## 1 Introduction

[2] There are multiple sources of error in numerical weather analysis and prediction including model error, observation instrument and representativeness error, errors introduced by the data-assimilation process itself, and physical-dynamical error growth. Because the true state of the atmosphere remains unknown, it is not possible to directly assess these errors or their impact on analysis quality or forecast skill. Many efforts have been made to investigate the impact of initial condition errors on forecast skill, such as with idealized identical or fraternal twin experiments [e.g., *Tribbia and Baumhefner*, 2004], but these studies have not considered errors in the context of data-assimilation systems.

[3] Previous studies [e.g., *Tyndall et al.* 2010; *Irvine et al.* 2011] have examined the role of observation error in data assimilation, primarily in the form of the weighting of observational data versus the background. Changing the specified observation error variance or background error variance in a data-assimilation system (DAS) alters how closely the analysis field draws to the observations compared to the background. This study instead is focused primarily on how the observation errors themselves impact qualities of the model analysis and forecast fields.

[4] There are many unanswered quantitative and qualitative questions about how observation error impacts the errors of analysis and subsequent forecasts given that the DAS is designed as an error filter and smoother [*Daley*, 1991]. Modern DAS are based on elegant mathematical theory, as outlined in the Appendix, that unfortunately offers only limited insight into answers to these questions because of the many unsupported assumptions generally implied for their computationally efficient application. Answers are also not forthcoming when using real observations since in that context the true state being analyzed is not sufficiently well known. In contrast, an observing system simulation experiment (OSSE) alleviates many of these difficulties since relevant errors can be directly calculated from the accurately known truth provided [*Errico et al.*, 2013]. As long as the OSSE is a faithful simulation of reality, it can provide valuable insight into these questions.

[5] An OSSE suitable for this problem has been developed at the National Aeronautics and Space Administration (NASA) Global Modeling and Assimilation Office (GMAO; *Errico et al.* [2013]; *Privé et al.* [2013]). It provides a tool for investigating how errors in sources of information or algorithms impact the analysis, background, and forecast errors. In addition, the observation errors in an OSSE can be directly manipulated to explore the impact of observation error on the analysis quality and forecast skill. In this work, a series of experiments with varied observation error are performed using the GMAO OSSE to explore the influence of observation error in an operational numerical weather forecasting system.

[6] The motivating factors for this study include both the design of OSSEs and the effects of observation error when assimilating real observations. The development of realistic observation errors for synthetic observations in OSSEs has been a challenging problem for decades. Here, the importance of accurately representing observation errors is investigated by testing the response of the OSSE framework to a range of observation error magnitudes from minimization of observation errors to gross overestimation of observation errors. A variety of metrics are employed, including explicit measures of analysis error. The importance of proper weighting of error covariance matrices is also explored.

[7] Details of the GMAO OSSE framework and the experimental setup are given in section 2. The influence of observation error on increment and error statistics of the data-assimilation products is described in section 3. Likewise, the effect of observation error on forecast skill is presented in section 4 and on observation impact metrics calculated with an adjoint model in section 5. Finally, the results are discussed in section 6.