Resolution and grids: why model accuracy depends on the numbers

Numerical Weather Prediction (NWP) models discretise the atmosphere into a three-dimensional grid of cells. Each cell represents a volume of air, and the model solves atmospheric equations for the average conditions within that cell. The horizontal resolution refers to the typical distance between the centres of these grid cells, often expressed in kilometres (km).

For instance, a model with a 9 km resolution has grid cells approximately 9 km by 9 km horizontally. This means that features smaller than this resolution cannot be explicitly represented. Instead, their effects are parameterised, meaning their influence is approximated based on larger-scale grid-cell averages. This process is necessary because explicitly modelling every small-scale atmospheric process would be computationally prohibitive.

Typical global models, such as the ECMWF Integrated Forecasting System (IFS) or the NOAA Global Forecast System (GFS), operate at horizontal resolutions ranging from approximately 9 km to 13 km. Regional or Limited Area Models (LAMs) can achieve much finer resolutions, sometimes down to 1 km or even a few hundred metres, to capture more localised phenomena. However, even these high-resolution models face fundamental limits on what they can resolve, and the computational cost increases exponentially with resolution.

A commonly cited rule in meteorology is that a feature needs to span at least 3 to 5 grid cells to be adequately resolved by a numerical model. This is not a hard physical limit but an empirical observation based on how numerical schemes handle gradients and interactions within the grid. Features smaller than this threshold are often smoothed out or their effects are parameterised, leading to a less accurate representation of local conditions.

Consider a small hill that is 5 km wide. In a 9 km resolution model, this hill would likely fall within a single grid cell or be spread across two. The model would struggle to represent its shape, its impact on airflow, or the localised wind effects like acceleration over the crest or shelter in the lee. Such a feature would be heavily smoothed or entirely missed, leading to an inaccurate wind forecast for that specific location.

However, in a a 1 km resolution model, the same 5 km hill would span 5 grid cells. This allows the model to capture the topography more accurately and, consequently, to simulate the wind flow around and over it with greater fidelity. This principle applies not only to terrain but also to atmospheric phenomena like convective cells, sea breezes, or frontal boundaries. Understanding this rule helps interpret model outputs, especially for microclimates.

One of the most significant impacts of model resolution is on the representation of terrain. Mountains, valleys, and even significant hills are often smoothed out or averaged over the area of a grid cell. This 'terrain smoothing' can lead to inaccuracies in wind forecasts, particularly in areas with complex topography. The model's internal representation of the Earth's surface is a simplified version of reality, especially at coarser resolutions.

For example, if a model has a 10 km resolution, a sharp, isolated peak like Carrauntoohil (Ireland's highest mountain, approximately 1038 m high) might be represented as a much broader, lower mound, or even just a slight elevation. The precise effects of its steep slopes on wind acceleration, turbulence, or shelter would be lost. The model would calculate wind speeds and directions based on this smoothed topography, which might differ significantly from the actual conditions experienced on the ground.

This is why forecasts for mountainous regions or areas with intricate coastlines often require higher-resolution models or local downscaling techniques to provide useful detail. The Wind Agent's Shear Glass, for instance, relies on model data that has already accounted for some level of terrain representation, but the underlying resolution still matters for the accuracy of that representation. Users should always cross-reference with local knowledge.

Coastal areas present a particular challenge for NWP models due to the sharp contrast between land and sea surfaces. Models use a land-sea mask to distinguish between these two types of surface. At lower resolutions, the coastline can appear blocky or jagged, leading to errors in how the model handles land-sea interactions. This is especially problematic for countries like Ireland with highly irregular coastlines.

For example, a model with a 10 km resolution might misrepresent a narrow headland or a complex estuary. A grid cell that is partly land and partly sea might be designated entirely as one or the other, or an average of their properties. This can lead to inaccuracies in:

• Sea breeze development: The model might misjudge the timing or strength of a sea breeze if the land-sea boundary is poorly defined, affecting local wind speeds and directions. This is critical for coastal activities.
• Funnelling effects: Narrow bays or inlets that channel wind might not be resolved, leading to underestimation of wind speeds in these areas.
• Shelter and exposure: Areas that are sheltered by a headland might be incorrectly exposed, or vice-versa, due to the smoothed coastline.

These errors are a common source of forecast discrepancy in coastal zones. The Wind Agent's agreement spine can highlight when models diverge in these complex areas, prompting closer inspection.

NWP models employ various grid types to cover the Earth's surface. The choice of grid impacts computational efficiency and how accurately different regions are represented:

• Regular Latitude-Longitude Grid: The simplest, with constant angular spacing. However, grid cells become smaller towards the poles, leading to computational redundancy and numerical instability. This type is less common in modern global models.
• Reduced Gaussian Grid: Used by models like the ECMWF IFS. This grid maintains roughly constant physical spacing by reducing the number of grid points towards the poles. This balances computational efficiency with a more uniform resolution across the globe.
• Icosahedral Grid: Used by models like DWD ICON. This grid uses a triangular tessellation of a sphere, offering a nearly uniform resolution across the globe without the pole singularity issues of latitude-longitude grids. It is well-suited for global models and nesting.

Each grid type has its advantages and disadvantages regarding computational cost, numerical stability, and how it handles atmospheric processes. The Wind Agent integrates data from models using different grid types, providing a comprehensive view that leverages the strengths of each. For example, the ICON model's icosahedral grid is designed for efficient global-to-regional nesting.

To achieve higher resolution over specific regions without the prohibitive computational cost of a global high-resolution model, meteorologists use nesting. This involves running a high-resolution Limited-Area Model (LAM) within the boundaries of a coarser-resolution global model.

The global model provides the boundary conditions (wind, temperature, pressure, humidity) for the LAM, which then calculates the atmospheric evolution at a finer scale within its domain. This allows the LAM to resolve smaller-scale features like local terrain effects, sea breezes, and convective storms that the global model cannot.

For example, Met Éireann runs HARMONIE-AROME, a LAM with a resolution of approximately 2.5 km, nested within a global model like the ECMWF IFS. This provides detailed forecasts for Ireland. The trade-off is that LAMs are dependent on the accuracy of their parent global model for their boundary conditions. Errors in the global model can propagate into the nested LAM. The Wind Agent often displays data from both global and regional models, allowing users to compare their outputs and understand the potential benefits and limitations of nesting.

While higher resolution allows models to represent smaller features, it does not automatically guarantee a better forecast. Several factors can limit the benefits of increased resolution:

• Initial Conditions: Even a high-resolution model needs accurate initial atmospheric observations. If the observational network is sparse, particularly over oceans, the model's starting point may be flawed, regardless of its resolution.
• Physics Parameterisations: Many atmospheric processes, such as cloud formation, precipitation, and turbulence, occur at scales smaller than even the highest resolution grids. These processes must be parameterised, and the accuracy of these parameterisations is crucial. A higher-resolution model with poor parameterisations might perform worse than a lower-resolution model with robust physics.
• Computational Cost: Higher resolution demands significantly more computational power and time. This can limit the number of ensemble members that can be run, reducing the ability to quantify forecast uncertainty.
• Error Growth: Small errors in initial conditions or parameterisations can grow rapidly in high-resolution models, leading to divergence from reality over time. Sometimes, a slightly coarser resolution can smooth out some of this 'noise'.

Therefore, the optimal resolution is a balance between resolving important features, computational feasibility, and the inherent predictability of the atmosphere. The Wind Agent provides ensemble forecasts to illustrate this uncertainty, even from high-resolution models.

NWP models provide forecasts on their grid points, but users typically want a forecast for a specific location, which rarely coincides exactly with a grid point. This requires interpolation, a mathematical process to estimate values between known grid points.

Common interpolation methods include:

• Nearest Neighbour: Simply takes the value from the closest grid point. This is computationally cheap but can lead to abrupt changes in values if the closest grid point shifts.
• Bilinear or Bicubic Interpolation: Uses values from multiple surrounding grid points (e.g., the four closest for bilinear) and weights them based on distance. This produces a smoother, more realistic estimate.

For example, if a model has grid points at (0,0), (0,10), (10,0), and (10,10) km, and you want a forecast for (3,4) km, interpolation will estimate the wind speed and direction at that precise point. The Wind Agent performs this interpolation to provide height-matched wind data at your exact specified location.

It is important to remember that interpolation does not add new information or resolution. It merely provides a smooth estimate based on the existing grid data. If the underlying grid cannot resolve a feature, interpolation will not magically create it. The quality of the interpolated forecast is fundamentally limited by the resolution and accuracy of the original model output.