### q 1998 American Meteorological Society Singular Vectors, Metrics, and Adaptive Observations

, 1996

"... Singular vectors of the linearized equations of motion have been used to study the instability properties of the atmosphere–ocean system and its related predictability. A third use of these singular vectors is proposed here: as part of a strategy to target adaptive observations to ‘‘sensitive’ ’ par ..."

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Singular vectors of the linearized equations of motion have been used to study the instability properties of the atmosphere–ocean system and its related predictability. A third use of these singular vectors is proposed here: as part of a strategy to target adaptive observations to ‘‘sensitive’ ’ parts of the atmosphere. Such observations could be made using unmanned aircraft, though calculations in this paper are motivated by the upstream com-ponent of the Fronts and Atlantic Storm-Track Experiment. Oceanic applications are also discussed. In defining this strategy, it is shown that there is, in principle, no freedom in the choice of inner product or metric for the singular vector calculation. However, the correct metric is dependent on the purpose for making the targeted observations (to study precursor developments or to improve forecast initial conditions). It is argued that for predictability studies, where both the dynamical instability properties of the system and the specification of the operational observing network and associated data assimilation system are important, the appropriate metric will differ from that appropriate to a pure geophysical fluid dynamics (GFD) problem. Based on two different sets of calculations, it is argued that for predictability studies (but not for GFD studies), a first-order approximation to the appropriate metric can be based on perturbation energy. The role of observations in data assimilation procedures (constraining large scales more than small scales) is fundamental in understanding reasons for the

### Chaos and weather prediction

, 2000

"... The weather is a chaotic system. Small errors in the initial conditions of a forecast grow rapidly, and affect predictability. Furthermore, predictability is limited by model errors due to the approximate simulation of atmospheric processes of the state-of-the-art numerical models. These two sources ..."

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The weather is a chaotic system. Small errors in the initial conditions of a forecast grow rapidly, and affect predictability. Furthermore, predictability is limited by model errors due to the approximate simulation of atmospheric processes of the state-of-the-art numerical models. These two sources of uncertainties limit the skill of single, deterministic forecasts in an unpredictable way, with days of high/ poor quality forecasts randomly followed by days of high/poor quality forecasts. Two of the most recent advances in numerical weather prediction, the operational implementation of ensemble prediction systems and the development of objective procedures to target adaptive observations are discussed. Ensemble prediction is a feasible method to integrate a single, deterministic forecast with an estimate of the probability distribution function of forecast states. In particular, ensemble can provide forecasters with an objective way to predict the skill of single deterministic forecasts, or, in other words, to forecast the forecast skill. The European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS), based on the notion that initial condition uncertainties are the dominant source of forecast error, is described. Adaptive observations targeted in sensitive regions can reduce the initial conditions ’ uncertainties, and thus decrease forecast errors. More generally, singular vectors that identify unstable regions of the atmospheric flow can be used to identify optimal ways to adapt the atmospheric observing system.

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"... Forecast influence of adaptive airborne observations in the environment of tropical cyclones in the western North Pacific basin Dissertation an der Fakultät für Physik der Ludwig–Maximilians–Universität ..."

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Forecast influence of adaptive airborne observations in the environment of tropical cyclones in the western North Pacific basin Dissertation an der Fakultät für Physik der Ludwig–Maximilians–Universität

### ABSTRACT Title of Document: APPLICATIONS OF THE LETKF TO ADAPTIVE OBSERVATIONS, ANALYSIS SENSITIVITY, OBSERVATION IMPACT AND THE ASSIMILATION OF MOISTURE

"... In this thesis we explore four new applications of the Local Ensemble Transform Kalman Filter (LETKF), namely adaptive observations, analysis sensitivity, observation impact, and multivariate humidity assimilation. In each of these applications we have obtained promising results. In the adaptive obs ..."

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In this thesis we explore four new applications of the Local Ensemble Transform Kalman Filter (LETKF), namely adaptive observations, analysis sensitivity, observation impact, and multivariate humidity assimilation. In each of these applications we have obtained promising results. In the adaptive observation studies, we found that ensemble spread strategy, where adaptive observations are selected among the points with largest ensemble spread (with the constraint that observations cannot be contiguous in order to avoid clusters of adaptive observations) is very effective and close to optimal sampling. The application on simulated Doppler Wind Lidar (DWL) adaptive observation studies shows that 3D-Var is as effective as LETKF with 10 % adaptive observations sampled with the ensemble spread strategy. With 2 % adaptive observations, 3D-Var is not as effective as the LETKF. In the analysis sensitivity study, we proposed to calculate this quantity within the LETKF with low additional computational time. Unlike in 4D-Var (Cardinali et al., 2004), in the LETKF, the computation is exact and satisfies the theoretical value limits (between 0 and 1). The results from simulated experiments show that the trace

### Nonlinear Processes in Geophysics c○European Geophysical Society 2001

, 2000

"... Using adjoint sensitivity as a local structure function in variational data assimilation ..."

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Using adjoint sensitivity as a local structure function in variational data assimilation

### Nonlinear Processes in Geophysics c○European Geophysical Society 2001 Sensitivity to observations applied to FASTEX cases

, 2000

"... Abstract. The concept of targeted observations was implemented during field experiments such as FASTEX, NORPEX or WSRP in order to cope with some predictability problems. The techniques of targeting used at that moment (adjointbased or ensemble transform methods) lead to quite disappointing results: ..."

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Abstract. The concept of targeted observations was implemented during field experiments such as FASTEX, NORPEX or WSRP in order to cope with some predictability problems. The techniques of targeting used at that moment (adjointbased or ensemble transform methods) lead to quite disappointing results: the efficiency of the additional observations deployed over sensitive areas did not turn out to remain consistent from one case to another. The influence of targeted observations on the forecasts could sometimes consist of strong improvements, or sometimes strong degradations. It turns out that the latter failure explains why the concept of optimal sampling arose. The efficiency of adaptive sampling appears to depend on the assimilation scheme that deals with the observations. It is then very useful to integrate the nature of the assimilation algorithm, as well as the deployment

### q 2004 American Meteorological Society Designing Efficient Observing Networks for ENSO Prediction

, 2003

"... The Tropical Atmosphere Ocean (TAO) array of moored buoys in the tropical Pacific Ocean is a major source of data for understanding and predicting El Niño–Southern Oscillation (ENSO). Despite the importance of the TAO array, limited work has been performed where observations are most important for ..."

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The Tropical Atmosphere Ocean (TAO) array of moored buoys in the tropical Pacific Ocean is a major source of data for understanding and predicting El Niño–Southern Oscillation (ENSO). Despite the importance of the TAO array, limited work has been performed where observations are most important for predicting ENSO effectively. To address this issue, this study performs a series of observing system simulation experiments (OSSEs) with a linearized intermediate coupled ENSO model, stochastically forced. ENSO forecasts are simulated for a variety of observing network configurations, and forecast skill averaged over many simulated ENSO events is compared. The first part of this study examined the relative importance of sea surface temperature (SST) and subsurface ocean observations, requirements for spacing and meridional extent of observations, and important regions for observations in this system. Using these results as a starting point, this paper develops efficient observing networks for forecasting ENSO in this system, where efficient is defined as providing reasonably skillful forecasts for relatively few observations. First, efficient networks that provide SST and thermocline depth data at the same locations are developed and discussed. Second, efficient networks of only thermocline depth observations are addressed, assuming that many SST observations are available from another source (e.g., satellites). The dependence of the OSSE results on the duration of the simulated data record is also explored. The results suggest that several decades of data may be sufficient for evaluating the effects of observing networks on ENSO forecast skill, despite being insufficient for evaluating the long-term potential predictability of ENSO. 1.

### unknown title

, 2002

"... The impact of various potential-vorticity anomalies on multiple frontal cyclogenesis events ..."

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The impact of various potential-vorticity anomalies on multiple frontal cyclogenesis events

### 2536 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 56 � 1999 American Meteorological Society Statistical Design for Adaptive Weather Observations

, 1997

"... Suppose that one has the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of ‘‘adaptive observations’ ’ is formulated as a problem i ..."

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Suppose that one has the freedom to adapt the observational network by choosing the times and locations of observations. Which choices would yield the best analysis of the atmospheric state or the best subsequent forecast? Here, this problem of ‘‘adaptive observations’ ’ is formulated as a problem in statistical design. The statistical framework provides a rigorous mathematical statement of the adaptive observations problem and indicates where the uncertainty of the current analysis, the dynamics of error evolution, the form and errors of observations, and data assimilation each enter the calculation. The statistical formulation of the problem also makes clear the importance of the optimality criteria (for instance, one might choose to minimize the total error variance in a given forecast) and identifies approximations that make calculation of optimal solutions feasible in principle. Optimal solutions are discussed and interpreted for a variety of cases. Selected approaches to the adaptive observations problem found in the literature are reviewed and interpreted from the optimal statistical design viewpoint. In addition, a numerical example, using the 40-variable model of Lorenz and Emanuel, suggests that some other proposed approaches may often be close to the optimal solution, at least in this highly idealized model. 1.