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## Statistical Design for Adaptive Weather Observations (1999)

Venue: | J. Atmos. Sci |

Citations: | 32 - 2 self |

### Citations

1507 | Bayesian Theory.
- Bernardo, Smith
- 1994
(Show Context)
Citation Context ...s arose in the MSE example of Section 2.) A statistician's tenet is that to design an optimal experiment, one must know what will be done with the data obtained. In the Bayesian statistics tradition (=-=Bernardo and Smith, 1994), all qua-=-ntities are treated as if they are random variables. Hence, Bayesian experimental design is virtually identical to design for prediction. Our use of the modifier "Bayesian" in this paper cou... |

383 |
Inverse Problem Theory: Methods of Data Fitting and Model Parameter Estimation, Elsevier Science Ltd, pp 630
- Tarantola
- 1987
(Show Context)
Citation Context ...articularly relevant to the formulation here.) It is well-known that they coincide with familiar results from the data assimilation literature, often known as the extended Kalman filter (Lorenc 1986; =-=Tarantola 1987; Courti-=-er 1997). In particular, the estimate given in (2.15) is obtainable as the solution to an optimization problem: Find the minimizer of J(x 1 ) = (x 1 \Gamma �� 1 ) T B \Gamma1 1 (x 1 \Gamma �� ... |

366 | Optimal Design of Experiments - Pukelsheim - 1993 |

319 | Bayesian experimental design: a review
- Chaloner, Verdinelli
- 1995
(Show Context)
Citation Context ... cannot be defined. To make the problem mathematically meaningful, some criterion function, generically denoted by F , taking B into a scalar must be specified. We present a brief overview here. (See =-=Chaloner and Verdinelli, 1995-=-, and Silvey, 1980 for in depth reviews; the following presentation relied heavily on that of Silvey.) As we develop these we suspend constantly writing that we optimize expected values (with respect ... |

253 |
Analysis methods for numerical weather prediction
- Lorenc
- 1177
(Show Context)
Citation Context ...for details particularly relevant to the formulation here.) It is well-known that they coincide with familiar results from the data assimilation literature, often known as the extended Kalman filter (=-=Lorenc 1986; Ta-=-rantola 1987; Courtier 1997). In particular, the estimate given in (2.15) is obtainable as the solution to an optimization problem: Find the minimizer of J(x 1 ) = (x 1 \Gamma �� 1 ) T B \Gamma1 1... |

155 |
Optimal Design
- Silvey
- 1980
(Show Context)
Citation Context ...blem mathematically meaningful, some criterion function, generically denoted by F , taking B into a scalar must be specified. We present a brief overview here. (See Chaloner and Verdinelli, 1995, and =-=Silvey, 1980-=- for in depth reviews; the following presentation relied heavily on that of Silvey.) As we develop these we suspend constantly writing that we optimize expected values (with respect to the data Y) of ... |

140 | Optimal sites for supplementary weather observations: simulation with a small model
- Lorenz, Emanuel
- 1998
(Show Context)
Citation Context ...oosing specific geographical areas in which specialized observational data will be obtained. We also present an example of optimal design for an idealized low-order model of the atmosphere (following =-=Lorenz and Emanuel 1998-=-) and compare that design against other proposed adaptive observation strategies. This work was motivated in part by the opportunity to test adaptive strategies during the Fronts and Atlantic Storm Tr... |

123 |
Singular vectors, metrics, and adaptive observations.
- Palmer, Gelaro, et al.
- 1998
(Show Context)
Citation Context ...ial intuitive value. Our results also lead to new interpretations of previously proposed strategies for adaptive observations (Langland and Rohaly 1996; Bishop and Toth 1996; Lorenz and Emanuel 1998; =-=Palmer et al. 1998-=-; see also Snyder 1996). 3.1 Computations for A-Optimal Designs Single Observation Setting. Suppose that a single adaptive observation is to be taken. That is, K is a single row vector. If that observ... |

106 |
Statistical Prediction Analysis.
- Aitchison, Dunsmore
- 1975
(Show Context)
Citation Context ...f the Euclidean norm squared prediction errors: MSE = E(jX \Gamma p(Y)j 2 ); (2.1) where the indicated expectation is taken with respect to both X and Y. A result from the theory of prediction (e.g., =-=Aitchison and Dunsmore, 1975-=-, pp. 47-50) tells us that we should choose the predictor to be the conditional expectation of X, given the observed data y: E(XjY = y): (2.2) This result is derived by noting that MSE = E(jX \Gamma E... |

61 |
Sequential Analysis and Optimal Design.
- Chernoff
- 1972
(Show Context)
Citation Context ... can in principle take a unified approach to the design of both routine and adaptive data collection. Though such fully sequential statistical designs have been studied and applied in other contexts (=-=Chernoff, 1972-=-), the complexities and size of weather forecasting applications may moderate the richness of the approach. 3 Results and Comparisons In this section we derive statistical design results for the A-opt... |

60 |
Dual formulation of four-dimensional variational assimilation.
- Courtier
- 1997
(Show Context)
Citation Context ...vant to the formulation here.) It is well-known that they coincide with familiar results from the data assimilation literature, often known as the extended Kalman filter (Lorenc 1986; Tarantola 1987; =-=Courtier 1997). In pa-=-rticular, the estimate given in (2.15) is obtainable as the solution to an optimization problem: Find the minimizer of J(x 1 ) = (x 1 \Gamma �� 1 ) T B \Gamma1 1 (x 1 \Gamma �� 1 ) + (y \Gamma... |

53 |
Optimal prediction of forecast error covariances through singular vectors
- Ehrendorfer, Tribbia
- 1997
(Show Context)
Citation Context ...follows from standard statistical theory that our implied, approximate distribution for X 1 is X 1 �� N(�� 1 ; B 1 ); (2.7) where �� 1 = f( 0 ) (2.8) and B 1 = F ( 0 )A 0 F ( 0 ) T : (2.9)=-= (Also, see Ehrendorfer and Tribbia 1997-=-.) At time t = t 0 we have the opportunity to design an experiment that will take place at time t = t 1 . We will observe a function of the state variables X 1 , with measurement error. In the adaptiv... |

45 | Recent advances it! nonlinear experimental design - Ford, Kitsos, et al. - 1989 |

18 | Distributed Parameter Systems: Theory and Applications. - Omatu, Seinfeld - 1989 |

11 | Sensors and control in the analysis of distributed systems (J.Wiley, - Jai, Pritchard - 1988 |

11 |
Adjoint-based targeting of observations for FASTEX cyclones. Preprints,
- Langland, Rohaly
- 1996
(Show Context)
Citation Context ...te variables), we obtain formulas for optimal designs that carry substantial intuitive value. Our results also lead to new interpretations of previously proposed strategies for adaptive observations (=-=Langland and Rohaly 1996-=-; Bishop and Toth 1996; Lorenz and Emanuel 1998; Palmer et al. 1998; see also Snyder 1996). 3.1 Computations for A-Optimal Designs Single Observation Setting. Suppose that a single adaptive observatio... |

9 | Comparison of two approaches of optimal design of an observation network - Fedorov, Müller - 1989 |

7 |
Using ensembles to identify observations likely to improve forecasts
- Bishop, Toth
- 1996
(Show Context)
Citation Context ...ormulas for optimal designs that carry substantial intuitive value. Our results also lead to new interpretations of previously proposed strategies for adaptive observations (Langland and Rohaly 1996; =-=Bishop and Toth 1996-=-; Lorenz and Emanuel 1998; Palmer et al. 1998; see also Snyder 1996). 3.1 Computations for A-Optimal Designs Single Observation Setting. Suppose that a single adaptive observation is to be taken. That... |

5 | Aspects of optimal design in dynamic systems - Titterington - 1980 |

1 | The Fronts and Atlantic Storm-Track Experiment (FASTEX): Scientific objectives and experimental - Lanland, Lynch, et al. - 1997 |

1 |
Linear Statistical Inference and Its Applications, 2/e
- Rao
- 1973
(Show Context)
Citation Context ...(3.9) The maximizer of ~ a is K Ts= (k T 1 ; : : : ; k T d ); (3.10) where k T 1 ; : : : ; k T d denote leading d eigenvectors corresponding to the eigen-problem G T 0 G 0 B 1 k T = k T : (3.11) (See =-=Rao, 1973, p.74.) A-=-s a closing comment, we note that if the unrestricted solutions k T j above are highly localized, they can direct the search for the restricted, "incidence" solutions. 3.2 A Simple Principle... |

1 | Summary of an informal workshop on adaptive observations and - Synder - 1996 |