Assimilation of Moderate-Resolution Imaging Spectroradiometer Level Two Cloud Products for Typhoon Analysis and Prediction

Abstract

A novel data assimilation technique is developed to assimilate MODIS (Moderate Resolution Imaging Spectroradiometer) level two (L2) cloud products, including cloud optical thickness (COT), cloud particle effective radius (Re), cloud water path (CWP), and cloud top pressure (CTP), into the Weather Research and Forecast (WRF) model. Its impact on the analysis and forecast of Typhoon Talim in 2023 at its initial developing stage is demonstrated. First, the conditional generative adversarial networks–bidirectional ensemble binned probability fusion (CGAN-BEBPF) model ) is applied to retrieve three-dimensional (3D) CloudSat CPR (cloud profiling radar) equivalent W-band (94 Ghz) radar reflectivity factor for the typhoons Talim and Chaba using the MODIS L2 data. Next, a W-band to S-band radar reflectivity factor mapping algorithm (W2S) is developed based on the collocated measurements of the retrieved W-band radar and ground-based S-band (4 Ghz) radar data for Typhoon Chaba at its landfall time. Then, W2S is utilized to project the MODIS-retrieved 3D W-band radar reflectivity factor of Typhoon Talim to equivalent ground-based S-band reflectivity factors. Finally, data assimilation and forecast experiments are conducted by using the WRF Hydrometeor and Latent Heat Nudging (HLHN) radar data assimilation technique. Verification of the simulation results shows that assimilating the MODIS L2 cloud products dramatically improves the initialization and forecast of the cloud and precipitation fields of Typhoon Talim. In comparison to the experiment without assimilation of the MODIS data, the Threat Score (TS) for general cloud areas and major precipitation areas is increased by 0.17 (from 0.46 to 0.63) and 0.28 (from 0.14 to 0.42), respectively. The fraction skill score (FSS) for the 5 mm precipitation threshold is increased by 0.43. This study provides an unprecedented data assimilation method to initialize 3D cloud and precipitation hydrometeor fields with the MODIS imagery payloads for numerical weather prediction models.

1. Introduction

Clouds and precipitation are important components of the atmospheric system, and they play a critical role in global and regional water cycles. Most disastrous weather events, including typhoons that have a significant impact on ecosystems and economic activities, are associated with cloud processes. The MODIS (Moderate Resolution Imaging Spectroradiometer) Imager payload provides broad swaths (2330 km) of cloud and precipitation observations that are widely used for monitoring the formation, structure, and trajectory of typhoons over the open oceans [1]. However, there are a lack of effective techniques for assimilating these data into numerical weather prediction models to improve the accuracy of typhoon prediction. This study develops an innovative approach to solve this issue.

Ground-based and airborne weather radars are currently the main instruments used to quantitatively observe three-dimensional (3D) cloud and precipitation structures [2]. Weather radars, including S (2–4 Ghz), C (4–8 Ghz), and X-band (8–12.5 Ghz) radio frequencies, are mainly deployed on land. Radar observations are particularly limited over oceans. To observe cloud and precipitation over the open oceans, several polar-orbiting satellites are equipped with cloud and precipitation radars, including the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR), the CloudSat Cloud Profiling Radar (CPR) [3], the Global Precipitation Measurement (GPM) Dual-frequency Precipitation Radar (DPR) [4], and the FY-3G Precipitation Measurement Radar (PMR) [5]. These radars are operated at Ku, Ka, and W radio frequency bands among which PR is Ku (13.8 Ghz), PMR and DPR are Ku (35.5 Ghz) and Ka (13.8 Ghz), and CPR is W-band (94 Ghz).

The radars onboarded on the polar-orbiting satellites can detect the vertical structure of clouds and precipitation, and previous works show that incorporating the vertical cloud observation from these instruments into numerical models helps to improve cloud and precipitation forecasting [6]. Nevertheless, the temporal resolution (typically 12 h) and spatial coverage of these observations are extremely limited. For example, CloudSat/CPR only provides a line of vertical profiles of the W-band radar reflectivity factor along the satellite trajectory; GMP/DPR and FY-3G/PMR provide a 3D cloud radar reflectivity factor but with spatial resolutions of 5–7 km and a swath width of 245–303 km. Such narrow spatiotemporal coverage severely limits the usage of the data for severe weather prediction. Thus, it is important to explore new methods to retrieve 3D cloud and precipitation structures from the passive Imager payload measurements of the weather satellites, which have a much broader swath coverage (e.g., 2330 km for MODIS).

The recent development of deep learning technology provides a new avenue for establishing reliable relationships between passive and active remote sensing data. Kou et al. integrated precipitation radar (PR) data from the TRMM satellite and ground-based radar (GR) reflectivity factor data using a neural network (NN) [7]. Yang et al. proposed a Hybrid Deep Neural Network (HDNN) model to reconstruct active radar data from passive microwave radiation [8]. They established a mapping relationship between the GPM Microwave Imager (GMI) and the Dual-frequency Precipitation Radar (DPR) onboard the Global Precipitation Measurement (GPM) satellite, thereby providing a broader range of 3D radar observation information. Brüning et al. utilized a Res-UNet model to merge high-resolution satellite images from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard the Meteosat Second Generation (MSG) geostationary satellite with the 2D radar reflectivity factor data from CloudSat to generate 3D cloud information [9].

Leinonen et al. applied a CGAN model to establish a relationship between MODIS cloud products (Re, COT, CWP, and CTP) and the two-dimensional vertical W-band cloud radar reflectivity factor of CloudSat CPR [10]; Wang et al. expanded the dataset based on Leinonen’s work and evaluated the model results for different cloud types [11]. They found that Leinonen et al.’s model successfully retrieves 3D deep convective and nimbostratus clouds based on MODIS cloud measurements. Qin et al. further analyzed the error characteristics of the CGAN-inverted cloud radar reflectivity factor and designed a bidirectional ensemble binning probability fusion (CGAN-BEBPF) technique. CGAN-BEBPF mitigates the spatial discontinuity and the errors of the cloud radar reflectivity factor caused by slicing and achieves an end-to-end automatic inversion capability of 3D W-band cloud radar reflectivity factor for entire MODIS granules [12].

Although the above machine learning technologies have made significant advances in the acquisition of 3D cloud information, there are very few efforts to develop data assimilation methods that are suitable for assimilating this 3D cloud information into numerical models. Our study’s purpose is to extend the Leinonen et al. [10], Wang et al. [11], and Qin et al. [12] works to assimilate the MODIS 3D W-band cloud and precipitation radar retrieval to improve WRF model initialization and typhoon prediction.

Data assimilation is a critical step to initialize numerical weather prediction (NWP) models for weather forecasting. Among the global leading operational weather prediction centers, ECMWF (the European Centre for Medium-Range Weather Forecasts) developed a four-dimensional variational data assimilation (4DVAR) system to initialize its IFS (Integrated Forecasting System) global forecast model [13,14], while NOAA (the National Oceanic and Atmospheric Administration) employed a GSI system (Gridpoint Statistical Interpolation, V3.2) that combines an ensemble-enhanced background error covariance with a three-dimensional variational scheme [15,16]. Although these data assimilation schemes are fundamental for global weather forecasting, they are not effective in assimilating cloud and precipitation observations for high-resolution NWP models [17].

Cloud and precipitation data assimilation is one of the most challenging research areas in contemporary numerical weather prediction [18,19]. In the last two decades, several techniques have been developed to assimilate ground-based weather radar data, primarily based on dynamic initialization methods [20]. Cloud analysis methods have also been developed to assimilate radar reflectivity factors. Albers et al. developed the Local Analysis and Prediction System (LAPS) [21], in which the radar reflectivity factor is used to estimate rainwater, snow, and hail in the analysis field, as well as to adjust water vapor. Hu et al. integrated the Advanced Regional Prediction System (ARPS) and Rapid Update Cycle (RUC) cloud analysis systems [22], which can synthesize ground weather station data, radar reflectivity factor, satellite cloud top height, and lightning observations to diagnose cloud cover and calculate the mixing ratios of hydrometeors for thermodynamical adjustment of the model initial conditions. Furthermore, nudging methods have been developed and proven to be effective for assimilating radar data in a time-continuous mode [23,24,25,26]. The National Science Foundation (NSF) National Center for Atmospheric Research (NCAR) developed a WRF four-dimensional data assimilation system (RTFDDA) [27,28,29] including a hydrometeor and latent heat nudging (HLHN) to assimilate weather radar data. HLHN has been evaluated by several researchers to assimilate weather radar reflectivity factor assimilation and achieves great improvements for severe precipitation prediction [23,24,25,26,30].

Unlike the ground-based weather radars that operate at S, C, and X-band radio wave frequencies and that have a great ability to detect precipitation particles in clouds, high-frequency W-band radar is sensitive to small hydrometeor particles and experiences severe signal attenuation and lower power returns (i.e., lower reflectivity [31]). Thus, the data assimilation methods for ground-based weather radars cannot be directly applied to W-band radar data. Some progress has been made to assimilate W-band radar reflectivity factor data with simplified indirect assimilation approaches. For example, in 2018, the Mediterranean experiment was conducted in Europe, which was based on the AROME model numerical simulation system and airborne W-band cloud radar observations [32]. A lookup table was established for the six hydrometeor types in the ICE microphysical using the cloud radar reflectivity factor. Borderies et al. used a 1D + 3Dvar method to establish a 1D Bayesian estimation of the relative humidity using the cloud radar reflectivity factor observed by the Radar Airborne System Tool for Atmosphere (RASTA) [33]. By assimilating the relative humidity with a 3Dvar method, they achieved a slight improvement in the water vapor initial conditions and precipitation forecasts. Finally, an empirical approach has been developed to include the CloudSat CPR data in a NWP model; the impact is minor because CPR only provides single-line radar beam profiling detection [34].

In this study, we develop a new and more effective approach to assimilate the MODIS-retrieved 3D W-band radar reflectivity factor for typhoon cloud and precipitation initialization. A statistical mapping function is established to project MODIS W-band radar reflectivity factor to pseudo-ground-based S-band radar reflectivity factor based on the collocated measurements of ground-based radars and MODIS for a landfall typhoon. This mapping function is used along with the NSF NCAR WRF-FDDA HLHN radar assimilation scheme to assimilate the MODIS L2 cloud products for Typhoon Talim and to demonstrate the value of our approach to assimilate the MODIS Imager L2 cloud products for severe weather events.

The structure of this paper is as follows: the next section introduces the data used in this study and the technology developed for the assimilation of the MODIS L2 cloud products. Section 3 introduces the components of the MODIS L2 cloud product data assimilation approach, including retrieving the 3D W-band radar reflectivity factor based on CGAN-BEBPF, mapping the MODIS 3D W-band cloud radar reflectivity factor to the ground-based S-band radar reflectivity factor, and using the HLHN radar data assimilation scheme. Section 4 presents the data assimilation results for Typhoon Talim and the verification of the WRF analyses and forecasts against Himawari and GMP satellite measurements. The impact of assimilating 3D cloud radar reflectivity factors along with different microphysical schemes is also analyzed. The limitation of the proposed data assimilation technology is discussed in Section 5. Finally, Section 6 summarizes the major findings and explores potential future research directions.

2. Materials and Methods

2.1. Data

The data used in this study include the NCEP (National Center for Environmental Center) Final Operational Global Analysis (FNL) reanalysis data, the ground-based radar reflectivity factor from the China Severe Weather Automatic Nowcasting (SWAN) system, the MODIS L2 cloud parameters, the GPM Integrated Multi-satellite Retrievals (IMERG) precipitation products, and the Himawari-9 cloud optical thickness.

FNL Reanalysis Data: FNL is used to derive the initial and lateral boundary conditions to drive the regional WRF simulations. Data from 21:00 UTC on 13 July 2023, to 09:00 UTC on 14 July 2023, at three-hour intervals, were used. The data resolution is 0.25° × 0.25°.

Ground-Based Radar Reflectivity factor: The 3D mosaic reflectivity data of the ground-based radars from the China Meteorological Administration (CMA) Severe Weather Automatic Nowcasting (SWAN) [35] are used to establish a mapping relationship between the S-band and W-band reflectivity factor. The SWAN radar reflectivity factor includes a network of S-band and C-band radars across China, and all data used in this study are from S-band radars.

MODIS L2 cloud products: The input data for the CGAN-BEBPF model consist of MODIS level 2 standard products, including cloud top pressure (CTP), cloud water path (CWP), cloud optical thickness (COT), effective particle radius (Re), and more. The data contain geographical coordinate information with a horizontal resolution of 1 km [36].

Using the pre-trained CGAN-BEBPF model [12] and inputting the MODIS L2 cloud products, 3D W-band cloud radar reflectivity factor fields are retrieved for the MODIS granules covering the typhoon cases selected in this study. The vertical resolution of the 3D radar reflectivity factor is 240 m with a total of 64 layers. The MODIS granules have grid numbers of 2030 × 1354 with a grid resolution of 1 km.

GPM Precipitation Estimation: The GPM Integrated Multi-satellite Retrievals for GPM (IMERG) precipitation products from 00:00 UTC to 07:00 UTC on 14 July 2023 were collected and used to evaluate the numerical simulation results. The IMERG final products are produced based on the data from all passive microwave instruments in the GPM [37]. The data resolution is 0.1° × 0.1°.

Himawari Satellite Cloud Optical Thickness: The cloud optical thickness from Himawari-9 is used to assess the simulation of the cloud and rain areas in the MODIS data assimilation experiments from 00:00 UTC to 09:00 UTC on 14 July 2023. The level-2 product of Himawari-9 cloud optical thickness has a temporal resolution of 10 min and a spatial resolution of 0.05° [38].

2.2. Typhoon Cases

This study employs two typhoon cases: Typhoon Talim, the 4th Typhoon of 2023, and Typhoon Chaba, the 3rd typhoon of 2022. Typhoon Talim is selected to assess the impact of the MODIS L2 cloud product data assimilation. The simulation time was at its initial development stage when it was located over the open ocean to the west of the Philippines, far from ground-based radar observations. The Himawari satellite visible image at that time is shown in Figure 1a. Thus, Typhoon Talim provides an adequate opportunity to demonstrate the value of the MODIS L2 data assimilation approach.

Typhoon Chaba was chosen because it was observed by both MODIS and ground-based radars at its landfall time. The satellite visible image for Typhoon Chaba is shown in Figure 1b. The collocated satellite and ground-based radar observations allow us to develop a mapping function between the 3D W-band radar reflectivity factor and the S-band radar reflectivity factor so that the MODIS retrieved 3D W-band radar reflectivity factor can be assimilated into the WRF model.

2.3. Technical Workflow

Figure 2 depicts the workflow of the technology developed in this study for assimilating MODIS L2 cloud products to initialize WRF for the Typhoon Talim simulation. The approach involves four key steps. First, the conditional generative adversarial networks–bidirectional ensemble binned probability fusion (CGAN-BEBPF) model developed by Qin is applied to retrieve three-dimensional (3D) CloudSat equivalent W-band (94 Ghz) radar reflectivity factor for both Talim and Chaba using the MODIS L2 data [12]. Then, a W-band to S-band mapping algorithm (W2S) is developed based on the collocated measurements of the retrieved W-band radar and ground-based S-band (4 Ghz) radars for Typhoon Chaba at its landfall time. Third, W2S is utilized to project the MODIS-retrieved 3D W-band radar reflectivity factor of Typhoon Talim to an equivalent ground-based S-band reflectivity factor which is in turn assimilated into a Hydrometeor and Latent Heat Nudging (HLHN) radar data assimilation technique. Finally, the assimilation results are evaluated using the GPM-IMERG precipitation data and Himawari satellite data.

This study employs the mesoscale Advanced Research WRF (ARW) Version 4.1.3 to conduct data assimilation experiments. The model is configured with two nested grids with an outer and an inner domain at grid intervals of 15 and 3 km, respectively. The model top pressure is set at 50 hPa with 33 vertical layers. The model domains and topography are shown in Figure 3. The WRF physical parametrization schemes chosen for this study are as follows: 1. The cumulus parameterization (for domain 1 only) uses the Betts–Miller–Janjic scheme, the microphysical process uses the Thompson scheme [39], the longwave radiation and shortwave radiation uses the RRTMG scheme [40], and the planetary boundary layer uses the YSU scheme [41]. These schemes are chosen for their overall reliable performance over tropical oceans.

Since radar data assimilation acts on the hydrometeor and temperature prognostic equations, three additional microphysical parameterization schemes are employed to conduct sensitivity experiments, including the Lin [42], Morrison [43], and WSM6 schemes [44]. Similar to the Thompson scheme, these three schemes also contain droplets, raindrops, ice crystals, snow, and graupel prognostic equations.

3. Mapping MODIS W-Band Cloud Radar Reflectivity Factor Retrieval to the S-Band Radar Reflectivity Factor

3.1. Retrieving 3D W-Band Radar Reflectivity Factor Based on CGAN-BEBPF

The MODIS L2 cloud products include cloud top pressure (CTP), cloud water path (CWP), effective radius of cloud particles (Re), and cloud optical thickness (COT). These variables only reflect the bulk characteristics of cloud systems and cannot be assimilated into NWP models. Leinonen et al. [10] first applied a CGAN deep learning model to retrieve vertical slices of the W-band radar reflectivity factor based on these cloud products. The retrieved W-band radar reflectivity factor is equivalent to the CloudSat CPR W-band radar measurements because the CGAN model was trained using the CloudSat CPR W-band radar measurements as labels. The CGAN model uses the Adam optimizer, which is computationally fast and requires fewer hyperparameters. The generator has an initial learning rate of 0.0002, and the discriminator has an initial learning rate of 0.0001. Wang et al. [11] conducted a detailed evaluation of the CGAN model and confirmed its satisfactory results for a deep, strong cloud system. Qin et al. further developed a bidirectional ensemble binning probability fusion (CGAN-BEBPF) technique that can automatically retrieve 3D W-band radar reflectivity factor for MODIS granules [12]. The training data for the CGAN-BEBPF model are from the CloudSat 2B-GEOPROF product and the MODIS product on the Aqua satellite (cloud effective radius, cloud top pressure, cloud optical thickness, cloud water path, and cloud mask). They include global data from 2010 to 2017, with a total of 251,456 samples, among which 90% are for training and 10% are for validation. The model in this study is used directly without any modification beyond Qin’s work [12]. The bidirectional, ensemble and binning probability fusion techniques effectively enhance the model retrieval accuracy and robustness. Figure 4 depicts the dataflow of the CGAN-BEBPF model.

In this study, we applied the CGAN-BEBPF model to retrieve the 3D W-band radar reflectivity factor for the MODIS granules containing Typhoon Talim and Typhoon Chaba at the observation times, respectively. The super-parameters of CGAN-BEBPF have been studied and tuned by Qin et al. [12], and we used their tuned-up model for the 3D cloud retrieval in the current study. Figure 5 shows the retrieved results for the two typhoons. For comparison, the MODIS cloud optical thickness (COT) is also presented.

Figure 5a shows the MODIS COT of typhoon Talim at 05:40 UTC on 14 July 2023, when it was featured by organized large strong convective clusters (within the red box). Figure 5b depicts the MODIS COT of Typhoon Chaba at its landfall time at 05:54 UTC on 2 July 2022, when the coastal ground-based S-band radars provide good coverage of its inner core. Chaba is a mature typhoon at its landfall time, featuring the eyewall (marked with a purple box) and the outer spiral rainband (marked with a red box).

The retrieved 3D W-band radar reflectivity factor extended from 240 m to 15,000 m ASL. The horizontal distribution of the typhoon rainband of the 3D retrievals is consistent with the MODIS COT measurements, and all major rainbands are retrieved. It recovers the cloud distribution at upper levels (e.g., 12,000 m ASL in Figure 5d) that is typically missed by ground-based radars. However, there are a couple of issues that need to be resolved before they can be assimilated into the WRF model. First, the magnitude of the W-band radar reflectivity factor is much lower than the typical S-band radar reflectivity factor, and there is a lack of a proper method to assimilate these data; second, the lower-level retrievals are apparently underestimated. In the following sections, we will examine these issues in detail and develop solutions to address them.

3.2. Characteristics of MODIS-Based W-Band Reflectivity Factor Retrievals

The MODIS 3D W-band cloud radar reflectivity factor retrieved by CGAN-BEBPF inherits an unwanted feature of the CloudSat CPR W-band radar (94 Ghz) detection—there is severe signal attenuation in the regions with intense precipitation. Figure 6 compares the MODIS-retrieved 3D W-band cloud radar reflectivity factor and the ground-based S-band radar reflectivity factor for Typhoon Chaba at its landfall time at 05:54 UTC on 2 July 2022. The MODIS 3D W-band cloud radar reflectivity factor retrieval overlaps with the ground-based S-band radar observations for the main parts of the typhoon.

Figure 6 shows that the MODIS cloud radar reflectivity factor generated by CGAN-BEBPF captures the overall inner-core rainbands observed by the ground-based S-band radar. Those at the middle layers (e.g., 7 km ASL, Figure 6b,e) are most consistent. However, due to the wavelength differences between the spaceborne W-band cloud radar and the ground-based S-band radar, they observed significantly different characteristics of the clouds at various altitudes. First, the MODIS cloud radar reflectivity factor generated by CGAN-BEBPF captures the entirety of the inner core rainbands of Typhoon Chaba whereas the ground radar misses the most offshore section, especially for the lower altitudes (such as the spiral rainbands labeled Area C at 2 km ASL, Figure 6d). Second, the W-band and S-band radars present significantly different reflectivity factor intensity. The ground-based radar reflectivity factor ranges from 20 to 50 dBZ, and the intense precipitation cores show over 40 dBZ (Areas A and B in Figure 6a). In contrast, the corresponding cloud radar reflectivity factor ranges from −20 to 15 dBZ. The intense rain cores in Areas A and B have a fake weak reflectivity factor, i.e., featuring “hollow” shaped rainbands at the lower altitude (Figure 6d). This effect is caused by the large attenuation of the W-band radar signal by the hydrometeors [45]. Lastly, the ground-based radar was not able to properly observe ice particles at higher altitudes such as 12 km ASL, resulting in scattered, weak echoes (Figure 6c); in contrast, the retrieved MODIS W-band cloud radar reflectivity factor recovers more upper-level cloud bodies (Figure 6f).

3.3. Mapping the W-Band to the S-Band Radar Reflectivity Factor Equivalent (W2S)

The above analysis indicates that it is challenging to assimilate the MODIS 3D W-band cloud radar reflectivity factor retrievals into NWP models because there are large differences to the ground-based S-band radar reflectivity factor. In fact, there is currently no effective algorithm to assimilate the W-band radar reflectivity factor into numerical weather prediction models. Herein, we developed an approach to assimilate the MODIS-retrieved W-band radar reflectivity factor. We first map the MODIS-retrieved W-band radar reflectivity factor to the equivalent S-band radar reflectivity factor (termed pseudo-S-band radar reflectivity factor) and then adopt the WRF-FDDA HLHN data assimilation scheme to assimilate these pseudo-S-band radar data. This approach not only allows us to convert the MODIS W-band radar reflectivity factor of hydrometeor water contents to be assimilated with the NSF-NCAR WRF HLHN radar data assimilation technique but also corrects the severe lower-level W-band signal attenuation.

Based on the collocated observation of MODIS and the ground-based radars for Typhoon Chaba at its landfall time, a tiered-mapping method is developed to map the MODIS W-band radar reflectivity factor profiles to the S-band profiles. The ground-based S-band radar reflectivity factor intensity is used for precipitation intensity tiering. Considering that the ground-based S-band radar reflectivity factor measurements often miss some lower-level data because of their lowest elevation angle is typically 0.5° and the earth has a curved surface, we use the S-band radar reflectivity factor averaged at heights between 2 and 4 km (including 2, 2.5, 3, 3.5, and 4 km, a total of 5 levels) for precipitation intensity tiering. A total of 12 bins are specified, varying from 20 to 44 dBZ at intervals of 2 dBZ. They roughly represent different portions of the rainbands. For each bin, the arithmetic means of the vertical profiles of the ground-based S-band radar reflectivity factor and the MODIS W-band cloud radar reflectivity factor are calculated and form a representative profile pair. The resultant representative profile pairs for all bins for Typhoon Chaba are shown in Figure 7a, and the individual profile samples used for constructing the representative means for bins 42–44 dBZ are shown in Figure 7b.

Figure 7 shows that the relationship between the S-band and W-band radar reflectivity factor profiles are quite distinct for the different bins. The ground-based S-band radar reflectivity factor decreases with height in general for all bins, and those in the intense reflectivity factor bins decrease more rapidly with the height. The MODIS W-band radar reflectivity factor behaves very differently. The stronger rainbands have a high W-band radar reflectivity factor above 6 km, but they have a lower reflectivity factor below 4 km, which again demonstrates the attenuation effects of the W-band reflectivity factor by the dense hydrometeors in the upper rain cores. The most intense bin (42–44 dBZ) has the largest attenuation, as shown in Figure 7b.

The representative profile pairs for the 12 rainband intensity bins establish a lookup table for mapping the MODIS 3D W-band radar reflectivity factor profiles to the corresponding ground-based S-band radar reflectivity factor profiles. Based on this table, the 3D pseudo-S-band radar reflectivity factor can be obtained from the MODIS 3D W-band cloud radar reflectivity factor. In practice, for each MODIS W-band cloud radar reflectivity factor profile, we identify the most similar curve in the table, i.e., the one that has the minimum absolute difference from the target profile. Then, the corresponding S-band radar reflectivity factor profile is picked from the lookup table and used as the projection output, i.e., a pseudo-S-band radar reflectivity factor profile.

3.4. Assessment of the 3D Pseudo-S-Band Radar Reflectivity Factor

To assess the reliability of the pseudo-S-band radar reflectivity factor retrieved with the mapping method, we compared them with the ground-based 3D S-band radar observation for Typhoon Chaba. Figure 8 shows the ground-based S-band radar reflectivity factor, the MODIS W-band cloud radar reflectivity factor, and the MODIS pseudo-S-band radar reflectivity factor for Typhoon Chaba at a height of 2 km at 00:54 UTC on 2 July 2022. The distribution of the pseudo-S-band radar reflectivity factor corresponds very well to the ground-based S-band radar observation, suggesting that it adequately represents the inner-core and outside rainband. In particular, the ground-based radar observed a convective area in region A and the pseudo-S-band reflectivity factor is over 40 dBZ at the corresponding position. In region B, the ground-based radar observations and the pseudo-S-band radar reflectivity factor are both over 40 dBZ. In both regions, the MODIS W-band radar reflectivity factor is very low and hollow.

Figure 8e,f show an independent validation of the MODIS W-band cloud radar reflectivity factor retrieval and the MODIS pseudo-S-band radar reflectivity factor against the ground-based S-band radar reflectivity factor (d) for the landfall Tropical Storm Mulan at 05:50 UTC on 10 August 2022. Mulan contains far less organized convective rainbands. The MODIS 3D cloud retrieval and the pseudo-S-band radar reflectivity factor reasonably capture the main rainbands (D, E, and F) observed by the coastal S-band radars.

It is evident that the mapping process not only projects the airborne W-band radar reflectivity factor to the ground-based S-band radar reflectivity factor but also effectively corrects the severe lower-level W-band attenuation in the rain cores. Furthermore, the pseudo-S-band retrieval fills in the gaps over the southeastern sea area that is out of reach by the ground-based radars. In the next section, we will illustrate how to assimilate these pseudo-S-band 3D radar reflectivity factor retrievals for the analysis and forecast of Typhoon Talim.

3.5. Assimilation of the Pseudo-S-Band Radar Reflectivity Factor

The pseudo-S-band radar reflectivity factor is assimilated with the WRF-FDDA [46] latent-heat and hydrometeor nudging (HLHN) scheme [23,24,25,26]. With WRF-FDDA HLHN, the hydrometeor (rain, snow, and graupel) mixing ratios are inverted based on the radar reflectivity factor; then, they are used to compute the nudging trend terms of the corresponding prognostic equations. The latent heat associated with the hydrometeor mixing ratio adjustments is added to the thermodynamic equations. The WRF equations with hydrometeor and latent heat nudging scheme can be written as follows:

$${\displaystyle \frac{d{Q}_r}{dt}}=D_{Qr}+S_{Qr}+Gr·Q_r^{anls},$$

(1)

$${\displaystyle \frac{d{Q}_s}{dt}}={D_{Qs}+S}_{Qs}+Gs·Q_s^{anls},$$

(2)

$${\displaystyle \frac{d{Q}_g}{dt}}={D_{Qg}+S}_{Qg}+Gg·Q_g^{anls},$$

(3)

$${\displaystyle \frac{dT}{dt}}=D_T{+S}_T+{\displaystyle \frac{L_{ce}·Gr·Q_r^{anls}+L_{ds}·(Gs·Q_s^{anls}+Gg·Q_g^{anls})}{C_p}}$$

(4)

where $Q_r$,$Q_s$, and ${ Q}_g$ represent specific mixing ratios of raindrops, snow, and graupel, respectively; $D_{Qr}$, $D_{Qs}$, and $D_{Qg}$ represent diffusion terms of these three variable equations due to sub-grid mixing processes; and $S_{Qr}$, $S_{Qs}$, and $S_{Qg}$ represent source/sink terms due to microphysical processes. T denotes temperature, $D_T$ represents diffusion terms of temperatures due to sub-grid mixing processes, and $S_T$ represent the source/sink term of the heat associated with microphysical phase changes and long- and short-wave radiation fluxes. The last terms in Equations (1)–(4) are the data assimilation nudging terms. $G_r$, $G_s$ and $G_g$ are the nudging coefficients for raindrops, snow, and graupel that control the relaxation intensity toward the observations. $Q_r^{anls}$, $Q_s^{anls}$, and $Q_g^{anls}$ are the analysis increments that are the differences between the model forecasts and the observations for raindrops, snow and graupel, respectively. $L_{ds}$ is the water deposition/sublimation specific latent heat, $L_{ce}$ is the water condensation/evaporation specific latent heat, and $C_p$ is the specific heat capacity of air.

It is important to note that an excessively large nudging coefficient Gx can cause significant disturbances, leading to imbalances in the model thermodynamics and dynamics. Huo et al. provides additional detailed discussions and numerous sensitivity tests. In general, Gx works well for being setting with a value in a fare large range, e.g., 0.0002 to 0.002 [25]. Thus, we prefer not to repeat these tests in the present study, and G is set as 0.007 in this study.

4. Assimilation Results and Evaluation

4.1. Data Assimilation Experiment Design

The time frame in the data assimilation experiments for Typhoon Talim is shown in Figure 9. An initial “spin-up” phase of 6 h is set to allow the model to adjust its state and achieve dynamic and physical balance [47]. The spin-up integration begins at 21:00 UTC on 13 July 2023, and ends at 03:00 UTC on 14 July 2023. Model simulations with and without radar data assimilation for the period between 03:00 and 05:40 UTC are carried out, which are followed by a forecast period ending at 09:00 UTC. For brevity, the experiment with MODIS-retrieved radar data assimilation is abbreviated as RDA, while that without is CTRL.

The RDA experiment is conducted to evaluate the impact of the MODIS L2 cloud products on the analysis and forecast of Typhoon Talim in 2023 at its early development stage over the open ocean to the west of the Philippines. Both CTRL and RDA are run with the Thompson microphysical scheme and initialized at 00:00 on 14 July 2023. CTRL is integrated from 00:00 UTC to 09:00 UTC without data assimilation, while RDA adds assimilation of the MODIS pseudo-S-band radar reflectivity factor between 03:00 and 05:40 UTC.

As a polar-orbiting satellite payload, the MODIS cloud measurements and its pseudo-S-band 3D radar reflectivity factor retrieval only provide a snapshot of Typhoon Talim at 05:40 UTC on 14 July 2023. The HLHN four-dimensional data assimilation approach adapted herein to assimilate the pseudo-S-band radar reflectivity factors is an indirect radar data assimilation algorithm. The pseudo-S-band radar reflectivity factors are used to derive specific mixing ratios of raindrops, snow, and graupel, which are nudged into the corresponding WRF prognostic equations (Equations (1)–(3)) and thermodynamic equation (Equation (4)). HLHN permits physically consistent adjustments by assimilating the observations within a time window in which it adds only a small fraction of the analysis increments into the model prognostic equation at each time step. Ideally, HLHN desires continuous observations to perform perfect forward synchronization between the model and observation states. Unfortunately, herein, we only obtained a single-time snapshot of pseudo-S-band radar reflectivity factors. Huo et al. (2021) conducted a series of experiments using 1, 2, 3, and 4 h time windows [25]. They found that using a time window of 3 and 4 h yields better results than using narrower time window. Since we only have on snapshot MODIS observation, it is not proper to use long time windows. Therefore, we set a time window of 2 h and 40 min (from 03:00 to 05:40 UTC) for RDA.

Figure 10 shows the composite reflectivity factor of CTRL and RDA, along with the cloud optical thickness observed by Himawari-9, for typhoon Talim (when it was in a category of tropical storm) at the end of assimilation (valid at 05:40 UTC on 14 July 2023). The wind barbs in Figure 10b,c depict winds at the 700 hPa level. The Himawari-9 cloud optical thickness indicates two heavy rain clusters on the northeast and south sides of the typhoon, reaching a value over 140. The data assimilation experiment yields a compact, strong convective storm in the south quadrant of the typhoon, and the radar reflectivity factor is above 50 dBZ. RDA outperforms CTRL significantly in the analysis of the main convection clusters in the northeastern and southern regions in both extent and intensity.

The wind field of RDA shows a cyclonic structure with a maximum wind speed of over 16 m/s located in the center region and a circulation center at 16.3°N, 119.7°E. There are several convective clusters in the center region with a maximum radar reflectivity factor exceeding 50 dBZ. In general, there are significant differences between the two experiments in the simulated typhoon structures. The typhoon simulated in CTRL has a compact rainband structure, while that in RDA has two core convection regions in the north and south, which is more consistent with the cloud optical thickness observation. CTRL captures the major rainband observed by Himawari-9 in the south quadrant but did not provide a good representation of the convection on the northeastern side. RDA also simulates a cyclonic wind field, but with slightly stronger wind speeds than CTRL. The maximum wind speed in the region for RDA exceeds 20 m/s.

Since there is no ground-based radar measurement that can be used to verify the model cloud forecasts, we compare the model radar reflectivity factor output with the Himawari-9 cloud optical thickness and conduct an objective analysis of the effect of the data assimilation on cloud and precipitation simulation of Typhoon Talim. Specifically, two sets of “coupled thresholds” are selected to compute TS scores: one set compares the model radar reflectivity factor at a threshold of 10 dBZ with a Himawari-9 COT at a threshold of 10, both of which roughly represent the general cloudy areas (Figure 10d–f); the other uses the radar reflectivity factor at a threshold of 30 with a Himawari-9 COT threshold of 40, both roughly representing the main rain areas (Figure 10g–i).

Threat scores (TS) are computed for the two threshold pairs. TS is one of the most used metrics for evaluating the accuracy of meteorological precipitation forecasts [48]. TS considers the true positives, false positives, and false negatives of a forecast for given thresholds and is calculated as follows:

$$TS={\displaystyle \frac{H}{H+F+M}},$$

(5)

where $H$ is the number of correctly forecasted events, $F$ is the number of incorrectly forecasted events, and $M$ is the number of events that occurred but were not forecasted.

The TS computed for the two threshold pairs are shown in Figure 11a and Figure 11b, respectively. Throughout the simulation period, for both the general cloudy areas and the main rain areas, the RDA TS scores are significantly greater than CTRL. From the beginning to the end of the data assimilation period, the RDA TS score for the general cloudy area increased from 0.46 to 0.63, while CTRL only increased to 0.5. The RDA TS score for the main rain area improved even more from 0.19 to 0.42, while CTRL decreased to 0.14. In the prediction stage, the TS scores of the RDA remained higher than CTRL. For the main rain area, the RDA TS scores decline significantly within the first 20 min of the prediction, but it stabilized later on and stayed much higher than CTRL.

Figure 12 compares hourly cumulative precipitation forecasts of the CTRL and RDA experiments from 06:00 to 07:00 UTC on 14 July 2023, with the GPM IMERG surface precipitation estimation. Figure 12a shows that during this period, Typhoon Talim contains a large area with over 10 mm of rainfall, and the maximum rainfall exceeds 30 mm. The precipitation areas in the CTRL experiment are concentrated in very narrow rainbands on the northwest and southwest quadrants, while the precipitation distribution and intensity of the RDA experiment are much more consistent with the observations. The objective comparison results show that the MODIS data assimilation (RDA) dramatically outperforms CTRL, which will be discussed in more details in the next section.

4.2. Impact of Microphysical Schemes on Data Assimilation

On the one hand, microphysical parameterization explicitly models the formation, growth, conversion, and decay processes of various hydrometeors and modulates dynamical and thermodynamical processes. On the other hand, the WRF-FDDA HLHN scheme assimilates the radar reflectivity factor by directly modifying the hydrometeor and thermodynamic equations (cf. Equations (1)–(4)). Thus, the interaction between microphysical parameterization and radar data assimilation processes can critically affect the model cloud and precipitation analysis and forecast. To investigate this issue, we conducted two sets of experiments by replacing the Thompson microphysical scheme with the Lin, Morison, and WSM6 schemes, respectively. The first set is the same as CTRL except for the other three are with different microphysical schemes and the second corresponds to RDA.

The four microphysical schemes simulate quite different characteristics of hydrometeors. Figure 13 compares the vertical profiles of the mixing ratios of rain, snow, and graupel simulated by the four different microphysical schemes with no data assimilation at 06:00 UTC, 14 July 2023. The profiles represent the average value over D02. The magnitude and distribution of hydrometeors of the four microphysical schemes vary greatly at different heights. The rain in all schemes is mostly distributed below the melting layer and decreases with height. Snow and graupel are distributed in the upper layers. The average peak values of the simulated rain mixing ratio from various schemes are around 0.07 g/kg, and the Thompson scheme and Lin scheme have slightly smaller values. In contrast, the differences between snow and graupel are much larger between the schemes. For snow, the average mixing ratio peaks at 0.25 g/kg for the Thompson scheme, with a maximum difference of 0.24 g/kg and a minimum difference of 0.1 g/kg to the other schemes. The differences range from 40% to 96%. These large variations in the hydrometeor distributions between the different microphysical schemes could affect the MODIS data assimilation because HLHN is applied to the prognostic equations of snow, graupel, and rain.

The TS scores for the simulated composite radar reflectivity factor of the eight experiments, i.e., the WRF runs with four microphysical schemes with and without assimilating the MODIS L2 cloud products, are calculated and shown in Figure 14. The verification is completed against the Himawari-9 COT observations. For the general cloudy area (Figure 14a), all MODIS radar data assimilation experiments present higher scores than those without radar data assimilation, with ~0.6 for the forecast periods. Among the experiments with the MODIS data assimilation, the TS score obtained using the Lin scheme remains at a high value. However, the Lin scheme performs the worst among the experiments without the data assimilation. For the main precipitation area (Figure 14b) in the data assimilation period, the TS scores are around 0.4, while those for the no radar data assimilation experiments are near 0.2. In general, the improvement from assimilating the MODIS data is over 30% for the forecast period. With the MODIS data assimilation, The Lin scheme achieves the best prediction for the first hour, but the other three microphysical schemes take over thereafter.

Fractions Skill Score (FSS) is a verification metric often used to quantify precipitation forecast accuracy by considering the contribution of the neighborhood predictions. It is specifically developed for the assessment of precipitation simulations with fine-resolution grids to avoid the double penalty of forecast accuracy due to small spatial displacements of forecast precipitation structures. The calculation formula for the FSS [49] score is as follows:

$$FSS=1-{\displaystyle \frac{\frac{1}{N_x{N}_y}{\sum }_{i=1}^{N_x}\sum _{j=1}^{N_y}{\left(O_{i,j}-M_{i,j}\right)}^2}{\frac{1}{N_x{N}_y}\left({\sum }_{i=1}^{N_x}\sum _{j=1}^{N_y}{O_{i,j}}^2+{\sum }_{i=1}^{N_x}\sum _{j=1}^{N_y}{M_{i,j}}^2\right)}},$$

(6)

where $N_x$ and $N_y$ represent the number of grid points in the horizontal directions of the domain, respectively. $O_{i,j}$ and $M_{i,j}$ are the observed fractions and model forecast fractions, respectively, for each grid point at the given precipitation thresholds and given neighborhood distance thresholds.

Figure 15 presents the FSS for an hour of accumulated precipitation of the MODIS data assimilation experiments with the four microphysical schemes and CTRL (without data assimilation) from 06:00 to 07:00 UTC, verified against GPM IMERG precipitation data. The FSSs for all experiments with the MODIS data assimilation are all significantly higher than CTRL and they decrease as the threshold increases. For all precipitation thresholds, the data assimilation experiment using the Lin scheme works best, with FSSs increasing by 0.55, 0.63, 0.63, 0.59, and 0.54 from CTRL for 0.1, 1, 2, 5, and 10 mm thresholds, respectively. It is interesting to see that the data assimilation experiment with Thompson scheme performs slightly worse than the other microphysical schemes. This result clearly reflects different responses of radar data assimilation for different microphysical schemes.

5. Discussion

This study represents the first attempt to assimilate satellite passive cloud remote sensing data (imager payload) into a mesoscale model to improve 3D cloud and precipitation structure modeling of typhoons. Although dramatic improvements in the initial conditions and short forecasts of the cloud and precipitation of typhoon Talim are achieved in this study, several limitations of the method are exposed and further improvements should be explored.

One of the obvious limitations is that MODIS is based on polar-orbiting satellites, which only provides single-time snapshot cloud products of typhoons every 12 or more hours, including the W-band cloud radar reflectivity factor retrievals. This seriously limits its usage for initializing the model cloud field with the four-dimensional data assimilation scheme and also explains why the effect of the MODIS cloud product data assimilation for Talim declines significantly in the first few hours of the model forecast.

I also wish to point out the uncertainties of the empirical mapping function from the MODIS W-band reflectivity factor retrievals to the ground-based S-band reflectivity factor developed in this study. Although the mapping method can correct the severe attenuation of the MODIS W-band reflectivity factor retrievals in the lower portions of the rainband, it could not resolve the desired fine-scale reflectivity texture that appeared in the MODIS W-band reflectivity factor retrievals. The mapping function could be refined by using more collocated MODIS observations and ground-based S-band radar measurements. Differences in mapping functions discriminated for different cloud systems, e.g., deep convection versus stratiform clouds, should be studied and employed for complex cloud fields. Furthermore, we are currently attempting to develop a machine-learning based mapping algorithm and process more convection cases that have collocated MODIS and ground-based radar observations to train it. We hope this new mapping function will greatly reduce the mapping uncertainties in the future.

Unlike the polar-orbiting satellites, the imager payload on the geostationary satellites provides highly frequent (e.g., every 10 min) cloud measurements similar to those of MODIS, but with lower spatial resolutions. We are currently extending our MODIS 3D cloud-retrieval and data assimilation scheme to process these data. The results will be reported in the future.

6. Conclusions

An innovative approach is developed to assimilate MODIS L2 cloud products to numerical weather models to improve cloud and precipitation initialization for typhoon prediction. Our approach includes retrieving the 3D W-band cloud radar reflectivity factor based on the MODIS L2 cloud product using a CGAN-BEBPF deep learning model, mapping this MODIS 3D W-band radar reflectivity factor to the ground-based S-band radar reflectivity factor, and assimilating these pseudo-S-band radar reflectivity factor to WRF with the WRF FDDA HLHN radar data assimilation scheme. The impact of the MODIS data assimilation on the analysis and forecast of Typhoon Talim is evaluated. The main conclusions are as follows:

(1)

Three-dimensional W-band cloud radar reflectivity factor of typhoons Talim and Chaba are retrieved based on the MODIS L2 cloud products by using the CGAN-BEBPF deep learning model. Taking advantage of collocated measurements of the ground-based weather radars and the retrieved MODIS W-band radar reflectivity factor at the landfall of typhoon Chaba, a mapping function between the MODIS-retrieved 3D W-band cloud radar reflectivity factor and the ground-based S-band radar reflectivity factor is constructed. This approach not only supports the use of WRF-FDDA HLHN to assimilate the MODIS data, but also effectively addresses the severe attenuation issue of the MODIS W-band cloud radar reflectivity factor retrievals in the lower portion of the intense precipitation cores.

(2)

Assimilating the MODIS L2 cloud products enables the WRF model to initialize the convective clusters of Typhoon Talim more accurately. By verifying the model results with the Himawari-9 cloud optical thickness and the GPM IMERG precipitation measurements, it is shown that during the data assimilation phase, the TS score of the MODIS data assimilation experiment is significantly increased for both general cloudy areas (from 0.46 to 0.63) and main precipitation areas (from 0.19 to 0.42), respectively; the TS score decreases during the forecasting phase, but it remains significantly higher than the experiment without data assimilation. There is also a significant improvement in precipitation analysis and forecasting, transforming the precipitation area from the narrow-rainband features in CTRL to the broader rainbands as observed. For the forecast period, the FSS score for the main precipitation core (>5 mm) is increased from 0.09 to 0.52.

(3)

The four microphysical parameterization schemes (Lin, Thompson, Morrison, and WSM6 schemes) present dramatically different distributions of rain, snow, and graupel mixing ratios. Since the HLHN radar data assimilation method assimilates the MODIS cloud products by modifying the model hydrometeors, the various microphysical schemes interact with the MODIS data assimilation differently. The results from the MODIS data assimilation experiments with the four microphysical schemes confirm that the microphysical schemes significantly affect the assimilation and forecasting performance of the model. Among the four microphysical schemes evaluated, the Lin microphysical scheme appears to be most compatible with the MODIS retrieved radar data assimilation.