Abstract

A variational method for retrieval of the three-dimensional wind field from single-Doppler radar observations is developed and tested. The method uses the conservation equation for reflectivity and the continuity equation as a constraining model. Weak and strong constraint formalisms in data analysis am reviewed and compared using a one-dimensional advection equation for reflectivity considered as a passive tracer. The authors show that a model equation should be used as a weak constraint when the model does not predict exactly the evolution of the observations (such as the conservation equation for reflectivity). Consequently, the variational method presented here combines both formalisms: the conservation equation for reflectivity is used as a weak constraint, while the continuity equation is used as a strong constraint. The method is applied to retrieve detailed three-dimensional wind field of a microburst observed by two C-band Doppler radars during the Phoenix II Convective Boundary Layer Experiment. Retrieved wind fields are compared with dual-Doppler wind analysis. Results of experiments show that the cost function has multiple minima, and consequently retrievals are sensitive to the initial guess. To find the true minimum the retrieval is performed from large to small scale. The results are very encouraging.

Abstract

Four methods for retrieval of the horizontal wind field are described and compared using single-Doppler observations of a sea-breeze front measured during the Convective and Precipitation/Electrification Experiment. The first method examined is the TREC (tracking radar echoes by correlation) technique similar to the one proposed by Tuttle and Foote. Two other methods, similar to TREC, in which wind vectors are estimated by minimizing the difference between successive patterns of reflectivity, are then examined. These methods conceptually link the TREC method and the velocity volume processing (VVP) approach to the variational wind retrieval method described here. The variational formulation uses the conservation of reflectivity and the radial momentum equation as physical constraints and in this way it incorporates the concepts on which TREC and VVP are based. The performance of the methods is compared using the dual-Doppler wind analysis as ground truth. Results show that the variational method can retrieve the wind field with higher resolution than the TREC method.

Abstract

Radiosonde observations employed in real-time numerical weather prediction (NWP) applications are disseminated through the Global Telecommunication System (GTS) using alphanumeric codes. These codes do not include information about the position and elapsed ascent time of the balloon. Consequently, the horizontal balloon drift has generally been either ignored or estimated in data assimilation systems for NWP. With the increasing resolution of atmospheric models, it is now important to consider the positions and times of radiosonde data in both data assimilation and forecast verification systems. This information is now available in the Binary Universal Form for the Representation of Meteorological Data (BUFR) code for radiosonde data. This latter code will progressively replace the alphanumeric codes for all radiosonde data transmitted on the GTS. As a result, a strategy should be adopted by NWP centers to deal with the various codes for radiosonde data during this transition. In this work, a method for estimating the balloon drift position from reported horizontal wind components and a representative elapsed ascent time profile are developed and tested. This allows for estimating the missing positions and times information of radiosonde data in alphanumeric reports, and then for processing them like those available in BUFR code. The impact of neglecting the balloon position in data assimilation and verification systems is shown to be significant in short-range forecasts in the upper troposphere and stratosphere, especially for the zonal wind field in the Northern Hemisphere winter season. Medium-range forecasts are also improved overall when the horizontal position of radiosonde data is retrieved.

Abstract

The degrees of freedom for signal (DFS) is used in data assimilation applications to measure the self-sensitivity of analysis to different observation types. This paper describes a practical method to estimate the DFS of observations from a posteriori statistics. The method does not require the consistency of the error statistics in the analysis system and it is shown that the observational impact on analyses can be estimated from observation departures with respect to analysis or the forecast. This method is first introduced to investigate the impact of a complete set, or subsets, of observations on the analysis for idealized one-dimensional variational data assimilation (1D-Var) analysis experiments and then applied in the framework of the three dimensional (3D)- and four-dimensional (4D)-Var schemes developed at Environment Canada.

Abstract

This study examines the linearization properties of a simplified planetary boundary layer parameterization based on the vertical diffusion equations, in which the exchange coefficients are a function of the local Richardson number and wind shear. Spurious noise, associated with this parameterization, develops near the surface in the tangent linear integrations. The origin of this problem is investigated by examining the accuracy of the linearization and the numerical stability of the scheme used to discretize the vertical diffusion equations. The noise is primarily due to the linearization of the exchange coefficients when the atmospheric state is near neutral static stability and when a long time step is employed. A regularization procedure based on the linearization error and a criterion for the numerical stability is proposed and tested. This regularization is compared with those recently adopted by Mahfouf, who neglects the perturbations of the exchange coefficients, and by Janisková et al., who reduce the amplitude of those perturbations when the Richardson number is in the vicinity of zero.

When the sizes of the atmospheric state perturbations are 1 m s⁻¹ for the winds and 1 K for the temperature, which is the typical size of analysis increments, regularizations proposed here and by Janisková et al. perform similarly and are slightly better than neglecting the perturbations of the exchange coefficients. On the other hand, when the state perturbations are much smaller (e.g., 3 orders of magnitude smaller), the linearization becomes accurate and a regularization is no longer necessary, as long as the time step is short enough to avoid numerical instability. In this case, the regularization proposed here becomes inactive while the others introduce unnecessary errors.

Abstract

The authors address the problem of optimization of the microphysical information extracted from a simulation system composed of high-resolution numerical models and multiparameter radar data or other available measurements. As a tool in the exploration of this question, a bulk microphysical scheme based on the general approach of scaling normalization of particle size distribution (PSD) is proposed. This approach does not rely on a particular functional form imposed on the PSD and naturally leads to power-law relationships between the PSD moments providing an accurate and compact PSD representation. To take into account the possible evolution of the shape/curvature of the distribution, ignored within standard one- and two-moment microphysical schemes, a new three-moment scheme based on the two-moment scaling normalization is proposed. The methodology of the moment retrieval included in the three-moment scheme can also be useful as a retrieval algorithm combining different remote sensing observations. The developed bulk microphysical scheme presents a unified formulation for microphysical parameterization using one, two, or three independent moments, suitable in the context of data assimilation. The effectiveness of the scheme with different combinations of independent moments is evaluated by comparison with a very high resolution spectral model within a 1D framework on representative microphysical processes: rain sedimentation and evaporation.

Abstract

Microphysical schemes based on the scaling normalization of the particle size distribution (PSD) are cast into a variational data assimilation method to assess their ability to retrieve the precipitation structure and humidity from moments of the PSD that can be derived from radar- and ground-based disdrometer measurements. The sedimentation and evaporation, which are the main processes below the cloud base, are examined. Various identical twin experiments are presented in the context of a column time-dependent model used to simulate the passage of precipitating cells over a short period of time. The relative humidity profile is assumed constant. The feedback of the microphysical processes on the thermodynamic fields is ignored. Observations are generated from a three-moment scheme having the zeroth, third, and sixth moments of the PSD as prognostic variables. The model is discretized in terms of the logarithms of the predictive moments, which render the adjustment of the model variables easier to the observations. An upper bound for the characteristic diameter for the sixth moment is however necessary to prevent numerical instabilities from developing during the data assimilation process.

The tangent linear model of the three-moment scheme reproduces well the difference between two nonlinear integrations over the assimilation window (8 min), which validates the use of its adjoint in the minimization of the cost function that measures the misfit between observations and corresponding model variables. A weak smoothness penalty function should be added to the cost function when noisy observations are assimilated.

When all the predicted moments are observed and assimilated, the minimization converges very well, even with 40% observation error. In this case, the reflectivity factor, which is related to the sixth moment, can be retrieved with 0.2-dB accuracy. When only the sixth moment is observed, the total number of concentration (related to the zeroth moment) cannot be recovered. However, the constant relative humidity can be obtained with 1% accuracy. When simpler one-moment and two-moment schemes are used to retrieve the precipitation structure from the observed sixth moment, the model error strongly projects on the nonobserved moments of the PSD.

Abstract

Real-time horizontal wind observations from the National Oceanic and Atmospheric Administration’s (NOAA’s) Profiler Network (NPN) are assessed in preparation for their assimilation in the Canadian Meteorological Centre (CMC) analysis systems. As a first step, radiosonde winds from 20 stations were compared to the central U.S. profiler stations over the 2001/02 winter season. It was found that profilers are at least as good as conventional radiosonde data. The 2001/02 winter season data were also used to examine the vertical correlation structure of the observation error for profilers. Using a statistical analysis of innovations, the observation error standard deviation of the wind components is estimated as 2.2 m s⁻¹ and the vertical correlation length is approximately 500 m. These results suggest that the data are vertically correlated because they are available every 250 m. Therefore, a thinning process is proposed in which one out of three data are selected in the vertical for each station.

Since January 2004, a close monitoring of NPN profiler data revealed significant errors at some stations in the lower and upper troposphere. Consequently, a monthly blacklist of NPN profilers is built based on data from the previous month.

A data impact study with both the three-dimensional variational data assimilation (3DVAR) and four-dimensional variational data assimilation (4DVAR) analysis systems was conducted using data from the 2003/04 winter season in which the vertical thinning was tested. It was found that the vertical thinning improves slightly the 6-h forecast error, especially in the 4DVAR over the central United States in which 6 times more profilers are assimilated. The impact of the vertical thinning is found to be neutral in the 3DVAR. Also, the impact of profiler data is significant over the central U.S. domain compared to a control run with the only difference being the addition of profiler data. These results were sufficiently good to implement NPN profilers in both the CMC global and regional analysis systems with the thinning process in fall of 2004.

Abstract

An analysis of the impact of GPS radio occultation observations on Environment Canada’s global deterministic weather prediction system is presented. Radio occultation data, as any other source of weather observations, have a direct impact on the analyses. Since they are assimilated assuming that they are well calibrated, they also impact the bias correction scheme employed for other data, such as satellite radiances. The authors estimate the relative impact of occultation data obtained from, first, their assimilation as atmospheric measurements and, second, their influence on the bias correction for radiance data. This assessment is performed using several implementations of the thermodynamic relationships involved, and also allowing or blocking this influence to the radiance bias correction scheme.

The current implementation of occultation operators at Environment Canada is presented, collecting upgrades that have been detailed elsewhere, such as the equation of state of air and the expression of refractivity. The performance of the system with and without assimilation of occultations is reviewed under conditions representative of current operations. Several denial runs are prepared, withdrawing only the occultation data from the assimilation, but keeping their influence on the radiance bias correction, or assimilating occultations but denying their impact on the bias correction procedure, and a complete denial.

It is shown that the impact of occultations on the analysis is significant through both paths—assimilation and radiance bias correction—albeit the first is larger. The authors conclude that the traceability link of the ensemble of occultations has an added value, beyond the value of each datum as an atmospheric measurement.

Abstract

This study examines the assimilation of near-surface wind observations over land to improve wind nowcasting and short-term tropospheric forecasts. A new geostatistical operator based on geophysical model output statistics (GMOS) is compared with a bilinear interpolation scheme (Bilin). The multivariate impact on forecasts and the temporal evolution of the analysis increments produced are examined as well as the influence of background error covariances on different components of the prediction system. Results show that Bilin significantly degrades surface and upper-air fields when assimilating only wind data from 4942 SYNOP stations. GMOS on the other hand produces smaller increments that are in better agreement with the model state. It leads to better short-term near-surface wind forecasts and does not deteriorate the upper-air forecasts. The information persists longer in the system with GMOS, although the local improvements do not propagate beyond 6-h lead time. Initial model tendencies indicate that the mass field is not significantly altered when using static error covariances and the boundary layer parameterizations damp the poorly balanced increment locally. Conversely, most of the analysis increment is propagated when using flow-dependent error statistics. It results in better balanced wind and mass fields and provides a more persistent impact on the forecasts. Forecast accuracy results from observing system experiments (assimilating SYNOP winds with all observations used operationally) are generally neutral. Nevertheless, forecasts and analyses from GMOS are more self-consistent than those from both Bilin and a control experiment (not assimilating near-surface winds over land) and the information from the observations persists up to 12-h lead time.