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A Tropical Cyclone Initialization in Multi-Scale Localization with Hybrid Four Dimensional Ensemble-Variational System: Preliminary Results

One way of the tropical cyclone (TC) initialization is assimilating the official advisory sea-level pressure observation to specify the initial structures of a TC with the aid of a background error covariance (BEC). In the hybrid four dimensional ensemblevariational data assimilation system, a static BEC explains the geostrophic and cyclostrophic wind-mass balance, and an ensemble BEC expresses the flow-dependent feature. Assimilation of the minimum sea-level pressure using a larger localization lengthscale with limited ensemble members yields the closest to the observations at the initial state, but an imbalance in the broad analysis increment distorts geopotential and wind fields. Moreover, the reduced central pressure of TC is rapidly returned to an intensity that a model resolution can represent during the prediction. We introduce the application of final-scale localization (FSL) at the last outer loop with the shortest one to improve the TC initialization. With the aid of FSL, we may conduct the shorter localization length-scale, especially adopted for the TC initialization. As preliminary results, both analysis and prediction become more stable and the large-scale environments are preserved better than in the control experiment. (Citation: Lim, S., H.-J. Song, and I.-H. Kwon, 2020: A tropical cyclone initialization in multi-scale localization with hybrid four dimensional ensemble-variational system: Preliminary results. SOLA, 16, 145−150, doi:10.2151/sola.2020-025.)


Introduction
Numerical weather prediction (NWP) models have been progressed to predict the tropical cyclone (TC) track and intensity; however, the initial condition (IC) with the combination of short-range forecast and observation still suffers to represent the structure and environment of realistic TCs (Torn 2010). Therefore, the DA uses a TC advisory data, minimum sea-level pressure (MinSLP) on central pressure of TC, to initialize the TC structure to improve the track and intensity (Barker et al. 2004;Kleist 2011). This allows a single observation to generate mass and wind analysis increments (AIs) by the background error covariance (BEC) relationship.
In this study, the TC initialization is performed on a hybrid four dimensional ensemble-variational DA system (hereafter H4DEV) using a global NWP model. In H4DEV, the ensemble BEC obviously helps to express the flow-dependent phenomena in the case of the TC (Hamill et al. 2010). However, the analysis result is occasionally exposed to the imbalance between wind and mass that leads to an unphysical evolution of the model states, at the early steps of the integration, and produces wider AIs distorting the environmental field. It eventually generates the unnecessary gravity waves around TC area, although the initial imbalance problem is weakened as the prediction proceeds. Song et al. (2018) introduced the multiple-resolution approach in the H4DEV. It conducts the analysis with different resolutions as the outer iteration progresses. It also helps to control the scaledependent observation network in its minimization process with cost-effective ways. Furthermore, Song (2019) represented a multi-scale localization (MSL) in the H4DEV, in which AIs are generated with different localization length-scales (LLS) as the outer iteration proceeds. The various LLS will determine how far observation information would be propagated in each outer loop (OL).
The TC is a part of the meso-α scale waves whose a horizontal length scale ranges from 200 to 2000 km (Orlanski 1975), but also the edge of synoptic scale whose a horizontal length scale is the order of 1000 km or more (AMS 2018). If we use a single large-scale localization even with a single observation for the TC initialization, this observation is propagated further than we expect. Otherwise, a single shorter-scale localization can hamper the use of the other observations that have longer-distant impacts (Song 2019). Here, we consider the final-scale localization (FSL) methods to restrict the TC advisory data only in the synoptic scale near the TC area.
The purpose of this work is to ensure that if the TC initialization assimilates with FSL at the last OL with the shortest LLS, it generates the appropriate AI to improve the TC structure.

Numerical weather prediction model
The Korea Institute of Atmospheric Prediction System (KIAPS) has been developing the global NWP model called the Korean Integrated Model (KIM, Hong et al. 2018). It is composed of non-hydrostatic governing equations that use the spectral element method on a cubed sphere implemented with state-of-the-art physics parameterization packages. The horizontal resolutions of deterministic and ensemble models in this study are 25 km and 50 km, respectively, with 91 vertical levels up to 80 km model top; the ensemble size is 50.

Hybrid four dimensional ensemble variationl data assimilation
H4DEV is one of the advanced DA schemes, which minimizes a cost function with a hybridized BEC between a static BEC and the ensemble BEC from a local ensemble transform Kalman filter (LETKF) (Hunt et al. 2007;Shin et al. 2016). While the static BEC explains the relationship of the geostrophic and cyclostrophic wind-mass balances, the ensemble BEC expresses the flow-dependent feature. The cost function in H4DEV ) is:

A Tropical Cyclone Initialization in Multi-Scale Localization with Hybrid Four Dimensional Ensemble-Variational System: Preliminary Results
excessive AI. The detailed method will be covered in the next subsection. Figure 1 illustrates the configuration of the multi-resolution OL composed of four iterations. During a cost function minimization, the OL contributes to updating the basic state with respect to which a nonlinear observation operator is linearized. At the first OL, static and ensemble AIs are generated with 42 and 10 total wave numbers, respectively, to fit the observation innovation. At the second (third) OL, they are generated with 85 (170) and 15 (20) total wavenumbers, and the last OL are made with 170 and 40 total wavenumbers.

Multi-scale localization
In this study, we use LLSs of 5, 7, 10 and 20 total wavenumbers for ensemble BEC, corresponding to approximately 7200 km, 5400 km, 3600 km and 1800 km, in each OL. It determines how far the observation could be propagated by the background error correlation. A recent study suggests that we need to consider the observation scales, which are covered from large-scale to smallscale motions , to make the best use of observation information. Since the TC advisory data, MinSLP, corresponds to the synoptic scale, we propose that the TC initialization should be assimilated at the last OL of the synoptic-scale localization (20 total wavenumber, the same as 1800 km). This approach enables the MinSLP observation to change the TC and its nearenvironment only, not large-scale features that are unwanted to be modified with the TC initialization.

Experimental design
Three experiments were performed to identify the response where ξ is the control variable that consists of stream function, unbalanced velocity potential, unbalanced temperature and surface pressure and pseudo relative humidity; α is an ensemble control variable determining localization of ensemble BEC; y o is the observation; h (x) is the observation operator; x g is a guess field for the analysis; U is an operator transforming the control variable into the model variable, which composed of the vertical (U v ), horizontal (U h ), and parameter transforms (U p ); O is the observation error covariance. For H4DEV, the localization function is generated as a gaussian type in wavenumber space and the localization is conducted in the same space . Currently, the weights β c (= 0.7) and β e (= 0.3) are used since the global performance was the best with them for the current system (Song et al. 2017), although a smaller weight on the ensemble BEC could be disadvantageous to represent the TC analysis. Except TC initialization is not conducted in LETKF, the same real observations are assimilated in both variational and ensemble systems .
As for the LETKF in H4DEV , the ICs for ensemble forecasts are generated by adding randomly selected perturbations from static BEC samples to the deterministic analysis . To prevent the filter divergence, the adaptive multiplicative and additive inflations are implemented. It autonomously has the horizontal localization functions given by a Gaussian-like piecewise fifth-order rational function (Gaspari and Cohn 1999;Miyoshi et al. 2011), varying 660 km to 1800 km depending on the level. The vertical localization functions are given by the Gaussian-like rational function with 0.1 (wind) or 0.2 hPa (mass) in logarithmic pressure for conventional data and a gradient of transmittance of the measured radiance for radiance data (Thepáut 2003).

Tropical cyclone initialization
The TC initialization (Kleist 2011) assimilates the estimates of MinSLP produced by the Regional Specialized Meteorological Center (RSMC) -Tokyo. 3-hourly generated TC advisory data covers the western North Pacific and the South China Sea (Muroi 2018). This single observation is treated as ordinary surface observation, but the quality controls (QC) are handled differently: 1) The conventional gross check is removed to prevent the observation from being filtered out due to a large observation innovation. 2) Only observations with good and fair QC indices can be used.
3) The observation over the land is not used because of the large uncertainty in surface pressure estimation. 4) The observation is assimilated when the background surface pressure of the TC center is higher than the TC advisory data.
Since the gross check in it is removed, it is hard to filter out the observation having the large observation innovation. This could produce excessive AI generating an unnecessary gravity wave and harming the large scale environment. It eventually occurs over the large uncertainty area to diagnose the TC in particularly in the ensemble system (Holt et al. 2015). To remedy excessive AIs, we devise an additional process: 1) The observation errors (OE) linearly vary with the TC intensity (Kleist 2011;Holt et al. 2015), then it diminishes with excessively fitted to observation (O where A = 400 (A + B, the maximum value) and B = 200 (the minimum value).
2) The observation innovation is empirically limited to 30 hPa at the maximum to suppress the initial shock. The incremental analysis updating (IAU, Bloom et al. 1996) is an alternative prescription, but currently, H4DEV does not have initialization methods.
3) The main idea in this study is the application of FSL to prevent Fig. 1. A schematic diagram for the multiple-resolution outer-loop (OL) frame with different localization length-scales (LLS). The width of each box with the wavenumber in parentheses implies each LLS in physical space. As a result, it has a combination of the analysis increments localized with 7200, 5400, 3600, and 1800 km LLS, which correspond to truncation wavenumbers 5, 7, 10, and 20 in wavenumber space, respectively. of TC initialization in the frame of MSL (Table 1). Basically, the first experiment (NOTC) without TC initialization is performed to demonstrate why the TC initialization is needed in the H4DEV. The second experiment (MUL1) assimilates the single MinSLP over the TC center during the whole OL processes with approximately 7200, 5400, 3600, and 1800 km LLSs as for the ordinary observations. Otherwise, the last experiment (MUL4; i.e., FSL) assimilates the MinSLP at the last OL, whose minimization is conducted with the highest resolution (T40 and T170, for ensemble and static control variables, respectively) and shortest LLS (approximately 1800 km) for ensemble BEC. Here, the other observations are minimized starting from the first OL as before. Through the comparison between the two experiments (MUL1 and MUL4), it is identified that the TC initialization needs to be conducted in the last OL, which has the shortest LLS (about 1800 km) with the highest resolution (about 900 km, T40, for the ensemble, and 212 km, T170, for the static control variables).
H4DEV system was performed in a warm cycle run from 1800 UTC on 22 June 2018 to 1200 UTC on 11 July 2018 during which TC Maria (2018) existed. Figure 2 shows the best track of TC Maria (2018) that reached a super typhoon, which is classified into category 5 on the Saffir-Simpson scale. Since the discernible difference between the MUL1 and MUL4 is emerging from 18 UTC on 5 July 2018 in the intensified TC with few cycles, a detailed analysis was conducted at 0000 UTC on July 7 2018.

TC analysis results
To demonstrate the advantage of the TC initialization at the last OL with the shortest LLS, we investigated which strategy is more appropriate for representing the TC structure. Figure 3 shows Table 1. Description of experiments: Yes (No) indicates that TC advisory data is used (not used) in the corresponding outer-loop (OL). The localization length-scale (LLS) in physical space is represented in parentheses. As a result, the MUL1 has a combination of the analysis increments (AIs) of TC advisory data localized with 7200, 5400, 3600, and 1800 km LLS while the AI of TC advisory in MUL4 is only obtained from 1800 km LLS, namely final-scale localization.

MUL1 MUL4
TC advisory data in 1st OL TC advisory data in 2nd OL TC advisory data in 3rd OL TC advisory data in 4th OL

No No No No
Yes (7200 km  the AIs of a mean sea-level pressure (MSLP) and a horizontal wind vector at 850 hPa. In the TC Maria (2018) area, we anticipate that the DA makes the TC stronger over the ocean where the observation is deficient. For the NOTC that does not conduct TC initialization, it generates an increased MSLP and an anti-cyclonic circulation increment (Fig. 3a). It weakens, rather than strengthens, the TC, because there was no observation to express the TC over the ocean. On the contrary, the TC initialization produces a decreased MSLP and a cyclonic circulation to strengthen the TC structure in cases of the MUL1 and MUL4. However, the magnitude and width of AIs depend on which OL the TC initialization is involved from. MUL1 decreases the MinSLP by 26 hPa and generates unnecessary wind vectors around the TC (Fig. 3b) since MUL1 has AIs obtained from longer LLS (Table 1). While the TC having a radius between 222 and 888 km is meso-α or synoptic scale, it is localized with longer length-scales in the first (7200 km), second (5400 km), and third (3600 km) OL in the frame of MSL. As a result, the single observation related to synoptic or less-scale has been over-propagated up to longer effective radii. On the other hand, the MUL4 experiment assimilates the MinSLP with at the last OL of the LLS of T20 or 1800 km; then it lowers the MinSLP by 13 hPa. Furthermore, a cyclonic wind vector is made while an unnecessary large-scale circulation is hard to be derived. The shorter LLS makes it reduced, which is the spurious error correlation due to the limited ensemble size. Figure  4 explains how these AIs are related to other atmospheric fields. To identify the results reasonable, we used the Integrated Forecast System (IFS) analysis data of the European Centre for Medium-Range Weather Forecasts (ECWMF), which is well known as the best quality of the forecast skill (https://apps.ecmwf.int/wmolcdnv/ scores/mean/500_z). It has the 0.25-degree latitude and longitude grids with 25 pressure levels from 1000 hPa to 1 hPa. At 0000 UTC on 7 July 2018, the IFS analysis simulates the central pressure of TC Maria (2018) as 948.5 hPa. Although it is higher than the RSMC best track information, 935 hPa, it well simulates, for a global NWP model result, lower-level TC structure at the analysis time. Compared to the IFS analysis, the MUL1 shows the best result of the central pressure of TC, 953.7 hPa, which the MUL4 follows as 957.1 hPa; NOTC is 984 hPa. While the geopotential height (GPH) at 500 hPa forms a closed contour in the Figs. 4a and 4d, the NOTC as well as MUL1 (Figs. 4b and 4c) similarly shows a wiggle in GPH in the southwest region of the TC. In particular, MUL1 has shown a distorted shape of TC due to an excessive AI along with the left side of the TC (Fig. 4c). These features were also identified as similar in the analysis of another experiment, which is with larger β e (= 0.7), at 0000 UTC on 7 July 2018 (not shown). Figure 5 shows the box plots of the RMSD of GPH at 500 hPa for NOTC, MUL1, and MUL4. In the vicinity of TC, excessive AI of MUL1 harms large-scale field and worsens the RMSD of GPH. However, the MUL4 may solve the imbalance problem, thereby tending to preserve the original GPH, resulting in the RMSD at a level similar to that of NOTC.

TC forecast results
We identified the 120-hour predicted tracks of TC Maria (2018) from 0000 UTC on 7 July 2018. The application of FSL (MUL4) at the last OL with the shortest LLS to TC initialization could not, however, reach to deriving improvements of prediction of the TC track (not shown). Next, we verified the time series of MinSLP for experiments, beginning at the same time (Fig. 6). At the initial time, the TC initialization (MUL1 and MUL4) leads to a decrease of about 30 hPa compared to NOTC; as a result, MUL1 produces MinSLP that was most similar to the RSMC best track; the MUL4 also generates MinSLP with similar performance. However, the reduced MinSLP could not be maintained during the forecast time especially in MUL1. In the case of MUL1, the strongest MinSLP among the experiments rapidly weakens during the initial 6-hours; however, its intensity is even weaker than NOTC after that. The excessive AI of 26 hPa is probably associated with an increase in acoustic and gravity wave activity, and the MinSLP eventually returns to a reduced intensity that the grid resolution can resolve (Kleist 2011). Otherwise, while the MUL4 shows the improved MinSLP at the analysis time, the reduced MinSLP is maintained until the 120-hour forecast lead time. The reduced central pressure of the assimilation of TC MinSLP is sustained during the prediction of the TC. Although the reduced MinSLP is increased from the analysis time, this amount is much smaller compared to MUL1. The changes in the track and intensity forecasts due to the multi-localization strategy for the TC initialization were modest but positive.

Conclusion
This study proposes the application of FSL at the last OL with the shortest LLS to improve the TC initialization. It is based on the idea that TC initialization should be assimilated with a LLS between meso-α and synoptic. Since the localization can reduce the propagation of unnecessary observation information (Anderson 2007), the shorter length-scale localization at the last OL with the minimum (1800 km) LLS is conducted. In TC Maria (2018) case, the mid-level GPH in the analysis shows a more stable TC structure and the reduced central pressure intensity is sustained during 120-hour forecast, compared to the experiment including the TC initialization with larger-scale localizations (3600, 5400, and 7200 km).
As a further study, experiments with increased ensemble ratio and resolution in H4DEV, including the TC initialization in LETKF as well, are planned. Besides, the additional impact of the IAU on suppression of initial shock can be investigated. With more TC cases, we anticipate the FSL in MSL will be more effective for TC initialization.