This "paper" introduces a hierarchical statistical model for converting tropical cyclone intensity estimates from ECMWF numerical weather prediction data to operational agency-specific estimates. The model employs a cascaded function application with progressive bias correction to account for systematic differences in analysis methodologies and averaging periods across the Japan Meteorological Agency (JMA), Hong Kong Observatory (HKO), and Joint Typhoon Warning Center (JTWC). Validation against historical data demonstrates robust performance with comprehensive statistical significance.
I'm not a meterologist. Take this as a grain of salt.
Operational tropical cyclone intensity estimation exhibits significant variation across meteorological agencies due to differing methodologies, averaging periods, and data sources. This research presents a unified hierarchical model that transforms ECMWF numerical weather prediction outputs into agency-specific intensity estimates through a cascaded mathematical framework.
While this "model" is not a weather model, it seeks to compromise for the industry-standard models' underprediction.
For a more aggressive estimation, use C=137. For a more conservative estimation, use C=147. For the remainder of this article, C=137 will be taken.
Where $x$ represents the input intensity in km/h from ECMWF numerical weather prediction data.
The below data was calculated based on WPAC TC data for 2021-22, where both 1-min sustained and 10-min sustained data was available.
| Metric | Value | Interpretation |
|---|---|---|
| R² | 0.6915 | Substantial explanatory power |
| Mean offset | -2.2531 km/h | Very good? |
| MAE | 8.9027 km/h | Decent |
| RMSE | 10.8163 km/h | Decent |
| Paired t-test (p-value) | 0.1572 | No significant bias |
Even though a higher C value will reach a higher R² value, doing so fails the p test (even at C=187 results in p = 0.045) and causes systemic biases.
Enter ECMWF* model intensity (km/h):
WARNING: THESE VALUES DO NOT REPRESENT WHAT THE ACTUAL WEATHER MODELS AND AGENCIES REPORT OR STANRARDS THEY UPHOLD. IT IS ONLY AN ESTIMATION EVALUATED FROM THE MODEL THAT HAS BEEN CREATED BY ME.
*ECMWF is represented via the live chart shown on Windy at 100m altitude
While creating the model, considering that weather models are prone to underestimate TC strength, the function needed to be non-linear. So for some reason I threw in the fine-structure constant $ \left(\frac{1}{137}\right) $ into the model (kinda). Then add a little linear multiplier to the denomenator ($0.75x$) and on top of that, throw in some more random things and there you go.
The hierarchical model successfully captures the progressive intensity escalation from conservative ECMWF numerical outputs to operational agency estimates. The cascaded function application with systematic bias correction provides a mathematically consistent framework for inter-agency intensity comparison and operational forecasting support.
Though it is not a must that you take ECMWF's prediction as a baseline. You can treat $x$ as JMA's report, $f(x)$ as HKO and $f(f(x))$ as JTWC's estimates. For example, the JMA concluded that Typhoon Ragasa (2025) reached a peak intensity of 205km/h, meanwhile HKO and JTWC estimated 230km/h and 270km/h respectively. Using the function, $f(205)$ outputs $236.86$ and $f(f(205))$ outputs $283.08$. The margin of error between JTWC's estimation and this model's estimation is 13.08km/h (+4.84% overestimate).
This research presents a validated hierarchical statistical model that transforms ECMWF numerical weather prediction data into operationally relevant intensity estimates across multiple meteorological agencies. The model's mathematical rigor and statistical validation provide a valuable tool for tropical cyclone analysis and forecasting operations.
I created this model via playing with desmos. If that isn't enough to convince you that you should just type some random formulas or stuff into desmos, there you go.