Statistics of the Z–R Relationship for Strong Convective Weather over the Yangtze–Huaihe River Basin and Its Application to Radar Reflectivity Data Assimilation for a Heavy Rain Event

The relationship between the radar reflectivity factor(Z) and the rainfall rate(R) is recalculated based on radar observations from 10 Doppler radars and hourly rainfall measurements at 6529 automatic weather stations over the Yangtze–Huaihe River basin. The data were collected by the National 973 Project from June to July 2013 for severe convective weather events. The Z–R relationship is combined with an empirical qr–R relationship to obtain a new Z–qr relationship, which is then used to correct the observational operator for radar reflectivity in the three-dimensional variational(3 DVar) data assimilation system of the Weather Research and Forecasting(WRF) model to improve the analysis and prediction of severe convective weather over the Yangtze–Huaihe River basin. The performance of the corrected reflectivity operator used in the WRF 3 DVar data assimilation system is tested with a heavy rain event that occurred over Jiangsu and Anhui provinces and the surrounding regions on 23 June 2013. It is noted that the observations for this event are not included in the calculation of the Z–R relationship. Three experiments are conducted with the WRF model and its 3 DVar system, including a control run without the assimilation of reflectivity data and two assimilation experiments with the original and corrected reflectivity operators. The experimental results show that the assimilation of radar reflectivity data has a positive impact on the rainfall forecast within a few hours with either the original or corrected reflectivity operators, but the corrected reflectivity operator achieves a better performance on the rainfall forecast than the original operator. The corrected reflectivity operator extends the effective time of radar data assimilation for the prediction of strong reflectivity. The physical variables analyzed with the corrected reflectivity operator present more reasonable mesoscale structures than those obtained with the original reflectivity operator. This suggests that the new statistical Z–R relationship is more suitable for predicting severe convective weather over the Yangtze–Huaihe River basin than the Z–R relationships currently in use.     

A Local Implementation of the POD-Based Ensemble 4DVar with R-Localization简

The purpose of this paper is to provide a robust and flexible implementation of a proper orthogonal decomposition-based ensemble four-dimensional variational assimilation method（PODEn4DVar） through Rlocalization.With R-localization,the implementation of the local PODEn4DVar analysis can be coded for parallelization with enhanced assimilation precision.The feasibility and effectiveness of the PODEn4DVar local implementation with R-localization are demonstrated in a two-dimensional shallow-water equation model with simulated observations（OSSEs） in comparison with the original version of the PODEn4DVar with B-localization and that without localization.The performance of the PODEn4DVar with localization shows a significant improvement over the scheme with no localization,particularly under the imperfect model scenario.Moreover,the R-localization scheme is capable of outperforming the Blocalization case to a certain extent.Further,the assimilation experiments also demonstrate that PODEn4DVar with R-localization is most efficient due to its easy parallel implementation.     

Variational Assimilation of GPS Precipitable Water Vapor and Hourly Rainfall Observations for a Meso-β Scale Heavy Precipitation Event During the 2002 Mei-Yu Season

Recent advances in Global Positioning System （GPS） remote sensing technology allow for a direct estimation of the precipitable water vapor （PWV） from delayed signals transmitted by GPS satellites, which can be assimilated into numerical models with four-dimensional variational （4DVAR） data assimilation. A mesoscale model and its 4DVAR system are used to access the impacts of assimilating GPS-PWV and hourly rainfall observations on the short-range prediction of a heavy rainfall event on 20 June 2002. The heavy precipitation was induced by a sequence of meso-β-scale convective systems （MCS） along the mei-yu front in China. The experiments with GPS-PWV assimilation cluster and also eliminated the erroneous rainfall successfully simulated the evolution of the observed MCS systems found in the experiment without 4DVAR assimilation. Experiments with hourly rainfall assimilation performed similarly both on the prediction of MCS initiation and the elimination of erroneous systems, however the MCS dissipated much sooner than it did in observations. It is found that the assimilation-induced moisture perturbation and mesoscale low-level jet are helpful for the MCS generation and development. It is also discovered that spurious gravity waves may post serious limitations for the current 4DVAR algorithm, which would degrade the assimilation efficiency, especially for rainfall data. Sensitivity experiments with different observations, assimilation windows and observation weightings suggest that assimilating GPS-PWV can be quite effective, even with the assimilation window as short as 1 h. On the other hand, assimilating rainfall observations requires extreme cautions on the selection of observation weightings and the control of spurious gravity waves.     

Assimilating All-sky Infrared Radiances from Himawari-8 Using the 3DVar Method for the Prediction of a Severe Storm over North China

Although radar observations capture storm structures with high spatiotemporal resolutions, they are limited within the storm region after the precipitation formed. Geostationary satellites data cover the gaps in the radar network prior to the formation of the precipitation for the storms and their environment. The study explores the effects of assimilating the water vapor channel radiances from Himawari-8 data with Weather Research and Forecasting model data assimilation system(WRFDA) for a severe storm case over north China. A fast cloud detection scheme for Advanced Himawari imager(AHI)radiance is enhanced in the framework of the WRFDA system initially in this study. The bias corrections, the cloud detection for the clear-sky AHI radiance, and the observation error modeling for cloudy radiance are conducted before the data assimilation. All AHI radiance observations are fully applied without any quality control for all-sky AHI radiance data assimilation. Results show that the simulated all-sky AHI radiance fits the observations better by using the cloud dependent observation error model, further improving the cloud heights. The all-sky AHI radiance assimilation adjusts all types of hydrometeor variables, especially cloud water and precipitation snow. It is proven that assimilating all-sky AHI data improves hydrometeor specifications when verified against the radar reflectivity. Consequently, the assimilation of AHI observations under the all-sky condition has an overall improved impact on both the precipitation locations and intensity compared to the experiment with only conventional and AHI clear-sky radiance data.     

Estimating the Soil Moisture Profile by Assimilating Near-Surface Observations with the Ensemble Kalman Filter （EnKF）

The paper investigates the ability to retrieve the true soil moisture profile by assimilating near-surface soil moisture into a soil moisture model with an ensemble Kalman filter （EnKF） assimilation scheme, including the effect of ensemble size, update interval and nonlinearities in the profile retrieval, the required time for full retrieval of the soil moisture profiles, and the possible influence of the depth of the soil moisture observation. These questions are addressed by a desktop study using synthetic data. The ＂true＂ soil moisture profiles are generated from the soil moisture model under the boundary condition of 0.5 cm d^-1 evaporation. To test the assimilation schemes, the model is initialized with a poor initial guess of the soil moisture profile, and different ensemble sizes are tested showing that an ensemble of 40 members is enough to represent the covariance of the model forecasts. Also compared are the results with those from the direct insertion assimilation scheme, showing that the EnKF is superior to the direct insertion assimilation scheme, for hourly observations, with retrieval of the soil moisture profile being achieved in 16 h as compared to 12 days or more. For daily observations, the true soil moisture profile is achieved in about 15 days with the EnKF, but it is impossible to approximate the true moisture within 18 days by using direct insertion. It is also found that observation depth does not have a significant effect on profile retrieval time for the EnKF. The nonlinearities have some negative influence on the optimal estimates of soil moisture profile but not very seriously.     

用一种新的同化方法同化降水量资料

Observations of accumulated precipitation are extremely valuable for effectively improving rainfall analysis and forecast. It is, however, difficult to use such observations directly through sequential assimilation methods, such as three-dimensional variational data assimilation or an Ensemble Kalman Filter. In this study, the authors illustrate a new approach that makes effective use of precipitation data to improve rainfall forecast. The new method directly obtains an optimal solution in a reduced space by fitting observations with historical time series generated by the model; it also avoids the implementation of tangent linear model and its adjoint. A lot of historical samples are produced as the ensemble of precipitation observations with the fully nonlinear forecast model. The results show that the new approach is capable of extracting information from precipitation observations to improve the analysis and forecast. This method provides comparable performance with the standard four- dimensional variational data assimilation at a much lower computational cost.     

Assimilating surface observations in a four-dimensional variational Doppler radar data assimilation system to improve the analysis and forecast of a squall line case

This paper examines how assimilating surface observations can improve the analysis and forecast ability of a fourdimensional Variational Doppler Radar Analysis System(VDRAS).Observed surface temperature and winds are assimilated together with radar radial velocity and reflectivity into a convection-permitting model using the VDRAS four-dimensional variational(4DVAR) data assimilation system.A squall-line case observed during a field campaign is selected to investigate the performance of the technique.A single observation experiment shows that assimilating surface observations can influence the analyzed fields in both the horizontal and vertical directions.The surface-based cold pool,divergence and gust front of the squall line are all strengthened through the assimilation of the single surface observation.Three experiments—assimilating radar data only,assimilating radar data with surface data blended in a mesoscale background,and assimilating both radar and surface observations with a 4DVAR cost function—are conducted to examine the impact of the surface data assimilation.Independent surface and wind profiler observations are used for verification.The result shows that the analysis and forecast are improved when surface observations are assimilated in addition to radar observations.It is also shown that the additional surface data can help improve the analysis and forecast at low levels.Surface and low-level features of the squall line—including the surface warm inflow,cold pool,gust front,and low-level wind—are much closer to the observations after assimilating the surface data in VDRAS.     

Dynamical and Microphysical Retrieval from Simulated Doppler Radar Observations Using the 4DVAR Assimilation Technique

Based on a cloud model and the four-dimensional variational (4DVAR) data assimilation method developed by Sun and Crook (1997), simulated experiments of dynamical and microphysical retrieval from Doppler radar data were performed. The 4DVAR data assimilation technique was applied to a cloud scale model with a warm rain parameterization scheme. The 3D wind, thermodynamical, and microphysical fields were determined by minimizing a cost function, defined by the difference between both radar observed radial velocities and reflectivities and their model predictions. The adjoint of the numerical model was used to provide the gradient of the cost function with respect to the control variables. Experiments have demonstrated that the 4DVAR assimilation method is able to retrieve the detailed structure of wind, thermodynamics, and microphysics by using either dual-Doppler or single-Doppler information. The quality of retrieval depends strongly on the magnitude of constraint with respect to the variables. Retrieving the temperature field, cloud water and water vapor is more difficult than the recovery of the wind field and rainwater. Accurate thermodynamic retrieval requires a longer assimilation period. The inclusion of a background term, even mean fields from a single sounding, helped reduce the retrieval errors. Less accurate velocity fields were obtained when single-Doppler data were used. It was found that the retrieved velocity is sensitive to the location of the retrieval domain relative to the radars while the other fields have very little changes. Two radar volumetric scans are generally adequate for providing the evolution, although the use of additional volumes improves the retrieval. As the amount of the observations decreases, the performance of the retrieval is degraded. However, the missing observations can be compensated by adding a background term to the cost function. The technique is robust to random errors in radial velocity and calibration errors in reflectivity. The boundary conditions from the dual-Doppler synthesized winds are sufficient for the retrieval. When the retrieval is mainly controlled by the observations in the regions away from the boundaries, the simple boundary conditions from velocity azimuth display (VAD) analysis are also available. The microphysical retrieval is sensitive to model errors.     

Impact of 4DVAR Assimilation of AIRS Total Column Ozone Observations on the Simulation of Hurricane Earl

The Atmospheric Infrared Sounder(AIRS) provides twice-daily global observations of brightness temperature, which can be used to retrieve the total column ozone with high spatial and temporal resolution.In order to apply the AIRS ozone data to numerical prediction of tropical cyclones, a four-dimensional variational(4DVAR) assimilation scheme on selected model levels is adopted and implemented in the mesoscale non-hydrostatic model MM5. Based on the correlation between total column ozone and potential vorticity(PV), the observation operator of each level is established and five levels with highest correlation coefficients are selected for the 4DVAR assimilation of the AIRS total column ozone observations. The results from the numerical experiments using the proposed assimilation scheme for Hurricane Earl show that the ozone data assimilation affects the PV distributions with more mesoscale information at high levels first and then influences those at middle and low levels through the so-called asymmetric penetration of PV anomalies.With the AIRS ozone data being assimilated, the warm core of Hurricane Earl is intensified, resulting in the improvement of other fields near the hurricane center. The track prediction is improved mainly due to adjustment of the steering flows in the assimilation experiment.     

EXPERIMENTS ON ASSIMILATION OF INITIAL VALUES IN NUMERICAL PREDICTION OF A WARM-SECTOR PRECIPITATION IN SOUTH CHINA

In order to understand the impact of initial conditions upon prediction accuracy of short-term forecast and nowcast of precipitation in South China, four experiments i.e. a control, an assimilation of conventional sounding and surface data, testing with nudging rainwater data and the assimilation of radar-derived radial wind, are respectively conducted to simulate a case of warm-sector heavy rainfall that occurred over South China, by using the GRAPES_MESO model. The results show that (1) assimilating conventional surface and sounding observations helps improve the 24-h rainfall forecast in both the area and order of magnitude; (2) nudging rainwater contributes to a significant improvement of nowcast, and (3) the assimilation of radar-derived radial winds distinctly improves the 24-h rainfall forecast in both the area and order of magnitude. These results serve as significant technical reference for the study on short-term forecast and nowcast of precipitation over South China in the future.     

Evaluation of the tropical variability from the Beijing Climate Center’s real-time operational global Ocean Data Assimilation System

The second-generation Global Ocean Data Assimilation System of the Beijing Climate Center(BCC_GODAS2.0) has been run daily in a pre-operational mode.It spans the period 1990 to the present day.The goal of this paper is to introduce the main components and to evaluate BCC_GODAS2.0 for the user community.BCC_GODAS2.0 consists of an observational data preprocess,ocean data quality control system,a three-dimensional variational(3DVAR) data assimilation,and global ocean circulation model[Modular Ocean Model 4(MOM4)].MOM4 is driven by six-hourly fluxes from the National Centers for Environmental Prediction.Satellite altimetry data,SST,and in-situ temperature and salinity data are assimilated in real time.The monthly results from the BCC_GODAS2.0 reanalysis are compared and assessed with observations for 1990-2011.The climatology of the mixed layer depth of BCC-GODAS2.0 is generally in agreement with that of World Ocean Atlas 2001.The modeled sea level variations in the tropical Pacific are consistent with observations from satellite altimetry on interannual to decadal time scales.Performances in predicting variations in the SST using BCC_GODAS2.0 are evaluated.The standard deviation of the SST in BCC-GODAS2.0 agrees well with observations in the tropical Pacific.BCC-GODAS2.0 is able to capture the main features of E1 Nino Modoki I and Modoki Ⅱ,which have different impacts on rainfall in southern China.In addition,the relationships between the Indian Ocean and the two types of E1 Nino Modoki are also reproduced.     

Variation of the North Equatorial Current,Mindanao Current,and Kuroshio Current in a High-Resolution Data Assimilation during 2008–2012

Outputs from a high-resolution data assimilation system,the global Hybrid Coordinate Ocean Model and Navy Coupled Ocean Data Assimilation （HYCOM＋NCODA） 1/12° analysis,were analyzed for the period September 2008 to February 2012.The objectives were to evaluate the performance of the system in simulating ocean circulation in the tropical northwestern Pacific and to examine the seasonal to interannual variations of the western boundary currents.The HYCOM assimilation compares well with altimetry observations and mooring current measurements.The mean structures and standard deviations of velocities of the North Equatorial Current （NEC）,Mindanao Current （MC） and Kuroshio Current （KC） also compare well with previous observations.Seasonal to interannual variations of the NEC transport volume are closely correlated with the MC transport volume,instead of that of the KC.The NEC and MC transport volumes mainly show well-defined annual cycles,with their maxima in spring and minima in fall,and are closely related to the circulation changes in the Mindanao Dome （MD） region.In seasons of transport maxima,the MD region experiences negative SSH anomalies and a cyclonic gyre anomaly,and in seasons of transport minima the situation is reversed.The sea surface NEC bifurcation latitude （NBL） in the HYCOM assimilation also agrees well with altimetry observations.In 2009,the NBL shows an annual cycle similar to previous studies,reaching its southernmost position in summer and its northernmost position in winter.In 2010 and 2011,the NBL variations are dominantly influenced by La Ni（n）a events.The dynamics responsible for the seasonal to interannual variations of the NEC-MC-KC current system are also discussed.     

EXPERIMENTAL APPLICATION OF A THINNING SCHEME FOR THE ASSIMILATION OF SURFACE OBSERVATION DATA IN GRAPES-3DVAR

To reduce the spatial correlation of representation error in observations and computational complexity, we propose a thinning scheme that can extract typical observations within a certain range. This scheme is applied to the Global/Regional Assimilation and Prediction System (GRAPES) with three-dimensional variation (3DVAR) to study the effect of the thinning radius on the assimilation results. The assimilation experiments indicate that when the ratio of the model resolution to the observational resolution is 1:3, the simulated results for precipitation are relatively good and have a relatively high equitable threat score (ETS). Moreover, the analysis errors in the temperature and the specific humidity are the smallest, the dependence of the norm gradient vector of the objective function on the number of iterations is slow, gentle, and close to 0, and the minimization results in improved conditions.     

MODIS brightness temperature data assimilation under cloudy conditions Ⅱ: Impacts on rainstorm forecasting

Although satellite observations provide large amount of information of clouds and precipitation and play an important role in the forecast of heavy rainfall, they have not been fully taken advantage of in data assimilation of numerical weather predictions, especially those in infrared channels. Assimilating radiances is common under clear-sky conditions since it is extremely difficult to simulate infrared transmittance in cloudy sky. Based on the Global and Regional Assimilation and Prediction Enhanced System 3-dimensional variance (GRAPES-3DVar), cloud liquid water content, ice-water content and cloud cover are employed as governing variables in the assimilation system. This scheme can improve the simulation of infrared transmittance by a fast radiative transfer model for TOVS (RTTOV) and adjust the atmospheric and cloud parameters based on infrared radiance observations. In this paper, we investigate a heavy rainfall over Guangdong province on May 26, 2007, which is right after the onset of a South China Sea monsoon. In this case, channels of the Moderate Resolution Imaging Spectroradiometer (MODIS) for observing water vapor (Channel 27) and cloud top altitude (Channel 36) are selected for the assimilation. The process of heavy rainfall is simulated by the Weather Research and Forecasting (WRF) model. Our results show that the assimilated MODIS data can improve the distribution of water vapor and temperature in the first guess field and indirectly adjust the upper-level wind field. The tendency of adjustment agrees well with the satellite observations. The assimilation scheme has positive impacts on the short-range forecasting of rainstorm.     

A Multivariate Empirical Orthogonal Function-Based Scheme for the Balanced Initial Ensemble Generation of an Ensemble Kalman Filter

The initial ensemble perturbations for an ensemble data assimilation system are expected to reasonably sample model uncertainty at the time of analysis to further reduce analysis uncertainty. Therefore, the careful choice of an initial ensemble perturbation method that dynamically cycles ensemble perturbations is required for the optimal performance of the system. Based on the multivariate empirical orthogonal function (MEOF) method, a new ensemble initialization scheme is developed to generate balanced initial perturbations for the ensemble Kalman filter (EnKF) data assimilation, with a reasonable consideration of the physical relationships between different model variables. The scheme is applied in assimilation experiments with a global spectral atmospheric model and with real observations. The proposed perturbation method is compared to the commonly used method of spatially-correlated random perturbations. The comparisons show that the model uncertainties prior to the first analysis time, which are forecasted from the balanced ensemble initial fields, maintain a much more reasonable spread and a more accurate forecast error covariance than those from the randomly perturbed initial fields. The analysis results are further improved by the balanced ensemble initialization scheme due to more accurate background information. Also, a 20-day continuous assimilation experiment shows that the ensemble spreads for each model variable are still retained in reasonable ranges without considering additional perturbations or inflations during the assimilation cycles, while the ensemble spreads from the randomly perturbed initialization scheme decrease and collapse rapidly.     

Comparative Experiments on the Effect of Radar Data Assimilation and Increasing Horizontal Resolution on Short-term Numerical Weather Prediction

To examine the effect of radar data assimilation and increasing horizontal resolution on the short-term numerical weather prediction, comparative numerical experiments are conducted for a Huabei (North China) torrential rainfall event by using the Advanced Regional Prediction System (ARPS) and ARPS Data Analysis System (ADAS). The experiments use five different horizontal grid spacings, i.e., 18, 15, 9, 6, and 3 km,respectively, under the two different types of analyses: one with radar data, the other without. Results show that, when radar data are not used in the analysis (i.e., only using the conventional observation data), increasing horizontal resolution can improve the short-term prediction of 6 h with better representation of the frontal structure and higher scores of the rainfall prediction, particularly for heavy rain situations. When radar data are assimilated, it significantly improves the rainfall prediction for the first 6 h, especially the locality and intensity of precipitation. Moreover, using radar data in the analysis is more effective in improving the short-term prediction than increasing horizontal resolution of the model alone, which is demonstrated by the fact that by using radar data in the analysis and a coarser resolution of the 18-km grid spacing, the predicted results are as good as that by using a higher resolution of the 3-km grid spacing without radar data. Further study of the results under the radar data assimilation with grid spacing of 18-3 km reveals that the rainfall prediction is more sensitive to the grid spacing in heavy rain situations (more than 40 mm) than in ordinary rain situations (less than 40 mm). When the horizontal grid spacing reduces from 6 to 3 km, there is no obvious improvement to the prediction results. This suggests that there is a limit to how far increasing horizontal resolution can do for the improvement of the prediction. Therefore, an effective approach to improve the short-term numerical prediction is to combine the radar data assimilation with an optimal horizontal resolution.     

Assessing the Performance of Separate Bias Kalman Filter in Correcting the Model Bias for Estimation of Soil Moisture Profiles

The performance of separate bias Kalman filter (SepKF) in correcting the model bias for the improvement of soil moisture profiles is evaluated by assimilating the near-surface soil moisture observations into a land surface model (LSM). First, an observing system simulation experiment (OSSE) is carried out, where the true soil moisture is known, two types of model bias (i.e., constant and sinusoidal) are specified, and the bias error covariance matrix is assumed to be proportional to the model forecast error covariance matrix with a ratio λ. Second, a real assimilation experiment is carried out with measurements at a site over Northwest China. In the OSSE, the soil moisture estimation with the SepKF is improved compared with ensemble Kalman filter (EnKF) without the bias filter, because SepKF can properly correct the model bias, especially in the situation with a large model bias. However, the performance of SepKF becomes slightly worse if the constant model bias increases or temporal variability of the sinusoidal model bias becomes large. It is suggested that the ratio λ should be increased (decreased) in order to improve the soil moisture estimation if temporal variability of the sinusoidal model bias becomes high (low). Finally, the assimilation experiment with real observations also shows that SepKF can further improve the estimation of soil moisture profiles compared with EnKF without the bias correction.     

A New Approach to Data Assimilation

A significant attempt to design a timesaving and efficient four-dimensional variational data assimilation (4DVar) has been made in this paper, and a new approach to data assimilation, which is noted as 'three-dimensional variational data assimilation of mapped observation (3DVM)' is proposed, based on the new concept of mapped observation and the new idea of backward 4DVar. Like the available 4DVar, 3DVM produces an optimal initial condition (IC) that is consistent with the prediction model due to the inclusion of model constraints and best fits the observations in the assimilation window through the model solution trajectory. Different from the 4DVar, the IC derived from 3DVM is located at the end of the assimilation window rather than at the beginning conventionally. This change greatly reduces the computing cost for the new approach, which is almost the same as that of the three-dimensional variational data assimilation (3DVar). Especially, such a change is able to improve assimilation accuracy because it does not need the tangential linear and adjoint approximations to calculate the gradient of cost function. Therefore, in numerical test, the new approach produces better IC than 4DVar does for 72-h simulation of TY9914 (Dan), by assimilating the three-dimensional fields of temperature and wind retrieved from the Advanced Microwave Sounding Unit-A (AMSU-A) observations. Meanwhile, it takes only 1/7 of the computing cost that the 4DVar requires for the same initialization with the same retrieved data.     

Assimilation of Doppler Radar Observations with an Ensemble Square Root Filter：A Squall Line Case Study

The effectiveness of using an Ensemble Square Root Filter（EnSRF） to assimilate real Doppler radar observations on convective scale is investigated by applying the technique to a case of squall line on 12July 2005 in midwest Shandong Province using the Weather Research and Forecasting（WRF） model.The experimental results show that：（1） The EnSRF system has the potential to initiate a squall line accurately by assimilation of real Doppler radar data.The convective-scale information has been added into the WRF model through radar data assimilation and thus the analyzed fields are improved noticeably.The model spin-up time has been shortened,and the precipitation forecast is improved accordingly.（2） Compared with the control run,the deterministic forecast initiated with the ensemble mean analysis of EnSRF produces more accurate prediction of microphysical fields.The predicted wind and thermal fields are reasonable and in accordance with the characteristics of convective storms.（3） The propagation direction of the squall line from the ensemble mean analysis is consistent with that of the observation,but the propagation speed is larger than the observed.The effective forecast period for this squall line is about 5-6 h,probably because of the nonlinear development of the convective storm.