The definition of ‘truth’ for Numerical Weather Prediction error statistics

Error covariance sensitivity and impact estimation with adjoint 4D‐Var: theoretical aspects and first applications to NAVDAS‐AR

“…Quantification of the loss of information as a result of suboptimal weighting, and implementation of efficient procedures to adjust the error covariance parameters to a configuration that improves the forecasts' skill, are areas of active research. Synergistic efforts include the development of error covariance models for NWP applications (Derber and Bouttier, 1999;Gaspari and Cohn, 1999;Lorenc, 2003;Fisher, 2003;Bannister, 2008aBannister, , 2008bFrehlich, 2011;Bishop et al, 2011;Raynaud et al, 2011) and of computationally feasible techniques for diagnosis, estimation, and tuning of the error covariance parameters (Wahba et al, 1995;Dee, 1995;Dee and Da Silva, 1999;Andersson et al, 2000;Desroziers and Ivanov, 2001;Cardinali et al, 2004;Buehner et al, 2005;Chapnik et al, 2006;Zupanski and Zupanski, 2006;Trémolet, 2007;Anderson, 2007;Liu and Kalnay, 2008;Desroziers et al, 2009;Li et al, 2009).…”

The error of representation: basic understanding

“…(4) much like that of the algorithms in the ensemble post-processing and bias-correction literature (e.g. Glahn and Lowry, 1972;Raftery et al, 2005) in which climatological information is used to build relationships between forecasts and observations. As such, this new framework has shown how to properly include the information normally obtained from 'bias-correction' algorithms within the data assimilation system.…”

“…First, even if we could give the forecast model the true state, it would not produce the correct forecast evolution because of incorrectly specified parameters and altogether missing physics. Second, what exactly is the appropriate true state to give the forecast model as an initial condition is ambiguous given the fact that this model can only represent states that are 'smoothed', or said another way, truncated with respect to the truth (Frehlich, 2011). More on this notion will be presented in Sections 3 and 4.…”

“…In practice, one would build eq. (49) by estimating its components using an archive of truthforecast pairs as is done in bias-correction algorithms (Glahn and Lowry, 1972). Moreover, this implies that we may view eq.…”

“…In addition to these, more theoretical works there have recently been attempts at estimating the structure of representation error from observational data and numerical model output (e.g. Richman et al, 2005;Frehlich, 2008;Oke and Sakov, 2008;Waller et al, 2013). This work has shown that there are a number of ways to see this error of representation in data.…”