Spectral Analysis of Forecast Error Investigated with an Observing System Simulation Experiment

The spectra of analysis and forecast error are examined using the observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASAGMAO). A global numerical weather prediction model, the Global Earth Observing System version 5 (GEOS-5) with Gridpoint Statistical Interpolation (GSI) data assimilation, is cycled for two months with once-daily forecasts to 336 hours to generate a control case. Verification of forecast errors using the Nature Run as truth is compared with verification of forecast errors using self-analysis; significant underestimation of forecast errors is seen using self-analysis verification for up to 48 hours. Likewise, self analysis verification significantly overestimates the error growth rates of the early forecast, as well as mischaracterizing the spatial scales at which the strongest growth occurs. The Nature Run-verified error variances exhibit a complicated progression of growth, particularly for low wave number errors. In a second experiment, cycling of the model and data assimilation over the same period is repeated, but using synthetic observations with different explicitly added observation errors having the same error variances as the control experiment, thus creating a different realization of the control. The forecast errors of the two experiments become more correlated during the early forecast period, with correlations increasing for up to 72 hours before beginning to decrease

Some General and Fundamental Requirements for Designing Observing System Simulation Experiments (OSSEs)

There is an increasing demand to provide OSSE support when seeking funding for new atmospheric observing instruments. Various individuals and groups are running or developing OSSEs with little experience in OSSEs in particular or DA in general. In this presentation we will describe some key issues that are often neglected and some of the poor practices to be avoided. These include issues regarding NR and OSSE validation, consideration of instrument, observation operator, and forecast model error, relationships between observations and synoptic conditions, and conflicts of interest

Some General and Fundamental Requirements for Designing Observing System Simulation Experiments (OSSEs)

The intent of this white paper is to inform WMO projects and working groups, together with the broader weather research and general meteorology and oceanography communities, regarding the use of Observing System Simulation Experiments (OSSEs). This paper is not intended to be either a critical or cursory review of past OSSE efforts. Instead, it describes some fundamental, but often neglected, aspects of OSSEs and prescribes important caveats regarding their design, validation, and application. Well designed, properly validated, and carefully conducted OSSEs can be invaluable for examining, understanding, and estimating impacts of proposed observing systems and new data assimilation techniques. Although significant imperfections and limitations should be expected, OSSEs either profoundly complement or uniquely provide both qualitative and quantitative characterizations of potential analysis of components of the earth system

The Role of Model and Initial Condition Error in Numerical Weather Forecasting Investigated with an Observing System Simulation Experiment

A series of experiments that explore the roles of model and initial condition error in numerical weather prediction are performed using an observing system simulation experiment (OSSE) framework developed at the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO). The use of an OSSE allows the analysis and forecast errors to be explicitly calculated, and different hypothetical observing networks can be tested with ease. In these experiments, both a full global OSSE framework and an 'identical twin' OSSE setup are utilized to compare the behavior of the data assimilation system and evolution of forecast skill with and without model error. The initial condition error is manipulated by varying the distribution and quality of the observing network and the magnitude of observation errors. The results show that model error has a strong impact on both the quality of the analysis field and the evolution of forecast skill, including both systematic and unsystematic model error components. With a realistic observing network, the analysis state retains a significant quantity of error due to systematic model error. If errors of the analysis state are minimized, model error acts to rapidly degrade forecast skill during the first 24-48 hours of forward integration. In the presence of model error, the impact of observation errors on forecast skill is small, but in the absence of model error, observation errors cause a substantial degradation of the skill of medium range forecasts

Status of the NASA GMAO Observing System Simulation Experiment

An Observing System Simulation Experiment (OSSE) is a pure modeling study used when actual observations are too expensive or difficult to obtain. OSSEs are valuable tools for determining the potential impact of new observing systems on numerical weather forecasts and for evaluation of data assimilation systems (DAS). An OSSE has been developed at the NASA Global Modeling and Assimilation Office (GMAO, Errico et al 2013). The GMAO OSSE uses a 13-month integration of the European Centre for Medium- Range Weather Forecasts 2005 operational model at T511/L91 resolution for the Nature Run (NR). Synthetic observations have been updated so that they are based on real observations during the summer of 2013. The emulated observation types include AMSU-A, MHS, IASI, AIRS, and HIRS4 radiance data, GPS-RO, and conventional types including aircraft, rawinsonde, profiler, surface, and satellite winds. The synthetic satellite wind observations are colocated with the NR cloud fields, and the rawinsondes are advected during ascent using the NR wind fields. Data counts for the synthetic observations are matched as closely as possible to real data counts, as shown in Figure 2. Errors are added to the synthetic observations to emulate representativeness and instrument errors. The synthetic errors are calibrated so that the statistics of observation innovation and analysis increments in the OSSE are similar to the same statistics for assimilation of real observations, in an iterative method described by Errico et al (2013). The standard deviations of observation minus forecast (xo-H(xb)) are compared for the OSSE and real data in Figure 3. The synthetic errors include both random, uncorrelated errors, and an additional correlated error component for some observational types. Vertically correlated errors are included for conventional sounding data and GPS-RO, and channel correlated errors are introduced to AIRS and IASI (Figure 4). HIRS, AMSU-A, and MHS have a component of horizontally correlated error. The forecast model used by the GMAO OSSE is the Goddard Earth Observing System Model, Version 5 (GEOS-5) with Gridpoint Statistical Interpolation (GSI) DAS. The model version has been updated to v. 5.13.3, corresponding to the current operational model. Forecasts are run on a cube-sphere grid with 180 points along each edge of the cube (approximately 0.5 degree horizontal resolution) with 72 vertical levels. The DAS is cycled at 6-hour intervals, with 240 hour forecasts launched daily at 0000 UTC. Evaluation of the forecasting skill for July and August is currently underway. Prior versions of the GMAO OSSE have been found to have greater forecasting skill than real world forecasts. It is anticipated that similar forecast skill will be found in the updated OSSE

Consideration of Dynamical Balances

The quasi-balance of extra-tropical tropospheric dynamics is a fundamental aspect of nature. If an atmospheric analysis does not reflect such balance sufficiently well, the subsequent forecast will exhibit unrealistic behavior associated with spurious fast-propagating gravity waves. Even if these eventually damp, they can create poor background fields for a subsequent analysis or interact with moist physics to create spurious precipitation. The nature of this problem will be described along with the reasons for atmospheric balance and techniques for mitigating imbalances. Attention will be focused on fundamental issues rather than on recipes for various techniques

Introduction to Data Assimilation

Atmospheric data assimilation is a class of techniques used for producing descriptions of fields of air temperature, pressure, humidity, wind, etc. on a spatial grid or in terms of a finite functional representation. These are then used to initialize numerical weather forecasts or to analyze the atmosphere for other purposes. The techniques combine past, present, and even future observations in an approximate statistically optimal way. Various types of statistical or physically-based models and their corresponding adjoints are employed to relate diverse fields in both time and space and to relate what is observed to what is being analyzed. Computationally, the problem is very demanding and onstraining on the techniques that can be employed on a routine basis

Towards an Understanding of Atmospheric Balance

During a 35 year period I published 30+ pear-reviewed papers and technical reports concerning, in part or whole, the topic of atmospheric balance. Most used normal modes, either implicitly or explicitly, as the appropriate diagnostic tool. This included examination of nonlinear balance in several different global and regional models using a variety of novel metrics as well as development of nonlinear normal mode initialization schemes for particular global and regional models. Recent studies also included the use of adjoint models and OSSEs to answer some questions regarding balance. lwill summarize what I learned through those many works, but also present what l see as remaining issues to be considered or investigated

Consideration of Dynamical Balances

The quasi-balance of extra-tropical tropospheric dynamics is a fundamental aspect of nature. If an atmospheric analysis does not reflect such balance sufficiently well, the subsequent forecast will exhibit unrealistic behavior associated with spurious fast-propagating gravity waves. Even if these eventually damp, they can create poor background fields for a subsequent analysis or interact with moist physics to create spurious precipitation. The nature of this problem will be described along with the reasons for atmospheric balance and techniques for mitigating imbalances. Attention will be focused on fundamental issues rather than on recipes for various techniques

Introduction to Adjoint Models

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization