Abstract

The impact of global positioning system (GPS) radio occultation (RO) soundings on the prediction of severe mei-yu frontal rainfall near Taiwan in June 2012 was investigated in this study using a developed local bending angle (LBA) operator. Two operators for local refractivity (REF) and nonlocal refractivity [excess phase (EPH)] were also used for comparisons. The devised LBA simplifies the calculation of the Abel transform in inverting model local refractivity without a loss of accuracy. These operators have been implemented into the three-dimensional variational data assimilation system of the Weather Research and Forecasting (WRF) Model to assimilate GPS RO soundings available from the Formosa Satellite Mission 3/Constellation Observing Systems for Meteorology, Ionosphere and Climate (FORMOSAT-3/COSMIC). The RO data are found to be beneficial to the WRF forecast of local severe rainfall in Taiwan. Characteristics of assimilation performance and innovation for the three operators are discussed. Both of the local operators performing assimilation at observation levels appear to produce mostly larger positive moisture increments than do the current nonlocal operators performing assimilation on the mean height of each model vertical level. As the information of the initial increments has propagated farther south with the frontal flow, the simulation for LBA shows better prediction of rainfall peaks in Taiwan on the second day than both REF and EPH, with a maximum improvement of about 25%. The positive impact of the RO data results partially from several RO observations near Mongolia and north China. This study provides an intercomparison among the three RO operators, and shows the feasibility of regional assimilation with LBA.

1. Introduction

Global positioning system (GPS) radio occultation (RO) soundings have been assimilated by global and regional models in recent years because of the fact that these data possess high vertical resolution, are free of calibration, and exhibit good accuracy in all weather conditions (Anthes 2011). Assimilations of different RO data (mainly refractivity and bending angle) have shown positive impacts on various predictions of global as well as regional weather phenomena including tropical cyclones (e.g., Zou et al. 1999, 2000; Liu and Zou 2003; Healy et al. 2005; Healy and Thépaut 2006; Healy 2008; Liu et al. 2008; Aparicio and Deblonde 2008; Ma et al. 2009; Chen et al. 2009; Huang et al. 2005, 2010; Chien and Kuo 2010; Poli et al. 2010; Cucurull 2010; Anlauf et al. 2011; Cucurull et al. 2006, 2013; Yang et al. 2014).

Among the RO data, refractivity is the intermediate product after applying the Abel inversion of the bending angle under local spherical symmetry. Conventionally, climatological background information is utilized for the bending angle in order to reduce its vertical variations in the RO retrieval (e.g., Sokolovskiy 2003; Kuo et al. 2004; Cucurull et al. 2013). Thus, assimilation of the bending angle may avoid such impacts from the imposed background, and more importantly, the inherited impacts of the local spherical symmetry assumption in the Abel inversion that may cause negative biases in retrieved refractivity under and near superrefraction (SR) in the lower troposphere (Kursinski et al. 1997, 2000; Sokolovskiy 2003) and in global RO data analyses as verified against conventional soundings (e.g., Kuo et al. 2004; Xie et al. 2006, 2012). By assimilating the bending angle with a local operator in a four-dimensional variational data assimilation system (4DVAR), global modeling showed noticeable improvement in initial temperature analysis in the upper troposphere and lower stratosphere (UTLS), greatly improving the anomaly correlation of global prediction in the European Centre for Medium-Range Forecasts (ECMWF) (e.g., Healy and Thépaut 2006; Healy 2008; Poli et al. 2010; Rennie 2010). Rennie (2010) further demonstrated that assimilating the bending angle indeed can provide a larger positive impact for global forecast than assimilating RO refractivity. Local bending angle assimilation also improved the operational global model performance at the National Centers for Environmental Prediction (NCEP) more than did local refractivity assimilation (Cucurull et al. 2013).

Nonlocal operators that perform a ray-tracing integration to obtain the bending angle have also been developed to improve the impact of RO data on global model prediction (e.g., Zou et al. 1999; Liu and Zou 2003; Healy and Thépaut 2006). In comparison to nonlocal operators for refractivity that take simplification on the actual RO raypath by a straight line (e.g., Sokolovskiy et al. 2005b; Chen et al. 2009; Ma et al. 2009; Anisetty et al. 2014), the nonlocal operator for the bending angle is more complex and time consuming. However, global predictions with 1D or 2D operators for the bending angle show no statistically significant differences in prediction performance, in spite of the tendency for the latter to further reduce the root-mean square of the initial innovations (observed minus model background) in the lower troposphere by around 5% (Healy et al. 2007). With a lower model top and rather limited lateral boundaries, use of a nonlocal operator for the bending angle in a regional model hence became more challenging and turned out to be less encouraging than in the past. Herein, it is reasonable to implement a local bending angle (LBA) operator into a regional model and present its feasibility in weather prediction with comparison to local and nonlocal refractivity operators.

The greater positive impacts on the prediction of global models at ECMWF and NCEP from assimilation of the bending angle has encouraged us to construct an LBA operator and implement it into data assimilation systems. In this paper, we aim to show the feasibility of the LBA operator in a regional model based on the simulation of one interesting case that exhibited severe frontal rainfall in Taiwan. Intercomparisons on the produced initial increments and the ensuing rainfall predictions for the RO operators provide a useful outline of their performance. Section 2 briefly describes the methodology, including the three RO operators. The case description and experimental design including datasets are given in section 3. Results are given in section 4, followed by conclusions in section 5.

2. The methodology

In this study, we focus on the impact of RO observations on regional models using the Weather Research and Forecasting (WRF) Model version 3.3 (Skamarock et al. 2008) along with the WRF Data Assimilation (WRFDA; Barker et al. 2012) system. The WRF Model has been an official regional model for daily operational prediction at the Central Weather Bureau (CWB) in Taiwan. The 3DVAR) technique is used in this study, and the three RO operators have been implemented into WRF 3DVAR with completed tangent linear and adjoint tests.

The RO refractivity is related to the atmospheric state such that

 
formula

where N is the refractivity for the neutral atmosphere, P the total pressure (hPa), T the air temperature (K), and Pw the water vapor pressure (hPa) related to the specific humidity q. The local refractivity operator uses (1) to convert model variables (P, T, q) to local refractivity for comparisons with the RO-retrieved refractivity (as observations) at each observation height (Chen et al. 2009; Huang et al. 2010). To account for the effects of horizontal gradients, the RO refractivity can be integrated along an RO raypath approximated by a straight line (Sokolovskiy et al. 2005a,b) as nonlocal refractivity—a new observable called excess phase. The current nonlocal refractivity operator has been applied on the mean height of each model vertical level to reduce computational cost in this study (see Chen et al. 2009). On average, such a nonlocal refractivity operator without parallelization takes about 100 times more computation than does a local refractivity operator (Zhang et al. 2014).

The bending angle α as a function of the impact parameter a is obtained from the Abel transform of a refractivity profile under a local spherical symmetry assumption given by

 
formula

where is the model refractive index and r is the radius of a point on the raypath from a local curvature center. Thus, this local realization of the bending angle is efficient without precisely modeling the actual raypath for comparison with the RO bending angle. For the LBA operator, we directly compute the contribution to the bending angle between two conjunctive model levels without assuming a smooth refractivity profile as in the RO Processing Package (ROPP) used in the ECMWF global model (Healy and Thépaut 2006). To overcome the singularity in (2) as x approaches a, the denominator can be simplified by evaluating the first factor as the average between the two model levels. Alternatively, Cucurull et al. (2013) has avoided the singularity by transforming the vertical coordinate in (2). We may use the layer intermediate values for both and so that the contribution, for example, from the interval between the ith and (i+1)th levels, can be easily calculated as

 
formula

where . The integral part in (3) for now has an exact form equal to . For a typical vertical interval within several kilometers, use of the layer average for may contribute to only a negligible error. The contribution of model perturbation (relative to the background) to the vertical refractivity gradient may also be ignored because of the inherent large gradient of the environmental background. Such simplifications can avoid perturbing both the factors and thus greatly reduce the complexity of the adjoint codes in 3DVAR. Finally, the contribution above the top of a regional model, as indicated by (2), is accounted for by an extrapolation of the model state following Healy and Thépaut (2006) and given in Yang et al. (2014).

The model assimilation is conducted in the x space with the input of observation impact parameters. However, the inversion [(3)] will incur a large spike on the bending angle for a large background refractivity gradient . An unbounded refractivity gradient would occur as x no longer monotonically increases with height, that is, under conditions of SR when or equivalently the refractivity gradient N km−1(Kursinski et al. 1997; Sokolovskiy 2003). SR may be observed near the top of the marine boundary layer where a large moisture gradient exists (Sokolovskiy 2003; Ho et al. 2015), which inevitably introduces a negative bias into the RO-retrieved refractivity below the SR. When SR is present in the model state, the model refractivity can still be invertible to obtain the bending angle outside the SR layer. However, assimilation of the bending angle through the Abel inversion in the presence of SR becomes an ill-conditioned problem, due to the fact that the original and other different Abel-retrieved refractivity profiles may correspond to the same bending angle. Hence, the RO data below the SR should be discarded as to avoid errors from ambiguity (Sokolovskiy 2003). In this study, the lower troposphere of the initial model state over the 20 RO points has not encountered the SR.

The developed LBA operator has been compared with the LBA operator in the Global Navigation Satellite System Receiver for Atmospheric Sounding (GRAS) Satellite Application Facility (SAF) ROPP for thousands of RO data points from the Taiwan Analysis Center for Constellation Observing Systems for Meteorology, Ionosphere and Climate (COSMIC) (TACC) at CWB, which is a mirror site of the COSMIC Data Analysis and Archive Center (CDAAC; Chen et al. 2010). This atmPrf file compiled in Network Common Data Form (NetCDF; see http://www.unidata.ucar.edu/packages/netcdf/index.html) and contains full-resolution profiles of physical parameters such as dry pressure, dry temperature, refractivity, bending angle, impact parameter, etc., versus the geometric height above mean sea level. Figure 1 shows an example of 31 samples. The larger variations in the deviation with decreased height below 20 km are simply due to the fact that the lower troposphere (LT) contains much higher moisture rates than does the UTLS, with almost linearly increasing temperature with decreasing height so that the LT bending angle by nature will be one order larger than the UTLS bending angle. In terms of fractional errors, the variations in LT may not always be stronger than in the UTLS. For the TACC atmPrf data, the results of the LBA operator agree well with observed bending angle profiles mostly within 2 × 10−5 rad, while the ROPP results are skewed to positive deviations with some overshooting outliers exceeding 5 × 10−4 rad. For TACC brfPrf data, which are routinely used in data assimilation, results of both operators are nearly identical with very good accuracy mostly within 5 × 10−4 rad. The brfPrf data are a low-resolution (currently about 200 m) atmospheric profile in Binary Universal Form for the Representation of Meteorological Data (BUFR) generated by interpolation from the higher-resolution atmPrf data. From the above comparisons, the implementation of (3) is well justified, and allows for conveniently constructing the adjoint codes of the operator in 3DVAR.

Fig. 1.

The difference between bending angles (rad) computed using the National Central University (NCU) forward operator and the observations from CWB TACC for (a) atmPrf (3–5-m resolution) and (b) brfPrf (200-m resolution). (c),(d) As in (a),(b), but using the ROPP operator of GRAS SAF. A total of 31 samples are compared.

Fig. 1.

The difference between bending angles (rad) computed using the National Central University (NCU) forward operator and the observations from CWB TACC for (a) atmPrf (3–5-m resolution) and (b) brfPrf (200-m resolution). (c),(d) As in (a),(b), but using the ROPP operator of GRAS SAF. A total of 31 samples are compared.

For simplicity, the observation errors of the bending angle used in this study essentially follow the specifications of the refractivity errors as described by Chen et al. (2014). At the surface, the bending angle errors of 2.5% and 1.5% are assumed for RO soundings located at the equator and poles, respectively, with a linear latitudinal interpolation in between. The observation errors decrease with height below 12 km, above which no vertical variation is assumed. The a priori bending angle errors specified herein are considerably smaller than the empirical value of 10% for the nonlocal 2D bending angle in Healy and Thépaut (2006). For a nonlocal bending angle, this large surface error of 10% may be assumed, when considering the effects of the horizontal gradient in contribution to ray tracing. The observation errors of the excess phase evaluated by Chen et al. (2011) have been employed in this study.

3. Case study and experimental design

a. Case study

Mei-yu frontal systems usually form during mid-May to mid-June and are one of the severe weather phenomena in East Asia. The mei-yu fronts that form in southeast China may migrate southward through Taiwan and produce heavy rainfall (Chen and Chen 2003). In this study, we chose such a frontal system with extremely heavy rainfall during 11–12 June 2012 over Taiwan. On 11 June, a stationary front extended from the western Pacific to the north of Taiwan and south China as shown in Fig. 2a. By 0600 UTC 12 June, the front moved southward toward Taiwan. Corresponding to the mei-yu front that was situated across southeast China, triggered along and ahead of the mei-yu front in this region are convective clouds associated with precipitation (Fig. 2b), with three major clusters located over southeast China, the East China Sea, and Taiwan, respectively. In response to the intense southwesterly flow and embedded convective systems, intense rainfall occurred over the southwest and central parts of Taiwan on 11 June (shown later). As the mei-yu front moved southward closer to Taiwan on 12 June, unexpected severe rainfall inundated the northern tip of Taiwan—the first nontyphoon weather event in the country calling for a national disaster warning meeting.

Fig. 2.

(a) Surface analysis chart from the Japan Meteorological Agency at 0600 UTC 11 Jun 2012 and (b) an enhanced infrared image from Multifunctional Transport Satellite-2 (MTSAT2; from CWB).

Fig. 2.

(a) Surface analysis chart from the Japan Meteorological Agency at 0600 UTC 11 Jun 2012 and (b) an enhanced infrared image from Multifunctional Transport Satellite-2 (MTSAT2; from CWB).

b. Experimental design

The datasets used for this study are the Formosa Satellite Mission 3 (FORMOSAT-3)/COSMIC RO soundings available from CDAAC, with the atmPrf dataset for the bending angle and the wetPrf dataset for refractivity. The wetPrf dataset is an atmospheric occultation profile interpolated to 100-m-height levels from atmPrf data, but with moisture information included for which gridded analyses or short-term forecasting are used to separate the pressure, temperature, and moisture contributions to the refractivity. The atmPrf dataset is at variable vertical resolutions of 3–5 m, while the wetPrf dataset is at a uniform resolution of 100 m. The wetPrf dataset does not contain bending angle information and operationally has been adopted for assimilation with RO refractivity. The initial background field for the experiments uses the global analysis (FNL) data from the NCEP Global Forecasting System (GFS) at horizontal resolution of 1° × 1°. Some conventional soundings (GTS) (mostly surface observations; see Table 1) were taken from the National Center for Atmospheric Research (NCAR) archive.

Table 1.

Summary of the experiments conducted.

Summary of the experiments conducted.
Summary of the experiments conducted.

The model simulation has three nested domains with horizontal resolutions of 45, 15, and 5 km, respectively (Fig. 3). The third domain of 5-km resolution will be helpful for resolving the motion at smaller scales over the topographical region in Taiwan. There are 35 vertically stretched layers (about half of the model levels are in the lower troposphere below 5-km height) with the model top at 50 hPa (~20-km height). All model domains employ the Yonsei University (YSU) boundary layer parameterization (Hong et al. 2006), the WRF single-moment (WSM) 3-class simple ice microphysics parameterization, and the Kain–Fritsch cumulus parameterization (except for domain 3). The model is integrated for 48 h from the initial time of 0600 UTC 10 June 2012. There are 20 GPS RO soundings found within a ±3-h window of the initial time in domain 1 (Fig. 3, where the plus sign indicates the location of the GPS RO sounding in the assimilation period). In this case, 10 RO soundings are available to the north of China where the colder air mass is located. The experiments are conducted by assimilating refractivity (denoted by REF), LBA, and excess phase (EPH) from the GPS RO data in combination of GTS data (see Table 1). A list of the numerical experiments is given in Table 1. At 0600 UTC 10 June, only two radiosonde soundings are available. The data assimilation is performed for all three of the domains. Most of the RO data are located in domain 1 at 45-km resolution and may still enhance the merits of the observations at higher resolution than GFS FNL. No data were assimilated in the control experiment (CTL). The climatological error covariances (CV3) were used for the background in 3DVAR for all of the assimilation experiments. CV3 is generated using the NCEP method that utilizes 24- and 12-h global forecasts to compute the climatological average difference in the forecasts at the same prediction time (Parrish and Derber 1992; Wu et al. 2002).

Fig. 3.

WRF triply nested domains at 45-, 15-, and 5-km resolution, respectively. The model winds at the lowest level at model initial time (0600 UTC 10 Jun 2012) are shown with GPS RO locations indicated by a plus sign for the location of the RO sounding observed within ±3 h of the initial time. The three green circles mark the removed RO soundings in the sensitivity experiments.

Fig. 3.

WRF triply nested domains at 45-, 15-, and 5-km resolution, respectively. The model winds at the lowest level at model initial time (0600 UTC 10 Jun 2012) are shown with GPS RO locations indicated by a plus sign for the location of the RO sounding observed within ±3 h of the initial time. The three green circles mark the removed RO soundings in the sensitivity experiments.

For the short-term rainfall forecast, application of a dynamic regional model is feasible since the model can resolve the highly nonlinear evolution of the flow over complex terrain. Artificial neural network models (ANNMs) are widely applied to forecasts of hydrological problems (e.g., reservoir inflow) because of the efficacy of these statistical methods in determining the best structure of the neural networks for a time series of data in the training phase and forecasting (test) phase (e.g., Valipour et al. 2013). Autoregressive moving average (ARMA) models (and their variants) have also been applied to forecasts of yearly rainfall over the United States (Valipour 2015). These statistical models work well for monthly or yearly forecasts when provided with a long-time series of observations to build a reliable regression. Since the 48-h rainfall forecasted by the dynamic WRF Model in this study varies significantly with topography and time, it may not be easy to construct a robust statistical regression for an improved forecast. Nevertheless, it is not a goal of this study to improve or extend the WRF Model forecast in combination with some statistical methods (like ANNM or ARMA).

4. Results and discussions

a. Initial modifications

Figure 4 shows the initial moisture increments at 913 hPa for the initialized model state of each experiment after the RO assimilation. The increments herein are the differences between the analysis and the background in the 3DVAR simulations. In general, LBA shows the largest magnitude of moisture increments up to 2.248 g kg−1 (Fig. 4b), followed by REF (Fig. 4a), and then EPH (Fig. 4c). We have also used the atmPrf refractivity data for comparison with assimilations with wetPrf refractivity data and found that the former assimilation with more dense observations results in slightly stronger increments (Fig. 4d). Because the RO refractivity does not vary abruptly in the vertical, the 100-m resolution for wetPrf is sufficient to resolve the vertical refractivity variation.

Fig. 4.

Initial moisture increments (interval of 0.1 g kg−1) at the 913-hPa model level at 0600 UTC 10 Jun 2012 for (a) REF, (b) LBA, (c) EPH, and (d) REFatm.

Fig. 4.

Initial moisture increments (interval of 0.1 g kg−1) at the 913-hPa model level at 0600 UTC 10 Jun 2012 for (a) REF, (b) LBA, (c) EPH, and (d) REFatm.

Near north China, both LBA and REF have larger positive moisture increments than EPH. Indeed, these positive increments are contributed to mostly by the RO soundings located in Mongolia and across northeast and northwest China. There are also noticeable moisture increments to the east of Japan and the Philippines for LBA. However, the impacts from these oceanic increments on local rainfall near Taiwan are significantly limited since they are not associated with precipitation over Taiwan as a result of the prevailing southwesterly wind flow that advects these moisture increments toward the east. Note that the concentration of moisture increments expands to a lateral extent of about 1500–2000 km. Since we have employed a larger horizontal assimilation length scale for moisture than the default in 3DVAR, a wider spreading of the effects of RO path observation is realized.

From Fig. 4, most of the moisture increments over the RO locations are primarily in phase at 913 hPa for the three operators (e.g., the Philippines and over northeast China). But, EPH increments can occasionally be out of phase relative to both LBA and REF increments (e.g., just east of Japan). Note that the EPH has performed an average on model mean height and a horizontal ray integration complicates the increment differences from those of the two local operators.

To further realize the different performance levels of the three operators, the vertical profiles of the initial moisture difference at each model level between CTL and the assimilation experiments (REF, LBA, and EPH) are shown in Fig. 5 at the locations of six selected RO soundings, four located on the northern continent and two over the ocean (just east of Japan and about 2000 km east of the Philippines). These six RO soundings were selected since Fig. 4 has revealed larger deviations at these locations. For RO soundings over land (Figs. 5a–d), the induced modifications are roughly similar for the two local operators (REF and LBA), with somewhat larger magnitudes as compared to those for the nonlocal operator (EPH). As is also revealed by Fig. 4, larger differences for the three operators are found over the ocean (Figs. 5e,f). Negative (positive) differences indicate that the CTL is drier (moister) than the assimilated states. Thus, the LBA results tend to exhibit greater moisture at lower levels when averaged over land and ocean for all 20 of the profiles (figures not shown), but both LBA and REF are still comparable for the soundings over land. In general, the EPH results appear to be drier as compared to those of the local operators.

Fig. 5.

Vertical profiles of moisture difference (g kg−1) at various sounding locations at the model initial time between CTL and the assimilation runs, REF (red), LBA (blue), and EPH (green).

Fig. 5.

Vertical profiles of moisture difference (g kg−1) at various sounding locations at the model initial time between CTL and the assimilation runs, REF (red), LBA (blue), and EPH (green).

Figure 6 shows the vertical profiles of the initial temperature differences between CTL and the assimilation experiments (REF, LBA, and EPH) at the locations of the six RO soundings. As a result of the tiny amount of moisture at the upper levels, the temperature is relatively more modified as compared to the moisture modifications (Fig. 5). We find that the characteristics of the vertical profiles of the temperature difference for the three operators are qualitatively similar. There is strong warming (herein large negative values) for REF below 5-km height at the sounding location (46.1°N, 111.18°E) while contrasting weaker warming is found for the other two operators (Fig. 6a). However, there is stronger cooling for REF around 10-km height at the nearby sounding (50.6°N, 125.11°E) (Fig. 6b). The modifications for the three operators are more similar over lower levels (e.g., lower than 6-km height) at the two other inland soundings (47.44°N, 84.77°E) and (54.04°N, 115.63°E). For the two oceanic soundings (33.2°N, 141.4°E and 11.72°N, 146.3°E), the modifications below 5-km height for both LBA and EPH are much less than those for REF (more warming). Throughout most of the upper levels, REF also provides generally larger modifications (up to 2°C) compared to LBA and EPH.

Fig. 6.

As in Fig. 5, but for the temperature difference (°C).

Fig. 6.

As in Fig. 5, but for the temperature difference (°C).

The assimilation performance can also be indicated by the data ingestion and innovation (the observation O minus the model background B or OB). Without loss of general characteristics, we may select the RO points where the moisture increments are more prominent. Figure 7 shows the vertical structures of OB at the two selected continental RO soundings over 46.1°N, 111.18°E and 50.6°N, 125.11°E for REF, LBA, and EPH. The innovation in WRF 3DVAR is generally marked as void data (reset to zero by default) when the magnitudes of the innovation exceed 5 times the observation error. Thus to avoid confusion, a zero line is not plotted in the figures. As can be seen in Fig. 7, almost all of the refractivity soundings are assimilated by the operator. The magnitude of the refractivity innovation increases with decreased height, but the data are still ingestible with respect to the specified observation error. With 100-m resolution (RO observations from wetPrf), many details in the vertical structure are indistinguishable from those of atmPrf (figures not shown). The magnitudes of the refractivity innovation are about the same as the observation errors below about 10-km height. Over these RO points, the innovations are mostly negative below about 7-km height, indicating the background possesses larger refractivity. Assimilation of these refractivity data thus will reduce the background refractivity by either increasing the temperature (as warming) or decreasing the moisture (as drying), or modulating both, according to (1).

Fig. 7.

Vertical profiles of innovation (OB) at two selected RO points over (left) 46.1°N, 111.18°E and (right) 50.6°N, 125.11°E for (top) REF, (middle) LBA, and (bottom) EPH. Red lines are a priori observation errors for REF, LBA (after being multiplied by 106), and EPH (after being multiplied by 10−3).

Fig. 7.

Vertical profiles of innovation (OB) at two selected RO points over (left) 46.1°N, 111.18°E and (right) 50.6°N, 125.11°E for (top) REF, (middle) LBA, and (bottom) EPH. Red lines are a priori observation errors for REF, LBA (after being multiplied by 106), and EPH (after being multiplied by 10−3).

The vertical profiles of bending angle innovation are similar to those of refractivity innovation, in spite of very sharp oscillations (most of them are caused by the resets). We observe that the bending angle data are more easily declined by the imposed strict quality control, especially at upper levels, indicating that either the background departure from the observation is relatively large or the observation error is set relatively small. Note that the current specification of the bending angle observation error is about 2.5% at the surface (as used for reflectivity). We found that with this criterion, the ingestion rates of the entire set of vertical observations for all 20 of the profiles range from 61% to 83%, while the ingestion rate below 5 km may exceed 90%. When a larger observation error of 10% is specified following Healy and Thépaut (2006), the maximum of the rejection rates for the 20 RO soundings may decrease to only 8.1% and most of them are less than 4%.

For the excess phase assimilation, all the data (herein averaged at each model mean height) have been assimilated with commensurable magnitudes of innovation and observation error. We found that as these two examples clearly show, except at much lower levels, the excess phase innovation varies essentially like the vertically smoothed refractivity innovation. However, over other oceanic RO soundings, the two innovations (EPH and REF) in the lower troposphere the deviation is relatively larger (figures not shown), which might indicate the importance of nonlocal RO modeling over oceanic regions with a stronger horizontal gradient (e.g., Sokolovskiy et al. 2005a,b; Chen et al. 2009). In this frontal case, the oceanic RO soundings play a much less influential role in the forecasting of local rainfall over Taiwan.

b. Comparison against global analysis

The performance of the devised LBA has been verified during the analysis against collocated radiosondes in simulations of the intense rainfall induced by southwesterly flow in south Taiwan (Yang et al. 2014). As in this study, LBA has moistened the boundary layer southwest of Taiwan more than REF. At 0600 UTC 10 June (the model initial time), there are no conventional GTS soundings available for the verification on the increments produced by the three RO operators. Because the initial background fields in the experiments use NCEP FNL with assimilation of RO data, we will compare the initial analyses from the three operators against the ECMWF interim reanalysis (Dee et al. 2011; ERA-Interim) at 0.75° × 0.75°, which assimilates RO data as well. Figure 8 shows the differences of the initial moisture (water vapor mixing ratio) from ERA-Interim at 850 hPa for the control and assimilation experiments (REF, LBA, and EPH). The moisture differences between the control experiment and ERA-Interim indicate that the NCEP FNL is mostly drier except for some sporadic regions, which include areas coincident with RO observations over the continent (Fig. 8a). The water vapor in these areas has been increased in the assimilation experiments, with the LBA demonstrating the greatest increase, followed by REF and then EPH. The larger increase northeast of China by LBA is also consistent with the previous results (cf. Figs. 4b and 5). Although these differences in terms of their magnitudes are not remarkable, as seen in the figures, they turn out to play an important role in influencing the ensuing model forecasts. The intercomparisons also substantiate that the regional RO assimilation has further contributed to initial moisture increments.

Fig. 8.

Initial moisture differences (g kg−1) at 850 hPa from ERA-Interim for (a) CTL, (b) REF, (c) LBA, and (d) EPH.

Fig. 8.

Initial moisture differences (g kg−1) at 850 hPa from ERA-Interim for (a) CTL, (b) REF, (c) LBA, and (d) EPH.

c. Simulated circulation

As mentioned before, the initial analyses with both atmPrf and wetPrf refractivity data in general are similar, which leads to similar forecast performance. Hereafter, we only show the forecast results with assimilation of the wetPrf refractivity data. We show the simulated cloud hydrometeor (vertically integrated cloud water) and flow at 956 hPa for CTL (Fig. 9a) and the difference between LBA and CTL at 24 h (Fig. 9b). At this time, the front is roughly aligned west–east from south China to the East China Sea (Fig. 2a). There is strong southwesterly flow at low levels that impinges Taiwan with no appreciable difference in the large-scale flow between CTL and LBA. Distributions of the convective clouds for both CTL and LBA agree well with the observed image (Fig. 2b). Convective clouds are somewhat more pronounced across southeast China at 24 h for LBA than CTL and move southward with time toward Taiwan (Fig. 9c). At 33 h, cloud hydrometeors exhibit positive and negative differences near the southeastern coast of China between CTL and LBA. These mixed results are reasonable since their associated clouds are not completely in phase. However, at 39 h, it becomes clearer that more convective clouds have reached the west coast of Taiwan for LBA (Fig. 9d). As shown later, these enhanced clouds lead to the most intense rainfall on the second day over the Central Mountain Range (CMR) in Taiwan for LBA. These differences in the resultant cloud convection are attributable to the initial differences in the RO vicinity over north China, as shown earlier.

Fig. 9.

Vertically integrated cloud hydrometeors (mm) in domain 2 at 24 h for (a) CTL and the difference between LBA and CTL at (b) 24, (c) 30, and (d) 39 h. The horizontal wind at 956 hPa is overlaid for CTL in (a) and for LBA in (b)–(d).

Fig. 9.

Vertically integrated cloud hydrometeors (mm) in domain 2 at 24 h for (a) CTL and the difference between LBA and CTL at (b) 24, (c) 30, and (d) 39 h. The horizontal wind at 956 hPa is overlaid for CTL in (a) and for LBA in (b)–(d).

When the front moves farther south, the differences among the four experiments become more pronounced, as seen in Fig. 10. At 42 h, both LBA and REF show more prefrontal onshore flow toward Taiwan, while the flow for both CTL and EPH is more parallel to the northwest coast of Taiwan. The moisture field exhibits a frontal boundary near northwest Taiwan, where the drier northerly flow is in confrontation with the moister southwesterly flow. It appears that this flow convergence takes place closest to north Taiwan for LBA, and the accompanying upslope wind is also most noticeable.

Fig. 10.

Moisture (g kg−1) and horizontal wind (m s−1) in domain 2 at 956 hPa at 42 h (1800 UTC 11 Jun 2012) for experiments (a) CTL, (b) REF, (c) LBA, and (d) EPH.

Fig. 10.

Moisture (g kg−1) and horizontal wind (m s−1) in domain 2 at 956 hPa at 42 h (1800 UTC 11 Jun 2012) for experiments (a) CTL, (b) REF, (c) LBA, and (d) EPH.

d. Local rainfall prediction

With the simulated flow patterns in mind, resultant local rainfall simulations are analyzed. Figure 11a shows the daily rainfall observations from the CWB on the first day (0600 UTC 10 June–0600 UTC 11 June) when the front is still north of Taiwan (Fig. 2a). Most of the observed rainfall occurred over the central and southern mountainous parts of Taiwan, with peaks of 421 and 642 mm, respectively, somewhat underpredicted by the CTL (Fig. 11b) and other experiments. The REF (Fig. 11c) and LBA (Fig. 11d) slightly improve the central rainfall on the first day compared to CTL. All three of the RO assimilation experiments in general obtain quite similar rainfall extremes and patterns. For investigation of the impact of additional available GTS data, we also conducted three experiments by combining GTS data (mostly surface observations) with REF, LBA, and EPH. As seen in Fig. 11, their combinations yield a small improvement with slightly enhanced amounts for the southern rainfall in Taiwan (Figs. 11f–h).

Fig. 11.

The (a) observed and simulated rainfall (with an interval of 50 mm) at domain 3 during 0–24 h (the first day) for experiments (b) CTL, (c) REF, (d) LBA, (e) EPH, (f) REF+GTS, (g) LBA+GTS, and (h) EPH+GTS.

Fig. 11.

The (a) observed and simulated rainfall (with an interval of 50 mm) at domain 3 during 0–24 h (the first day) for experiments (b) CTL, (c) REF, (d) LBA, (e) EPH, (f) REF+GTS, (g) LBA+GTS, and (h) EPH+GTS.

Figure 12 shows the daily rainfall on the second day (0600 UTC 11 June–0600 UTC 12 June) as the front had already migrated to the northern tip of Taiwan. The observed rainfall (Fig. 12a) shows that the rainfall extends to northern Taiwan on the second day as a result of the impingement of the front toward north Taiwan (Fig. 2a). As seen in Fig. 10, the intense southwesterly flow has encountered the front near north Taiwan. Consequently, a peak in accumulated rainfall of 506 mm is observed near the northwest coast of Taiwan, while the earlier extremes are still present to the south. The predicted accumulated rainfall over the central and southern parts of Taiwan are 359.6 and 316.2 mm, respectively, for CTL (Fig. 12b), which are considerably smaller than LBA. In fact, compared to the other experiments, LBA (Fig. 12d) appears to better capture the observed rainfall with four peaks (Fig. 12a). For example, it obtains more intense central and southern peaks (403.7 and 465.2 mm, respectively), which are in better agreement with the observed values (431 and 656 mm, respectively). In addition, LBA appears to show some capability in predicting the intense prefrontal rainfall (194.9 mm) near the northwest coast of Taiwan. REF also captures well the central and southern peaks (303.9 and 449.6 mm, respectively), and the northern peak (188.4 mm), as shown in Fig. 12c. EPH exhibits similar patterns of major rainfall, but with considerably reduced intensity (Fig. 12e). For the northern rainfall, the nonlocal operator seems to produce weaker intensity (around 100 mm) than do the two local operators, possibly as a result of the effects of the decreased moisture increments over north China at the aforementioned initial time. In summary for the RO impacts, the improvement realized by LBA is about 24% over REF and EPH for the observed central rainfall peak (431 mm) and about 25% over EPH for the observed farthest south rainfall peak (548 mm). On the second day, assimilations of combining GTS data and RO data have not improved the prediction of the three major rainfall areas (Figs. 12f–h) as compared to assimilations with the RO data only.

Fig. 12.

As in Fig. 11, but for the second day.

Fig. 12.

As in Fig. 11, but for the second day.

With more than 399 automatic rain gauges over Taiwan, we can further evaluate the performances of the experiments for local rainfall prediction. The verification is conducted on model grids covering Taiwan only. The equitable threat score (ETS) is computed for rainfall verification, which is defined as

 
formula

where H is the number of hits (correct forecasts); F and O are the numbers of samples (i.e., grid points) in which the rainfall amounts are greater than the specified threshold for the forecast and the observations, respectively; and R = FO/N, representing the random forecast for a given N (the number of points being verified). The forecast skill increases with higher ETS, which will be equal to 1 for a perfect prediction, with both F and O completely overlapping with each other. Chien and Kuo (2010) also used ETS to evaluate the impact of the RO refractivity on 2007 mei-yu system predictions. Figure 13 shows the ETS against the rainfall observations with respect to different thresholds. For the first day (Fig. 13a), the ETSs are best for EPH until 25 mm, followed by CTL. Both EPH and CTL are better than REF and LBA until 130 mm. For larger thresholds beyond 130 mm, the CTL, REF, LBA, and EPH results are similar. When GTS data are combined with RO data, ETS is greatly improved for the thresholds of 70–350 mm. Indeed, EPH+GTS shows the highest skill for 50–100 mm, while REF+GTS improves the larger rainfall above 130 mm.

Fig. 13.

(a) The ETSs for experiments CTL, REF, LBA, EPH, REF+GTS, LBA+GTS, and EPH+GTS during 0–24 h. (b) As in (a), but for 24–48 h.

Fig. 13.

(a) The ETSs for experiments CTL, REF, LBA, EPH, REF+GTS, LBA+GTS, and EPH+GTS during 0–24 h. (b) As in (a), but for 24–48 h.

For the second day (Fig. 13b), EPH outperforms the others for the thresholds of 100–150 mm, above which its ETSs drop more quickly than for either LBA or REF. REF is better than LBA until 100 mm and LBA is superior for thresholds between 130 and 150 mm; above that level it ranks second behind REF. Indeed, REF performs best in predicting the rainfall larger than 200 mm and outperforms LBA by about 0.02–0.06 in ETS; this may indicate the fact that REF is associated with slightly smaller phase errors of such intense rainfall compared to the observations (Fig. 12). The combination of GTS data with RO data has generally improved local rainfall predictions for smaller thresholds. It is noticeable that REF+GTS obtains the highest ETSs for thresholds below 100 mm. All the ETSs on the second day for the three RO operators are considerably higher than CTL, and they are generally about 0.25 for intense rainfall in the range of 100–200 mm. The forecast skill for intense rainfall in this study is reasonable and acceptable compared to other mei-yu frontal rainfall predictions (e.g., Chien and Kuo 2010).

e. Impact of continental RO observations

To understand how the induced rainfall extremes might differ with respect to the RO soundings, we have conducted two sensitivity experiments. LBA-REM2 removes the two RO soundings near east Mongolia (46.1°N, 111.18°E) and northeast China (50.6°N, 125.11°E) from the LBA experiment, and LBA-REM3 removes one more sounding north of Lake Baikal (56.53°N, 106.49°E) from the LBA-REM2 (Fig. 3). These two experiments were considered for LBA since it already highlighted better rainfall predictions. Figure 14 shows the daily rainfall on the second day for the two experiments. Compared to LBA, both LBA-REM2 and LBA-REM3 have similar rainfall patterns, but with slightly reduced maxima over north Taiwan. Note that such reductions in local rainfall prediction are the results of the initial tiny differences, due to the removal of two or three remote RO soundings away from Taiwan. These two experiments illustrate the sensitivity of local rainfall predictions to assimilated RO data.

Fig. 14.

Simulated rainfall totals (with an interval of 50 mm) during 24–48 h for experiments (a) LBA-REM2 and (b) LBA-REM3.

Fig. 14.

Simulated rainfall totals (with an interval of 50 mm) during 24–48 h for experiments (a) LBA-REM2 and (b) LBA-REM3.

The remote connection of the induced moisture increments with the downstream weather is physically based. As the moisture increments introduced by the three continental RO soundings have been transported upward and well mixed with the frontal system, the moisture information may propagate farther southward toward Taiwan by the flow near northern China (see Fig. 3). As seen in Fig. 4, moisture increments from the RO soundings may extend from the RO location with a radius of about 600–800 km. Such a wide spreading of moisture facilitates mixing with the frontal system. The remote connection built by the induced moisture increments then depends on whether the downstream weather development is sensitive to the locally modified upstream atmospheric condition.

5. Conclusions

The RO data are found to have a positive impact on the local rainfall prediction of a mei-yu frontal system near Taiwan in June 2012 when assimilated by 3DVAR with a newly developed local operator for the bending angle. LBA results are compared to a local operator for refractivity, and a nonlocal operator for excess phase (integrated refractivity along a RO raypath), the latter of the two having been investigated (e.g., Chen et al. 2009), and the results are found to comparable. The performance of LBA has compared well to that of the ROPP LBA in GRAS SAF used by ECMWF. Part of the positive impact in the weather forecast is found to result from assimilation of the RO observations near Mongolia and north China, where initial moisture increments are mostly positive as produced by the RO data. Both LBA and REF assimilate RO data at their observation levels, but for computational efficiency EPH currently assimilates excess phase data on the mean height of each model level. Both LBA and REF produce more intense initial positive moisture increments over the northern continent than EPH. Consequently, the prediction of intense rainfall in Taiwan is improved by LBA and, to a lesser extent, by REF. However, in terms of evaluations of forecast skill for various rainfall thresholds, EPH generally shows some advantages at medium-range thresholds. For this case, assimilation with LBA slightly outperforms or is comparable to that with REF for the prediction of severe rainfall in Taiwan. A similar conclusion was also found when using an ensemble Kaman filter assimilation with LBA that better predicts severe rainfall in south Taiwan associated with a strong southwesterly flow in early summer (Yang et al. 2014).

The improvement on rainfall prediction for LBA is mainly attributed to the larger positive moisture increments over north China. Larger increments may be produced by the RO operator in the presence of larger innovations (the difference between B and O ) when taking into account the minimization of the cost function with specified a priori observation errors and estimated background errors. In this sense, the different responses of the increments from the three RO operators are a complicated combination of the processes involved in the minimization. For a larger innovation, the resulting increment may not be larger when the a priori observation errors are specified as being relatively larger. Since both REF and LBA have shown about the same magnitudes of the increments, we believe that these comparable increments are reasonable as a reflection of large departures between B and O. The smaller increments for EPH may be partially due to the fact that the current operator assimilates the average observation on model mean height.

To improve the accuracy of the initial analysis, specifying the a priori observation errors for the bending angle is essentially important. In this study, without realistic estimation, the bending angle observation errors have simply been assumed to have a value of 2.5% at the surface, as does the estimated error used for local refractivity. Such observation errors for the bending angle remain relatively smaller compared to the typical magnitudes of the innovation, thus sometimes leading the bending angle to be an outlier. With larger observation errors, bending angle assimilation using the current operator may acquire approximately the same data acceptance rate as in refractivity assimilation. In this sense, the bending angle assimilation will be as robust as refractivity assimilation. In the future, an optimal assimilation strategy that takes into account the uncertainty of physically based observation errors should help better us to utilize the RO bending angle (e.g., Kuo 2014).

Another challenge associated with LBA assimilation is superrefraction (SR) present in the model state. SR may occur in the lower troposphere (e.g., Sokolovskiy 2003; Xie et al. 2006; Ho et al. 2015) and will introduce a negative bias in the Abel-retrieved refractivity below the layer of SR. However, the inverted bending angle will become unbounded when approaching an SR layer and produce an unrealistic artifact for assimilation. Furthermore, with an SR layer, the model refractivity may also not correspond to the true RO bending angle, because of the ill-conditioned problem (Sokolovskiy 2003). In this study, the initial model background did not encounter SR even for the oceanic RO points. In cycling assimilations, however, the background from the regional model forecast may likely produce local SR. The COSMIC follow-on mission (COSMIC-2), commencing in 2016, will provide much more RO sounding data over lower latitudes than COSMIC, thus enriching the volume of observation information for marine boundary layers that are potentially associated with SR. This demands further investigation of LBA assimilation in the presence of SR.

Acknowledgments

This research is supported by Ministry of Science and Technology, Taiwan. Discussions with Dr. Bill Kuo at UCAR were beneficial to this study. Our laboratory team—I-Hsin Wu, Wen-Sen Teng, and Chun-Tze Wu—helped on this research work.

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