Assimilation of GPM Microwave Imager Radiance for Track Prediction of Typhoon Cases with the WRF Hybrid En3DVAR System

The accuracy in track and intensity forecast for tropical cyclones (TC) is crucial for the reduction of casualty and property loss. Over the past 20 years, remarkable improvements have been made in TC forecasts with more advanced numerical weather prediction (NWP) models along with the increased use of multi-source observations especially of the remote sensing data (Rappaport et al., 2009; Xu et al., 2013, 2016). As one of the significant sources of the observations for NWP model, satellite radiance data provide useful thermal and moist information, particularly over oceans to supplement the conventional observations (McNally et al., 2000, 2006; Bouttier and Kelly, 2006). Among the satellite data, microwave channels are uniquely able to depict moisture structures and processes (Liu et al., 2012; Chambon et al., 2014; Shen and Min, 2015).

The Global Precipitation Measurement (GPM) mission is a constellation-based satellite mission initiated by National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA). GMI (GPM Microwave Imager) is a conical-scanned, multichannel, microwave imager sensor launched on 28 February 2014. It has been found to be quite useful for understanding moist processes with its unique capability for detecting the precipitation structure (Pu et al., 2019). It is superior to its predecessors, the Tropical Rainfall Measurement Mission (TRMM) because of its improved spectral band resolution and higher spatial resolution. GMI not only inherits the 9 channels from TRMM to detect heavy to light precipitation but also includes 4 high-frequency channels for the detection of the snowfall (Mangla and Jayaluxmi, 2018). In a recent study of GMI data assimilation, the statistical properties of GMI all-sky simulation was explored with promising results (Mangla and Indu, 2019). Chambon et al. (2014) assimilated microwave precipitation observations from a pre-GPM satellite constellation with an ensemble data assimilation system. Pu et al. (2019) (P19) investigated the impact of clear-sky assimilation of GMI radiances for two TC cases in the framework of HWRF using a hybrid method. In this study, we further examine the impact of assimilating clear-sky GMI radiance data on TC track forecasts with the Weather Research and Forecast Data Assimilation system (WRFDA) based on the hybrid ensemble three-dimensional variational data assimilation method (Lorenc et al., 2000; Barker et al., 2004, 2012). The present study differs from P19 in that it concerns more typhoon cases in the western North Pacific, which made landfall along China’s coast and commonly caused severe damage. P19 solely studied the impact of GMI radiance data assimilation on two Atlantic hurricanes during the 2015 and 2016 hurricane seasons. Although GMI radiance data are able to cover most areas on the globe, their potential contribution to analyses and forecasts of landfalling TCs in the western North Pacific has not been fully examined.

The hybrid method is popular owing to its easier implementation even for non-local and non-conventional observations compared to the pure ensemble Kalman filter (EnKF; Zhang et al., 2013; Pan et al., 2014). Recently, numerous studies have illustrated that forecasts initialized from the ensemble-based DA are able to generate comparable or better forecasts than those from the three-dimensional variational (3DVAR) method with various observations for many types of weather applications (e.g., Li and Liu, 2009; Weng et al., 2011; Dong and Xue, 2013). Hybrid DA method is able to generate complex flow-dependent background error covariance (BEC) for various weather systems (Hamill and Snyder, 2000; Hamill et al., 2011). Thus, the hybrid method is better able to reflect the strong vortical and nongeostrophic motions of TCs (Wang, 2011; Schwartz et al., 2013; Lu et al, 2017). However, there are several technical issues about the hybrid DA method that need to be further investigated and confirmed (Schwartz et al., 2015). For example, the ensemble updating techniques and the options to determine the first guess for the hybrid experiments are the key steps for the hybrid data assimilation configurations. On the other hand, there is no study published currently applying the WRF hybrid En3DVAR to the assimilation of radiance data from the GMI for enhancing TC track forecasts. This initial study seeks to investigate the skills of applying the 3DVAR and the hybrid method for improving TC track forecast when assimilating the GMI radiance data.

The rest of this paper is arranged as follows. A brief introduction to the hybrid method is provided as well as the GMI radiance data assimilation methodology in section 2. An overview of typhoon cases along with the experimental design is described in section 3. Section 4 gives the main results before conclusions and discussions are elaborated in the last section.

The WRF hybrid DA system is based on the 3DVAR framework by including the extended control variables a (Lorenc, 2003). The traditional 3DVAR is framed to provide an analysis increment ${{x}}{'}$ with the following cost function,

where ${{{J}}_1}$ is associated with the static covariance matrix ${{B}}$ and ${{{J}}_{\rm{o}}}$ is the observation term that is associated with observation error covariance matrix ${{R}}$. ${{{y}}'_{\rm{o}}} = {{{y}}_{\rm{o}}} - {{H}}\left({{{{x}}_{^{\rm{b}}}}} \right)$ is the innovation vector. Here ${{{y}}_{\rm{o}}}$ and ${{{x}}_{\rm{b}}}$ is the observation vector and the background state vector respectively. ${{H}}$ is the observation operator, while ${{H}}$ is the linearized observation operator. For the hybrid En3DVAR system, a sum of two terms is the final analysis increment ${{x}}'$, described as

The first term ${{x}}{'_1}$ in Eq. (2) represents the increment associated with the static BEC in 3DVAR and the second term of Eq. (2) is a linear combination of the extended control variable ${{{a}}_k}$($k = 1, \cdots,K$) with the kth ensemble perturbations ${({{{x}}_k})_{\rm{e}}}$. Symbol. denotes the element-by-element product of the vectors. With the necessity of the ensemble covariance localization, the coefficients of ${{{a}}_k}$ vary in space as a vector. Otherwise, the coefficients of ${{{a}}_k}$ can be represented by scalars (Lorenc, 2003) in the absence of any localization. The above-mentioned increment ${{x}}{'_1}$ and the extended control variable ${{{a}}_k}$ are obtained by minimizing the following cost function for hybrid

where ${{{J}}_{\rm{e}}}$ is associated with the ensemble covariance that is used to constrain the extended control vector ${{a}}$. A is applied for the spatial correlation as the block diagonal matrix. The two coefficients, $\,{\beta _1}$ and $\,{\beta _2}$, determine corresponding weights prescribed to the flow-dependent ensemble covariance and static covariance (Wang et al., 2008), with the constraint as,

The GMI 1b radiance data are assimilated into the WRFDA system for both 3DVAR and hybrid methods in this study. GMI is a microwave radiometer with 13 channels, ranging from 10 GHz to 183 GHz (Table 1). The first 9 channels are standard microwave imager channels sensitive to precipitation and total column water vapor. Channel 8–9 at 89.0 GHZ are sensitive to convective rain areas. Channels 10–13 are responsible for detection of light precipitation and snowfall. In this study, only channels 3–7 are chosen to be assimilated carefully. It has been proven that raw radiance observations thinned to a grid with 2–6 times the model grid resolution are able to remove the potential error correlations between adjacent observations (Schwartz et al., 2012). A thinning mesh with 90 km is determined as an initial attempt to the assimilation of GMI radiances data.

The Community Radiative Transfer Model (CRTM; Liu and Weng, 2006) coupled within the WRFDA was applied as the observation operator for GMI radiances. The temperature and humidity information from the model states are essential inputs for CRTM to calculate the simulated brightness temperature. The procedures of quality control and bias correction were conducted before data assimilation. For quality control: 1) Radiance data over mixed surfaces or with large bias were rejected. 2) Radiance observations were rejected if the retrieved level-2 cloud water liquid path (CLWP) exceeded the threshold listed in Table 2. The CLWP thresholds refers to those in Yang et al. (2016) and Kazumori et al. (2008). The systematic biases from the observed radiances were corrected before assimilation with 7 predictors (Liu et al., 2012; Xu et al., 2013) using the variational bias correction (VarBC) scheme. The applied predictors are the scan position, the square and cube of the scan position, the 200–50 hPa and 1000–300 hPa layer thicknesses, total column water vapor, and surface skin temperature. The quality control procedure works effectively for the criteria by checking the GMI observations after the quality control. In addition, the bias correction scheme was able to remove the systematic bias for the typhoon cases in our current study (not shown). The observation errors calculated offline are listed in Table 2 with GMI observations samples over 0000 UTC 1 July 2014 to 1200 UTC 21 July 2014. The statistics of the observation error is obtained by estimating the standard deviation between the observed and the simulated brightness temperature.

Four typhoon cases are employed in this study to validate the impact of GMI data assimilation with the hybrid method. The first case is Typhoon Matmo (2014) and the second case is Typhoon Chan-hom (2015). The other two cases are Meranti (2016) and Mangkhut (2018). The case Matmo (2014) is selected for the detailed comparison of the 3DVAR and the hybrid method. These typhoon cases are selected since they are effectively observed by the GMI radiance data.

From the record of the China Meteorological Administration (CMA), Matmo (2014) is the 10th typhoon, which occurred in the Western North Pacific Ocean. It made landfall in eastern Taiwan at 1600 UTC 22 July 2014 and then made its second landfall along the China coast near Fujian Province with the MSW reaching 30 m/s at 0700 UTC 23 July 2014. The landfall location was approximately 100 km away from Quanzhou Bay. Subsequently, Matmo (2014) passed through Fujian and Jiangxi Provinces, and continued northward to Shandong Province. Under the influence of Matmo (2014), heavy rainstorms occurred in northwest and southeast Quanzhou. Over its inland path, Matmo (2014) brought heavy precipitation, causing severe damage to 10 provinces in China.

Chan-hom (2015) was reported as the strongest TC landfall in Zhejiang Province since 1949. On 1 July, Chan-hom (2015) was clarified as a severe tropical storm. Early on 2 July, Chan-hom (2015) began to turn to the west-southwest with increasing intensity. Late on 9 July, Chan-hom (2015) reached its peak strength with estimated winds of 165 km/h and minimum sea level pressure of 935 hPa. Chan-hom (2015) made its landfall in Zhoushan, Zhejiang Province on 11 July around 0840 UTC.

Typhoon Meranti (2016) was one of the most powerful tropical cyclones on record and caused extensive damage to the Batanes in the Philippines, Taiwan, as well as Fujian Province in September 2016. Similarly, Typhoon Mangkhut (2018) was an extremely intense and catastrophic tropical cyclone that impacted Guam, the Philippines and South China in September 2018.

All experiments were conducted with the WRF (Skamarock et al., 2008), which is a compressible and non-hydrostatic atmospheric model in three dimensions. A single domain was applied with 57 vertical levels and a model top at 10 hPa for all experiments. The horizontal grid spacing was 15-km for all cases. For the physics parameterizations, the Kain-Fritsch cumulus parameterization (Kain and Fritsch, 1990; Kain, 2004) with a modified trigger function (Ma and Tan, 2009) and the WRF Single-Moment 6-Class microphysics scheme (Hong et al., 2004) were applied along with the Yonsei University (YSU) boundary layer scheme (Hong et al., 2006) and the 5-layer thermal diffusion model for land surface processes scheme. For the radiation scheme, the MM5 shortwave radiation scheme (Dudhia, 1989) and the Rapid Radiative Transfer Model (RRTM) longwave radiation scheme (Mlawer et al., 1997) were utilized.

For Typhoon Matmo (2014), three experiments were configured to evaluate the impact of assimilating GMI radiance data with the 3DVAR and the hybrid method on the subsequent forecasts in Table 3. The 3d-gts experiment assimilates only conventional observations from the operational Global Telecommunication System dataset in the National Centers for Environmental Prediction (NCEP) with the traditional 3DVAR method (Fig. 1a). The 3d-gmi experiment not only assimilates the conventional observations but also assimilates the GMI radiance data (Fig. 1b). Similar to the 3d-gmi experiment, h-gmi experiment employs the hybrid method with 40 ensemble members using the mean of the ensemble forecasts as the background.

Figure 1.  (a) The distribution of observations from 1400 UTC 21 July to 1800 UTC 21 July. The numbers of each observation are marked on the right, (b) The GMI observations at 1600 UTC 21 July 2014. The red typhoon signals show the best track from 1800 UTC 21 July 2014 to 1200 UTC 24 July 2014 for Typhoon Matmo (2014).

Both 3DVAR and hybrid DA experiments were initialized using the NCEP operational 0.5º$ \times $0.5º degree GFS analysis data as the initial and lateral boundary conditions. The initial conditions for Matmo (2014) are valid at 0600 UTC 21 July 2014. For 3DVAR, the background for DA is the 10 h spin-up forecast from 0600 UTC 21 July to 1600 UTC 21 July. Similarly, the initial ensemble members at 0600 UTC 21 July were generated by adding Gaussian random perturbations to the GFS analysis for the hybrid DA experiments. The Gaussian perturbations were drawn based on the static BECs (Torn et al., 2006). The h-gmi experiment employs the hybrid method using the ensemble mean as the background, and 10-h ensemble forecasts were launched to generate the ensemble members at 1600 UTC 21 July for the hybrid experiments. A 68-h deterministic forecast was launched at 1600 UTC 21 July by the analysis in 3DVAR and hybrid experiments, respectively.

For the other three typhoons cases, only the two experiments 3d-gmi and h-gmi were conducted for each case. The analysis time for Chan-hom (2015) and Meranti (2016) are at 1800 UTC 9 July 2015 and at 0000 UTC 12 September 2016, respectively. For Mangkhut (2018), the valid time for the analysis is at 1800 UTC 15 September 2018.

With the limited ensemble members, horizontal and vertical localizations were applied to reduce spurious correlations caused by sampling error with a 750 km horizontal localization radius. The vertical localization scheme was based on an empirical function that considered the distance between two levels and the model height-dependent localization radius (Shen et al., 2017). The full 100% weight was prescribed to the ensemble-based BEC for the hybrid experiments. Observations within ±2 h were applied to the analysis time. The static BEC statistics used in the 3DVAR were derived based on the “NMC” method from the differences between 24-h and 12-h forecasts (Parrish and Derber, 1992) by using the WRFDA utility (Barker et al., 2012) for five control variables (velocity potential, stream function, unbalanced temperature, surface pressure and relative humidity).

In this section, the ensemble spread, as well as the analyses and forecasts for Typhoon Matmo (2014) for each DA experiment are investigated. RMSE using conventional observations as reference for the 24-h forecasts are also evaluated.

For the hybrid DA experiments, for a prior ensemble to be reliable in providing the flow-dependent background error, it is important to evaluate the ensemble performance to see if the prior ensemble spread is sufficient. The ensemble spread of wind and temperature at 500 hPa is shown in Fig. 2 for the 10-h forecast valid at 1600 UTC 21 July, when typhoon Matmo (2014) intensified. It is found that near the typhoon center, a local maximum of spread was obvious for wind and temperature, since the forecast uncertainties are large for both the typhoon and its environment. Observations are most likely to have larger impact for areas with more obvious ensemble spread. Conversely, observations will have less influence in the areas with smaller spread. Wind and temperature spread were both larger over western China, where few observations were available to constrain the model. By contrast, spread was smaller in eastern China because of the plentiful observations.

Figure 2.  Ensemble spread for (a) wind speed (m s⁻¹) and (b) temperature (K) valid at 1600 UTC 21 July 2014 at 500 hPa for Typhoon Matmo (2014).

To further understand why the analyses and forecasts from the 3DVAR and hybrid simulations were different, we examined the analysis increments directly. In Fig. 3, the geopotential height analysis increments at 850 hPa are shown for the three DA experiments. The pattern of the increments in 3d-gts and 3d-gmi are quite similar, except for the existence of a noticeable positive height increment center to the north of the TC center in the 3d-gts (Figs. 3a and 3b). This positive geopotential height difference to the north of typhoon Matmo (2014) is better revealed in the 3d-gts minus 3d-gmi field shown in Fig. 3d. The area with the large difference in the geopotential height is covered by a swath of the GMI observations, indicating the contribution from the data assimilation of the GMI radiance.

Figure 3.  Geopotential height increments (color shades, units: m² s⁻²) and the geopotential height (contours, units: m² s⁻²) for the background at 850 hPa for (a) 3d-gts, (b) 3d-gmi, (c) h-gmi, and (d) the difference between the geopotential height increments from 3d-gts and 3d-gmi (3d-gts minus 3d-gmi) at 1600 UTC 21 July 2014 for Typhoon Matmo (2014). A notable dipole structure is marked with a black circle.

For h-gmi, a notable dipole structure is observed with a positive increment and a negative increment to the southwest and northeast of the TC center, respectively, marked in Fig. 3c. The geopotential height increments tend to make the typhoon move northeastward. The increments of the geopotential height suggest the assimilation of GMI radiance observations with the flow-dependent ensemble covariance is able to adjust the location of the typhoon in the background by moving the vortex with low geopotential height northeastward.

The differences of water vapor flux (WVF) at 850 hPa between analyses and background from different data assimilation experiments are illustrated in Fig. 4 along with the wind from the background. Compared with the 3d-gts, 3d-gmi provides increase of the WVF around the east of TC center around 135°E and 20°N and the area in the southwest of the domain. These two areas closely correspond to the distributions of the GMI data. The results indicate that the assimilation of GMI data is able to improve the water vapor content fields in the analyses. In Fig. 4c, the spiral pattern of the WVF is found with the introduction of the flow dependent background error.

Figure 4.  The water vapor flux (shaded; g cm⁻¹ hPa⁻¹ s⁻¹) difference between analyses and background for (a) 3d-gts, (b) 3d-gmi, and (c) h-gmi at 850 hPa at 1600 UTC 21 July 2014 for Typhoon Matmo (2014). The vectors show the direction and magnitude of the wind from the background.

The RMSEs profiles of temperature, specific humidity, and horizontal wind of the 24-h forecasts compared to the conventional observations are evaluated in Fig. 5. A set of conventional observations including the atmospheric motion vector winds from geostationary satellites (GeoAMV) and radiosondes were applied. The largest RMSE of u-wind, v-wind, and temperature appear near the 70 hPa~100 hPa. Generally, GMI data assimilation is able to improve the temperature and humidity forecast consistently for lower levels. The hybrid DA experiment is superior to the 3DVAR experiment 3d-gmi.

Figure 5.  Vertical profiles of the root mean square error (RMSE) of the 24-h forecasts versus conventional observations for (a) u-wind (units: m s⁻¹), (b) v-wind (units: m s⁻¹), (c) temperature (units: K), and (d) water vapor mixing ratio (units: g kg⁻¹) for 3 experiments for Typhoon Matmo (2014).

The predicted typhoon tracks and track errors from 3d-gts, 3d-gmi, and h-gmi are shown respectively for the 66-h forecast against the best track from CMA. 3d-gts and 3d-gmi experiments have a similar south bias while h-gmi DA experiment has a north bias track forecasts for the first 48 hours in Fig. 6a. With the flow- dependent ensemble background error covariance, the tracks for hybrid experiment h-gmi with the ensemble mean as the first guess fit more closely to the best track data. The result of the track forecast is consistent with what is observed in Fig. 3, which shows that the geopotential height increments lead the typhoon to move northeastward with the GMI radiance data assimilation, especially with the hybrid DA method. It should also be noted that the track error from the hybrid DA is not necessarily smallest at the initial time, since these multi-variant increments usually require essential spin-up time to achieve balance between model variables.

Figure 6.  The 66-h predicted (a) tracks and (b) track errors from 1800 UTC 21 July to 1200 UTC 24 July 2014 for Typhoon Matmo (2014).

The temporal evolution of the track forecasts errors for all the experiments are displayed in Fig. 6b. It is found that 3d-gts yields largest track errors for most of the time, which means that the track forecasts are improved with the assimilation of GMI observations. Generally, the track errors from h-gmi are consistently smaller than those from 3d-gmi experiment.

To validate the robustness of the results based on the case Matmo (2014), statistical results from the four typhoon cases are illustrated. Averaged vertical profiles of the difference of analysis and background of the total water vapor and hydrometeor mixing ratio (sum of water vapor, ice, snow, graupel, rain water, and cloud water mixing ratio) are provided for Typhoon Matmo (2014), Chan-hom (2015), Meranti (2016), and Mangkhut (2018) in Fig. 7. It is found that assimilating of GMI observations increases the water vapor and hydrometeor content to some extent with 3DVAR. It should be pointed out that when hybrid is applied, the water vapor and hydrometeor contents are greatly enhanced.

Figure 7.  Averaged vertical profile of the total water vapor and hydrometeor mixing ratio (sum of water vapor, ice, snow, graupel, rain water, and cloud water mixing ratio) difference of analysis and background (units: g kg⁻¹) for Matmo (2014), Chan-hom (2015), Meranti (2016), and Mangkhut (2018).

The 36-h predicted tracks from Typhoon Chan-hom (2015), Typhoon Meranti (2016) and Typhoon Mangkhut (2018) are shown in Fig. 8a. The mean track errors throughout the forecast period averaged over the four typhoon cases are also displayed in Fig. 8b. The tracks from the h-gmi fit better with the best track compared to those from the 3d-gmi. Overall, the track error for h-gmi are consistently smaller than those from the 3d-gmi, especially after 6-h forecast.

Figure 8.  (a) The predicted tracks for Chan-hom (2015), Meranti (2016) and Mangkhut (2018), (b) the averaged track errors for multiple typhoon cases including Matmo (2014), Chan-hom (2015), Meranti (2016), and Mangkhut (2018) with the forecast leading time.

In this study, several DA experiments related to the assimilation of GMI radiance data for four typhoons were conducted to investigate the impact of the hybrid method on TC track prediction for Typhoon Matmo (2014), Typhoon Chan-hom (2015), Typhoon Meranti (2016), and Typhoon Mangkhut (2018). Detailed diagnostics were conducted to evaluate the impact of the GMI data assimilation on the analyses and the subsequent forecasts for Matmo (2014). Aspects of the ensemble spread from the ensemble forecasts were examined to show the flow-dependent ensemble background error covariance. The 24-h forecasts were also verified against a set of conventional observations. Statistical results based on the four typhoon cases were also presented to obtain solid conclusions. It is found that, after assimilating the GMI radiance data under the clear sky condition with 3DVAR, the model fields are effectively adjusted for the geopotential height and the water vapor flux, leading to improved forecast skills of the typhoon track. The hybrid method has the capability of further adjusting the location of the typhoon systematically with the typhoon-specific background error covariance. The improvement of the track forecast is even obvious for later forecast hours. These improvements are validated based on the four typhoon cases. The water vapor and hydrometeor contents are enhanced with the assimilation of GMI radiances. The tracks from the hybrid DA experiments with GMI radiance data fit better with the best track compared to those from the 3d-gmi experiments, especially after 6-h forecast.

These findings are encouraging and suggest that GMI data assimilation is able to improve the skills of the typhoon analyses and forecasts. Hybrid DA method is superior to the 3DVAR method due to the flow-dependent ensemble background error as well as the use of the ensemble mean as the background. The typhoon intensity forecast improvements depend on the accuracy of the high-resolution cloud-resolving mesoscale models and data assimilation techniques over a variety of scales to represent the internal dynamics. Thus, only track forecasts are emphasized in this study, since the assimilation of GMI radiance data to improve the internal dynamic information for the vortex structure is limited. Further investigations on applying other advanced radiance data assimilation techniques for improving typhoon intensity forecasts are ongoing. Additional study on assimilating the radiance data for enhancing the typhoon intensity and precipitation forecasts are planned with other approaches, such as applying the all-sky GMI data and advanced data assimilation methods.

Acknowledgements. This research was primarily supported by the Chinese National Natural Science Foundation of China (G41805016), the Chinese National Key R&D Program of China (2018YFC1506404), the Chinese National Natural Science Foundation of China (G41805070), the Chinese National Key R&D Program of China (2018YFC1506603), the research project of Heavy Rain and Drought-Flood Disasters in Plateau and Basin Key Laboratory of Sichuan Province in China (SZKT201901, SZKT201904), the research project of the Institute of Atmospheric Environment, China Meteorological Administration, Shenyang in China (2020SYIAE07, 2020SYIAE02). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Nanjing University of Information Science & Technology.