1. Introduction
There are many diagnostic parameters developed in meteorology to diagnose or predict various weather elements in short-range (from hours to a few days) forecasts, such as convective available potential energy (CAPE) for convection (Moncrieff and Miller 1976), Haines index for fire weather (Haines 1988), the fog-diagnostic scheme (Zhou and Du 2010), and the icing scheme for aviation weather (S. Silberberg 2014, personal communication). For long-range forecasts, there is the monsoon index (Wang and Fan 1999), El Niño–Southern Oscillation (ENSO) index (Wolter and Timlin 1993), Madden–Julian oscillation (MJO) index (Ventrice et al. 2013; Kiladis et al. 2014), and North Atlantic Oscillation (NAO) index (Hurrell 1995). In this study we will propose two new parameters, moist vorticity and moist divergence, for diagnosing heavy rain locations.
Heavy rain is an outcome of combined favorable dynamic and moisture conditions. It has been shown that combining dynamic and moisture factors together in a forecast method can greatly improve heavy rain prediction [e.g., Doswell et al. (1996), where precipitation efficiency and duration are another two important elements considered in their method]. The extension of potential vorticity (PV) to moist potential vorticity (MPV) is an example of combining dynamic and moisture factors (Bennetts and Hoskins 1979). Another example is the generalization of the MPV, that is, generalized moist potential vorticity (GMPV; Gao et al. 2004a). Both the MPV and GMPV will be further explored in our study. How to properly include moisture effects into a dynamic factor is not obvious. We use this study to demonstrate a feasible way to include moisture effects within a dynamical parameter and how this inclusion improves the parameter’s performance through a case study and systematic evaluation. The goal of this study is not to suggest that the application of this parameter can replace a conceptual model–based, multiscale forecast process, but simply to demonstrate how the incorporation of moisture effects in the parameter can improve the correlation between areal coverage of the parameter and the observed rainfall location. In the study, a regional heavy rain event that occurred on 1 July 1991 is used for a detailed analysis and method test. An independent dataset of 41 daily regional heavy rain cases from the notorious flooding year of 1998 in eastern China is used for a systematic evaluation to confirm the robustness of our approach. In the rest of this paper, the datasets and the heavy rain cases will be described in section 2, the results are presented in section 3, and a summary and discussion are provided in section 4.
2. Dataset and case description
Two datasets are used in this study. The first one is the observed precipitation from 754 weather stations across mainland China (Fig. 1). The stations are relatively uniformly spaced throughout eastern China and more sparsely distributed across western China. Most stations in eastern China are located in the East Asian monsoon region and experienced at least 1 day of heavy rain (filled circles) during the period 1960–2010. A daily local heavy rain (LHR) event is defined when the precipitation amount accumulated over a 24-h period (from 1200 UTC to 1200 UTC on the following day) exceeds 50 mm at a station. When two or more adjacent stations (less than 200 km apart) meet the LRH criteria at the same time, a daily regional heavy rain (RHR) event is defined. The term heavy rain used in this study refers to a daily RHR event. These observed precipitation data are interpolated onto a 0.5° latitude–longitude grid using the ordinary Kriging method of Chen et al. (2010), which is used for the threat score (TS) calculation in section 3. The second dataset is the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim), which is used for calculating various diagnostic parameters. The ERA-Interim is on a 0.75° (~80 km) latitude–longitude grid with standard pressure levels from 1000 to 50 hPa (Dee et al. 2011). This dataset is available online (http://apps.ecmwf.int/datasets/data/interim-full-daily). Given that the ERA-Interim is about 0 km in spatial resolution, only long-lasting (24 h) large-scale widespread regional heavy rain events (more than 10 adjacent stations with observed rainfall exceeding 50 mm day−1) caused by obvious synoptic-scale circulation systems (Qian 2013) are used in this study (see Table 1), while those isolated local heavy rain events probably caused by individual convective systems are excluded.
Distribution of 754 weather stations in China. Filled (open) circles indicate stations with (without) heavy rain days (≥50 mm day−1) from 1960 to 2010.
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
Description of the 41 daily regional heavy rain events that occurred in eastern China in 1998.
From 30 June to 12 July 1991, a prolonged heavy rain event occurred over the lower Yangtze River basin, in response to a series of short waves moving eastward across the area (Ding 1993). On 1 July 1991, 22 stations exceeded 50 mm day−1 of rainfall with a precipitation maximum of 201.8 mm day−1 and an average precipitation total of 96.5 mm day−1. The event on 1 July (from 1200 UTC 30 June to 1200 UTC 1 July) is showcased in this study. During the summer of 1998, heavy rain events frequently occurred over the Yangtze River basin, resulting in the most severe flooding on record and leading to the deaths of more than 3000 people. Direct economic losses of about CNY 167 billion [equivalent to about $28 billion (U.S. dollars)] were associated with the flooding (National Climate Center of China 1998). There were 41 daily regional heavy rain episodes during that summer based on the criterion of having at least 10 adjacent stations exceeding 50 mm day−1 (a 24-h period centered at 0000 UTC of a day) rainfall at each station. These 41 cases are listed in Table 1 with a brief description including the date and number of stations with precipitation exceeding 25, 50, or 100 mm day−1, as well as associated synoptic-scale systems. On 7 July 1998, there were two regional heavy rain events over northwestern and northeastern China. Among these 41 cases, most of them occurred along or south of the Yangtze River. They were mainly associated with the synoptic-scale frontal boundary (horizontal wind shear, convergence zone, and reversed trough) and extratropical cyclones (Table 1). These 41 cases are used for systematic evaluation in this study.
3. Dynamic and moisture parameters in diagnosing heavy rain
a. Vorticity, divergence, and relative humidity
Horizontal distribution of vorticity at 850 hPa (s−1; contours with an interval of 2 × 10−5 s−1) at (a) 1200 and (b) 1800 UTC 30 Jun and at (c) 0000, (d) 0600, and (e) 1200 UTC 1 Jul 1991; (f) the average of (a)–(e). Filled (open) circles indicate the stations with rainfall exceeding 50 (25–50) mm during the 24-h period from 1200 UTC 30 Jun to 1200 UTC 1 Jul 1991.
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
As in Fig. 2, but for divergence at 850 hPa (s−1; contours with an interval of 1 × 10−5 s−1).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
Horizontal distribution of relative humidity 
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
b. Moist potential vorticity and generalized MPV
MPV has been extensively used in studies of conditional symmetric instability (Emanuel 1983, 1988; Bennetts and Sharp 1982; Schultz and Schumacher 1999) and the generation of MPV in extratropical cyclones (Cao and Cho 1995; Martínez-Alvarado et al. 2010). MPV has also been used in the analysis of heavy rainfall (Shou and Li 1999; Clark et al. 2002; Gao et al. 2004a,b; Deng and Gao 2009; Novak et al. 2009; Zhou et al. 2010). Gao et al. (2004b) argued that maximum MPV and maximum surface rainfall are nearly collocated as a result of the impact of heat and mass forcing on the development of MPV and argued that MPV can, therefore, be used to track the propagation of rain systems (see their Figs. 1–4). However, there is only one case visually examined in Gao et al. (2004b). In this study, we will systematically and quantitatively examine the performance of MPV in diagnosing heavy rain locations. Figure 5 shows the vertical cross section of MPV along with its two components (MPV1 and MPV2) for the 1 July 1991 regional heavy rain case. MPV has virtually no ability to depict a heavy rain area (Fig. 5a) because of the opposite signals coming from the MPV1 (Fig. 5b) and MPV2 (Fig. 5c) over the heavy rain region. The two components can depict the heavy rain location better than MPV can itself (e.g., the maximal axes of positive MPV1 and negative MPV2 extend to the lower level right over the heavy rainband). To examine their horizontal distribution, Fig. 6 shows the MPV and its two components at 850 and 925 hPa. Consistent with Fig. 5, the MPV (Figs. 6a,d) does not match the heavy rain area because of the opposite signs of the two components. Although the MPV1 (Figs. 6b,e) does cover most or at least part of the heavy rain area, it is too widespread spatially, resulting in a high false alarm rate. The MPV2 (Figs. 6c,f) is the best among the three with much reduced false alarms but misses many heavy rain spots such as the heavy rainband in the western end of the Yangtze River and the heavy rain area in northeastern China because of a lack of coverage. For the MPV, MPV1, and MPV2, their performance is better at 850 than 925 hPa. Therefore, they will be evaluated at 850 hPa hereafter.
Vertical–latitude cross sections of (a) MPV, (b) MPV1, and (c) MPV2 [potential vorticity units (PVU); where 1 PVU = 10−6 K kg−1 m2 s−1; contours with an interval of 0.5 PVU] along 114.75°E at 0000 UTC 1 Jul 1991. The thick horizontal line at the surface represents the area of heavy rain. The shading indicates positive PV with values larger than 0.5 PVU.
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
(a) MPV, (b) MPV1, and (c) MPV2 at 850 hPa (contours with an interval of 0.5 PVU) at 0000 UTC 1 Jul 1991. (d)–(f) As in (a)–(c), but for 925 hPa. Filled (open) circles indicate the stations with rainfall exceeding 50 (25–50) mm day−1. Positive (negative) PV is shown by solid (dashed) lines, where cyan (brown) shading covers values >0.5 PVU (<−0.5 PVU).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
Impact of k value on the relative humidity–based weight at 0000 UTC 1 Jul 1991: (a) k = 1, (b) k = 10, and (c) k = 20 for horizontal distribution (unitless; contours with an interval of 0.1) and (d) k = 1, (e) k = 10, and (f) k = 20 for vertical distribution (unitless; contours with an interval of 0.2). Filled (open) circles indicate the stations with rainfall exceeding 50 (25–50) mm day−1 in (a)–(c), and the heavy rain area is indicated by the filled triangles in (d)–(f).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
As in Fig. 5, but for (a) GMPV, (b) GMPV1, and (c) GMPV2 (k = 10).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
As in Fig. 6, but for (a),(d) GMPV; (b),(e) GMPV1; and (c),(f) GMPV2 (k = 10).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
Variation of TS with the threshold of parameters, averaged over the 41 daily heavy rain cases occurring in eastern China during 1998. The black dots correspond to the optimal thresholds for (a) MPV, (b) MPV1, (c) MPV2, (d) GMPV, (e) GMPV1, and (f) GMPV2, respectively.
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
Average TS of various parameters from the MPV and GMPV groups in depicting the heavy precipitation area (≥25 mm day−1) based on 41 daily heavy rain cases occurring in eastern China during 1998. The TS difference between MPV and GMPV is statistically significant at the 99% level based on the Student’s t test.
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
TS and std dev (with respect to mean) of various parameters in depicting heavy rain locations (≥25 mm day−1) based on 41 daily cases occurring in eastern China in 1998. Here, TSmean, TSbest, and TSworst are the mean, best, and worst TS for a parameter. Statistical significance of an improvement is based on a Student’s t test. The optimal threshold used for each parameter is also listed based on the 41-case average.
The reason why the GMPV is superior to the MPV is in the more realistic treatment of moisture in the heavy rain area when replacing the equivalent potential temperature with the generalized equivalent potential temperature. To demonstrate this, Figs. 12 and 13 compare the horizontal and vertical distributions and gradients of 
(left) The equivalent potential temperature and (right) the generalized equivalent potential temperature (k = 10) at 850 hPa at 0000 UTC 1 Jul 1991 (K; contours with an interval of 4 K).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
Vertical–latitude cross sections of (a) the equivalent potential temperature (K; contours with an interval of 4 K), (b) the generalized equivalent potential temperature (K; contours with an interval of 4 K), (c) the vertical gradient of 
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
c. Moist vorticity and moist divergence
Vertical–latitude cross sections (s−1; contours with an interval of 2 × 10−5 s−1) of (a) vorticity, (b) MV, (c) divergence, and (d) MD at 0000 UTC 1 Jul 1991. The heavy rain area is indicated by the filled triangles.
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
As in Fig. 2, but for MV (k = 10).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
As in Fig. 3, but for MD (k = 10).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
As in section 3b, TS is again calculated based on the 41 daily regional heavy rain cases to quantitatively measure how well a vorticity- or a divergence-related parameter overlaps with a heavy precipitation area (≥25 mm day−1) within China. Similar to the situations for vorticity and divergence in Figs. 2 and 3, although the MV and MD are similar to each other in general at different times during the event, the midpoint 0000 UTC (Figs. 15c, 16c) seems to match the heavy rain area the best (at least as well as others). Therefore, the midpoint is again used as a representative time for a daily regional heavy rain event in the following statistics. The optimal threshold for each parameter is shown in Fig. 17. Based on these optimal thresholds, Fig. 18 shows the averaged TS results for the three groups (note the MPV vs GMPV group is the same as in Fig. 11 and is listed for comparison purposes). After incorporating the effects of moisture into the vorticity and divergence, the improvements of MV or MD over the vorticity or divergence are significant: about a 60% increase in TS for MD (from 0.169 to 0.27) and 24% for MV (from 0.196 to 0.262). This result is also statistically significant at the 99% confidence level. The averaged TS as well as the best and worst scores and their variance (standard deviation with respect to mean) for each parameter out of the 41 cases are also listed in Table 2 along with the statistical significance levels.
As in Fig. 10, but for (a) vorticity, (b) MV, (c) divergence, and (d) MD.
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
As in Fig. 11, but for vorticity vs MV and divergence vs MD (MPV vs GMPV is taken from Fig. 11).
Citation: Weather and Forecasting 30, 6; 10.1175/WAF-D-14-00154.1
4. Conclusions and discussion
Heavy precipitation is an outcome of combined favorable dynamic and moisture conditions. Our study demonstrated that a parameter containing either a dynamic or moisture factor alone, such as vorticity, divergence, or relative humidity, cannot accurately depict heavy rain areas (often leading to too many false alarms), but properly including moisture effects into a dynamical parameter can significantly increase a parameter’s ability to diagnose heavy rain locations. In this study, a regional heavy rain event that occurred along the Yangtze River on 1 July 1991 is used as a case study, and another 41 daily regional heavy rain events during the notorious flooding year of 1998 in eastern China are used for systematic evaluation. TS is used to quantitatively measure the overlap between a parameter and the heavy rain areas. Because of the limited spatial resolution (~80 km) of the reanalysis data, only long-lasting large-scale widespread regional heavy rain events associated with synoptic-scale weather systems are investigated.
Although the GMPV was proposed about 10 years ago (Gao et al. 2004a), it is still unfamiliar to many. Therefore, the concept of GMPV is introduced first. The empirical relative humidity–based weighting approach used to modify the effects of moisture in the MPV to become a GMPV is then analyzed. It is found that the GMPV is superior to the MPV in depicting heavy rain locations; for example, GMPV can increase TS by 194% over the MPV on average (increasing from 0.064 to 0.188), which is statistically significant at the 99% confidence level. The two components of the MPV are also improved by those of the GMPV: a 16% increase in TS for the GMPV1 over the MPV1 (from 0.111 to 0.129), and 18% for the GMPV2 over the MPV2 (from 0.131 to 0.154), results that are statistically significant at the 65% and 80% confidence levels, respectively.
Following the same empirical relative humidity–based weighting approach, two new diagnostic parameters (MV and MD) are proposed for the first time by incorporating moisture effects into the traditional vorticity and divergence. Results show that after the moisture effects are properly incorporated, the improved ability of the vorticity and divergence to capture heavy rain areas is significant. For example, MV is superior to the vorticity by 24% (from 0.196 to 0.262), and MD to the divergence by 60% (from 0.169 to 0.27) in terms of TS, averaged over the 41 cases. Many spurious areas are eliminated. These improvements are statistically significant at the 99% confidence level. Both MV and MD are superior to GMPV in depicting heavy rain locations. Although MV and MD perform similarly to each other on average, the performance of MV seems to be more stable than that of MD. For example, the range in TS variation is narrower for MV (from 0.121 to 0.498) than for MD (from 0.073 to 0.548).
Although application of MV and MD in assessing heavy rain potential is not intended to replace a complete, multiscale forecasting methodology, such as that of Doswell et al. (1996), the two new parameters could be used to postprocess a model forecast to potentially improve heavy rain location predictions in the following three possible ways. First, they could be directly applied to numerical weather prediction model outputs. Since the performance levels of the analysis-based MV and MD (TS = 0.26 and 0.27, respectively) are similar to that of the current operational day-1 forecasts of 24-h accumulated precipitation exceeding 25–50 mm at NCEP, which is about 0.20–0.30 (NCEP/WPC 2014), it might be hard to add value over short-range (1–2 days) heavy rain forecasts. However, it could be valuable for longer-range (beyond a few days) forecasts given the fact that atmospheric circulation (wind, temperature, humidity, and pressure) is more predictable than precipitation. If their application is further combined with ensemble forecasts (Du et al. 1997), the performance of MV and MD could be even more reliable and extended to longer forecast ranges. Second, they could be used to replace the conventional vorticity and divergence in model’s statistical postprocessing such as model output statistics (Glahn and Lowry 1972) and other machine-learning schemes. Third, they could be used to calibrate model forecasts such as physically based bias and displacement error correction to greatly improve heavy rain prediction (Du et al. 2000). At the same time, it will also be necessary to further examine how the performance of MV and MD varies with weather systems (such as smaller-scale convection) and for different geographical regions. Our final hope is that the approach of combining dynamic and moisture factors together as demonstrated in this study could inspire similar works in the future to advance our understanding of atmospheric behavior and improve diagnostic and prediction tools.
Acknowledgments
The authors wish to thank the editors and anonymous reviewers for their valuable comments and suggestions to improve the paper. This work is supported by the National Natural Science Foundation of China (41375073), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDA0509400), and the Key Technologies R&D Program (201306032). Ms. Mary Hart of NCEP is appreciated for her help in improving the readability of the manuscript.
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