Search Results
Abstract
A data assimilation strategy based on feedback control has been developed for the geophysical sciences—a strategy that uses model output to control the behavior of the dynamical system. Whereas optimal tracking through feedback control had its early history in application to vehicle trajectories in space science, the methodology has been adapted to geophysical dynamics by forcing the trajectory of a deterministic model to follow observations in accord with observation accuracy. Fundamentally, this offline (where it is assumed that the observations in a given assimilation window are all given) approach is based on Pontryagin’s minimum principle (PMP) where a least squares fit of idealized path to dynamic law follows from Hamiltonian mechanics. This utilitarian process optimally determines a forcing function that depends on the state (the feedback component) and the observations. It follows that this optimal forcing accounts for the model error. From this model error, a correction to the one-step transition matrix is constructed. The above theory and technique is illustrated using the linear Burgers’ equation that transfers energy from the large scale to the small scale.
Abstract
A data assimilation strategy based on feedback control has been developed for the geophysical sciences—a strategy that uses model output to control the behavior of the dynamical system. Whereas optimal tracking through feedback control had its early history in application to vehicle trajectories in space science, the methodology has been adapted to geophysical dynamics by forcing the trajectory of a deterministic model to follow observations in accord with observation accuracy. Fundamentally, this offline (where it is assumed that the observations in a given assimilation window are all given) approach is based on Pontryagin’s minimum principle (PMP) where a least squares fit of idealized path to dynamic law follows from Hamiltonian mechanics. This utilitarian process optimally determines a forcing function that depends on the state (the feedback component) and the observations. It follows that this optimal forcing accounts for the model error. From this model error, a correction to the one-step transition matrix is constructed. The above theory and technique is illustrated using the linear Burgers’ equation that transfers energy from the large scale to the small scale.
Abstract
A new approach is described for calculating the mass (m) and terminal velocity (V t ) of ice particles from airborne and balloon-borne imaging probe data as well as its applications for remote sensing and modeling studies. Unlike past studies that derived these parameters from the maximum (projected) dimension (D) and habit alone, the “two-parameter approach” uses D and the particle's projected cross-sectional area (A). Expressions were developed that relate the area ratio (A r ; the projected area of an ice particle normalized by the area of a circle with diameter D) to its effective density (ρ e ) and to V t .
Habit-dependent, power-law relationships between ρ e and A r were developed using analytic representations of the geometry of various types of planar and spatial ice crystals. Relationships were also derived from new or reanalyzed data for single ice particles and aggregates observed in clouds and at the ground.
The mass relationships were evaluated by comparing calculations to direct measurements of ice water content (IWC). The calculations were from Particle Measuring Systems (PMS) 2D-C and 2D-P probes of particle size distributions in ice cloud layers on 3 days during an Atmospheric Radiation Measurement (ARM) field campaign in Oklahoma; the direct measurements were from counterflow virtual impactor (CVI) observations in ice cloud layers during the field campaign. Agreement was generally to within 20%, whereas using previous mass–dimension relationship approaches usually produced larger differences. Comparison of ground-based measurements of radar reflectivity with calculations from collocated balloon-borne ice crystal measurements also showed that the new method accurately captured the vertical reflectivity structure. Improvements in the accuracy of the estimates from the earlier mass–dimension relationships were achieved by converting them to the new form. A new, more accurate mass–dimension relationship for spatial, cirrus-type crystals was deduced from the comparison.
The relationship between V t and A r was derived from a combination of theory and observations. A new expression accounting for the drag coefficients of large aggregates was developed from observational data. Explicit relationships for calculating V t as a function of D for aggregates with a variety of component crystals were developed.
Abstract
A new approach is described for calculating the mass (m) and terminal velocity (V t ) of ice particles from airborne and balloon-borne imaging probe data as well as its applications for remote sensing and modeling studies. Unlike past studies that derived these parameters from the maximum (projected) dimension (D) and habit alone, the “two-parameter approach” uses D and the particle's projected cross-sectional area (A). Expressions were developed that relate the area ratio (A r ; the projected area of an ice particle normalized by the area of a circle with diameter D) to its effective density (ρ e ) and to V t .
Habit-dependent, power-law relationships between ρ e and A r were developed using analytic representations of the geometry of various types of planar and spatial ice crystals. Relationships were also derived from new or reanalyzed data for single ice particles and aggregates observed in clouds and at the ground.
The mass relationships were evaluated by comparing calculations to direct measurements of ice water content (IWC). The calculations were from Particle Measuring Systems (PMS) 2D-C and 2D-P probes of particle size distributions in ice cloud layers on 3 days during an Atmospheric Radiation Measurement (ARM) field campaign in Oklahoma; the direct measurements were from counterflow virtual impactor (CVI) observations in ice cloud layers during the field campaign. Agreement was generally to within 20%, whereas using previous mass–dimension relationship approaches usually produced larger differences. Comparison of ground-based measurements of radar reflectivity with calculations from collocated balloon-borne ice crystal measurements also showed that the new method accurately captured the vertical reflectivity structure. Improvements in the accuracy of the estimates from the earlier mass–dimension relationships were achieved by converting them to the new form. A new, more accurate mass–dimension relationship for spatial, cirrus-type crystals was deduced from the comparison.
The relationship between V t and A r was derived from a combination of theory and observations. A new expression accounting for the drag coefficients of large aggregates was developed from observational data. Explicit relationships for calculating V t as a function of D for aggregates with a variety of component crystals were developed.
