Limitations of wind extraction from 4D-Var assimilation of ozone

Abstract

Time-dependent variational data assimilation allows the possibility of extracting wind information from observations of ozone or other trace gases. Since trace gas observations are not available at sufficient resolution for deriving feature-track winds, they must be combined with model background information to produce an analysis. If done with time-dependent variational assimilation, wind information may be extracted via the adjoint of the linearized tracer continuity equation. This paper presents idealized experiments that illustrate the mechanics of tracer–wind extraction and demonstrate some of the limitations of this procedure. We first examine tracer–wind extraction using a simple one-dimensional advection equation. The analytic solution for a single trace gas observation is discussed along with numerical solutions for multiple observations. The limitations of tracer–wind extraction are then explored using highly idealized ozone experiments performed with a development version of the Navy Global Environmental Model (NAVGEM) in which globally distributed hourly stratospheric ozone profiles are assimilated in a single 6 h update cycle in January 2009. Starting with perfect background ozone conditions, but imperfect dynamical conditions, ozone errors develop over the 6 h background window. Wind increments are introduced in the analysis in order to reduce the differences between background ozone and ozone observations. For "perfect" observations (unbiased and no random error), this results in root-mean-square (RMS) vector wind error reductions of up to ~4 m s⁻¹ in the winter hemisphere and tropics. Wind extraction is more difficult in the summer hemisphere due to weak ozone gradients and smaller background wind errors. The limitations of wind extraction are also explored for observations with imposed random errors and for limited sampling patterns. As expected, the amount of wind information extracted degrades as observation errors or data voids increase. In the case of poorly specified observation error covariances, assimilation of ozone data with imposed errors may result in increased RMS wind error, since the assimilation is constrained too tightly to the noisy observations

Wind extraction potential from ensemble Kalman filter assimilation of stratospheric ozone using a global shallow water model

“…For each successive height observation, the sampling occurs at one of 3840 latitude/longitude points on an icosahedral equal-area grid. This allows the observations to not be too clumped together and provides a way to scale upward to a global equal area grid sampling, as was used in Allen et al (2013). We choose the average data frequency for the height observations to be the same as the MLS sampling frequency (∼ 3450 day −1 ).…”

“…The investigation of algorithms to extract wind information from tracers started with 1-D and 2-D simulations by Daley (1995Daley ( , 1996 and Riishøjgaard (1996). These studies showed that wind information could be extracted from tracer observations when the continuity equation was coupled to the dynamical equations via either a 4D-Var (four-dimensional variational assimilation) algorithm or an extended Kalman filter (EKF) Semane et al (2009), and Allen et al (2013). These further supported the potential of tracer assimilation to benefit the winds but also highlighted limitations due to paucity of observations, insufficient data quality, and inadequate modeling of tracers in the forecast model, as well as phenomenological limitations due to geophysical variability.…”

Hybrid ensemble 4DVar assimilation of stratospheric ozone using a global shallow water model

“…In addition, we would like to explore eliminating the tangent linear model and adjoint using different ensemble variational approaches (e.g., Buehner et al, 2010Buehner et al, , 2013Buehner et al, , 2015Lorenc et al, 2015;Frolov and Bishop, 2016). Finally, we plan to apply what we have learned from these SWM studies to devise experiments with an operational hybrid 4DVar system, building on the work of Allen et al (2013), who examined wind benefits from O 3 assimilation in a pre-operational version of the Navy Global Environmental Model 4DVar system.…”

“…Since trace gas observations are not generally available at sufficient resolution for deriving feature-track winds, they must be combined with model background information to produce an analysis using a 4-D data assimilation system. A pilot study using a full 3-D NWP model with a 4DVar system (Allen et al, 2013) not only showed that wind extraction from ozone assimilation in the stratosphere is possible but also highlighted limitations due to geophysical conditions, tracer observation quality and error specifications, and limited observing sampling patterns. These results motivated the authors to pursue a more detailed theoretical study of the problem using the shallow water model framework with a variety of data assimilation systems.…”

“…The tracer-wind relationship has been examined with a variety of DA systems including the extended Kalman filter (EKF; Daley, 1995Daley, , 1996, 4-D variational assimilation (4DVar; Riishøjgaard, 1996;Peuch et al, 2000;Andersson et al, 2007;Peubey and McNally, 2009;Semane et al, 2009;Han and McNally, 2010;Dragani and McNally, 2013;Allen et al, 2013Allen et al, , 2014, and ensemble Kalman filter (EnKF; Milewski and Bourqui, 2011;Allen et al, 2015). While idealized studies have shown strong potential for wind extraction from tracer assimilation, attempts to assimilate O 3 using realistic numerical weather prediction (NWP) systems have produced mixed results (see Allen et al, 2015, for a discussion).…”