The retrieval of ice water content from radar reflectivity factor and temperature and its use in evaluating a mesoscale model

Ice clouds are an important yet largely unvalidated component of weather forecasting and climate models, but radar offers the potential to provide the necessary data to evaluate them. First in this paper, coordinated aircraft in situ measurements and scans by a 3-GHz radar are presented, demonstrating that, for stratiform midlatitude ice clouds, radar reflectivity in the Rayleigh-scattering regime may be reliably calculated from aircraft size spectra if the "Brown and Francis" mass-size relationship is used. The comparisons spanned radar reflectivity values from -15 to +20 dBZ, ice water contents (IWCs) from 0.01 to 0.4 g m(-3), and median volumetric diameters between 0.2 and 3 mm. In mixed-phase conditions the agreement is much poorer because of the higher-density ice particles present. A large midlatitude aircraft dataset is then used to derive expressions that relate radar reflectivity and temperature to ice water content and visible extinction coefficient. The analysis is an advance over previous work in several ways: the retrievals vary smoothly with both input parameters, different relationships are derived for the common radar frequencies of 3, 35, and 94 GHz, and the problem of retrieving the long-term mean and the horizontal variance of ice cloud parameters is considered separately. It is shown that the dependence on temperature arises because of the temperature dependence of the number concentration "intercept parameter" rather than mean particle size. A comparison is presented of ice water content derived from scanning 3-GHz radar with the values held in the Met Office mesoscale forecast model, for eight precipitating cases spanning 39 h over Southern England. It is found that the model predicted mean I WC to within 10% of the observations at temperatures between -30 degrees and - 10 degrees C but tended to underestimate it by around a factor of 2 at colder temperatures.

Independent evaluation of the ability of spaceborne radar and lidar to retrieve the microphysical and radiative properties of ice clouds

The combination of radar and lidar in space offers the unique potential to retrieve vertical profiles of ice water content and particle size globally, and two algorithms developed recently claim to have overcome the principal difficulty with this approach-that of correcting the lidar signal for extinction. In this paper "blind tests" of these algorithms are carried out, using realistic 94-GHz radar and 355-nm lidar backscatter profiles simulated from aircraft-measured size spectra, and including the effects of molecular scattering, multiple scattering, and instrument noise. Radiation calculations are performed on the true and retrieved microphysical profiles to estimate the accuracy with which radiative flux profiles could be inferred remotely. It is found that the visible extinction profile can be retrieved independent of assumptions on the nature of the size distribution, the habit of the particles, the mean extinction-to-backscatter ratio, or errors in instrument calibration. Local errors in retrieved extinction can occur in proportion to local fluctuations in the extinction-to-backscatter ratio, but down to 400 m above the height of the lowest lidar return, optical depth is typically retrieved to better than 0.2. Retrieval uncertainties are greater at the far end of the profile, and errors in total optical depth can exceed 1, which changes the shortwave radiative effect of the cloud by around 20%. Longwave fluxes are much less sensitive to errors in total optical depth, and may generally be calculated to better than 2 W m(-2) throughout the profile. It is important for retrieval algorithms to account for the effects of lidar multiple scattering, because if this is neglected, then optical depth is underestimated by approximately 35%, resulting in cloud radiative effects being underestimated by around 30% in the shortwave and 15% in the longwave. Unlike the extinction coefficient, the inferred ice water content and particle size can vary by 30%, depending on the assumed mass-size relationship (a problem common to all remote retrieval algorithms). However, radiative fluxes are almost completely determined by the extinction profile, and if this is correct, then errors in these other parameters have only a small effect in the shortwave (around 6%, compared to that of clear sky) and a negligible effect in the longwave.

Efficient tree construction for the multicast problem

A new heuristic for the Steiner Minimal Tree problem is presented here. The method described is based on the detection of particular sets of nodes in networks, the “Hot Spot” sets, which are used to obtain better approximations of the optimal solutions. An algorithm is also proposed which is capable of improving the solutions obtained by classical heuristics, by means of a stirring process of the nodes in solution trees. Classical heuristics and an enumerative method are used CIS comparison terms in the experimental analysis which demonstrates the goodness of the heuristic discussed in this paper.

Efficient tree construction for the multicast problem

A new heuristic for the Steiner minimal tree problem is presented. The method described is based on the detection of particular sets of nodes in networks, the “hot spot” sets, which are used to obtain better approximations of the optimal solutions. An algorithm is also proposed which is capable of improving the solutions obtained by classical heuristics, by means of a stirring process of the nodes in solution trees. Classical heuristics and an enumerative method are used as comparison terms in the experimental analysis which demonstrates the capability of the heuristic discussed

A fuzzy approach for the network congestion problem

In the recent years, the unpredictable growth of the Internet has moreover pointed out the congestion problem, one of the problems that historicallyha ve affected the network. This paper deals with the design and the evaluation of a congestion control algorithm which adopts a FuzzyCon troller. The analogyb etween Proportional Integral (PI) regulators and Fuzzycon trollers is discussed and a method to determine the scaling factors of the Fuzzycon troller is presented. It is shown that the Fuzzycon troller outperforms the PI under traffic conditions which are different from those related to the operating point considered in the design.

A parallel genetic algorithm for the Steiner Problem in Networks

This paper presents a parallel genetic algorithm to the Steiner Problem in Networks. Several previous papers have proposed the adoption of GAs and others metaheuristics to solve the SPN demonstrating the validity of their approaches. This work differs from them for two main reasons: the dimension and the characteristics of the networks adopted in the experiments and the aim from which it has been originated. The reason that aimed this work was namely to build a comparison term for validating deterministic and computationally inexpensive algorithms which can be used in practical engineering applications, such as the multicast transmission in the Internet. On the other hand, the large dimensions of our sample networks require the adoption of a parallel implementation of the Steiner GA, which is able to deal with such large problem instances.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.