Beijing wind direction model shows small bias but surprisingly large errors

A kilometer-scale reanalysis of weather over Beijing can reproduce temperature, humidity and wind speed with impressive accuracy, yet it still struggles to pin down the direction the wind blows from. A new evaluation published in Geoscience Letters reports that the East Asia Reanalysis System at 1-km resolution, known as EARS1km, shows a mean wind-direction bias of only about minus two degrees over the Beijing metropolitan region, while the mean absolute error reaches 49 degrees and the root-mean-square error climbs to 66 degrees. The researchers call this counterintuitive combination Small Bias, Large Errors: positive and negative directional deviations largely cancel out when averaged, but individual hourly forecasts can be wildly off.

The study, led by Hekun Yang with colleagues including Jinfang Yin, examined the summers of 2022 and 2023 using hourly observations from 134 automatic weather stations across Beijing, northern Hebei Province, northern Tianjin and the transitional zone between the Yanshan and Taihang Mountains. The stations, drawn from the China Meteorological Administration’s quality-controlled network, cover four dominant land-cover types: cropland, urban built-up areas, grassland and mixed forest, each represented by roughly 30 or more stations. The two summers of hourly records yielded several hundred thousand quality-assured observation-simulation pairs, making this one of the densest evaluations of its kind for a megacity region.

EARS1km itself is a regional reanalysis product generated with the Weather Research and Forecasting model in a two-way nested configuration at 3-km and 1-km resolutions, initialized and bounded by ERA5 data. The 1-km inner domain uses the Mellor-Yamada-Janjic turbulence scheme for the planetary boundary layer, coupled to a Monin-Obukhov surface-layer scheme and the Noah land-surface model, with convection represented explicitly rather than parameterized. Notably, no urban canopy model was activated, a choice the authors acknowledge introduces uncertainty in how building-scale flow is represented.

For the variables the model handles well, the numbers are striking. Two-meter air temperature showed a bias of minus 0.11 degrees Celsius and an RMSE of 1.38 degrees Celsius; relative humidity a bias of minus 0.07 percent with RMSE of 8.29 percent; and ten-meter wind speed a bias of plus 0.21 meters per second with RMSE of 1.42 meters per second. Wind direction, by contrast, stood out as the problem variable, with monthly decompositions from June to August showing consistently high RMSE and near-zero bias throughout the season.

The first of the study’s two diagnostic perspectives concerns weak winds. When the team stratified all hourly pairs by observed wind speed, they found a pronounced, monotonic dependence of directional error on that speed. Under weak winds of zero to two meters per second, wind-direction MAE and RMSE reached 56 and 73 degrees respectively; in the moderate regime of two to four meters per second these fell to 39 and 54 degrees; and above four meters per second they dropped further to 31 and 44 degrees. Weak winds made up 63.21 percent of the total dataset, with moderate and relatively strong winds accounting for 27.21 and 9.58 percent, so calm conditions dominate the record both in frequency and in per-sample error magnitude.

The authors are careful to frame this as geometric amplification rather than an independent physical error source. Wind direction depends nonlinearly on the horizontal wind components, so a fixed cross-wind component error produces a larger angular deviation as the background wind weakens. Their worked example is vivid: a one-meter-per-second cross-wind error corresponds to about 14 degrees of directional error against a four-meter-per-second background wind, but exceeds 45 degrees once wind speed falls below one meter per second. The same amplification pattern appeared across all four land-cover types, and reduced background flow also weakens the synoptic constraint on surface direction, allowing unresolved terrain effects, roughness transitions and thermally driven circulations to influence local flow.

The second perspective examines land-surface heterogeneity. The team calculated four metrics for circular buffers of 1, 3, 5 and 10 kilometers around each station: the number of land-cover types, Shannon entropy, the Simpson diversity index and the proportion of the dominant type. The association between heterogeneity and directional error strengthened monotonically as buffer radius increased, with the strongest links at the 5-to-10-kilometer scale, likely because these buffers capture roughness and thermal contrasts across urban-agricultural and forest-grassland transitions. Grouping stations by the number of land-cover types, wind-direction RMSE reached 68 degrees in the high-heterogeneity group versus 60 degrees in the low-heterogeneity group, an eight-degree difference; the Shannon entropy grouping gave a seven-degree difference. Heterogeneity metrics correlated only weakly with directional bias, indicating a stronger association with error magnitude than with any consistent shift in direction.

Intriguingly, the sign of the heterogeneity association flipped across land-cover types. Over cropland, high-heterogeneity sites had larger RMSE than low-heterogeneity sites, rising from 57 to 65 degrees. Urban built-up areas showed a modest difference in the opposite direction, grassland showed RMSE 14 degrees lower in high-heterogeneity sites, and mixed forest showed the largest reduction at 17 degrees. The authors suggest this counterintuitive pattern may reflect localized flow over homogeneous, continuous canopies, including valley winds and canopy drag that are difficult for the model to reproduce.

The two perspectives turned out to be coupled. Stratifying by wind speed showed that heterogeneity correlates more tightly with directional error under weak winds: at the 10-kilometer scale, Spearman correlations of the land-cover-type count, Shannon entropy and Simpson index with RMSE were 0.35, 0.28 and 0.26 under weak winds, all statistically significant, but fell to 0.22, 0.18 and 0.17 under non-weak winds. In a two-by-two comparison, weak winds raised RMSE from 51 to 67 degrees at low-heterogeneity sites and from 55 to 74 degrees at high-heterogeneity sites, widening the gap between the groups from 4 to 7 degrees. A Welch t-test confirmed the extra weak-wind increment at heterogeneous sites was significantly larger, but a two-way analysis of variance identified wind regime as the dominant control, with a partial eta-squared of 0.2541 against 0.0343 for heterogeneity and a non-significant interaction.

A finer three-by-three classification, sorting stations into tertiles of weak-wind frequency and ten-kilometer Shannon entropy, told a subtler story. Wind-direction RMSE climbed sharply with weak-wind frequency, with row means of 55, 65 and 73 degrees, while heterogeneity column means rose more gently from 61 to 69 degrees. Here both main effects were significant and, unlike the binary analysis, the interaction was too, with a partial eta-squared of 0.0757 and p equal to 0.042. RMSE reached 72 degrees in the high-high group versus 50 degrees in the low-low group. The authors interpret this as non-additive, category-dependent variation rather than a uniformly positive heterogeneity effect, and they caution that planform land-cover classification alone is a poor predictor of directional error under weak winds.

The team also acknowledges an important caveat: the surface observations used are routinely assimilated into the EARS system, so the evaluation measures how closely the reanalysis matches the observed state rather than testing against fully independent data. Because assimilation pulls the analysis toward observations, the diagnosed errors should be treated as a conservative lower bound, meaning the Small Bias, Large Errors pattern would likely be at least as pronounced against independent observations. The authors further stress that the operational implication is diagnostic rather than a demonstrated precipitation-forecast impact: high directional RMSE in calm, heterogeneous settings can flag low confidence in local wind direction, but it should not be translated directly into moisture-transport displacement or rainfall error without dedicated case-based verification. Scheme-sensitivity experiments with refined boundary-layer and urban-canopy treatments, they conclude, are the logical next step for determining which unresolved processes materially affect forecasts over megacity regions.

Subject of Research: Evaluation of near-surface wind direction errors in a kilometer-scale reanalysis over Beijing

Article Title: Small bias, large errors: a dual-perspective evaluation of numerical model near-surface wind direction over beijing megacity

Article References: Yang, H., Yin, J., Kang, Y., Li, F., Zhang, H., & Wei, X. (2026). Small bias, large errors: a dual-perspective evaluation of numerical model near-surface wind direction over beijing megacity. Geoscience Letters, 13(1), Article 62. https://doi.org/10.1186/s40562-026-00514-w

Image Credits: AI Generated

DOI: 10.1186/s40562-026-00514-w

Keywords: wind direction, reanalysis, Beijing, EARS1km, weak winds, land-surface heterogeneity, numerical weather model, urban meteorology, error metrics, boundary layer, kilometer-scale modeling, summer monsoon