# Enhanced parallelization of the incremental 4D-Var data assimilation algorithm using the Randomized Incremental Optimal Technique (RIOT)

## TL;DR

This paper introduces RIOT, a parallelized version of incremental 4D-Var using randomized SVD, significantly reducing computation time in atmospheric data assimilation while increasing energy use, with promising results in models and real-world problems.

## Contribution

The paper presents RIOT, a novel parallelization method for incremental 4D-Var that replaces CG with RSVD, improving efficiency and enabling faster data assimilation in weather prediction.

## Key findings

- RIOT reduces wall-time by 2-3 times in black carbon source inversion.
- Performance gains increase with non-linearities in the Lorenz-96 model.
- Analysis covariance computation is 40 times faster with RIOT.

## Abstract

Incremental 4D-Var is a data assimilation algorithm used routinely at operational numerical weather predictions centers worldwide.This paper implements a new method for parallelizing incremental 4D-Var, the Randomized Incremental Optimal Technique (RIOT), which replaces the traditional sequential conjugate gradient (CG) iterations in the inner-loop of the minimization with fully parallel randomized singular value decomposition (RSVD) of the preconditioned Hessian of the cost function. RIOT is tested using the standard Lorenz-96 model (L-96) as well as two realistic high-dimensional atmospheric source inversion problems based on aircraft observations of black carbon concentrations. A new outer-loop preconditioning technique tailored to RSVD was introduced to improve convergence stability and performance. Results obtained with the L-96 system show that the performance improvement from RIOT compared to standard CG algorithms increases significantly with non-linearities. Overall, in the realistic black carbon source inversion experiments, RIOT reduces the wall-time of the 4D-Var minimization by a factor 2-3, at the cost of a factor 4-10 increase in energy cost due to the large number of parallel cores used. Furthermore, RIOT enables reduction of the wall-time computation of the analysis error covariance matrix by a factor 40 compared to a standard iterative Lanczos approach. Finally, as evidenced in this study, implementation of RIOT in an operational numerical weather prediction system will require a better understanding of its convergence properties as a function of the Hessian characteristics and, in particular, the degree of freedom for signal (DOFs) of the inverse problem.