• Cao, J., , and Gao S. T. , 2008: Generalized potential temperature in non-uniformly saturated atmosphere (in Chinese). Chin. J. Geophys., 51, 16511656.

    • Search Google Scholar
    • Export Citation
  • Chen, X. H., , Yu J. L. , , Qiu X. X. , , and Zhang J. , 2007: Vapor investigation of a heavy rainfall event in the Huaihe River basin 2005. Meteor. Mon., 33, 4752.

    • Search Google Scholar
    • Export Citation
  • Department of Geophysics, 1976: Weather Analyses and Forecasts (Meteorology for Undergraduate Students in Peking University). Scientific Press, 570 pp.

  • Doswell, C. A., III, , and Schultz D. M. , 2006: On the use of indices and parameters in forecasting severe storms. Electron. J. Severe Storms Meteor., 1 (3). [Available online at http://www.ejssm.org/ojs/index.php/ejssm/article/viewarticle/11/12.]

    • Search Google Scholar
    • Export Citation
  • Doswell, C. A., III, , Brooks H. E. , , and Maddox R. A. , 1996: Flash flood forecasting: An ingredients-based methodology. Wea. Forecasting, 11, 560581, doi:10.1175/1520-0434(1996)011<0560:FFFAIB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gao, S. T., , Wang X. R. , , and Zhou Y. S. , 2004: Generation of generalized moist potential vorticity in a frictionless and moist adiabatic flow. Geophys. Res. Lett., 31, L12113, doi:10.1029/2003GL019152.

    • Search Google Scholar
    • Export Citation
  • Holton, B. J. R., 2012: An Introduction to Dynamic Meteorology. 4th ed. Academic Press, 535 pp.

  • Qian, W., , Li J. , , and Shan X. , 2013: Application of synoptic-scale anomalous winds predicted by medium-range weather forecast models on the regional heavy rainfall in China in 2010. Sci. China Earth Sci., 56, 10591070, doi:10.1007/s11430-013-4586-5.

    • Search Google Scholar
    • Export Citation
  • Qian, W., , Du J. , , Shan X. , , and Jiang N. , 2015: Incorporating the effects of moisture into a dynamical parameter: Moist vorticity and moist divergence. Wea. Forecasting, 30, 14111428, doi:10.1175/WAF-D-14-00154.1.

    • Search Google Scholar
    • Export Citation
  • Qian, W., , Jiang N. , , and Du J. , 2016: Anomaly-based weather analysis versus traditional total-field-based weather analysis for depicting regional heavy rain events. Wea. Forecasting, 31, 7193, doi:10.1175/WAF-D-15-0074.1.

    • Search Google Scholar
    • Export Citation
  • Schultz, D. M., , and Schumacher P. N. , 1999: The use and misuse of conditional symmetric instability. Mon. Wea. Rev., 127, 27092732, doi:10.1175/1520-0493(1999)127<2709:TUAMOC>2.0.CO;2; Corrigendum, 128, 1573, doi:10.1175/1520-0493(1999)127<1573:CORRIG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schultz, D. M., , and Spengler T. , 2016: Comments on “Incorporating the effects of moisture into a dynamical parameter: Moist vorticity and moist divergence.” Wea. Forecasting, 31, 13931396, doi:10.1175/WAF-D-16-0067.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X. R., , Wu K. J. , , and Shi C. E. , 1999: The introduction of condensation probability function and the dynamic equations on non-uniform saturated moist air. J. Trop. Meteor., 15, 6470.

    • Search Google Scholar
    • Export Citation
  • Wetzel, S. W., , and Martin J. E. , 2001: An operational ingredients-based methodology for forecasting midlatitude winter season precipitation. Wea. Forecasting, 16, 156167, doi:10.1175/1520-0434(2001)016<0156:AOIBMF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, G., 2016: The progress of fog forecast operation in China. Adv. Meteor. Sci. Technol., 6 (2), 4248.

  • View in gallery

    Horizontal distributions of the (a) moisture advection and (b) moisture convergence terms at 0000 UTC 1 Jul 1991. Contour interval is 0.1 × 10−6 s−1. Black-filled and open circles indicate the stations with observed rainfall ≥50 and 25–50 mm day−1 (1200 UTC 30 Jun–1200 UTC 1 Jul 1991), respectively.

  • View in gallery

    (a) DQ, (b) MD, (c) VQ, and (d) MV at 850 hPa at 0000 UTC 1 Jul 1991. The contour intervals are 1 × 10−5 s−1 for MD and 2 × 10−5 s−1 for MV, with k = 10, and 20 × 10−5 s−1 g kg−1 for DQ and 25 × 10−5 for VQ. Red, green, and blue open circles (dots) indicate the stations with rainfall ≥50, 25–50, and 10–25 mm day−1 (1200 UTC 30 Jun–1200 UTC 1 Jul 1991), respectively. [These plots are adopted from Figs. 12a, 10a, 13a, and 11a in Qian et al. (2016).]

  • View in gallery

    Verification of the heavy-rain (≥25 mm day−1) location forecasts for (a1),(a2) ECMWF model precipitation, (b1),(b2) MD, and (c1),(c2) MV. The observed and model precipitation totals were accumulations over a 24-h period from 0000 UTC 18 Jun to 0000 UTC 19 Jun 2010. (left) The day-1 forecast initialized at 0000 UTC 18 Jun and (right) the day-10 forecast initialized at 0000 UTC 9 Jun. MD and MV were calculated at the midpoint (1200 UTC 18 Jun). The red, blue, and green colors represent HIT, FA, and MISS areas, which were verified against an analyzed precipitation dataset. The observed station precipitation was also plotted for reference, where the black dots and open circles indicate the stations with rainfall ≥50 and 25–50 mm day−1. The box (20°–35°N, 100°–125°E) is the southeast China domain covering the major heavy rainband. Both the entire domain and the southeast China domain were used for calculating Figs. 4 and 5.

  • View in gallery

    As in Fig. 3, but for the domain-summary scores: (a1),(a2) HIT rate or TS, (b1),(b2) FA rate, and (c1),(c2) MISS rate at forecast lengths from days 1 through 10. The averages over (left) the entire China domain and (right) the southeast China domain, where the black curve is for the ECMWF model precipitation, the blue curve is for MD, and the red curve is for MV.

  • View in gallery

    As in Fig. 4, but averaged over the twelve 10-day forecasts of daily heavy rain events, which were initialized daily from 0000 UTC 14 Jun to 0000 UTC 25 Jun 2010.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 11 11 0
PDF Downloads 5 5 0

Reply to “Comments on ‘Incorporating the Effects of Moisture into a Dynamical Parameter: Moist Vorticity and Moist Divergence’”

View More View Less
  • 1 Department of Atmospheric and Oceanic Sciences, Peking University, Beijing, China
  • 2 NOAA/NCEP/Environmental Modeling Center, College Park, Maryland
© Get Permissions
Full access

Abstract

Mathematical derivation, meteorological justification, and comparison to model direct precipitation forecasts are the three main concerns recently raised by Schultz and Spengler about moist divergence (MD) and moist vorticity (MV), which were introduced in earlier work by Qian et al. That previous work demonstrated that MD (MV) can in principle be derived mathematically with a value-added empirical modification. MD (MV) has a solid meteorological basis. It combines ascent motion and high moisture: the two elements necessary for rainfall. However, precipitation efficiency is not considered in MD (MV). Given the omission of an advection term in the mathematical derivation and the lack of precipitation efficiency, MD (MV) might be suitable mainly for heavy rain events with large areal coverage and long duration caused by large-scale quasi-stationary weather systems, but not for local intense heavy rain events caused by small-scale convection. In addition, MD (MV) is not capable of describing precipitation intensity. MD (MV) worked reasonably well in predicting heavy rain locations from short to medium ranges as compared with the ECMWF model precipitation forecasts. MD (MV) was generally worse than (though sometimes similar to) the model heavy rain forecast at shorter ranges (about a week) but became comparable or even better at longer ranges (around 10 days). It should be reiterated that MD (MV) is not intended to be a primary tool for predicting heavy rain areas, especially in the short range, but is a useful parameter for calibrating model heavy precipitation forecasts, as stated in the original paper.

Corresponding author address: Prof. Weihong Qian, Dept. of Atmospheric and Oceanic Sciences, Peking University, Beijing 100871, China. E-mail: qianwh@pku.edu.cn

The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/WAF-D-14-00154.1.

Abstract

Mathematical derivation, meteorological justification, and comparison to model direct precipitation forecasts are the three main concerns recently raised by Schultz and Spengler about moist divergence (MD) and moist vorticity (MV), which were introduced in earlier work by Qian et al. That previous work demonstrated that MD (MV) can in principle be derived mathematically with a value-added empirical modification. MD (MV) has a solid meteorological basis. It combines ascent motion and high moisture: the two elements necessary for rainfall. However, precipitation efficiency is not considered in MD (MV). Given the omission of an advection term in the mathematical derivation and the lack of precipitation efficiency, MD (MV) might be suitable mainly for heavy rain events with large areal coverage and long duration caused by large-scale quasi-stationary weather systems, but not for local intense heavy rain events caused by small-scale convection. In addition, MD (MV) is not capable of describing precipitation intensity. MD (MV) worked reasonably well in predicting heavy rain locations from short to medium ranges as compared with the ECMWF model precipitation forecasts. MD (MV) was generally worse than (though sometimes similar to) the model heavy rain forecast at shorter ranges (about a week) but became comparable or even better at longer ranges (around 10 days). It should be reiterated that MD (MV) is not intended to be a primary tool for predicting heavy rain areas, especially in the short range, but is a useful parameter for calibrating model heavy precipitation forecasts, as stated in the original paper.

Corresponding author address: Prof. Weihong Qian, Dept. of Atmospheric and Oceanic Sciences, Peking University, Beijing 100871, China. E-mail: qianwh@pku.edu.cn

The original article that was the subject of this comment/reply can be found at http://journals.ametsoc.org/doi/abs/10.1175/WAF-D-14-00154.1.

1. Introduction

Qian et al. (2015, hereafter Q15) recently introduced two parameters, moist divergence (MD) and moist vorticity (MV), to compare with their dry versions of divergence and relative vorticity in diagnosing locations of daily large-scale heavy rains in eastern China:
e1
e2
where u and υ are the zonal and meridional wind components, respectively; q is the air specific humidity; qs is the saturated specific humidity; x and y are, respectively, the zonal and meridional distances; and k = 10. By incorporating a moisture factor into a dynamical diagnostic parameter, MD and MV yield significant improvement over the original pure-dynamic parameters in locating heavy rain areas. Q15 have successfully demonstrated the superiority of MD (MV) over the divergence (relative vorticity) in their Table 2 and Fig. 18. Schultz and Spengler (2016, hereafter SS16), however, questioned the work in three aspects: “moist vorticity and moist divergence are flawed mathematically,” “no meteorological evidence is presented for why areas of moist vorticity and moist divergence should overlap with regions of 24-h accumulated rainfall,” and “all three quantities have not been verified against the output of precipitation directly from the model nor is the approach of combining meteorological quantities into a single parameter appropriate in an ingredients-based forecasting approach.” The first two points concern scientific justification mathematically and meteorologically, while the third point is about the method’s application to predictions. Therefore, we will focus on these three aspects in this paper.

In sections 2 and 3, the mathematical and meteorological justifications, respectively, are illustrated. The application of MD and MV to heavy rain predictions is demonstrated by comparing it with the ECMWF model’s direct precipitation forecasts in section 4. A summary and discussion are given in section 5.

2. Mathematical justification

From the moisture budget equation of an air parcel in pressure coordinates,
e3
where ; ; ω is the vertical velocity in pressure p coordinates; E and P are the evaporation rate and the precipitation rate, respectively; and t is time. In eastern China regional heavy rainfall, particularly in summer, occurs frequently along a persistent shallow (below 700 hPa) front (called the mei-yu front). The evaporation E and local tendency of specific humidity are small when associated with the mei-yu front during the rainfall period when the air has almost become saturated (Chen et al. 2007). Thus, Eq. (3) can be simplified as
e4
If we integrate Eq. (4) from the surface (p = ps) to the top (p = 0) of the atmosphere, the local precipitation amount is proportional to the vertically integrated horizontal water vapor convergence or moisture flux convergence (MFC) because . In the rainfall process, the precipitation is achieved through the ascending motion ω in the lower troposphere where the maximum MFC is located. The horizontal MFC can be written as
e5
Along the mei-yu front, the advection term (Fig. 1a) is much smaller than the convergence term (Fig. 1b) because of the quasi-stationary circulation system. Thus, the convergence term [called DQ, as in Eq. (7) in Qian et al. (2016)] in the lower troposphere is directly associated with rainfall P:
e6
Therefore, precipitation is directly proportional to the product of divergence and moisture. MD [Eq. (1)] is also a product of divergence and moisture, except that the moisture term is in the form of relative humidity (RH; q/qs) instead of specific humidity q. Thus, the physical principle behind MD is exactly the same as Eq. (6). An analog to DQ, the product of relative vorticity and q was called VQ, as in Eq. (8) in Qian et al. (2016).
Fig. 1.
Fig. 1.

Horizontal distributions of the (a) moisture advection and (b) moisture convergence terms at 0000 UTC 1 Jul 1991. Contour interval is 0.1 × 10−6 s−1. Black-filled and open circles indicate the stations with observed rainfall ≥50 and 25–50 mm day−1 (1200 UTC 30 Jun–1200 UTC 1 Jul 1991), respectively.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-16-0111.1

Why is RH used instead of specific humidity in MD (MV)? Admittedly, this is based on empirical work done by Gao et al. (2004). Gao et al. (2004) proposed an empirical formula of (q/qs)-based weighting called the condensation probability function (CPF), where (q/qs)k. The CPF can better describe the location of high-moisture areas associated with heavy rain than does specific humidity itself. This advantage was also demonstrated by Q15 using 42 daily regional heavy rain cases. For example, Fig. 7 in Q15 showed the impact of varying the k value on the relationship between RH-based weight and heavy rainfall areas in both horizontal and vertical structures. By varying the k value, one can effectively control the impact level of moisture to better match a parameter with the observed precipitation area. First of all, higher RH is often more likely associated with heavy rain. For a fixed RH, since q/qs is normally less than 1, the impact of moisture is reduced when the k value increases. For example, when k varied from 1 to 20, the area of MD shrinks from a large area at lower RH to a small area at higher RH. Theoretically and statistically, the spatial distribution of (q/qs)k changes more slowly when k ≥ 9 (Wang et al. 1999). This process of obtaining an optimal k value is what we referred to as “proper” in Q15, in answer to the issue raised in SS16: “The article does not define what is proper, why this approach is proper, and what the scientific justification for this inclusion is. Besides heavy rain cases, the CPF can also clearly distinguish the difference between lighter fog and denser fog, as demonstrated by Cao and Gao (2008, p. 1652) and Zhang (2016).

How does this technique perform after replacing specific humidity with CPF? Figure 2a is calculated based on Eq. (6), and Fig. 2b is based on MD for the 1 July 1991 heavy rain case (Qian et al. 2016). It can be seen that both DQ and MD are generally similar to each other but MD is more concentrated on the major precipitation area with fewer isolated maximum convergence centers in the nonprecipitation area. This phenomenon is more obvious for the two relative vorticity terms (VQ versus MV; cf. Figs. 2c and 2d). To have a robust and quantitative result, Table 1 displays some verification results averaged over 41 daily heavy rain events [taken in part from Table 1 in Qian et al. (2016)]. MD has a significantly higher detection rate (POD) and accuracy [threat score (TS)] in capturing heavy rain areas than DQ, although MD’s bias is higher. The same is true for MV versus VQ. The fact that using CPF instead of q yielded an improved outcome shows an added value from an empirical modification of exact mathematics in a real-world application such as weather forecasting, as long as the modified parameter follows the same underlying physical principle. The empirical modification may have helped by taking statistical correction into account.

Fig. 2.
Fig. 2.

(a) DQ, (b) MD, (c) VQ, and (d) MV at 850 hPa at 0000 UTC 1 Jul 1991. The contour intervals are 1 × 10−5 s−1 for MD and 2 × 10−5 s−1 for MV, with k = 10, and 20 × 10−5 s−1 g kg−1 for DQ and 25 × 10−5 for VQ. Red, green, and blue open circles (dots) indicate the stations with rainfall ≥50, 25–50, and 10–25 mm day−1 (1200 UTC 30 Jun–1200 UTC 1 Jul 1991), respectively. [These plots are adopted from Figs. 12a, 10a, 13a, and 11a in Qian et al. (2016).]

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-16-0111.1

Table 1.

Averaged TS, POD, areal bias (bias), and false alarm ratio (FAR) of the two divergence terms (DQ and MD) and two vorticity terms (VQ and MV) at 850 hPa in depicting heavy rain locations (≥25 mm day−1) based on 41 cases (see Table 1 in Q15) that occurred across eastern China in 1998. The optimal thresholds used for each parameter are listed. The percentage values in parentheses indicate the statistical significance levels of the differences between MD (MV) and DQ (VQ). The boldface represents the better performance of MD and MV over DQ and VQ. [This table is extracted from Table 1 in Qian et al. (2016).]

Table 1.

3. Meteorological justification

Doswell et al. (1996) stated that “high rainfall rates involve the rapid ascent of air containing substantial water vapor and also depend on the precipitation efficiency.” These three elements (ascending motion, high moisture, and precipitation efficiency) form the ingredients-based methodology used to predict heavy rainfall events, as reviewed by Schultz and Schumacher (1999). Therefore, MD and MV were analyzed and compared with these three elements in this section.

a. Ascending motion

The ascending motion in the lower troposphere can be described by the omega function (Holton, 2012, p. 167). For a short-wave system where relative vorticity advection is larger than the planetary vorticity f advection, the vertical motion at 500 hPa forced by the advection of geostrophic vorticity ςg by the thermal wind is
e7
where w is the vertical velocity in geometric z coordinates, z is the vertical height, and is the horizontal geostrophic wind vector. Thus, there is ascending motion (w > 0) above the surface low (positive relative vorticity; ςg > 0 in the lower troposphere) and descending motion (w < 0) above the surface high (negative relative vorticity; ςg < 0 in the lower troposphere). The ascending motion or surface low (positive relative vorticity) is located in the front of the trough (east of the trough and west of the ridge). This relates the relative vorticity directly to ascending motion. Dynamically, a surface cyclonic vorticity system causes flow to converge to its center, resulting in ascending motion. Therefore, either vorticity (MV) or divergence (MD) is physically related to ascending motion.

b. High moisture

The second condition for producing heavy rainfall is an area of high-moisture content contained in the air (Schultz and Schumacher 1999). This is a necessary condition commonly used by forecasters and researchers including Doswell et al. (1996) and Gao et al. (2004). As we have discussed at length in the previous section, identifying a high-moisture area is a critical part of MD and MV methodology.

c. Precipitation efficiency

Precipitation efficiency is a contributor to rainfall intensity, especially for intense rainfall during a short time period causing flash floods. For a mesoscale convective system the precipitation efficiency is potentially linked with various vertical instabilities, which have been reviewed by Schultz and Schumacher (1999). This element is obviously missed in MD and MV. Since MD and MV are designed to diagnose heavy rain locations rather than rainfall intensity, the lack of precipitation efficiency might be acceptable. As the focus of Q15 is on synoptic scale, quasi-stationary (e.g., Figs. 2 and 3 in Q15), and long-duration (24 h) events, precipitation efficiency could be a much less important factor.

In summary, two of the three meteorological elements that were contained in the ingredients-based method are also included in MD and MV. The concept of MD (MV) also agrees well with forecaster experience in both China (Department of Geophysics 1976) and the United States (Wetzel and Martin, 2001). For example, cyclonic vorticity and strong convergence accompanied by high moisture (a dewpoint depression smaller than 2°C is often used as a criterion) in the lower troposphere (usually ~850 hPa) are commonly regarded as favorable conditions for heavy rain to occur. Therefore, we disagree with the comments of SS16 that “Any coincidence would appear to be due to a loose relationship between low-level vorticity, divergence, and high relative humidity in precipitating regions.” and “In particular, Doswell and Schultz (2006) discussed the problems when combining two separate quantities that may not even be collocated and can evolve largely independently of each other.”

4. Comparison between model precipitation forecasts and MD (MV) diagnoses

Although directly using MD and MV to predict heavy rain locations is not the intention of Q15, in this section we compared MD (MV) fields derived from model-predicted wind and RH fields with direct model precipitation output, as suggested by SS16. Based on the available THORPEX Interactive Grand Global Ensemble (TIGGE; http://tigge.ecmwf.int) dataset, a long-lasting heavy rain event in 2010 was chosen and the corresponding ECMWF model forecasts of days 1–10 were verified against an analyzed precipitation dataset (Qian et al. 2013).

In 2010, 78 regional heavy rain events occurred in China. Among them the longest-lasting regional heavy rain event started on 14 June and continued for 12 consecutive days (ending on 25 June), resulting in heavy rainfall at 122 stations in eastern China (the station distribution can be found in Fig. 1 in Q15). During this period the highest daily rainfall amount (251.7 mm) occurred on 19 June in Fujian Province. Therefore, this 12-day period was verified with an illustration of the daily event of 19 June in particular.

Figure 3 shows the hit (HIT), miss (MISS), and false alarm (FA) areas of the ECMWF model precipitation forecast and MD and MV, respectively, for day 1 (left panel, initialized at 0000 UTC 18 June 2010) and day 10 (right panel, initialized at 0000 UTC 9 June 2010) forecasts of the locations of 24-h accumulated precipitation exceeding 25 mm. Generally speaking, the three forecasts had a similar ability to capture heavy rain areas for day 1, while MD and MV captured more heavy rain areas than the model precipitation forecast for day 10. MD and MV had larger HIT areas and smaller MISS areas but more false alarms than the model precipitation forecast. To have a quantitative measure, the HIT, FA, and MISS rates are further calculated as follows (note that the HIT rate defined here is the commonly known TS):
e8
e9
e10
Fig. 3.
Fig. 3.

Verification of the heavy-rain (≥25 mm day−1) location forecasts for (a1),(a2) ECMWF model precipitation, (b1),(b2) MD, and (c1),(c2) MV. The observed and model precipitation totals were accumulations over a 24-h period from 0000 UTC 18 Jun to 0000 UTC 19 Jun 2010. (left) The day-1 forecast initialized at 0000 UTC 18 Jun and (right) the day-10 forecast initialized at 0000 UTC 9 Jun. MD and MV were calculated at the midpoint (1200 UTC 18 Jun). The red, blue, and green colors represent HIT, FA, and MISS areas, which were verified against an analyzed precipitation dataset. The observed station precipitation was also plotted for reference, where the black dots and open circles indicate the stations with rainfall ≥50 and 25–50 mm day−1. The box (20°–35°N, 100°–125°E) is the southeast China domain covering the major heavy rainband. Both the entire domain and the southeast China domain were used for calculating Figs. 4 and 5.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-16-0111.1

For the 19 June case the HIT rate (or TS), FA rate, and MISS rate are shown in Fig. 4 for both the entire China domain (left panel) and a smaller southeast China domain (20°–35°N, 100°–125°E; see the small box in Fig. 3) covering the heavy rain event only (right panel), for the day 1–10 forecasts. For the China domain (Fig. 4a1), MD (MV) generally performs worse than the model precipitation from days 1 to 5, was comparable from days 6 to 9, and was better at day 10. For the southeast China domain (Fig. 4a2), MD (MV) was comparable to the model precipitation from days 1 to 9 and better at day 10. For a more robust result, Fig. 5 shows the averaged HIT rate (TS), FA rate, and MISS rate over the 12 daily heavy rain events (14–25 June) for both domains. In terms of TS (Figs. 5a1 and 5a2), MD (MV) was generally worse than the model direct precipitation forecasts but the difference between MD (MV) and the model precipitation forecast becomes smaller as forecast length increases. This is consistent with the reasoning of Q15: “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” (p. 1427 in Q15). The poorer performance of MD and MV is mainly due to the higher FA rate (Figs. 5b1 and 5b2). Systematic evaluation with a wider range of cases is still needed to confirm this.

Fig. 4.
Fig. 4.

As in Fig. 3, but for the domain-summary scores: (a1),(a2) HIT rate or TS, (b1),(b2) FA rate, and (c1),(c2) MISS rate at forecast lengths from days 1 through 10. The averages over (left) the entire China domain and (right) the southeast China domain, where the black curve is for the ECMWF model precipitation, the blue curve is for MD, and the red curve is for MV.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-16-0111.1

Fig. 5.
Fig. 5.

As in Fig. 4, but averaged over the twelve 10-day forecasts of daily heavy rain events, which were initialized daily from 0000 UTC 14 Jun to 0000 UTC 25 Jun 2010.

Citation: Weather and Forecasting 31, 4; 10.1175/WAF-D-16-0111.1

The above results perfectly echo the original intention of Q15: “Although application of the MV and MD to assess heavy rain potential is not intended to replace a complete, multiscale forecasting methodology such as Doswell et al. (1996), the two new parameters could be used to postprocess a model forecast to potentially improve heavy-rain location prediction…” (p. 1426, the last paragraph of Q15). Therefore, we want to reemphasize here that MD (MV) is not intended to be a primary tool to directly predict heavy rain areas, especially in the short range (although it might do from the medium to long ranges), but is a useful parameter for calibrating model precipitation forecasts through postprocessing. For example, the right panel in Fig. 3 shows that the western part of the heavy rainband was completely missed by the model precipitation forecast but was mostly covered by both MD and MV at day 10. Apparently, such information from MD and MV could be potentially used to improve model precipitation forecasts. How to extract useful information from MD (MV) to calibrate a model precipitation forecast needs to be studied.

5. Summary and discussion

Mathematical derivation, meteorological justification, and comparison to model direct precipitation forecasts are the three main concerns raised by SS16 about MD and MV. We have therefore addressed these three aspects, one by one, in this paper. Sections 24 showed that MD and MV are not random parameters but can be derived mathematically in principle (with a value-added empirical modification), have a meteorological basis, and have worked reasonably well in predicting heavy rain locations from the short to medium range.

Specifically, section 2 showed an exact mathematical derivation and then demonstrated the merit of replacing specific humidity with a RH-based weight (but under the same physical principle) based on previous studies. It proved that such a modification of moisture content format can improve performance. This result illustrated that exact mathematics with an empirical modification could yield an improved outcome in a real-world application such as weather forecasting as long as the modification follows the same underlying physical principle. The beauty of an empirical modification is that it could take statistical corrections into account.

Section 3 compared MD and MV with an ingredients-based approach (Doswell et al. 1996). MD (MV) contains two of the three elements: ascending motion and high moisture, but precipitation efficiency is not considered. The concept of MD (MV) also agrees well with forecaster experience. Given the omission of an advection term in deriving Eq. (6) and the lack of a precipitation efficiency factor, MD (MV) might be suitable mainly for heavy rain events with large areal coverage and long duration caused by large-scale quasi-stationary strong weather systems. Whether it works for local intense heavy rain events caused by small-scale convection needs to be investigated further. In addition, MD (MV) has no ability to describe precipitation intensity.

In section 4, MD (MV) was compared with the ECMWF model direct precipitation forecasts. MD (MV) was generally worse than (or sometimes similar to) the model heavy rain forecast in the short range (about a week) but became comparable to or better than the model in the medium range (around day 10). This is consistent with the fact that atmospheric circulation (wind, temperature, humidity, and pressure) has a longer predictability length than precipitation. The poorer performance of MD and MV is mainly due to the higher FA rate. A more systematic evaluation involving various types of heavy rain cases is needed in the future. We also challenge the authors of SS16 to compare their ingredient-based method with direct model precipitation forecasts. As was stated in Q15, we want to reiterate that MD (MV) is not intended to be a primary tool to directly predict heavy rain areas, especially in the short range (although it might do so from the medium to long ranges), but is a useful parameter for calibrating model direct precipitation output to improve heavy rain predictions. The best method for using MD and MV to calibrate model precipitation forecasts would be valuable to explore. In this study MD and MV were calculated only at one representative time point (the midpoint of a daily rainfall event) and one vertical level (850 hPa). More information can be obtained if they can be calculated for multiple time points throughout an entire heavy rain process and at multiple vertical levels.

Finally, we would like to point out that the original goal of Q15 was to examine if a dynamic parameter’s ability to locate heavy rain areas can be significantly improved when it incorporates a moisture factor. MD and MV are two such examples. Q15 has successfully demonstrated the superiority of MD (MV) over the original divergence (relative vorticity). We invite the authors of SS16 to independently verify such improvements using other heavy rain cases of their choice.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (41375073). We appreciate Ms. Mary Hart of NCEP for reading through the manuscript to improve its readability.

REFERENCES

  • Cao, J., , and Gao S. T. , 2008: Generalized potential temperature in non-uniformly saturated atmosphere (in Chinese). Chin. J. Geophys., 51, 16511656.

    • Search Google Scholar
    • Export Citation
  • Chen, X. H., , Yu J. L. , , Qiu X. X. , , and Zhang J. , 2007: Vapor investigation of a heavy rainfall event in the Huaihe River basin 2005. Meteor. Mon., 33, 4752.

    • Search Google Scholar
    • Export Citation
  • Department of Geophysics, 1976: Weather Analyses and Forecasts (Meteorology for Undergraduate Students in Peking University). Scientific Press, 570 pp.

  • Doswell, C. A., III, , and Schultz D. M. , 2006: On the use of indices and parameters in forecasting severe storms. Electron. J. Severe Storms Meteor., 1 (3). [Available online at http://www.ejssm.org/ojs/index.php/ejssm/article/viewarticle/11/12.]

    • Search Google Scholar
    • Export Citation
  • Doswell, C. A., III, , Brooks H. E. , , and Maddox R. A. , 1996: Flash flood forecasting: An ingredients-based methodology. Wea. Forecasting, 11, 560581, doi:10.1175/1520-0434(1996)011<0560:FFFAIB>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Gao, S. T., , Wang X. R. , , and Zhou Y. S. , 2004: Generation of generalized moist potential vorticity in a frictionless and moist adiabatic flow. Geophys. Res. Lett., 31, L12113, doi:10.1029/2003GL019152.

    • Search Google Scholar
    • Export Citation
  • Holton, B. J. R., 2012: An Introduction to Dynamic Meteorology. 4th ed. Academic Press, 535 pp.

  • Qian, W., , Li J. , , and Shan X. , 2013: Application of synoptic-scale anomalous winds predicted by medium-range weather forecast models on the regional heavy rainfall in China in 2010. Sci. China Earth Sci., 56, 10591070, doi:10.1007/s11430-013-4586-5.

    • Search Google Scholar
    • Export Citation
  • Qian, W., , Du J. , , Shan X. , , and Jiang N. , 2015: Incorporating the effects of moisture into a dynamical parameter: Moist vorticity and moist divergence. Wea. Forecasting, 30, 14111428, doi:10.1175/WAF-D-14-00154.1.

    • Search Google Scholar
    • Export Citation
  • Qian, W., , Jiang N. , , and Du J. , 2016: Anomaly-based weather analysis versus traditional total-field-based weather analysis for depicting regional heavy rain events. Wea. Forecasting, 31, 7193, doi:10.1175/WAF-D-15-0074.1.

    • Search Google Scholar
    • Export Citation
  • Schultz, D. M., , and Schumacher P. N. , 1999: The use and misuse of conditional symmetric instability. Mon. Wea. Rev., 127, 27092732, doi:10.1175/1520-0493(1999)127<2709:TUAMOC>2.0.CO;2; Corrigendum, 128, 1573, doi:10.1175/1520-0493(1999)127<1573:CORRIG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Schultz, D. M., , and Spengler T. , 2016: Comments on “Incorporating the effects of moisture into a dynamical parameter: Moist vorticity and moist divergence.” Wea. Forecasting, 31, 13931396, doi:10.1175/WAF-D-16-0067.1.

    • Search Google Scholar
    • Export Citation
  • Wang, X. R., , Wu K. J. , , and Shi C. E. , 1999: The introduction of condensation probability function and the dynamic equations on non-uniform saturated moist air. J. Trop. Meteor., 15, 6470.

    • Search Google Scholar
    • Export Citation
  • Wetzel, S. W., , and Martin J. E. , 2001: An operational ingredients-based methodology for forecasting midlatitude winter season precipitation. Wea. Forecasting, 16, 156167, doi:10.1175/1520-0434(2001)016<0156:AOIBMF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Zhang, G., 2016: The progress of fog forecast operation in China. Adv. Meteor. Sci. Technol., 6 (2), 4248.

Save