The Improvement of Short-Term Quantitative Precipitation Forecast in Mountainous Areas by the Assimilation of Meteorological State Variables Retrieved by Multiple Doppler Radar Data

Yu-Chieng Liou aDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan

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Tzu-Jui Chou aDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan

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Yu-Ting Cheng bCentral Weather Administration, Taipei, Taiwan

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Yung-Lin Teng aDepartment of Atmospheric Sciences, National Central University, Taoyuan, Taiwan

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Abstract

This study presents a sequential procedure formulated by combining a multiple-Doppler radar wind synthesis technique with a thermodynamic retrieval method, which can be applied to retrieve the three-dimensional wind, pressure, temperature, rainwater mixing ratio, and moisture over complex terrain. The retrieved meteorological state variables are utilized to reinitialize a high-resolution numerical model, which then carries out time integration using four different microphysical (MP) schemes, including the Goddard Cumulus Ensemble (GCE), Morrison (MOR), WRF single-moment 6-class (WSM6), and WRF double-moment 6-class (WDM6) schemes. It is found that through this procedure, the short-term quantitative precipitation forecast (QPF) skill of a numerical model over mountainous areas can be significantly improved up to 6 h. The moisture field plays a crucial role in producing the correct rainfall forecast. Since no specific microphysical scheme outperforms the others, a combination of various rainfall scenarios forecasted by different MP schemes is suggested in order to provide a stable and reliable rainfall forecast. This work also demonstrates that, with the proposed approach, radar data from only two volume scans are sufficient to improve the rainfall forecasts. This is because the unobserved meteorological state variables are instantaneously retrieved and directly used to reinitialize the model, thereby the model spinup time can be effectively shortened.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yu-Chieng Liou, tyliou@atm.ncu.edu.tw

Abstract

This study presents a sequential procedure formulated by combining a multiple-Doppler radar wind synthesis technique with a thermodynamic retrieval method, which can be applied to retrieve the three-dimensional wind, pressure, temperature, rainwater mixing ratio, and moisture over complex terrain. The retrieved meteorological state variables are utilized to reinitialize a high-resolution numerical model, which then carries out time integration using four different microphysical (MP) schemes, including the Goddard Cumulus Ensemble (GCE), Morrison (MOR), WRF single-moment 6-class (WSM6), and WRF double-moment 6-class (WDM6) schemes. It is found that through this procedure, the short-term quantitative precipitation forecast (QPF) skill of a numerical model over mountainous areas can be significantly improved up to 6 h. The moisture field plays a crucial role in producing the correct rainfall forecast. Since no specific microphysical scheme outperforms the others, a combination of various rainfall scenarios forecasted by different MP schemes is suggested in order to provide a stable and reliable rainfall forecast. This work also demonstrates that, with the proposed approach, radar data from only two volume scans are sufficient to improve the rainfall forecasts. This is because the unobserved meteorological state variables are instantaneously retrieved and directly used to reinitialize the model, thereby the model spinup time can be effectively shortened.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Yu-Chieng Liou, tyliou@atm.ncu.edu.tw

1. Introduction

In the past few decades, numerous efforts have been made to improve short-term convective-scale forecasts of rainfall. Methods developed include the three-dimensional variational data assimilation (3DVAR; e.g., Xiao et al. 2005; Hu et al. 2006; Chung et al. 2009; Gao and Stensrud 2012; Lai et al. 2020), four-dimensional variational data assimilation (4DVAR; e.g., Sun and Crook 1997; Sun and Zhang 2008; Thiruvengadam et al. 2020; Tai et al. 2011, 2017; Wu et al. 2021), ensemble Kalman filter (EnKF; e.g., Snyder and Zhang 2003; Tong and Xue 2005; Xue et al. 2006; Jung et al. 2008; Tsai et al. 2014; Do et al. 2023), and hybrid systems (e.g., Li et al. 2012; Gao and Stensrud 2014; Li et al. 2015; Lee et al. 2022). These techniques have been widely used to assimilate weather radar data into a high-resolution numerical model, thereby significantly increasing the model’s forecasting skill for severe rainfall events.

However, a numerical model needs spinup time after initialization, meaning that a certain period of time is required before the model reaches a stable status. For EnKF, sufficient time is also needed for the ensemble members to generate correct correlations among different variables. Given this requirement, the radar echo extrapolation technique represents another effective way to provide very short-term (usually 1–3 h) precipitation forecasts (e.g., Dixon and Wiener 1993; Li and Lai 2004; Germann and Zawadzki 2002, 2004; Chung and Yao 2020).

On the other hand, the work of Gal-Chen (1978, hereafter G78) demonstrated that the thermodynamic parameters (i.e., pressure and temperature perturbations) could be derived from the multiple-Doppler radar-synthesized three-dimensional winds, and these fields can be utilized to initialize a numerical model. Further research based on this concept to improve the weather analysis and model forecast can be found in Lin et al. (1993), Crook (1994), Crook and Tuttle (1994), Protat et al. (2001), Weygandt et al. (2002), Liu et al. (2005), Zhao et al. (2006), Liou et al. (2014), and Shimizu et al. (2019). The advantage of this approach is that the model spinup time can be effectively reduced because the unobserved meteorological variables are instantaneously retrieved and directly inserted into the model.

The first author (YCL) of this manuscript had developed a variational-based multiple-Doppler radar wind analysis method (Liou and Chang 2009; Liou et al. 2012) and a new thermodynamic retrieval scheme (Liou et al. 2019). These two methods are specifically designed to perform the retrievals directly over a nonflat surface from which to generate a set of three-dimensional wind, temperature, and pressure perturbation fields over complex terrain (see section 2 for more details). To improve the analysis and forecast in mountainous areas, in this current study, a sequential procedure is formulated by combining the aforementioned two advanced wind synthesis and thermodynamic retrieval methods. The meteorological state variables over the terrain can be retrieved and then applied to reinitialize a high-resolution numerical model. The goal of this study is to assess the impact of this approach on model prediction, in particular for the improvement of the short-term (0–6 h) quantitative precipitation forecast (QPF) skill over mountainous regions. It should be emphasized that with this procedure, the unobserved state variables being assimilated into the numerical model are obtained instantaneously from the Doppler radar wind measurements, rather than through internal adjustment of the model during a long-term time integration. As a result, even with fewer radar data, this approach is still able to shorten the model spinup time (Liou et al. 2014).

In the next section, the methods for retrieving the three-dimensional wind, pressure, and temperature perturbations and diagnosing the water vapor are introduced. The experimental design is described in section 3, along with detailed investigations of the performance of the proposed procedure for improving the model QPF using a real case study. The role played by water vapor is also discussed. The rainfall forecasts under different microphysical schemes are explored in section 4, followed by a second case study in section 5. A summary is given in section 6.

2. Methodology

a. WISSDOM: A multiple-Doppler radar three-dimensional wind synthesis method for use over complex terrain

The Wind Synthesis System using Doppler Measurements (WISSDOM; see Liou et al. 2012, 2019) is used for wind analysis. In the WISSDOM algorithm, the wind fields are solved by variationally minimizing a cost function in which a set of equations is implemented as weak constraints. These include the geometric relationship between the radial wind observed by each Doppler radar and the retrieved Cartesian wind components (u, υ, w), the anelastic continuity equation, the vertical vorticity equation, and a background flow field obtained from a selected mesoscale numerical model output (Liou and Teng 2023). WISSDOM can recover the wind fields along and near the radar baseline (Liou and Chang 2009). The immersed boundary method (Tseng and Ferziger 2003) is employed to take into account topographic forcing on the fluid during the computation. WISSDOM has demonstrated its capability of synthesizing wind fields over complex terrain (Liou et al. 2012). It is also easy to merge wind observations from any number of radars and surface stations (Liou et al. 2016, 2019). Furthermore, by implementing the vertical vorticity equation to constrain the retrieved three-dimensional winds, one can avoid the problem associated with the production of a residual term when performing the vorticity budget analysis (Liou et al. 2012), leading to better thermodynamic retrieval results with higher accuracy (Protat and Zawadzki 2000). WISSDOM has been applied for a variety of purposes, ranging from the study of the convective structure (Liou et al. 2013; Lee et al. 2014), precipitation efficiency (Chang et al. 2015), and orographic effects on rainfall (Liou et al. 2016; Lee et al. 2018; Tsai et al. 2018), to high-resolution (50 m) wind retrievals in mountainous areas (Tsai et al. 2023). WISSDOM has also been implemented in operation at the Korea Meteorological Administration (Park et al. 2023). An ongoing work is to test WISSDOM with data collected by a single Doppler radar, provided a reliable background wind field is available.

b. TPTRS: A thermodynamic retrieval scheme over complex terrain

Thermodynamic retrieval schemes use the multiple-Doppler synthesized wind fields to derive the three-dimensional pressure and temperature perturbations. In the widely used G78 method, a two-dimensional Poisson equation needs to be solved in each horizontal plane to obtain the pressure perturbations. However, when topography exists, it is very difficult to solve the Poisson equation on a horizontal plane with embedded hollows caused by the intersection of the domain with the mountains. To deal with this problem, Liou et al. (2019) developed a new method, named the Terrain-Permitting Thermodynamic Retrieval Scheme (TPTRS), in which one can directly use the wind field synthesized by WISSDOM to derive the three-dimensional thermodynamic fields over complex terrains.

The TPTRS thermodynamic retrieval starts with the equations of motion:
F1θυ0[ut+Vufυ+turb(u)]=πx,
G1θυ0[υt+Vυ+fu+turb(υ)]=πy,
H1θυ0[wt+Vw+turb(w)+g(qr+qs)]=πz+gθcθυ0θ0,
where the subscript “0” represents a horizontally homogeneous basic state and depends only on height, which can be determined by a prestorm environmental sounding. The perturbations relative to the basic state are written with variables with a prime. In (1)(3), (u, υ, w) are the Cartesian wind components, f stands for the Coriolis parameter, g is the gravitational acceleration, and turb() denotes an operator for subgrid turbulence parameterization. The mixing ratio of rainwater qr and snow qs can be calculated using the radar reflectivity through empirical equations such as those suggested in Tong and Xue (2005), or by more sophisticated ways using dual-polarimetric radar data as proposed in Carlin et al. (2016). The parameter π′ is the perturbation of the normalized pressure defined as
π=ππ0=Cp(PP00)κCp(P0P00)κ,
where P is the total pressure, P0 is the basic-state pressure, P00 = 1000 hPa, κ = R/Cp, R (=287 J kg−1 K−1) stands for the gas constant, and Cp (=1005 J kg−1 K−1) represents the specific heat capacity under constant pressure.
The virtual potential temperature θυ and virtual cloud potential temperature perturbation θc as defined in Roux (1985) are expressed as follows:
θυ=θ(1.0+0.61qυ),
θc=θ+(0.61qυqc)θ0,
where θ is the potential temperature, qυ denotes the perturbation of the water vapor mixing ratio from its basic state qυ0, and qc is the cloud water mixing ratio. The virtual cloud potential temperature perturbation θc is treated as a retrievable parameter. From (5), the basic-state virtual potential temperature can be expressed as
θυ0=θ0(1.0+0.61qυ0).
The values of F, G, and H in (1)(3) can be computed once the three-dimensional wind field is obtained from WISSDOM.

The quasi-Newtonian conjugate-gradient algorithm developed by Liu and Nocedal (1989) was adopted to variationally minimize a cost function that contains (1)(3). This approach allows one to conduct the minimization only at those grid points located in the flow regions of the analysis domain. The design of TPTRS can be traced back to the work done previously by Liou (2001) and Liou et al. (2003), but with a significant modification in terms of implementing the terrain-resolving capability.

c. A moisture/temperature adjustment scheme and rainwater estimation

The initiation and development of convection is known to be highly sensitive to the moisture amount and the structure in the boundary layer (Crook 1996; Weckwerth 2000). In this study, the moisture adjustment scheme proposed by Liou et al. (2014) is applied and outlined in detail in the following.

  1. Step (i): Set qυ=0 in (6).

  2. Step (ii): Convert the retrieved π′ to total P following the procedures introduced in the appendix.

  3. Step (iii): Use the retrieved θc from TPTRS and the simulated qc from the model to compute θ′ from (6). After adding θ0 to θ′, one gets the total θ, which can be converted into total temperature T (see the appendix).

  4. Step (iv): Use the retrieved total pressure P and temperature T at the surface from TPTRS to estimate the dewpoint temperature Td, as
    Td=Bln(Aε/qυP)sfc,
    where A = 2.533 × 108 kPa, B = 5.417 × 103 K, ε = 0.622, and qυ=qυ+qυ0. The subscript sfc stands for the surface level.
  5. Step (v): Estimate the height H of the lifting condensation level (LCL) using the following relation (Rogers and Yau 1989, p. 57):
    H(km)(TTd)sfc8.
  6. Step (vi): Saturation is assumed when the radar reflectivity is greater than 10 dBZ, and the height is above LCL. For those saturated grid points, the TPTRS-retrieved temperature can be applied to compute the saturation water vapor pressure es using the Clausius–Clapeyron equation (Rogers and Yau 1989, p. 14):
    es(T)=AeB/T.
    Then, the es is transformed into saturation water vapor mixing ratio qvs by
    qvs=εesP.
    By subtracting the basic state from qvs, a new qυ can be obtained, followed by an update of θ′ in (6).
  7. Step (vii): Compute Δqυ and Δθ′, the differences between the old and updated qυ and θ′. If both are smaller than the prescribed thresholds (in this study, |Δqυ|<5×105kgkg1 and |Δθ′| < 1 × 10−2 K), the adjustments are completed. Otherwise, steps (iii)–(vii) are repeated.

The aforementioned procedure forms an iterative loop until the solutions converge. It is noticed that step (vi) is similar to the approaches by Xu et al. (2010) and Montmerle et al. (2001), except in their studies the vertical velocity is also utilized as an additional criterion to determine the extent of the saturation.

Starting from the radial velocities and reflectivity measured by multiple-Doppler radars, the aforementioned methods provide a set of three-dimensional winds, thermodynamic parameters (i.e., pressure and temperature perturbations), rainwater, and water vapor mixing ratio within the analysis domain. Based on this set of data, one can reinitialize a numerical model, with time integration continuing to predict the rainfall. This approach can be considered an extension of Liou et al. (2014). However, the main improvement over Liou et al. (2014) is that the methods employed in this study are capable of retrieving winds and thermodynamic variables directly over complex terrain, thus avoiding the requirement of data interpolation from the retrieval domain to the model domain, particularly over the mountainous regions. In addition, four different microphysical schemes are applied in the following simulations after model initialization. The performances of each scheme and a combination of all schemes for forecasting rainfall are evaluated. Finally, the rainfall forecast time in this study is extended up to 6 h, rather than only 3 h as in Liou et al. (2014).

3. Benchmark experiment using a real case study—SoWMEX IOP8

a. Model settings and experimental design

The model settings and experimental design for a benchmark experiment are described below. The WRF Model (v3.8.1) used in the experiments was comprised of two nested domains (labeled D01 and D02; see Fig. 1). Both domains contained 165 × 183 horizontal grid points and 52σ levels in the vertical direction. The horizontal resolutions for D01 and D02 were 6.0 and 2.0 km, respectively. The Yonsei University (YSU) scheme (Hong et al. 2006) and the Kain–Fritsch scheme (Kain 2004) were employed for the planetary boundary layer and convective parameterization, respectively. In this benchmark experiment (named RAD_INIT), the WSM6 microphysical scheme was tested first. Figure 1 shows the coverage of D01 and D02, while the locations of the various observational instruments including weather radar, sounding, rain gauge, and surface station are displayed in Fig. 2.

Fig. 1.
Fig. 1.

The D01 and D02 domain settings for the WRF simulations in this study.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Fig. 2.
Fig. 2.

Locations of various observational instruments in D02. The red dots represent three weather radars (SPOL of NCAR, RCCG, and RCKT operated by the Taiwan CWA). The blue squares denote the TN and LG sounding stations. The pink crosses stand for surface stations, and the small black dots are rain gauges. Topography (m) is shown by the color shading.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

The first case selected for this study was from the intensive observation period (IOP) 8 during the Southwestern Monsoon Experiment (SoWMEX) conducted in Taiwan from May to June 2008. This particular IOP was a prefrontal squall-line system, which produced over 200 mm of rainfall within 24 h in southern Taiwan. The study period started at 0600 UTC 14 June and ended at 1800 UTC. The WRF Model was first initialized using ERA-Interim data at 0600 UTC, followed by a 6-h integration until 1200 UTC. Then, the model states in D02 at 1200 UTC were reinitialized using the radar observed and retrieved (by WISSDOM and TPTRS) parameters (i.e., wind, temperature, pressure, rainwater, and vapor), followed by a 6-h forecast of the rainfall. Note that at 1200 UTC, the wind field from the WRF simulation is also utilized by WISSDOM as the background wind field to fill in the radar data-void regions. Furthermore, the cloud water mixing ratio qc, which is needed in the moisture adjustment scheme, is also obtained from the model.

A basic state is required for thermodynamic retrieval. A series of sensitivity tests were performed to select the model-simulated atmosphere a few hours before 1200 UTC as the basic state. It was found that by changing the basic state, TPTRS would retrieve different thermodynamic fields. However, through the radar data assimilation procedure proposed in section 2, the model’s rainfall forecasts could always be improved, only to a different extent. Therefore, in this study, the model-simulated atmospheric state at 0900 UTC, or 3 h before the data assimilation occurred at 1200 UTC, was selected as an example to compute the basic state. It should be mentioned that those basic-state variables such as P0, θ0, and qυ0 [see (4) and (7) in section 2b] needed for computing π0 and θυ0 are obtained by performing a horizontal average of P, θ, and qυ produced by the model simulation at 0900 UTC.

In addition to RAD_INIT, two more tests (named No_RAD and RAD_INIT_NoQv) were conducted. No_RAD represented a pure model simulation without data assimilation. In RAD_INIT_NoQv, the same data assimilation procedures were used as in the RAD_INIT experiment, but the moisture adjustment was not performed.

b. Indices for quantitative comparison

The indices utilized for conducting a quantitative comparison between the forecasted/retrieved and observed variables include the root-mean-square error (RMSE) and the spatial correlation coefficient (SCC):
RMSE=(AfAO)2M,
SCC=(AfAf¯)(AOAO¯)(AfAf¯)2(AOAO¯)2,
where subscripts “f” and “o” denote the forecasted/retrieved and observed values for a certain parameter A, respectively, and M stands for the total number of grid points used for the calculation. In (13), the overbar stands for an average over the grids.
The model-forecasted rainfall amounts distributed at the model grid points are interpolated to each rain gauge site. The equitable threat score (ETS), as proposed by Schaefer (1990), is computed to provide a quantitative assessment of the QPF capability. Following Wang (2014), this index is defined as
ETS=HRF+OHR,
where H, F, and O are the number of correctly predicted, forecasted, and observed points above a certain threshold, respectively, while R is the number of hits obtained by random guessing, which can be written as
R=F×ON,
where N is the total number of points in the verification domain. When H is equal to R, the model has no forecast skill, whereas ETS = 1.0 indicates a perfect forecast.
Finally, the fraction skill score (FSS; Roberts and Lean 2008) is also utilized to evaluate the performance of the forecast. As in Do et al. (2023), this score is calculated as follows:
FSS=11Ni=1N(PfPo)21Ni=1NPf2+1Ni=1NPo2,
where Pf and Po are the forecasted and observed fractions over a certain number of grids (N: 10 × 10 points in this study) surrounding each grid point, respectively. The FSS ranges from 0.0 to 1.0, with 0.0 representing zero forecasting ability and 1.0 a perfect forecast.

c. Retrieved results and verification

Figure 3 shows an example of the model-simulated background and WISSDOM-retrieved wind fields at a height of 1.0 km at 1200 UTC. It can be seen that the prevailing wind was from the southwest. In the background wind field, the distribution of the horizontal wind speed was rather smooth and gradually decreased toward the land (Fig. 3a). Updrafts can be found only on the land. By contrast, in the retrieved wind field (Fig. 3b), the horizontal flows were deflected more northward over the plain area (∼23.5°N, 120.5°E). The distribution of the horizontal wind speed exhibits more spatial variations. Updrafts can be identified not only over the land near the mountains but also over the ocean within the regions of strong radar reflectivity (not shown). The increments of the horizontal wind (Fig. 3c) computed by subtracting the background from the retrieved field revealed that the southwesterly flows were significantly accelerated/decelerated over the ocean/land through WISSDOM retrievals.

Fig. 3.
Fig. 3.

The flow fields at 1.0 km in height during SoWMEX IOP8 at 1200 UTC 14 Jun 2008. (a) Model-simulated background horizontal wind vectors (black arrow; m s−1), horizontal wind speed (color shading; m s−1), and updraft (blue contour; 0.3 m s−1 interval); (b) as in (a), but for WISSDOM-retrieved results; and (c) increments of horizontal wind (black arrow; m s−1) and speed (color shading; m s−1). Gray-shaded areas illustrate where the altitude exceeds 1.0 km.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Figure 4 shows the model-simulated background and TPTRS-retrieved total pressure and potential temperature fields along with their increments. Similar to the wind fields, the distribution of the retrieved pressure and potential temperature fields also reveal more spatial variations than their background counterparts. The retrieved pressure modifies the background pressure field with the positive increments reaching approximately 10 hPa. The retrieved temperature field generally cools down the background field and exhibits a clear cold pool feature near the coastal area. The cold pool’s magnitude can reach −4 K, and its coverage is roughly consistent with the regions of higher pressure.

Fig. 4.
Fig. 4.

The pressure (contour; hPa) and potential temperature fields (color shading; K) at 1.0 km in height during SoWMEX IOP8 at 1200 UTC 14 Jun 2008. (a) Model-simulated background fields, (b) TPTRS-retrieved fields, and (c) increment fields. Gray-shaded areas illustrate where the altitude exceeds 1.0 km.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Figures 5 and 6 compare the wind and thermodynamic variables measured by Tainan (TN) and Liouguei (LG) soundings with their counterparts retrieved by WISSDOM and TPTRS at 1200 UTC. The RMSE of the wind fields before and after the adjustment by using radar radial velocity data and WISSDOM can be reduced from 3.43 to 1.74 m s−1 for the Tainan sounding and remains similar for the Liouguei sounding (∼3.1 m s−1). On the other hand, the application of TPTRS does lead to a significant improvement in the pressure and temperature fields. The RMSE of the pressure perturbation for the Tainan station is reduced from 15.3 to 0.15 hPa, and from 12.2 to 0.13 hPa for the Liouguei station, respectively. The RMSE of the temperature decreases from 1.41 to 1.05 K for Tainan, and from 1.14 to 0.97 K for the Liouguei station.

Fig. 5.
Fig. 5.

Sounding-observed (black line), WISSDOM-retrieved (blue line), and model-produced background (red line) horizontal u and υ winds at 1200 UTC 24 Jun 2008. (a),(b) The results from the TN sounding station. (c),(d) The results from the LG sounding station.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Fig. 6.
Fig. 6.

Sounding-observed (black line), TPTRS-retrieved (blue line), and model-produced background (red line) pressure (hPa) and potential temperature (K) at 1200 UTC 24 Jun 2008. (a),(b) The results from the TN sounding station. (c),(d) The results from the LG sounding station. Note that in (a) and (c), the black and blue lines are mostly overlapped.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Figure 7 shows a comparison of the retrieved temperature obtained by TPTRS at the first grid point immediately above the terrain against the limited number of surface observations. It can be seen that the TPTRS-retrieved result correctly captures the overall pattern of the temperature distribution, with the value decreasing from the plain area to the mountainous region. The SCC between the retrieved and observed fields can reach 0.75, while the RMSE is 3.2°C. These differences can be explained by the fact that TPTRS does not assimilate any surface temperature observations, and the radars usually do not provide the low-level wind measurements that are needed for thermodynamic retrieval. In addition, the altitudes of the surface stations do not exactly correspond to the TPTRS grids. All these factors may contribute to the discrepancies.

Fig. 7.
Fig. 7.

The temperature (°C) observed by surface stations (numbers) and retrieved (color shading) by TPTRS at the first grid point immediately above the terrain at 1200 UTC 24 Jun 2008.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

d. A comparison of model simulations from experiments No_RAD, RAD_INIT_NoQv, and RAD_INIT

The results of the model simulations from three experiments (No_RAD, RAD_INIT_NoQv, and RAD_INIT) are first examined before the rainfall forecast skill is evaluated. Figure 8 shows the RMSE of the total temperature, total pressure, and water vapor mixing ratio between the 6-h model simulations and observations from surface stations located below 250-m height. It should be mentioned that the number of available surface stations (not shown) is 51 for temperature and pressure, and 19 for water vapor measurements, respectively. It can be seen that except for pressure where the RMSE from three experiments are comparable, the RMSEs of temperature and water vapor from RAD_INIT are significantly lower than those from No_RAD and RAD_INIT_NoQv over the entire 6-h period. The RMSEs of temperature and water vapor fields from RAD_INIT_NoQv are generally between those from No_RAD and RAD_INIT. This intercomparison indicates that using the radar-data-retrieved pressure, temperature, and moisture information to reinitialize the model can provide a positive impact on the following model simulation for at least 6 h.

Fig. 8.
Fig. 8.

Compared against ground stations, the RMSEs of temperature, pressure, and moisture during 0–6-h model simulation produced by three experiments No_RAD (without data assimilation), RAD_INIT_NoQv (without assimilating water vapor), and RAD_INIT (with data assimilation).

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

e. Rainfall forecasts in experiments No_RAD, RAD_INIT_NoQv, and RAD_INIT

Figure 9 displays the rainfall accumulated over 3 and 6 h as observed at surface stations, as well as by model forecasts in No_RAD, RAD_INIT_NoQv, and RAD_INIT experiments. The major features to note in Figs. 9a and 9e are that the observed heaviest precipitations exhibit a λ-shaped pattern, marked as rainbands A and B, respectively. It can be seen that without data assimilation (No_RAD), the model significantly underestimates the rainfall amount at 3 h and produces an inaccurate rainfall pattern at 6 h (Figs. 9b,f). Without the moisture adjustment process (RAD_INIT_NoQv), even when the retrieved wind, temperature, and pressure are assimilated into the model, the forecasted rainfall is still incorrect in terms of both spatial distribution and amount (Figs. 9c,g). In contrast, with the information for the retrieved parameters assimilated into the model, the major λ-shaped rainfall pattern and the intensity can be accurately captured, although rainband A is somewhat narrower than its observed counterpart (Figs. 9d,h). Figure 10 depicts the hourly statistics including ETS, FSS, and SCC. Note that when computing the ETS, the threshold of 5.42 mm h−1 is converted from the criterion for heavy rain used by Taiwan’s Central Weather Administration (CWA). It can be seen that with data assimilation, the model’s forecast skill can be significantly improved, as revealed by all three indices. The ETSs at the third and fourth hours are close to 0.5. These scores are much better than those reported by Liou et al. (2014), in which the multiple-Doppler wind synthesis algorithm and thermodynamic retrieval scheme employed for that research were not designed to deal with terrain. Thus, in Liou et al. (2014), data interpolation from the retrieval domain to the mountainous area of the model was required during the assimilation, which would introduce errors. Furthermore, the FSSs obtained in the RAD_INIT experiment range between 0.4 and 0.7 with a 30-mm accumulated rainfall criterion during the 6-h period. These scores are higher than the results obtained by Do et al. (2023), who explored the impact of assimilating the radar-derived refractivity on the short-term QPF for the same case using the ensemble Kalman filter technique. Note that in Do et al. (2023), the FSS at the first hour was low (see Fig. 12e of that paper), while in our RAD_INIT experiment, this value immediately reached almost 0.5. This is an indication that the model spinup time can be effectively reduced by assimilating the retrieved thermodynamic parameters. Finally, the SCCs from the RAD_INIT experiment are higher than those obtained from No_RAD and RAD_INIT_NoQv experiments, exceeding 0.6 during the entire 6-h forecast period.

Fig. 9.
Fig. 9.

Accumulated precipitation over (a)–(d) 3 and (e)–(h) 6 h produced by (a),(e) rain gauge observations, (b),(f) No_RAD, (c),(g) RAD_INIT_NoQv, and (d),(h) RAD_INIT experiments for SoWMEX IOP8.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Fig. 10.
Fig. 10.

(a) ETS (with 5.42 mm h−1 criterion), (b) FSS (with 30-mm accumulated rainfall criteria), and (c) SCC for No_RAD, RAD_INIT_NoQv, and RAD_INIT experiments for SoWMEX IOP8. The forecast started from 1200 UTC 14 Jun 2008.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

4. QPF with different microphysical schemes

Although the RAD_INIT experiment produced encouraging QPF results, it is known that the selection of a different microphysical (MP) scheme would have generated a different rainfall scenario and that the performance of the MP scheme is often case dependent. Thus, in addition to using the WSM6 scheme, as in the RAD_INIT experiment, the WRF double-moment 6-class (WDM6), Goddard Cumulus Ensemble (GCE), and Morrison (MOR) schemes were also utilized for rainfall forecast after the radar-derived parameters were assimilated into the model. Furthermore, the so-called probability matching (PM; Ebert 2001) method was also employed to merge the QPF results from four different MP schemes. PM is known to have the advantage of being able to maintain the rainfall pattern while at the same time keeping the extreme values.

Figure 11 displays the rainfall distributions after accumulating for 3 and 6 h obtained by using different MP schemes and the PM method. A visual comparison with the observations (Figs. 9a,e) reveals that the main λ-shaped structure of the rainfall can be captured by all four MP schemes and PM, except that GCE fails to reproduce rainband A (Figs. 11a,e). GCE also overforecasts the rainfall amount in the coastal area near 23.0°N. Figure 12 shows a comparison of the ETS, FSS, and SCC scores. It can be seen that none of the MP schemes outperform the others at all time levels. However, the ETS scores from PM can reach almost 0.6 at the third and fourth hour, becoming the highest for three out of six time levels, and are comparable to those obtained with other schemes at the first, second, and sixth hour (except for GCE which is significantly higher at the second hour). The FSS and SCC scores of PM are also found to be similar to those obtained with the other schemes and are never the worst ones.

Fig. 11.
Fig. 11.

Model-generated accumulated precipitation after assimilating radar-retrieved parameters for SoWMEX IOP8 by using the (a),(e) GCE, (b),(f) WDM6, (c),(g) MOR, and (d),(h) PM. The forecast period is 3 h in (a)–(d) and 6 h in (e)–(h). The PM also combines the rainfall forecasts from the WSM6 scheme in the RAD_INIT experiment displayed in Figs. 9d and 9h.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Fig. 12.
Fig. 12.

(a) ETS (with 5.42 mm h−1 criterion), (b) FSS (with 30-mm accumulated rainfall criteria), and (c) SCC scores from the experiments with different microphysical schemes for SoWMEX IOP8. They include WSM6, GCE, WDM6, MOR, and PM.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

5. The second real case study—SoWMEX IOP4

To provide more evidence to support the proposed assimilation procedures introduced in the previous sections, the same experimental design is applied to a second case observed during IOP 4 of SoWMEX. This IOP started at 2100 UTC 1 June and ended at 1500 UTC 3 June. According to Tai et al. (2011), in this case, a stationary front stretching from south of Japan to southern Taiwan was identified. Several lines of convective storms that had formed over the ocean began to interact with the topography as they approached the landmass of Taiwan.

Similar to the first case study introduced in section 3, the WRF Model was reinitialized with the retrieved three-dimensional wind, temperature, pressure, rainwater, and moisture fields at 0600 UTC 2 June, followed by a 6-h forecast of the rainfall.

Figure 13a depicts the accumulated rainfall measured by rain gauges over 6 h. The observed results reveal that the major precipitation area extends over the southwestern plain area, which can be successfully reproduced in the model forecasts after assimilating the radar-retrieved parameters (Fig. 13d). However, the pure model simulation (Fig. 13b) and the experiment without assimilating water vapor (Fig. 13c) fail to forecast the rainfall both qualitatively and quantitatively. Figures 13e–h show the 6-h accumulated rainfall forecasted by repeating the RAD_INIT experiment but using different microphysical schemes and the PM method. It can be seen that even though a different microphysical scheme is employed, the major precipitation area can be well captured by the model after performing the radar data assimilation. Figure 14 provides a quantitative comparison. It is shown that by using PM, the ETS score can reach 0.5 at the third hour, while the FSS approaches 0.7 after the third hour, and the SCC score exceeds 0.5 over the entire 6-h period.

Fig. 13.
Fig. 13.

For SoWMEX IOP4, the accumulated precipitation over 6 h from (a) rain gauge observation, (b) No_RAD, (c) RAD_INIT_NoQv, and (d) RAD_INIT. Using different MP schemes, the model-generated rainfall after assimilating radar-retrieved parameters is denoted in (e) GCE, (f) WDM6, (g) MOR, and (h) PM. The PM also combines the results from RAD_INIT which utilizes the WSM6 scheme.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

Fig. 14.
Fig. 14.

As in Fig. 12, but for SoWMEX IOP4.

Citation: Monthly Weather Review 152, 6; 10.1175/MWR-D-23-0230.1

An overall evaluation of the performance of each MP scheme at every hour for both cases (IOP 8 in Fig. 12 and IOP 4 in Fig. 14) shows that actually, WSM6 yields a better rainfall forecast than the other schemes, followed by PM. However, in theory, double-moment schemes are physically more reasonable than single-moment schemes (Li et al. 2020). Moreover, previous studies also indicated the performance of different MP schemes on rainfall forecast is usually case dependent (Du et al. 2022; Luo et al. 2023). Under this condition, it is suggested to use PM instead of any specific MP scheme for future rainfall forecasts in other cases.

6. Summary and future work

In this study, a multiple-Doppler radar wind synthesis technique and a thermodynamic retrieval method are combined so that one can utilize radar data from only two volume scans to retrieve the three-dimensional wind, pressure, temperature, rainwater mixing ratio, and moisture fields over complex terrain. By using these retrieved meteorological state variables to reinitialize a high-resolution numerical model, it is shown in two real case studies that the model’s spinup time can be effectively reduced, and the accuracy of the forecasted precipitation can be significantly improved up to 6 h. The moisture field is found to play a critical role in correct rainfall forecasting. It is suggested that a combination of different MP schemes (the PM method) be applied to obtain stable and reliable rainfall forecasts. The method proposed in this study can be considered as an alternative to other sophisticated data assimilation schemes (e.g., 4DVAR and EnKF) or simple extrapolation techniques [e.g., McGill Algorithm for Precipitation nowcasting using Lagrangian Extrapolation (MAPLE); Germann and Zawadzki 2002]. The cases selected for this research represent two events with widespread precipitation. In the future, the proposed procedure will be tested on events with scattered convective cells leading to heavy rainfall.

Acknowledgments.

This research is supported by the National Science and Technology Council of Taiwan, under NSTC 112-2111-M-008-025 and NSTC 112-2625-M-008-002.

Data availability statement.

The observational datasets used in this research are obtained from the Atmospheric Science Research and Application Databank (ASRAD; https://asrad.pccu.edu.tw) funded and maintained by the National Science and Technology Council and Chinese Culture University of Taiwan, respectively. The numerical model setups and experimental results are available from the corresponding author Dr. Yu-Chieng Liou (tyliou@atm.ncu.edu.tw). The codes of WISSDOM and TPTRS for retrieving three-dimensional wind and thermodynamic fields can be obtained by request to the corresponding author.

APPENDIX

Pressure and Temperature Conversion Procedures

This appendix introduces the procedures to convert π′ and θc into total pressure P and temperature T and their perturbations. The definitions of all variables can be found in section 2b of the context. The π′ and θc are retrieved by TPTRS. By adding the basic state π0, one gets the total π, followed by computing the total pressure P:
π0=Cp(P0P00)κ,
π+π0=π=Cp(PP00)κ,
P=P00(πCp)1/κ.
The virtual cloud potential temperature perturbation θc retrieved by TPTRS is
θc=θ+(0.61qυqc)θ0.
The iterative procedure explained in section 2c of the context yields the θ′. By adding the basic-state potential temperature θ0, one gets the total potential temperature θ, followed by computing the total temperature T:
θ0=T0(P00P0)κ,
θ+θ0=θ=T(P00P)κ,
T=θ(PP00)κ.
Finally, the pressure and temperature perturbations can also be obtained:
P=PP0,
T=TT0.

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