Assimilating AMSU-A Radiance Data with the WRF Hybrid En3DVAR System for Track Predictions of Typhoon Megi(2010)

SHEN Feifeiand MIN Jinzhong

Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science&Technology,Nanjing 210044

Assimilating AMSU-A Radiance Data with the WRF Hybrid En3DVAR System for Track Predictions of Typhoon Megi(2010)

SHEN Feifei∗and MIN Jinzhong

Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science&Technology,Nanjing 210044

The impact of assimilating radiances from the Advanced Microwave Sounding Unit-A(AMSU-A)on the track prediction of Typhoon Megi(2010)was studied using the Weather Research and Forecasting(WRF)model and a hybrid ensemble threedimensional variational(En3DVAR)data assimilation(DA)system.The influences of tuning the length scale and variance scale factors related to the static background error covariance(BEC)on the track forecast of the typhoon were studied. The results show that,in typhoon radiance data assimilation,a moderate length scale factor improves the prediction of the typhoon track.The assimilation of AMSU-A radiances using 3DVAR had a slight positive impact on track forecasts,even when the static BEC was carefully tuned to optimize its performance.When the hybrid DA was employed,the track forecast was significantly improved,especially for the sharp northward turn after crossing the Philippines,with the flow-dependent ensemble covariance.The flow-dependent BEC can be estimated by the hybrid DA and was capable of adjusting the position of the typhoon systematically.The impacts of the typhoon-specific BEC derived from ensemble forecasts were revealed by comparing the analysis increments and forecasts generated by the hybrid DA and 3DVAR.Additionally,for 24 h forecasts, the hybrid DA experiment with use of the full flow-dependent background error substantially outperformed 3DVAR in terms of the horizontal winds and temperature in the lower and mid-troposphere and for moisture at all levels.

data assimilation,radiance,observation operator

1.Introduction

The accuracy of tropical cyclone(TC)track prediction is one of the most important tasks in weather forecasting,crucial for saving lives and property.Over the past two decades, significant improvements have been made in TC track forecasts due to the increased use of remote sensing data,other advanced observations,and improved numerical weather prediction(NWP)models(Houze et al.,2007;Singh et al.,2008; Rappaport et al.,2009;Cangialosi and Franklin,2011).However,great challenges remain,especially for recurving tracks (George and Gray,1977;Thu and Krishnamurti,1992;Holland and Wang,1995;Zhang et al.,2013b),because a recurving track of a TC involves more uncertainties than an nonrecurving one.As one of the most important types of observations for NWP,satellite radiance data can provide valuable temperature and humidity information,especially over areas where conventional observations are limited(Derber and Wu, 1998;English et al.,2000;McNally et al.,2000;Bouttier and Kelly,2001;Le Marshall et al.,2006;McNally et al.,2006). Satellite radiances can be assimilated into NWP models with retrieval assimilation or direct assimilation(DA)methods. With the retrieval assimilation method,the retrieved temperature and humidity information from radiances using physical or statistical retrieval methods(Goldberg,1999)are applied in a similar way as with conventional data.The DA method involves assimilating radiance observations directly into NWP models,and is considered superior to retrieval assimilation because the observational error statistics are more accurate(Eyre,1989;Andersson et al.,1994;Derber and Wu, 1998;English et al.,2000;Bouttier and Kelly,2001).Moreover,its rapid,real-time processing without the retrieval steps is an advantage for operational data usage,enabling the early introduction of the radiance data into operational systems.

For most operational centers,a three-dimensional variational(3DVAR;e.g.,Parrish and Derber,1992;Lorenc et al., 2000;Barker et al.,2004)DA scheme is employed to obtain the initial conditions.In 3DVAR,observational information is spread to model grid points to correct the background field with the assumption of an isotropic,nearly homogeneous, static,time-invariant with flow-independent background error covariances(BECs).However,these assumptions cannot generally be used for TC assimilation applications due to thestrong vortical and nongeostrophic motions of TCs(Hamill and Snyder,2000);the true flow-dependent nature of the background errors is not captured.Recently,several studies have demonstrated that forecasts from ensemble-based DA can produce comparable or better forecasts than those from 3DVAR in a variety of weather applications(e.g.,Li and Liu, 2009;Torn and Hakim,2009;Hamill et al.,2011;Weng et al.,2011;Zhang et al.,2011;Dong and Xue,2012).

Ensemble Kalman filter(EnKF)methods benefit from the use of flow-dependent BEC but suffer from rank deficiency due to the smaller ensemble members used.The covariance localization method is often adopted to alleviate this problem.The variational technique is quite efficient and able to process complex nonlinear observations and apply physical constraints,but it is lacking in terms of the inclusion of flow-dependent BECs.To reconcile the advantages and disadvantages of the variational and EnKF methods,increasing effort is being made to hybridize the two approaches,rather than settling for one particular method.A hybrid DA approach that couples the ensemble DA technique into the variational framework(e.g.,Hamill and Snyder,2000;Lorenc, 2003;Wang et al.,2008a;Zhang et al.,2009;Wang,2010; Schwartz et al.,2013)has shown great promise for weather applications.Many previous studies have shown that hybrid approaches yield comparable or better forecasts than those based purely on 3DVAR that do not incorporate ensemble BECs,and can outperform forecasts initialized by standalone EnKFs(e.g.,Buehner,2005;Buehner et al.,2010;Hamill et al.,2011;Wang,2011;Li et al.,2012;Zhang and Zhang, 2012;Schwartz et al.,2013;Wang et al.,2013;Zhang et al., 2013a;Pan et al.,2014;Schwartz and Liu,2014).

The hybrid approach is popular for the following three reasons.First,the hybrid technique can be easily implemented in pre-existing variational DA frameworks(e.g., Wang et al.,2007b;Zhang et al.,2013a;Pan et al.,2014). Second,with a model-space covariance localization technique,the assimilation of non-local observations,such as satellite radiance data,may be more effective in hybrid frameworks than in EnKFs that use observation-space localization(Campbell et al.,2010).And third,the hybrid method can save computational cost by using the ensembles at a coarser resolution than deterministic hybrid analysis(e.g., Rainwater and Hunt,2013),and by producing similar results as EnKFs but with a smaller ensemble compared to the traditional EnKF.

However,to the best of our knowledge,no study has yet been published that applies the Weather Research and Forecasting(WRF)Hybrid En3DVAR DA to the assimilation of radiance data from the Advanced Microwave Sounding Unit-A(AMSU-A)for improving TC track prediction.Accordingly,this preliminary study examines the potential benefits of this computationally efficient procedure for improving TC track forecasting when assimilating AMSU-A radiance data.

More specifically,this study investigates the impacts of DA on TC track forecasting within the WRF Hybrid DA system(Barker et al.,2012),similar to in Wang(2011).However,this work differs from that of Wang(2011)in several important ways.First,this work investigates the effect of assimilating AMSU-A radiance observations on track predictions,while Wang(2011)did not assimilate any satellite radiance data.Second,in this study,each ensemble member is updated by running the hybrid analysis system multiple times with perturbed observations,whereas Wang(2011)used an ensemble transformation Kalman filter(ETKF)to generate the analysis ensemble.Moreover,we systematically examined the influence of the static BEC related length scale factor and variance scale factor on the prediction of the track of a typhoon for radiance DA.

The remainder of this paper is organized as follows.In section 2,we provide a brief introduction to the WRF Hybrid DA system system,together with aspects on radiance data assimilation.An overview of Typhoon Megi(2010)and the experimental settings are described in section 3.Section 4 presents the main results.Conclusions and further discussion are provided in the last section.

2.The WRF Hybrid En3DVAR DA system and radiance data assimilation

2.1.The WRF Hybrid En3DVAR DA system

2.2.AMSU-A radiance assimilation procedures

The AMSU-A 1b radiance data are ingested into the WRF 3DVAR and WRF Hybrid DA system in this study.AMSU-A is a line-scanned microwave sensor with 15 sensitive channels,each with a 2343 km swath width.It measures 30 pixels in each swath,with an approximate 48 km diameter footprint at nadir.In this study,a subset of AMSU-A channels is chosen to be assimilated.Channels 1–2 and 15 are located in window regions and are thus not assimilated since they are sensitive to uncertain surface parameters,cloud and precipitation.Channels 3–14 are sensitive to temperature,among which only channels 5–7 are assimilated because they peak under the model top(20 hPa).

The Community Radiative Transfer Model(CRTM;Han et al.,2006;Liu and Weng,2006)is coupled within the WRFDA system(Barker et al.,2012)described in section 2.1 as the observation operator for AMSU-A radiance.This is then used to calculate the simulated radiances with the temperature and moisture information from model states.Radiance data over mixed surfaces and observations with large scan angles are rejected.A radiance observation with large bias(the bias-corrected observation minus the CRTM modeled radiance),exceeding either 15 K or 5r is rejected,where r is the specified observation error standard deviation for brightness temperature.Following Liu et al.(2012),we use the full-sky AMSU-Aradiancesin thisstudy withoutany special cloud detection procedure.Better results for track forecasts are obtained when the thinning mesh is set to roughly 6–8 times the grid resolution for the Typhoon Megi(2010) case.Thus,we determine a 120 km thinning mesh as the first attempt to study assimilating AMSU-A radiances using hybrid methods.We correct the systematic biases from observed radiances before assimilation using the same method as in Liu et al.(2012)and Xu et al.(2013).The radiance bias is expressed inside a modified forward operator with a linear combination of several predictors(the scan position,the square and cube of the scan position,the 1000–300 hPa and 200–50 hPa layer thicknesses,surface skin temperature,and total column water vapor)and their coefficients.The coefficients are updated via a variational minimization process by including them in the cost function[Eq.(2)]as control variables(Derber and Wu,1998;Aulign´e et al.,2007;Dee and Uppala,2009).

3.Case description and experimental design

3.1.Overview of Typhoon Megi(2010)

Super Typhoon Megi(2010)—one of the most destructive TCs over the western North Pacific and South China Sea in 2010—was chosen for our experiments in this study.Megi (2010)was identified as a tropical disturbance by the Joint Typhoon Warning Center(JTWC)when it was about 600 km to the east of the Philippines at 0000 UTC 12 October 2010.Megi(2010)then developed quickly that same day. The JTWC classified the vortex as a tropical depression before 0900 UTC 13 October.Then,later,on 14 October,the Japan Meteorological Agency(JMA)upgraded Megi(2010) to a severe tropical storm and the JTWC upgraded it to a category-1 typhoon.On 15 October,Megi(2010)moved northwestwards and gradually intensified into a typhoon over the Pacific to the east of the Philippines.As shown in Figs.1 and 2,Megi(2010)initially moved northwestward,and then turned west-southwestward.It experienced a rapid intensification during 16–18 October,reaching its peak intensity at 1200 UTC 17 October,with minimum sea level pressure (MSLP)of 895 hPa and maximum surface wind(MSW)of up to 72 m s−1.Megi(2010)made landfall over Luzon Island as a super typhoon at 0425 UTC 18 October and became weaker after crossing the island.After that,it re-intensified rapidly from category-2 to category-4(MSLP:935 hPa)earlyon 19 October.At 0000 UTC 20 October,Megi(2010)experienced a sharp turn from westward to northward,an unusual track change that was not forecast by any of the leading operational centers.On 23 October,it made a second landfall as a tropical storm at Zhangpu in Fujian Province,and finally dissipated gradually the next day.

3.2.WRF model configuration

Table 1.List of experiments.

The WRF model(Skamarock et al.,2008)was used to conduct all the experiments.WRF is a three-dimensional, compressible,non-hydrostatic atmospheric model using terrain-following,mass-based sigma coordinate levels;its governing equations are written in flux form.All experiments were conducted over the single domain with a 15 km horizontal grid spacing.There were 450×400 grid points horizontally and 43 vertical levels with the model top at 20 hPa.The following parameterizations were used:the WRF Single-Moment6-Class scheme(Hong etal.,2004);the Kain–Fritsch cumulus parameterization(Kain and Fritsch, 1990,1993;Kain,2004)with a modified trigger function (Ma and Tan,2009);the Yonsei University(YSU)boundary layer scheme(Noh et al.,2003);the 5-layer thermal diffusion model for land surface processes scheme;the RRTM longwave radiation scheme(Mlawer et al.,1997);and the MM5 shortwave radiation scheme(Dudhia,1989).

3.3.Data assimilation setup

Several initial experiments were configured to compare the fundamentaldifference in using flow-dependentand static BEC and to evaluate the impact of DA when assimilating AMSU-A data on the subsequent forecast of Typhoon Megi (2010).Table 1 summarizes the design of the experiments.

To reduce spurious correlations caused by sampling error due to the limited ensemble member,a 750 km horizontal localization radius was applied to the ensemble covariance, and a standard vertical localization described in Wang et al. [2014,Eq.(12)]was applied.In all the DA experiments,all observations within±1.5 h were assumed to be valid at the analysis time.The static BEC statistics in the 3DVAR system were derived from the differences between the 24 h and 12 h forecasts valid at the same time,using the National Meteorological Center(NMC)method(Parrish and Derber,1992). These forecasts were generated using the WRF model on the same model grid for each day of September 2010,usingthe GFS(Global Forecast System)analyses as the initial and boundary conditions.The static BEC matrix was obtained using the WRFDA utility called CV5(Barker et al.,2012)for five control variables(stream function,unbalanced temperature,surface pressure and velocity potential,and relative humidity).Allexperiments were initialized at1800 UTC 17 October 2010(Fig.3),using the NCEP operational 0.5◦×0.5◦GFS analysis data as the initial and lateral boundary conditions.With the initial and lateral boundary conditions at this time,the initial ensemble was generated by taking Gaussian random draws with the static BECs and zero mean(Torn et al.,2006)and adding the perturbations to the GFS analysis. The deterministic and ensemble fields produced at 1800 UTC 17 October initialized the 6-h WRF forecasts,which served as backgrounds for the first 3DVAR,and hybrid analyses at 0000 UTC 18 October.A 120 h deterministic forecast was separately initialized at 0000 UTC 18 October by the analysis with 3DVAR and the hybrid con figurations.The 6 h cycling forecast-analysis experiments were carried out for all experiments until 0000 UTC 23 October.For the following cycles, the background was the previous cycle’s 6 h WRF forecast (initialized from the hybrid mean analysis).For those cycles, 24 h deterministic forecasts were carried out to evaluate the impact of cycling assimilation on forecasts.Digital filter initialization(DFI;Lynch and Huang,1992;Huang and Lynch, 1993)using a twice-DFI scheme and the Dolph filter(Lynch, 1997)with a 2 h backward integration were applied to all 120 h forecasts.Each ensemble member was updated by running the hybrid analysis system multiple times with perturbed observations.The covariance relaxation method of Zhang et al. (2004)wasemployed to maintain ensemble spread,where the final in flated ensemble perturbation is a weighted average of prior perturbation(as the background ensemble)and posterior perturbation(the ensemble analysis).In this study,the weight for the posterior perturbation was set to 0.8.

4.Results and discussions

In this section,we evaluate the analyses and forecasts of each of the DA experiments.The model predictions of Megi(2010)’s track were verified against the best-track analyses of the China Meteorological Administration(CMA)(Yu et al.,2007).Aspects of the ensemble spread performance were also examined since the key with ensemble-based DA is the use of an ensemble to estimate the flow-dependent forecast error.The differences in the analyses increments from 3DVAR and the hybrid DA are further diagnosed to evaluate how these differences contribute to the difference in the track forecasts.RMSE profiles of the 24-h forecasts are also displayed when using a set of conventional observations as reference.

4.1.Sensitivity to the length scale

4.2.Ensemble performance

Since a high-quality prior ensemble is the key to successful hybrid analyses,it is important to evaluate the ensemble performance.Figure 6 shows the ensemble spread of windand temperature on the 19th model level after the 6 h forecast valid at 0000 UTC 18 October,when Typhoon Megi (2010)intensified.The 6 h forecast ensemble directly provides the flow-dependent background error in the hybrid system.Since there are more forecast uncertainties where the spread is large,observations in areas with large ensemble spread are most likely to have a large impact in the hybrid system.Likewise,observations are less likely to influence the analysesin areaswhere the spread issmaller.The patterns reflecting the features of the observation locations and meteo-rological conditions can be seen in Figs.6a and b.The spread was large over the Tibetan Plateau in the west,where few observations were available to constrain the model.Conversely, spread was smallest over Eastern China,where observations were plentiful.A local maximum of spread was obvious for wind and potential temperature in the northeast of the Philippines,where Typhoon Megi(2010)moved,reflecting the forecast uncertainty for a TC.The ensemble spread also suggests larger forecast uncertainties around Megi(2010)than in its environment.

The ensemble spread can represent the ensemble mean forecast error in a well-calibrated system(Houtekamer et al., 2005).The forecast RMSEs,ensemble spread,and the static background error from the WRFDA(Wang et al.,2014)using the NMC method and the WRFDAmodeling are shown in Figs.7a and b.The forecast RMSEs were obtained by comparing the forecast ensemble mean with the GFS analyses. The static background error from the WRFDA modeling was estimated based on the ensemble perturbations using Gaussian random draws with the static BECs and zero mean.The ensemble mean RMSEs of wind were less than 3 m s−1and the temperature was less than 1 K at most levels.For winds, the static background error from the WRFDA modeling was largely underestimated,consistent with the results in Wang et al.(2014);whereas,the ensemble spread was much closer to the RMSEs compared to the static background error.For temperature,both the ensemble spread and the static background error were greater than the corresponding RMSEs between model level 34 and model level 41.For other levels, the ensemble spread was much closer to the RMSEs,while the static background error underestimated the forecast errors.Overall,the ensembles were reasonably well calibrated. The final background error from the hybrid system,as a mix of the flow-dependent and the static background error,plays an important role in the data assimilation procedure.

4.3.TC track forecasts

4.4.Forecast veri fication against conventional observations

5.Summary and conclusions

In this study,several experiments involving the assimilation of AMSU-A radiance data for Super Typhoon Megi (2010)were performed to investigate the effect of the hybrid DA approach on TC track forecasts.Instead of using an EnKF to update the ensemble,as in earlier studies,in this study each ensemble member was updated by running the hybrid analysis system multiple times with perturbed observations.Model predictions of Megi(2010)’s track were verified against the best-track analyses of the CMA.Further diagnostics were conducted to evaluate how the analyses increment differences contributed to the subsequent forecast differences.Aspects of the flow-dependent error covariance represented by the ensemble spread from the ensemble forecasts were examined.The 24 h forecasts were also verified against a set of conventional observations.The main findings from the experiments can be summarized as follows:

(1)The tuning of length scale factor is a necessary task to optimize the performance of radiance data assimilation,even with the background error calculated locally using the NMC method.In the case of Typhoon Megi(2010),a moderate length scale factor with roughly 50%of the default value improved the prediction of the typhoon track,but how the forecast error depended on the variance scale factor was more mixed.

(3)The increments for both the fields around the typhoon and the large-scale environment produced by the hybrid DA and 3DVAR were different.The hybrid DA is capable of systematically adjusting the position of the typhoon with the typhoon-specific BEC used.

(4)For 24 h forecasts,the hybrid DA experiment with the use of full flow-dependent background error substantially outperformed 3DVAR in terms of the horizontal winds and temperature in the lower and mid-troposphere and for moisture at all levels,though we tuned the static BEC to optimize its performance.

The findings of this study are encouraging and suggest that hybrid DA can initialize higher quality forecasts than the 3DVAR system.Given that any improvements in the typhoon intensity forecast were not obvious due to the limitations of NWP modeling related to aspects such as dynamics, physical parameterizations,and spatial resolution,only track forecasts are emphasized in this paper.Further investigations into the use of the hybrid radiance data assimilation system for improving typhoon intensity forecasts are ongoing.In this study,we used just one outer loop during the variational minimization process.In the future,we intend to focus on employing multiple outer loops in 3DVAR frameworks and retuning the scale length for the 3DVAR recursive filter to assess the relative contributions of the static and ensemble BECs.To understand the relative advantages and disadvantages of different techniques in typhoon forecasts,direct and thorough comparisons with other DA techniques such as the EnKF,4DVAR,and En-4DVAR are also planned.

Acknowledgements.This research was primarily supported by the National Fundamental 973 Research Program of China (Grant No.OPPAC-2013CB430102),Natural Science Foundation of China(41375025),and the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions.The SGI Altix3700 BX2 supercomputers at Nanjing University of Information Science&Technology were used.

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10.1007/s00376-014-4239-4.

28 October 2014;revised 12 December 2014;accepted 29 December 2014)

∗Corresponding author:SHEN Feifei

Email:ffshen.nuist@gmail.com