration effects. This final step bridges the gap between the model's physics and the user's specific needs.

The Wind Agent acts as an intelligent layer on top of these foundational NWP principles, providing a refined and actionable view of wind conditions. It does not run its own atmospheric model; instead, it ingests data from multiple leading global and regional NWP models, including ECMWF IFS, GFS, and DWD ICON-EU. This multi-model approach is crucial because no single model is always superior in all situations or for all parameters.

By comparing forecasts from different models for the same location and time, The Wind Agent's Agreement Spine highlights areas of consensus or divergence, giving you a clearer picture of forecast uncertainty. When models agree, confidence is higher; when they diverge, it signals greater uncertainty, prompting closer attention to the ensemble spread.

Furthermore, The Wind Agent addresses the critical issue of wind shear by providing height-matched wind speeds. The Shear Glass displays wind at 10, 80, 120, and 180 metres, allowing users to specify their exact working height and receive an interpolated wind speed relevant to their operation, rather than relying solely on the standard 10 m forecast. This is particularly vital for activities like crane operations or drone flights where wind changes significantly with height.

Finally, the exceedance fan integrates ensemble forecast data with your specified wind limits. Instead of a single 'best guess' forecast, it presents the probability of exceeding your operational limits, offering a probabilistic view that aligns with risk-based decision-making. This moves beyond deterministic forecasts to provide a more nuanced understanding of potential impacts.