This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored.

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system’s time evolution. Rather than solving the problem from scratch each time new observations become available, one uses the model to “forecast ” the current state, using a prior state estimate (which incorporates information from past data) as the initial condition, then uses current data to correct the prior forecast to a current state estimate. This Bayesian approach is most effective when the uncertainty in both the observations and in the state estimate, as it evolves over time, are accurately quantified. In this article, I describe a practical method for data assimilation in large, spatiotemporally chaotic systems. The method is a type of “Ensemble Kalman Filter”, in which the state estimate and its approximate uncertainty are represented at any given time by an ensemble of system states. I discuss both the mathematical basis of this approach and its implementation; my primary emphasis is on ease of use and computational speed rather than improving accuracy over previously published approaches to ensemble Kalman filtering. 1

A Doppler radar data assimilation system is developed based on ensemble Kalman filter (EnKF) method and tested with simulated radar data from a supercell storm. As a first implementation, we assume the forward models are perfect and radar data are sampled at the analysis grid points. A general purpose nonhydrostatic compressible model is used with the inclusion of complex multi-class ice microphysics. New aspects compared to previous studies include the demonstration of the ability of EnKF method in retrieving multiple microphysical species associated with a multi-class ice microphysics scheme, and in accurately retrieving the wind and thermodynamic variables. Also new are the inclusion of reflectivity observations and the determination of the relative role of radial velocity and reflectivity data as well as their spatial coverage in recovering the full flow and cloud fields. In general, the system is able to reestablish the model storm extremely well after a number of assimilation cycles, and best results are obtained when both radial velocity and reflectivity data, including reflectivity information outside precipitation regions, are used. Significant positive impact of the reflectivity assimilation

This paper describes the Simple Ocean Data Assimilation (SODA) reanalysis of ocean climate variability. In the assimilation, a model forecast produced by an ocean general circulation model with an average resolution of 0.25 ° 0.4 ° 40 levels is continuously corrected by contemporaneous observations with corrections estimated every 10 days. The basic reanalysis, SODA 1.4.2, spans the 44-yr period from 1958 to 2001, which complements the span of the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis (ERA-40). The observation set for this experiment includes the historical archive of hydrographic profiles supplemented by ship intake measurements, moored hydrographic obser-vations, and remotely sensed SST. A parallel run, SODA 1.4.0, is forced with identical surface boundary conditions, but without data assimilation. The new reanalysis represents a significant improvement over a previously published version of the SODA algorithm. In particular, eddy kinetic energy and sea level variability are much larger than in previous versions and are more similar to estimates from independent observations. One issue addressed in this paper is the relative importance of the model forecast versus the observations for the analysis. The results show that at near-annual frequencies the forecast model has a strong influence, whereas at decadal frequencies the observations become increasingly dominant in the analysis. As a consequence, interannual variability in SODA 1.4.2 closely resembles interannual variability in SODA 1.4.0. However, decadal anomalies of the 0–700-m heat content from SODA 1.4.2 more closely resemble heat content anomalies based on observations. 1.

Abstract—Operations with multiple autonomous underwater vehicles (AUVs) have a variety of underwater applications. For example, a coordinated group of vehicles with environmental sensors can perform adaptive ocean sampling at the appropriate spatial and temporal scales. We describe a methodology for cooperative control of multiple vehicles based on virtual bodies and artificial potentials (VBAP). This methodology allows for adaptable formation control and can be used for missions such as gradient climbing and feature tracking in an uncertain environment. We discuss our implementation on a fleet of autonomous underwater gliders and present results from sea trials in Monterey Bay in August, 2003. These at-sea demonstrations were performed as part of the Autonomous Ocean Sampling Network (AOSN) II project. Index Terms—Adaptive sampling, autonomous underwater vehicles (AUVs), cooperative control, formations, gradient climbing, underwater gliders. I.

Modifications to the Atlantic and east Pacific versions of the operational Statistical Hurricane Intensity Prediction Scheme (SHIPS) for each year from 1997 to 2003 are described. Major changes include the addition of a method to account for the storm decay over land in 2000, the extension of the forecasts from 3 to 5 days in 2001, and the use of an operational global model for the evaluation of the atmospheric predictors instead of a simple dry-adiabatic model beginning in 2001. A verification of the SHIPS operational intensity forecasts is presented. Results show that the 1997–2003 SHIPS forecasts had statistically significant skill (relative to climatology and persistence) out to 72 h in the Atlantic, and at 48 and 72 h in the east Pacific. The inclusion of the land effects reduced the intensity errors by up to 15 % in the Atlantic, and up to 3 % in the east Pacific, primarily for the shorter-range forecasts. The inclusion of land effects did not significantly degrade the forecasts at any time period. Results also showed that the 4–5-day forecasts that began in 2001 did not have skill in the Atlantic, but had some skill in the east Pacific. An experimental version of SHIPS that included satellite observations was tested during the 2002 and 2003 seasons. New predictors included brightness temperature information from Geostationary Operational

Ensemble Kalman filtering was developed as a way to assimilate observed data to track the current state in a computational model. In this paper we show that the ensemble approach makes possible an additional benefit: the timing of observations,

Recent studies (Patil et al. 2001, 2002) have shown that, when the Earth’s surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector. In this paper we show how this finding can be exploited to formulate a potentially accurate and efficient data assimilation technique. The basic idea is that, since the expected forecast errors lie in a locally low dimensional subspace, the analysis resulting from the data assimilation should also lie in this subspace. This implies that operations only on relatively low dimensional matrices are required. The data assimilation analysis is done locally in a manner allowing massively parallel computation to be exploited. The local analyses are then used to construct global states for advancement to the next forecast time. Potential advantages of the method are discussed. 1

Some of the most complex models routinely run are numerical weather prediction models. These models are based on a discretisation of a coupled set of partial differential equations (the dynamics) which govern the time evolution of the atmosphere, described in terms of temperature, pressure, velocity,

Abstract A data assimilation system based on the ensemble square-root Kalman filter (EnSRF) is extended to include the additional capability of assimilating polarimetric radar variables. It is used to assess the impact of simulating additional polarimetric observations on convective storm analysis in an OSSE (Observing System Simulation Experiment) framework. The polarimetric variables considered include differential reflectivity Z DR , reflectivity difference Z dp , and specific differential phase K DP . To simulate the observational data more realistically, a new error model is introduced for characterizing the errors of the non-polarimetric and polarimetric radar variables. The error model includes both correlated and uncorrelated error components for reflectivities at horizontal and vertical polarizations (Z H and Z V ). It is shown that the storm analysis is improved when polarimetric variables are assimilated in addition to Z H or in addition to both Z H and radial velocity V r . Positive impact is largest when Z DR , Z dp , and K DP are assimilated all together. Improvement is generally larger in vertical velocity, water vapor and rainwater mixing ratios. The rain water field benefits the most while the impacts on horizontal wind components and snow mixing ratios are smaller. Improvement is found at all model levels even though the polarimetric data, after the application of thresholds, are mostly limited to the lower levels. Among Z DR , Z dp , and K DP , Z DR is found to produce the largest positive impact on the analysis. It is suggested that Z DR provides more independent information than the other variables. The impact of polarimetric data is also expected to be larger when they are used to retrieve drop size distribution parameters. This study is believed to be the first to directly assimilate (simulated) polarimetric data into a numerical model. 1