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Extracting multiple-scale observational information is critical for accurately reconstructing the structure of mesoscale circulation systems such as typhoon. The Space and Time Mesoscale Analysis System (STMAS) with multigrid data assimilation developed in Earth System Research Laboratory (ESRL) in National Oceanic and Atmospheric Administration (NOAA) has addressed this issue. Previous studies have shown the capability of STMAS to retrieve multiscale information in 2-dimensional Doppler radar radial velocity observations. This study explores the application of 3-dimensional (3D) Doppler radar radial velocities with STMAS for reconstructing a 3D typhoon structure. As for the first step, here, we use an idealized simulation framework. A two-scale simulated “typhoon” field is constructed and referred to as “truth,” from which randomly distributed conventional wind data and 3D Doppler radar radial wind data are generated. These data are used to reconstruct the synthetic 3D “typhoon” structure by the STMAS and the traditional 3D variational (3D-Var) analysis. The degree by which the “truth” 3D typhoon structure is recovered is an assessment of the impact of the data type or analysis scheme being evaluated. We also examine the effects of weak constraint and strong constraint on STMAS analyses. Results show that while the STMAS is superior to the traditional 3D-Var for reconstructing the 3D typhoon structure, the strong constraint STMAS can produce better analyses on both horizontal and vertical velocities.

Doppler radar has long been a valuable observational tool in meteorology. Three-dimensional (3D) Doppler radar radial velocity data can provide an opportunity to estimate both horizontal and vertical velocities. Therefore, in recent years, Doppler radar data assimilation for short-term numerical weather forecasting or called nowcasting has become a focal point of research [

In Doppler radar radial velocity data assimilation used in the above literatures, in a three-dimensional variational (3D-Var) framework, a background error covariance matrix is always needed to determine the spatial spreading of observational information. It is well known that an analysis field at different locations may have different correlation scales [

To minimize the errors of long and short waves in turn, a sequential 3D-Var approach has been proposed by Xie et al. [

Here, we study the analysis of 3D Doppler radar radial velocities using the STMAS to reconstruct the 3D wind structure. As for the first step, this study is performed in a twin experiment framework. In the next section, we first briefly review the theory of the multigrid 3D-Var data assimilation scheme in the STMAS. Some important aspects of the STMAS techniques such as smoothing, constraint, and Doppler radar radial wind operators used in the cost function of the STMAS multigrid 3D-Var are described. Section

In this study, the STMAS implemented by the multigrid 3D-Var is applied to the analysis of 3D Doppler radar radial velocities. This method can extract long and short wavelength information in turn efficiently from observations and provide objective and accurate analysis. The basic idea of this multigrid implementation can be referred to Li et al. [

To assimilate 3D Doppler radar radial velocities, with the control variables being

During the procedure of sequential multiscale analyses, the operators

To make a strong constraint on these three components of wind vector, incompressible continuity equation

The study domain covers a ^{2}
^{−1}, ^{2}
^{−1},

The typhoon center

The synthetic “typhoon” field (serving as the “truth”) at middle vertical level (5 km). (a) Radial velocity, (b)

Then, Doppler radar radial velocity data are generated from the “truth” typhoon field with one-degree azimuth angle increment and 2500 m gate spacing and 2-degree elevation angle increment from 1 degree to 20 degrees by interpolating the “truth” velocity field to the radial velocity observations’ points and using the equation

In the following, the above observational data are used to retrieve the simulated “typhoon” structure by the STMAS analysis method with weak or strong constraint and the traditional 3-dimensional variance (3D-Var) analysis with different correlation scales, respectively, and by comparing the analyzed results with the “truth,” performances of different analysis methods are discussed.

The error variances of radial velocity observations and conventional observations can be determined by the measurement error of instruments. But, here for simplicity, the same error variance is set for each kind of data. However, because the amount of radial velocity data is much larger than that of conventional data, a scaling scheme is used to balance the weights of these two types of observations. Thus, the conventional observation can have the same weight as that of radial velocity observation, which may comprise these two types of observations to get to a reasonable wind analysis.

The limited memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) method [

Three level grids are employed ranging from about 31.25 km × 31.25 km × 2.5 km (

The STMAS analyses with the above 3D Doppler radar radial velocity data or conventional data which vary from coarse to dense are shown in Figures

Root mean square errors (RMSE) of

Experiment | RMSE of |
RMSE of |
RMSE of |
---|---|---|---|

MG_RADAR | 15.7032 | 14.5197 | 2.3663 |

MG_COARSE | 9.2592 | 9.2195 | 1.4610 |

MG_RADAR_COARSE | 7.9500 | 7.6029 | 1.3757 |

MG_MODERATE | 3.2196 | 3.1966 | 0.8228 |

MG_RADAR_MODERATE | 3.0649 | 2.6148 | 0.7930 |

MG_DENSE | 1.0707 | 1.0849 | 0.5494 |

MG_RADAR_DENSE | 1.0514 | 1.0135 | 0.5373 |

MG_RADAR_DENSE_WEAK | 1.0747 | 1.0254 | 2.0840 |

T50_RADAR_DENSE | 6.8944 | 7.1118 | 1.3832 |

T25_RADAR_DENSE | 2.8425 | 2.7135 | 0.8172 |

T12_RADAR_DENSE | 3.7725 | 3.6773 | 0.7787 |

T06_RADAR_DENSE | 10.2998 | 10.2631 | 1.3669 |

STMAS analyses at middle vertical level. From left to right, these columns represent radial wind,

(a) and (b) are similar to Figures

(a) and (b) are similar to Figures

To compare the performance of the STMAS with a strong constraint or weak constraint, the continuity equation is added as penalty term to make a weak constraint case (otherwise, the STMAS analysis is a strong constraint of the three components of wind vector). Then, the control variables become

Assimilating the whole simulated Doppler radar radial velocity data and dense conventional data, the STMAS analyses with continuity equation as strong constraint or weak constraint are shown in Figures

As shown in Figure

For a traditional 3D-Var analysis, the cost function takes the form

Based on Gaussian distribution, the traditional 3D-Var using correlation scale usually constructs the background error covariance matrix by an empirical correlation scale. Therefore, the traditional 3D-Var with a certain correlation scale only can analyze this kind of scale information. However, the “truth” typhoon field in this study contains two different spatial scales wind speed information (~35 km and ~10 km). The traditional 3D-Var with 50 km horizontal correlation scale can only capture the main pattern of this typhoon field (i.e., the long wave information) but lose the small-scale information and produce a smooth analysis (Figure

Similar to Figure

From the vertical velocity distribution as well as wind vector shown in Figure

Vertical velocity section (color shade) and wind vector in this section across the typhoon center. (a) STMAS; (b) tradition 3D-Var with

Within an idealized simulation framework, the role of 3D Doppler radar radial velocity data for reconstructing 3D typhoon structures has been examined using the Space and Time Mesoscale Analysis System (STMAS). A two-scale simulated “typhoon” field is constructed and referred to as “truth,” from which randomly distributed conventional wind data and 3D Doppler radar radial wind data are generated. These data are used to reconstruct the synthetic 3D “typhoon” structure by the STMAS or the traditional 3D variational (3D-Var) analysis. The degree by which the “truth” 3D typhoon structure is recovered is an assessment of the impact of data type or analysis scheme being evaluated. The effects of weak or strong constraint on STMAS analysis have also been examined. We found that (

This study gives us promising results. Challenges still remain when 3D radar radial velocity data are assimilated for the reconstruction and initialization of real typhoon structures in the future. First, given the fact that the real atmosphere is compressive, the wind vector may not satisfy the nondiffusivity continuity equation used in this study. Therefore, a full continuity equation should be used to make a more general strong constraint in future study. Second, the model error has not been taken into account in this study. The influence of model errors on typhoon reconstruction and initialization has to be addressed and how to deal with model errors could be an important research topic in the follow-up studies.

The authors declare that there are no competing interests regarding the publication of this paper.

This research was jointly supported by grants of National Basic Research Program (2013CB430304), National Natural Science Foundation (41376013, 41376015, 41306006, 41541041, and 41506039), National High-Tech R&D Program (2013AA09A505), and National Programme on Global Change and Air-Sea Interaction (GASI-01-01-12 and GASI-IPOVAI-04) of China.