Climate and Wind Statistics¶

A CFD wind study produces dimensionless results – pressure, force and comfort coefficients that are independent of the actual wind speed. To turn those into design values (design pressures, return-period accelerations, pedestrian-comfort verdicts) they must be combined with the local wind climate: how often the wind blows, how hard, and from which direction.

The cfdmod.climate module provides that statistical layer – long-term speed distributions, extreme-value analysis, directional statistics and the Lawson pedestrian-comfort criterion. Climate ingestion is deliberately kept outside the pipeline (it is small tabular data), and combined with the pipeline’s dimensionless output in a downstream step.

Parent distribution (Weibull)¶

The long-term distribution of mean wind speed at a site is well described by a Weibull distribution, whose probability density is

\[ f(U) = \frac{k}{c}\left(\frac{U}{c}\right)^{k-1} \exp\!\left[-\left(\frac{U}{c}\right)^{k}\right] \]

with shape parameter \(k\) and scale parameter \(c\) (a characteristic speed). fit_weibull fits \((k, c)\) to a speed record and directional_weibull_fit fits one Weibull per wind-direction sector. The helpers weibull_shape_from_mean_and_std / weibull_scale_from_mean_and_shape recover parameters from summary statistics, and get_weibull_quantile / get_weibull_probability_between_velocities read probabilities off the fitted distribution – the exceedance frequencies a comfort or fatigue assessment integrates over.

Extreme values (Gumbel)¶

Design wind loads are governed not by the typical speed but by the extreme speed for a chosen return period. The maxima (annual, or per independent storm) follow a Type I / Gumbel extreme-value distribution,

\[ F(U) = \exp\!\left[-e^{-(U - \mu)/\beta}\right] \]

with location \(\mu\) and scale \(\beta\). The design speed for a return period \(R\) (years) follows from the reduced variate \(y_R = -\ln\!\left[-\ln\!\left(1 - 1/R\right)\right]\) (get_reduced_variate()), giving the return level

\[ U_R = \mu + \beta\, y_R \]

(type_I_return_level()). fit_gumbel fits the distribution; two estimators are provided – fit_gumbel_BR_MIS (the Method of Independent Storms after Vallis, 2019) and fit_gumbel_MLE_MIS (maximum-likelihood) – and directional_gumbel_fit fits per sector.

Storm declustering and direction¶

Extreme-value fitting assumes the maxima are independent. A raw time series is not: one storm contributes many correlated hourly peaks. The Method of Independent Storms extracts one peak per storm event (get_storm_peaks()) and removes an event’s samples before picking the next (remove_storm_from_series()), so the fit sees independent maxima.

Directional statistics are handled by the wind-rose helpers (cfdmod.climate.wind_rose), which count wind occurrences per direction sector – the weights that combine per-sector fits into an omnidirectional result, and that drive the pedestrian-comfort assessment below. Analytical mean-velocity profiles (code-based \(U(z)\) laws) live alongside in WindProfile.

Pedestrian comfort (Lawson)¶

Pedestrian wind comfort combines the CFD velocity field at pedestrian level with the site climate. The pipeline extracts per-probe velocity statistics (mean / rms / peak) at pedestrian-level probes (the PedestrianComfortConfig recipe); those per-direction amplification ratios are then weighted by the local directional Weibull climate into an effective velocity per probe (fit_average_velocity in cfdmod.climate.lawson). That effective velocity is what the Lawson comfort criterion classifies against its activity-category speed thresholds (sitting, standing, strolling, walking) to produce the pedestrian-comfort verdict at each location.