Four-dimensional data assimilation and numerical weather prediction (original) (raw)
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Four-dimensional variational data assimilation for Doppler radar wind data
Journal of Computational and Applied Mathematics, 2005
All forecast models, whether they represent the state of the weather, the spread of a disease, or levels of economic activity, contain unknown parameters. These parameters may be the model's initial conditions, its boundary conditions, or other tunable parameters which have to be determined. Four dimensional variational data assimilation (4D-Var) is a method of estimating this set of parameters by optimizing the fit between the solution of the model and a set of observations which the model is meant to predict. Although the method of 4D-Var described in this paper is not restricted to any particular system, the application described here has a numerical weather prediction (NWP) model at its core, and the parameters to be determined are the initial conditions of the model. The purpose of this paper is to give a review covering assimilation of Doppler radar wind data into a NWP model. Some associated problems, such as sensitivity to small variations in the initial conditions or du...
Quarterly Journal of the Royal Meteorological Society, 1998
Results of four-dimensional variational assimilations, 4D-Var, in cycling mode, over a few two-week assimilation periods are presented. 4D-Var is implemented in its incremental formulation, with a high-resolution model with the full physical parametrization package to compare the atmospheric states with the Observations, and a lowresolution model with simplified physics to minimize the cost-function. The comparison of 4D-Var using several assimilation windows (6, 12 and 24 hours) with 3D-Var (the equivalent of 4D-Var with no time-dimension) over a two-week period shows a clear benefit from using 4D-Var over a 6 or 12-hour window compared to the static 3D-Var scheme. It also exhibits some problems with the forecasts started using 4D-Var over a 24-hour window. The poorer performance of 4D-Var over a relatively long assimilation window can be partly explained by the fact that, in these experiments, the tangent-linear and adjoint models used in the minimization are only approximations of the assimilating model (having lower resolution and crude physics). The error these approximations introduce in the time evolution of a perturbation affects the convergence of the incremental 4D-Var, with larger discontinuities in the values of the cost-function when going from low to high resolution for longer assimilation windows. Additional experiments are performed comparing 4D-Var using a 6-hour window with the 3D-Var system. Two additional 2-week periods show a consistent improvement in extratropical forecast scores with the 4D-Var system. The main 4D-Var improvements occur in areas where the 3D-Var errors were the largest. Local improvement can be as large as 35% for the root-mean-square of the 5-day-forecast error, averaged over a two-week period. A comparison of key analysis errors shows that, indeed, 4D-Var using a 6-hour window is able to reduce substantially the amplitude of its fast-growing error components. The overall fit to observations of analyses and short-range forecasts from 3D-Var and 4D-Var is comparable. In active baroclinic areas, the fit of the background to the data is considerably better for the 4D-Var system, resulting in smaller increments. It appears that in these areas (and in particular over the west Atlantic), 4D-Var is able to better use the information contained in the observations. The ability of 4D-Var to extrapolate some aircraft data in the vertical with a baroclinic tilt is illustrated. Problems exist in the tropics and mountainous areas due partly to a lack of physics in the tangent-linear model. Possible improvements to the system (the introduction of more physics; better behaviour of the incremental approach owing to a line search at high resolution) are also discussed.
Atmospheric Science Letters
The effects of tuning of length-scale and observation-error on heavy rainfall forecasts are investigated. Length scale and observation error are tuned based on observation minus background (O − B) covariances and theoretically expected cost function values, respectively. Tuned length scale and observation error are applied to radar data assimilation using the Four Dimensional Variational (4D-Var) method. Length-scale tuning leads to improved Quantitative Precipitation Forecast (QPF) skill for heavy precipitation, better analyses, and reduced errors of wind, temperature, humidity, and hydrometeor forecasts. The effects of observation-error tuning are not as significant as those of length-scale tuning, and they are limited to improvements in QPF skill. This is because tuned observation errors are close to pre-assumed values. Proper tuning of length-scale and observation-error is essential for radar data assimilation using the 4D-Var method.
CIRA/CSU Four-Dimensional Variational Data Assimilation System
Monthly Weather Review, 2005
A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Predic...
Development of an efficient regional four-dimensional variational data assimilation system for WRF
This paper presents the development of a single executable four-dimensional variational data assimilation (4D-Var) system based on the Weather Research and Forecasting (WRF) Model through coupling the variational data assimilation algorithm (WRF-VAR) with the newly developed WRF tangent linear and adjoint model (WRFPLUS). Compared to the predecessor Multiple Program Multiple Data version, the new WRF 4D-Var system achieves major improvements in that all processing cores are able to participate in the computation and all information exchanges between WRF-VAR and WRFPLUS are moved directly from disk to memory. The single executable 4D-Var system demonstrates desirable acceleration and scalability in terms of the computational performance, as demonstrated through a series of benchmarking data assimilation experiments carried out over a continental U.S. domain. To take into account the nonlinear processes with the linearized minimization algorithm and to further decrease the computational cost of the 4D-Var minimization, a multi-incremental minimization that uses multiple horizontal resolutions for the inner loop has been developed. The method calculates the innovations with a high-resolution grid and minimizes the cost function with a lowerresolution grid. The details regarding the transition between the high-resolution outer loop and the low-resolution inner loop are introduced. Performance of the multi-incremental configuration is found to be comparable to that with the full-resolution 4D-Var in terms of 24-h forecast accuracy in the week-long analysis and forecast experiment over the continental U.S. domain. Moreover, the capability of the newly developed multi-incremental 4D-Var system is further demonstrated in the convection-permitting analysis and forecast experiment for Hurricane Sandy (2012), which was hardly computationally feasible with the predecessor WRF 4D-Var system.
Impact of Assimilation of Doppler Radial Velocity on a Variational System and on its Forecasts
Quarterly Journal of the Royal Meteorological Society
An approach to the assimilation of Doppler radar radial winds into a high resolution Numerical Weather Prediction (NWP) model is described. In this paper, we discuss the types of errors which might occur in radar radial winds. A new approach to specifying the radial velocity observation error is proposed based upon the radial gradient of the velocity across the pulse volume. The variation of this error with range is derived for a specific case. The production of "super-observations" for the input to a 3D-Var assimilation system is discussed. Impact of the assimilation of Doppler velocities on the 3D-Var analysis and on the model forecasts, for a case study, is investigated.
Monthly Weather Review, 2000
The formulation of the National Centers for Environmental Prediction four-dimensional variational dataassimilation (4D-Var) system is described. Results of applying 4D-Var over a one-week assimilation period, with a full set of physical parametrizations, are presented and compared with those of 3D-Var. The linearization has been performed without simplifications and, therefore, the tangent-linear and adjoint codes are consistent with the nonlinear physical parametrizations. The 4D-Var assimilation is similar in formulation to the 3D-Var analysis, except that observations are used at the appropriate time in 4D-Var. Compared with the 3D-Var runs, the 4D-Var results showed good convergences, smaller analysis increments, and a comparable fit of analyses and short-range forecasts to observations. A consistent improvement with the 4D-Var system is observed in short-range (six-hour) forecasts of all model variables except the specific humidity. The temperature analyses from 4D-Var were found to be better in most of the areas where the analysis errors from 3D-Var were largest, although the globally averaged root-mean-square difference in the 4D-Var temperature analysis was larger due to a very small degradation in some parts of the globe that include data-rich areas. The globally averaged root-mean-square difference in the 4D-Var specific-humidity analysis, compared with that of 3D-Var, was larger and was found to result from slightly increased analysis-error maxima in the 4D-Var results over data-sparse tropical regions. The 3 4 day forecasts from 4D-Var analyses compared more favourably than forecasts from the 3D-Var analyses with the targeted mid-Pacific dropwindsonde observations available from the 1998 North Pacific Experiment. Compared with conventional observations, a consistent improvement in the 1-5 day forecasts of wind and temperature was shown in the tropics and the southern hemisphere.