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Abstract Assimilating radar reflectivity into convective-scale NWP models remains a challenging topic in radar data assimilation. A primary reason is that the reflectivity forward observation operator is highly nonlinear. To address this challenge, a power transformation function is applied to the WRF Model’s hydrometeor and water vapor mixing ratio variables in this study. Three 3D variational data assimilation experiments are performed and compared for five high-impact weather events that occurred in 2019: (i) a control experiment that assimilates reflectivity using the original hydrometeor mixing ratios as control variables, (ii) an experiment that assimilates reflectivity using power-transformed hydrometeor mixing ratios as control variables, and (iii) an experiment that assimilates reflectivity and retrieved pseudo–water vapor observations using power-transformed hydrometeor and water vapor mixing ratios (qυ) as control variables. Both qualitative and quantitative evaluations are performed for 0–3-h forecasts from the five cases. The analysis and forecast performance in the two experiments with power-transformed mixing ratios is better than the control experiment. Notably, the assimilation of pseudo–water vapor with power-transformedqυas an additional control variable is found to improve the performance of the analysis and short-term forecasts for all cases. In addition, the convergence rate of the cost function minimization for the two experiments that use the power transformation is faster than that of the control experiments. Significance StatementThe effective use of radar reflectivity observations in any data assimilation scheme remains an important research topic because reflectivity observations explicitly include information about hydrometeors and also implicitly include information about the distribution of moisture within storms. However, it is difficult to assimilate reflectivity because the reflectivity forward observation operator is highly nonlinear. This study seeks to identify a more effective way to assimilate reflectivity into a convective-scale NWP model to improve the accuracy of predictions of high-impact weather events.
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This content will become publicly available on October 28, 2026
Direct Assimilation of Radar Reflectivity Data in Logarithmic Scale or Power Transform?
Abstract To cover its large dynamic range, radar reflectivity factors have historically been displayed and used on a logarithmic scale, that is, decibels of reflectivity (dBZ). Logarithmic reflectivity has also been used for data assimilation without being questioned or well validated. However, fundamental limitations exist with directly assimilating logarithmic reflectivity, such as strong nonlinearity of the observation forward operator and the fact that the impacts of small reflectivity values are amplified, leading to exaggerated increments when mapped back into physical space. In this study, we power‐transform both reflectivity and hydrometeor mixing ratios to alleviate the aforementioned issues with using conventional logarithmic reflectivity. Forecast evaluation across eight severe convection events demonstrates that applying the Box‐Cox power transformations to both reflectivity and hydrometeor mixing ratios effectively reduces the nonlinearity between the observations and control variables. This approach significantly improves analyses of model hydrometeor variables and forecasts of composite reflectivity and hourly precipitation.
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- Award ID(s):
- 2527406
- PAR ID:
- 10656735
- Publisher / Repository:
- American Geophysics Union
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 52
- Issue:
- 20
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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