A data assimilation algorithm for predicting rain

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 147; no. 736; pp. 1949 - 1963
• Main Authors: Janjić, Tijana, Ruckstuhl, Yvonne, Toint, Philippe L.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.04.2021; Wiley Subscription Services, Inc
• Subjects: Algorithms; Computer applications; Convection; convective‐scale predictions; Data; Data assimilation; Data collection; disjoint linear constraints; Hydrometeors; Meteorological satellites; Physical properties; Prediction models; preservation of non‐negativity; quadratic optimization; Rainfall forecasting; Weather forecasting
• ISSN: 0035-9009; 1477-870X; 1477-870X
• DOI: 10.1002/qj.4004

Convective‐scale data assimilation uses high‐resolution numerical weather prediction models and temporally and spatially dense observations of relevant atmospheric variables. In addition, it requires a data assimilation algorithm that is able to provide initial conditions for a state vector of large size with one third or more of its components containing prognostic hydrometeors variables whose non‐negativity needs to be preserved. The algorithm also needs to be fast as the state vector requires a high updating frequency in order to catch fast‐changing convection. A computationally efficient algorithm for quadratic optimization (QO, or formerly QP) is presented here, which preserves physical properties in order to represent features of the real atmosphere. Crucially for its performance, it exploits the fact that the resulting linear constraints may be disjoint. Numerical results on a simple model designed for testing convective‐scale data assimilation show accurate results and promising computational cost. In particular, if constraints on physical quantities are disjoint and their rank is small, further reduction in computational costs can be achieved. Convective scale data assimilation requires a data assimilation algorithm that is able to provide initial conditions for a state vector of large size with one third or more of its components containing prognostic hydrometeors variables whose non‐negativity needs to be preserved. Governed by the principal of preservation of physical properties in order to represent features of real atmosphere and the computational efficiency, a specialized algorithm that focuses on predicting rain is presented and tested on idealized convective scale data assimilation example.