1. Introduction
Heavy rainfall events can be associated with significant societal disruption (e.g., Ashley and Ashley 2008; Gourley et al. 2013; Smith et al. 2013), therefore it is important to understand both the dynamical processes and predictability of these events. Ensemble prediction systems (EPSs) can be used to represent the predictability of atmospheric phenomena by accounting for uncertainties in the initial conditions or dynamical formulation of a numerical weather prediction (NWP) model (Sivillo et al. 1997; Toth et al. 1997; Schwartz et al. 2015). EPSs provide added value over deterministic forecasts, and can be beneficial in particularly disruptive events (e.g., Evans et al. 2014; Golding et al. 2016; Greybush et al. 2017). While it has been established that forecasts of heavy rainfall have benefitted from the development of convection-permitting NWP (e.g., Clark et al. 2010; Yan and Gallus 2016), convection-permitting EPSs are still characterized by a combination of model biases and insufficient ensemble variability (e.g., Buizza et al. 2005; Novak et al. 2008; Berner et al. 2011; Bouttier et al. 2012; Romine et al. 2014).
Parameterizations of subgrid-scale processes can contribute to the deficiency in spread, or underdispersiveness, of EPSs. Numerical parameterization schemes typically consist of statistical and climatological assumptions in conjunction with explicitly resolved dynamics to provide approximations to subgrid-scale processes (Holton 2004). Due to the nature of these assumptions, the output of parameterization schemes can artificially constrain ensemble variability by imposing assumed statistical restrictions on uncertain physical parameters, while simultaneously subjecting the ensemble to the biases of chosen parameterization schemes (e.g., Palmer et al. 2009). Stochastic methods, such as stochastic perturbed parameterization tendencies (SPPT), can be used to account for the model error associated with parameterized processes, and hence can increase ensemble dispersion (Buizza et al. 1999). SPPT can increase ensemble variability by multiplying the sum of the parameterized physical tendencies at each grid point by a tunable, spatially and temporally correlated, red-noise perturbation field. This field is a function of an initial random number seed, decorrelation time scale, length scale, and amplitude scale (Buizza et al. 1999). Each ensemble member is characterized by a unique stochastic perturbation field dependent on the initial seed, therefore these perturbations act to cast the output tendencies of the deterministic parameterization schemes as a probability distribution (Palmer et al. 2009; Romine et al. 2014). Moreover, unlike multimodel or multiphysics ensembles, the use of a single model with consistent physics parameterizations permits all members to be considered equally likely outcomes (e.g., Romine et al. 2014). While most implementations multiply the total parameterized tendencies by the stochastic pattern, the SPPT method can be applied independently to individual parameterization schemes (independent SPPT or iSPPT; Christensen et al. 2015, 2017). The use of iSPPT removes the implicit assumption of SPPT that errors across different parameterization schemes are correlated, while also allowing for sensitivity experiments in which perturbations may be applied to one parameterization scheme at a time (Christensen et al. 2017).
Stochastic model error schemes have been applied to operational NWP on the medium-range, seasonal, and climate scales. Buizza et al. (1999) discussed the implementation of an early version of SPPT in the European Center for Medium-Range Weather Forecasts (ECMWF) EPS during 1998. Ensemble forecasts using this early SPPT scheme proved to be more skillful than those based on initial condition uncertainty alone, particularly in terms of rainfall predictability. The current operational version of the ECMWF SPPT scheme (Leutbecher et al. 2017) retains the conceptual design introduced by Buizza et al. (1999) and introduces tendency perturbations on multiple scales. In addition to the ECMWF EPS, a version of the SPPT scheme is incorporated in EPSs produced by Environment and Climate Change Canada, Météo-France, and the Japan Meteorological Agency, and has been tested in the Weather Research and Forecasting (WRF) Model, Global Forecast System (GFS) model, and the UKMET Unified Model (Leutbecher et al. 2017).
Despite the increasing prevalence of SPPT schemes in operational NWP, relatively less attention has been given to the implementation and tuning of SPPT for mesoscale heavy rainfall events. Bouttier et al. (2012) investigated the impact of SPPT on temperature, humidity, wind, and cloud forecasts over two 14-day forecast periods using the convection-permitting Applications of Research to Operations at Mesoscale (AROME) model, and found that SPPT improves ensemble reliability by increasing ensemble dispersion at the expense of the ensemble mean forecast for all parameters except for precipitation. For precipitation, particularly light rainfall, the AROME-SPPT scheme acts to suppress an inherent wet bias in the model and reduces the false alarm ratio for rainfall observations exceeding 2 mm (Bouttier et al. 2012). In a study by Romine et al. (2014), the stochastic kinetic energy backscatter scheme (SKEB) and SPPT are introduced in a 30-member convection-permitting WRF ensemble over the central United States for a one-month period during May–June 2012. Similar to Bouttier et al. (2012), SPPT tends to improve forecast skill of low rainfall rates; however, unlike the AROME-SPPT scheme, a wet bias is introduced into the WRF Model, and forecast skill diminishes with increasing rainfall rate. Despite these biases, the ensembles using the stochastic schemes are generally more reliable (Romine et al. 2014).
Since the introduction of SPPT by Buizza et al. (1999), the amplitude, temporal, and spatial scale tuning parameters of the stochastic pattern continue to be incompletely understood parameters. The results of Buizza et al. (1999) indicate that “medium” scale perturbations in the 1998 ECMWF EPS (i.e., amplitude = 0.5, decorrelation time = 3 h, decorrelation length = 5°) were associated with reliable probabilistic forecasts which did not significantly reduce deterministic skill. It is further demonstrated by Buizza et al. (1999) that “high” values of the tuning parameters (i.e., amplitude = 1.0, decorrelation time = 12 h, decorrelation length = 10°) can increase ensemble dispersion. Tuning experiments conducted by Bouttier et al. (2012) indicate that ensemble dispersion is particularly sensitive to the perturbation amplitude and time scales, while a case study of banded snowfall events by Greybush et al. (2017) suggests that dispersion of ensemble precipitation forecasts may not be sensitive to the SPPT tuning parameters. Tuning experiments were not conducted by Romine et al. (2014), which used tunable parameters that were empirically selected for meso–synoptic-scale processes. Leutbecher et al. (2017) indicate that errors simulated by stochastic perturbations may be flow dependent, and Bouttier et al. (2012) further suggest that the SPPT tuning parameters should be based on observed weather conditions and that further research is required to understand their appropriate configuration.
While the preceding studies have addressed the effects of adjustments to the stochastic pattern tuning parameters, to the authors’ knowledge, a systematic documentation on the sensitivity of the ensemble mean and spread of heavy rainfall forecasts to adjustments of SPPT tuning parameters is not present in the published literature. Moreover, there appear to be few studies of the sensitivity of ensemble rainfall forecasts to the tuning and implementation of iSPPT schemes as well. Motivated by the potential improvement that these stochastic schemes can provide for probabilistic rainfall forecasts, this paper investigates the sensitivity of WRF ensemble forecasts to the tuning configuration and implementation of SPPT and individual iSPPT schemes, with specific focus on how these parameters impact ensemble rainfall variability. This study is conducted as part of the U.S.–Taiwan Partnership for International Research and Education (PIRE) program, with the goal of improving heavy rainfall forecasts in both the eastern United States and Taiwan.
Section 2 summarizes the design of the ensemble system used in this paper, including both an outline of the model configuration and a description of the stochastic perturbation schemes. Section 2 also includes a visualization of the effects of the tuning parameters on the perturbation field. A detailed overview of the heavy rainfall events selected for this study is provided in section 3. Section 4 presents the results of this study in terms of total accumulated rainfall and rainfall rate, with emphasis on the ensemble mean and standard deviation. A description of forecast skill with respect to each heavy rainfall event is also included in section 4. Further discussion is included in section 5, followed by a summary and concluding remarks in section 6.
2. Methodology
Three synoptically similar heavy rainfall events are utilized in this study to explore the sensitivity of ensemble rainfall forecasts to the configuration of SPPT and iSPPT schemes. These cases include 1) the remnants of Tropical Storm (TS) Lee (2011) over the northeastern United States, 2) IOP 8 (Tu et al. 2014) of the Southwest Monsoon Experiment (SoWMEX; Jou et al. 2011) over southern Taiwan during 2008, and 3) a mei-yu front heavy rainfall event over northern Taiwan during 2017. Though the three cases occur in spatially disparate areas, each is characterized by heavy rainfall that occurs in association with poleward flow of a warm and moist air mass toward a preexisting convergent boundary.
a. Model setup
SPPT and iSPPT ensembles as well as an unperturbed control forecast are produced for each event using version 3.7.1 of the WRF Model (Skamarock et al. 2008; Powers et al. 2017). TS Lee experiments use 15–3-km domain nesting and initial and boundary conditions provided by a National Centers for Environmental Prediction (NCEP) GFS deterministic forecast. The 2017 mei-yu front event similarly uses a 15–3-km domain configuration, but initial and boundary conditions are taken from member 01 of the Global Ensemble Forecast System (GEFS) as this forecast most accurately simulates the orientation and evolution of the observed heavy rainfall band. For this case, uncertainty in the location and evolution of the front can dominate rainfall forecast variability, therefore, the use of member 01 of the GEFS for initial and boundary conditions is intended to isolate the contribution of SPPT and iSPPT to the spread of ensemble rainfall forecasts. SoWMEX-IOP8 experiments use a triply nested domain setup of 27–9–3-km horizontal resolution and initial and boundary conditions generated from the analysis mean of a WRF-LETKF data assimilation procedure outlined in Yang et al. (2014), except using WRF version 3.7.1. Figure 1 provides a depiction of the domain configuration and regional topography. Additional details on the WRF Model configuration used for each case are provided in Table 1. An overview of each case, including a summary of their respective societal impacts and physical evolution, follows in section 3.
WRF Model domain configurations and terrain height (m) for the (a) remnants of TS Lee, (b) SoWMEX-IOP8, and (c) June 2017 mei-yu front cases. The inset image in (b) is a zoomed-in depiction of the innermost domain.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
WRF Model configuration for each case. Convective parameterization is only used on the coarse domain(s) for each case, and not on the 3-km domain. Rainfall accumulation period refers to the 18-h period over which rainfall forecasts and observations are examined for each case.
b. Forecast verification
Rainfall forecasts of each event are each verified against a different observational dataset, thus, verification metrics are computed separately for each case. Gridded multisensor rainfall analyses are only available for the TS Lee and 2017 mei-yu front events, which are verified against Stage IV rainfall analyses (ST4; Lin 2011) and Quantitative Precipitation Estimation and Segregation Using Multiple Sensors (QPESUMS) estimates (Gourley et al. 2001), respectively. The SoWMEX-IOP8 event is compared to observations made by a network of rain gauge (RG) stations over Taiwan (e.g., Yang et al. 2014). As in Romine et al. (2014), rainfall observations are bilinearly interpolated to the 3-km model grid for each event in order to compute verification metrics. Rainfall forecast skill is evaluated in terms of the areal coverage of a specified total rainfall threshold relative to the observations as well as fractions skill scores (FSSs) over neighborhood squares with a length of 63 km (e.g., Roberts and Lean 2008; Romine et al. 2014; Jankov et al. 2019).1
c. SPPT and iSPPT
The stochastic perturbation field evolves via red-noise process dictated by an initial random number seed, and a tunable decorrelation time scale, length scale, and amplitude scale (i, t, l, and σ). The initial random number seed i determines the initial spatial configuration of the perturbation field and is different for each ensemble member. Decorrelation time t refers to the duration of time that elapses before the temporal autocorrelation function (ACF) of the perturbation field at a grid point diminishes to e−1. Similarly, the decorrelation length scale l is an isotropic parameter that defines the distance spanned away from a point before the spatial ACF of the perturbation field reaches e−1. Consequently, large t and l scales describe perturbations that evolve slowly with time or have a large spatial extent, respectively. Adjustments to the amplitude parameter σ simply scale the perturbations by changing the grid point standard deviation of the stochastic pattern. In all cases, the amplitude is capped to 2 × σ, so the perturbations do not become too large.
d. Experiment design
For each case, there are 32 combinations of four SPPT and iSPPT parameterization schemes (Table 2), and eight configurations of the stochastic pattern tuning parameters (Table 3). SPPT perturbations are applied to the sum of the physical tendencies associated with only the radiation, PBL, and convection (coarse domain only) parameterization schemes. The iSPPT perturbations are applied individually to PBL, radiation, and microphysics tendencies (Table 2). The choice to perturb individual schemes in isolation was made to leverage the ability of iSPPT to conduct sensitivity experiments (Christensen et al. 2017), in this case to examine the sensitivity of rainfall forecasts to individual parameterization schemes in conjunction with the stochastic pattern tuning parameters. While analysis of ensemble reliability is outside of the scope of the three case studies included in this paper, it is expected that these rainfall forecasts will be underdispersive since perturbations are only directly applied to a single process, unlike in an operational setting where iSPPT patterns would be applied to all parameterization schemes.
Parameterized physics tendencies perturbed by each of the SPPT and individual iSPPT schemes. SPPT perturbs the sum of each tendency across n parameterization schemes p (i.e., PBL, radiation, and cumulus convection), while the iSPPT schemes only perturb tendencies associated with a single parameterization scheme.
Values of the decorrelation time scale, length scale, and amplitude scale for each tuning experiment. The REF and EEPS configurations refer to the SPPT configuration utilized by Romine et al. (2014) and a configuration used operationally in the ECMWF EPS (Leutbecher et al. 2017), respectively. The asterisk indicates that the EEPS amplitude scale is adjusted to σ = 0.40 when paired with iSPPTMP in order to maintain model stability.
Each “L,” “T,” and “A” experiment (Table 3) represents an isolated adjustment to the tunable decorrelation length scale, time scale, and amplitude scale, respectively, with respect to a reference configuration (REF) employed by Romine et al. (2014). The choice to vary parameters independently was made to examine how the rainfall forecast variability responds to the scaling of each tuning parameter. For comparison, the EEPS configuration employs the smallest-scale stochastic perturbations used in the ECMWF SPPT scheme (Leutbecher et al. 2017). For a given case and ensemble, each of the twenty ensemble members are identically configured and use the same initial and boundary conditions, and differ only by the initial seed of the perturbation field. Thus, ensemble spread arises solely as a result of the stochastic perturbations. The choice to use the same initial and boundary conditions for each member of a given case was made to isolate the effect of changing the stochastic pattern alone. Similar to the application of iSPPT to individual parameterization schemes, it is presumed that this choice would lead to underdispersive forecasts, as uncertainty in the initial state is essential to EPSs (e.g., Sivillo et al. 1997).
The TS Lee experiments are used to provide an illustrative example of how the SPPT tuning parameters affect the structure and evolution of the perturbation pattern (Fig. 2). Figures 2a–h depict the stochastic pattern of a single ensemble member (same initial seed) at the same forecast time. Figures 2a and 2b represent the REF and the EEPS configurations, respectively, and demonstrate that the relatively large l, t, and σ scales of the EEPS configuration (Table 3) are realized in spatially large, high-amplitude perturbations relative to the REF configuration. Figure 2i compares the temporal ACF of each tuning configuration. It is clear that the EEPS perturbation field evolves more slowly in time relative to the REF configuration, which is expected given the longer decorrelation time of the EEPS relative to the REF configuration. Examined individually, adjustments to the σ parameter simply scale the amplitude of the perturbations (Figs. 2c,d) and do not alter the spatial or temporal evolution, demonstrated by the identical temporal ACF of the A0.4, A0.3, and REF configurations (Fig. 2i). Adjustments to l modify the spatial scale of the perturbations, with a small l resulting in perturbations that vary rapidly in space, and a large l resulting in more gradual spatial variations (Figs. 2e,f). Increasing or decreasing t does not modify the spatial scale or perturbation amplitude, but does result in different spatial patterns at the same forecast time (Figs. 2g,h) due to the adjusted decorrelation time (Fig. 2i).
Snapshot of the stochastic perturbation pattern (unitless; shaded) over the outer model domain at 0000 UTC 7 Sep 2011 during the remnants of TS Lee case for member 000 of the iSPPTMP ensemble using the (a) REF, (b) EEPS, (c) A0.3, (d) A0.4, (e) L15km, (f) L500km, (g) T900s, and (h) T21600s configurations (see Table 3 for parameter settings). The green box in (a) outlines the innermost, convection permitting domain. (i) The mean temporal autocorrelation function (ACF) of the stochastic pattern at all points in the coarse domain at 0900 UTC during the TS Lee simulations, where the long-dashed gray line corresponds to a correlation of zero, and the short-dashed gray line represents a correlation of e−1. The temporal ACFs of the REF, A0.4, and A0.3 configurations are indistinguishable in (i), as these configurations differ only by perturbation amplitude.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
3. Case selection and overview
a. Remnants of TS Lee: 7–8 September 2011
In the United States, disruptive heavy rainfall events frequently occur during the warm season and can be associated with tropical cyclone activity (e.g., Ashley and Ashley 2008). In these situations, interactions of remnant tropical moisture with the background synoptic-scale flow can yield potentially damaging rainfall hundreds to thousands of kilometers away from the immediate landfall location or track of the TC (e.g., Galarneau et al. 2010; Villarini et al. 2014). One such example is TS Lee (2011), which made landfall along the Louisiana coast on 4 September 2011, and subsequently dissipated by 0000 UTC on 7 September over northwestern Georgia. Remnant moisture from TS Lee interacted with a stationary front over the Mid-Atlantic and northeastern United States, producing in excess of 200–300 mm of rainfall over portions of Maryland, Pennsylvania, New York, and southern New England during 5–10 September. This yielded historic flooding within the Susquehanna River watershed, including 12 flood-related fatalities, evacuations of more than 100 000 people, and total damages exceeding $1 billion (Avila and Stewart 2013).
The remnants of TS Lee produced widespread heavy rainfall over the northeast United States through the interaction between the warm and moist remnant tropical air mass and a preexisting quasi-stationary boundary (Avila and Stewart 2013). The tropical air mass associated with TS Lee, characterized by broad southeasterly flow and a large region of 925-hPa θe > 335 K at 1200 UTC 7 September 2011 (Fig. 3a), progressed northward during 7 September, reorienting and strengthening an area of low-level convergence and the θe gradient along the preexisting boundary. Six-hour rainfall (not shown) exceeding 40 mm was observed in the vicinity of the strong 925-hPa θe gradient and frontal convergence over central Pennsylvania at 1200 UTC (Fig. 3a). Eighteen-hour rainfall exceeding 50 mm extended from central Pennsylvania to the northeast through central and eastern New York, with an embedded band exceeding 90 mm over central Pennsylvania and south-central New York (Fig. 3d).
(top) Control forecast 925 hPa θe (K; shaded) and wind (m s−1; barbs) and (bottom) observed 18-h rainfall (mm) during the three heavy rainfall events. Representative times for each event are (a) 1200 UTC 7 Sep 2011 during the remnants of TS Lee, (b) 0700 UTC 16 Jun 2008 during SoWMEX-IOP8, and (c) 0000 UTC 2 Jun 2017 over northern Taiwan. Stage IV and QPESUMS gridded rainfall products are used for the (d) TS Lee and (f) 2017 mei-yu front events, respectively. Hourly rain gauge observations are used to represent (e) SoWMEX-IOP8.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
b. SoWMEX-IOP8: 15–16 June 2008
The mei-yu season in Taiwan (15 May–15 June) is associated with the climatological northward progression of the southwest monsoon and is characterized by persistent heavy rainfall over the island (Chen and Chen 2003; Chen et al. 2007). Heavy rainfall events during the mei-yu season primarily result from interactions between mesoscale features of the southwesterly monsoon, the topography of Taiwan, and transient southward displacements of the mei-yu front. The mei-yu front is a boundary defined as a zonally elongated axis of cyclonic vorticity, moisture flux convergence, and upward vertical motion separating the southwest monsoon air mass to its south from a continental air mass to its north (Chen 2004). SoWMEX-IOP8 (15–16 June 2008) represents one type of mei-yu season event, characterized by an MCS embedded in the southwest monsoon, and produced in excess of 300 mm of rainfall in 15 h over the coast of southwestern Taiwan.
Xu et al. (2012) provide a comprehensive summary of the physical mechanisms associated the heavy rainfall during SoWMEX-IOP8, focusing on the quasi-stationary MCS offshore of the southwestern coast of Taiwan. The heavy rainfall associated with the MCS (Fig. 3e) was maintained by a warm and moist southwesterly low-level jet continuously interacting with a cold pool along the southern Taiwan coast (Xu et al. 2012). The cold pool was established by evaporative cooling from earlier rainfall as well as local offshore flow associated with a land breeze (Tu et al. 2014). In the unperturbed control simulation, the cold pool identified by Xu et al. (2012) is located over southern Taiwan at 0700 UTC (Fig. 3b) and moves to the north along the western side of the island by 0900 UTC [not shown; see also Fig. 19 of Xu et al. (2012)]. The heaviest rainfall during SoWMEX-IOP8 was restricted to the coastal plain by the cold pool associated with the MCS as well as terrain blocking (Xu et al. 2012).
c. Northern Taiwan mei-yu front event: 1–2 June 2017
The heavy rainfall event during 1–2 June 2017 is characterized by a southward displacement of the mei-yu front over northern Taiwan. This event produced in excess of 700 mm of rain and resulted in significant flooding as well as the loss of power to more than 10 000 homes, the evacuation of more than 250 people in New Taipei City, damage to roads, five injuries, and one fatality (Chung 2017).
The 2017 mei-yu front event produced heavy rainfall over northern Taiwan through interactions between the mei-yu front and the complex terrain of northern Taiwan. The heaviest rainfall through the duration of this event was persistently observed along the convergent baroclinic zone associated with the mei-yu front (Figs. 3c,f). A topographically enhanced barrier jet (e.g., Li and Chen 1998) was associated with locally strong low-level convergence as well as greater rainfall production over northwestern Taiwan (Figs. 3c,f). As the mei-yu front progressed to the south, rainfall occurred primarily over the center of the island as the warm and moist prefrontal monsoon air mass interacted with the Central Mountain Range (CMR), while heavy rainfall over northern Taiwan subsided by 1200 UTC 2 June.
4. Results
The results presented in this section address how different configurations of SPPT and iSPPT impact the ensemble rainfall forecast, with specific focus on ensemble standard deviation as well as the ensemble mean. Results of the TS Lee experiments are described in section 4a, followed by SoWMEX-IOP8 and the 2017 mei-yu front cases in sections 4b and 4c, respectively. Ensemble skill is evaluated in terms of both FSSs and areal coverage of a particular total rainfall threshold, and is discussed for each case in section 4d.
a. Remnants of TS Lee: 0000–1800 UTC 7 September 2011
During the TS Lee event, the quantity and location of the accumulated rainfall standard deviation during 0000–1800 UTC 7 September 2011 varies depending on which parameterization(s) are perturbed. The iSPPTMP experiments tend to be associated with larger ensemble rainfall standard deviation over a larger area than other non-MP experiments, likely on account of the presence of large parameterized microphysics tendencies in areas of clouds and precipitation. The greatest ensemble standard deviation is located over central Pennsylvania in the REF configuration experiments, exceeding 25 mm with SPPT and iSPPTPBL, and 40 mm with iSPPTMP (Figs. 4a–c).The iSPPTMP experiment is associated with a more zonally elongated region of standard deviation exceeding 25–30 mm over central Pennsylvania than the non-iSPPTMP experiments, as well as a more extensive region of rainfall standard deviation exceeding 25 mm over southeastern New York (Fig. 4). The iSPPTRad ensemble is associated with the smallest rainfall standard deviation of the four REF configuration experiments, with rainfall standard deviation exceeding 20 mm only in isolated locations (Fig. 4d).
Accumulated rainfall standard deviation (mm; shaded) over an 18-h period (0000–1800 UTC 7 Sep 2011) during the remnants of TS Lee event for the REF configuration of the (a) SPPT, (b) iSPPTPBL, (c) iSPPTMP, and (d) iSPPTRad ensembles. The solid black and dashed magenta contours indicate where the accumulated rainfall is at least 40 mm for the control forecast and ensemble mean, respectively.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
Beyond the choice of parameterization scheme, rainfall standard deviation is also a function of the stochastic pattern tuning parameters, particularly the decorrelation time scale and amplitude scale. For SPPT, decreasing the perturbation amplitude scale or decorrelation time scale (Figs. 5c,g, respectively) results in a decrease of the rainfall standard deviation compared to the REF configuration (Fig. 5a), while increasing these parameters is associated with larger ensemble standard deviation (Figs. 5d,h, respectively). Experiments which modify the decorrelation length scale, that is, L15km and L500km, are associated with lower ensemble standard deviation relative to the REF experiment; though, the L500km experiment is associated with greater standard deviation than the L15km experiment (Figs. 5e,f). Generally speaking, the EEPS configuration, which is characterized by the largest decorrelation time, length, and amplitude scales, produces the largest rainfall standard deviation, such that the standard deviation exceeds 45 mm over northeastern and central Pennsylvania (Fig. 5b). The behavior of the EEPS configuration is not necessarily surprising in light of the time and amplitude scale-only experiments, which demonstrate that increasing either of these parameters can yield greater rainfall forecast variability. The EEPS configuration used in this study is derived from a multiscale, global SPPT scheme designed to represent errors on larger scales, including those associated with convective parameterization (Leutbecher et al. 2017). Consequently, the perturbation pattern produced by the EEPS configuration, while appropriately tuned for the ECMWF-EPS, may not be as compatible for use in regional, convection-permitting NWP.
As in Fig. 4, but using only SPPT with the (a) REF, (b) EEPS, (c) A0.3, (d) A0.4, (e) L15km, (f) L500km, (g) T900s, and (h) T21600s configurations.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
The results of the 32 SPPT and iSPPT experiments can be generalized by examining area-averaged ensemble rainfall means and standard deviations over the area where the total rainfall exceeds 40 mm in the control forecast. This region is chosen to quantitatively compare the results within the location of the heaviest rainfall. Examining first the hourly evolution of the ensemble rainfall forecasts for the TS Lee case (Fig. 6), it is evident that the ensemble standard deviation generally increases with forecast lead time nearly independent of the mean rainfall rate, indicating that SPPT and individual iSPPT perturbation schemes may affect processes related to rainfall timing and evolution in this case, as well as rainfall intensity. Excluding iSPPTMP experiments, the area-average mean rainfall rate is relatively unaffected by the stochastic pattern tuning parameters. Under all configurations of iSPPTMP (Fig. 6c), the mean rainfall rate as well as the standard deviation are characterized by frequent, high-amplitude variations, with the mean rainfall rate approximately 0.5 mm h−1 greater than other non-iSPPTMP experiments for the duration of the event (Fig. 6c).
Area-averaged hourly ensemble mean rainfall rate (mm h−1; top panels) and standard deviation (mm h−1; bottom panels) for all configurations of (a) SPPT, (b) iSPPTPBL, (c) iSPPTMP, and (d) iSPPTRad for the remnants of TS Lee event during 0000–1800 UTC 7 Sep 2011. Mean rainfall rate is labeled along the left vertical axis, and rainfall rate standard deviation is labeled along the right vertical axis. Forecast time (UTC) increases to the right on the horizontal axis. Area averages are computed over the region where the control forecast total rainfall was at least 40 mm.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
The rainfall standard deviation is particularly sensitive to the perturbation time scale and amplitude scale for the duration of the forecast period, with comparatively less sensitivity to the perturbation length scale. Similar to the spatial distribution of rainfall standard deviation for all SPPT configurations (Fig. 5), experiments which increase the perturbation amplitude or time scale yield a larger ensemble standard deviation than the REF configuration at nearly all forecast lead times for all SPPT and iSPPT experiments (dashed blue and green lines in Fig. 6), while experiments that reduce these parameters are characterized by smaller ensemble standard deviation (solid blue and green lines in Fig. 6). The L500km and L15km experiments are characterized by smaller ensemble standard deviation than the REF configuration at nearly all lead times for all experiments (Fig. 6).
The area-averaged standard deviation of the accumulated rainfall for all TS Lee experiments is summarized in Fig. 7a. iSPPTMP is associated with the greatest rainfall standard deviation for REF configuration experiments (16.5 mm), followed by SPPT (14.0 mm), iSPPTPBL (11.9 mm), and iSPPTRad (9.2 mm). This ranking is consistent for all configurations except for T900s, for which SPPT is associated with the largest standard deviation. Similar to the spatial and hourly results, large amplitude and long decorrelation time scale perturbations increase the area-averaged rainfall standard deviation compared to the REF configuration, increasing or decreasing the decorrelation length scale decreases the standard deviation relative to the REF configuration, and unsurprisingly, the EEPS configuration is associated with the largest standard deviation (Fig. 7a).
Area-averaged ensemble standard deviation (mm) of the 18-h rainfall accumulation during all experiments of (a) the remnants of TS Lee (0000–1800 UTC 7 Sep 2011), (b) SoWMEX-IOP8 (0000–1800 UTC 16 Jun 2008), and (c) the 2017 mei-yu front event (1800 UTC 1 Jun–1200 UTC 2 Jun 2017). Individual bar colors correspond to the SPPT or individual iSPPT scheme, and clusters of bars correspond to the tuning configuration, labeled on the horizontal axis. Horizontal reference lines are colored according to SPPT or iSPPT scheme, and refer to the area-averaged ensemble standard deviation associated with the REF configuration. Area averages are computed over the region where the control forecast total rainfall was at least 40 mm. Area averages are further restricted to northern Taiwan during the 2017 mei-yu front event, defined by the dashed rectangle between 25.6° and 24.6°N and between 120.0° and 122.5°E in Figs. 11 and 12.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
b. SoWMEX-IOP8: 0000–1800 UTC 16 June 2008
The SoWMEX-IOP8 experiments are associated with greater rainfall standard deviation than corresponding TS Lee experiments; though, this standard deviation is similarly sensitive to the choice of perturbed parameterization scheme. The SPPT ensemble is characterized by the most dispersive rainfall forecast of the REF configuration experiments (Fig. 7b), with an area-averaged rainfall standard deviation of 32.7 mm, followed by iSPPTMP (29.5 mm), iSPPTPBL (29.1 mm), and iSPPTRad (26.4 mm). Spatially, the SPPT-REF experiment has rainfall standard deviation exceeding 30 mm over most of the southern third of the island and along the east-central coastline, with isolated areas exceeding 50–60 mm (Fig. 8a). The iSPPTPBL experiment appears to reduce the spatial extent of 30 mm standard deviation over southern Taiwan as well as the frequency of standard deviation exceeding 50 mm (Fig. 8b). While the iSPPTMP experiment (Fig. 8c) is associated with rainfall standard deviation exceeding 70–80 mm in isolated areas over coastal northeastern and southwestern Taiwan, this experiment appears to generally reduce the area of standard deviation greater than 40 mm over southern Taiwan. The iSPPTRad experiment generally reduces ensemble standard deviation over all of Taiwan (Fig. 8d).
As in Fig. 4, but for 0000–1800 UTC UTC 16 Jun 2008 during SoWMEX-IOP8.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
To a lesser degree than the TS Lee experiments, SoWMEX-IOP8 rainfall standard deviation also depends on the stochastic pattern tuning parameters, with the greatest sensitivity to the decorrelation time scale and amplitude scale. Excluding the EEPS configuration, the T21600s and A0.4 configurations are characterized by the largest area-averaged ensemble standard deviation for the SPPT, iSPPTPBL, and iSPPTMP experiments (Fig. 7b). Furthermore, only the T21600s and EEPS configurations are associated with an area of rainfall standard deviation exceeding 70 mm along the eastern coast of Taiwan when using SPPT (Figs. 9b,h). As in the TS Lee experiments, the L15km and L500km experiments each reduce ensemble rainfall standard deviation relative to the REF configuration in all experiments (Figs. 7b and 9e,f).
As in Fig. 8, but using only SPPT with the (a) REF, (b) EEPS, (c) A0.3, (d) A0.4, (e) L15km, (f) L500km, (g) T900s, and (h) T21600s configurations.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
Hourly rainfall variability scales more strongly with mean rainfall rate during SoWMEX-IOP8 experiments than TS Lee experiments (Fig. 10), possibly suggesting that the large-scale timing and evolution during SoWMEX-IOP8 is relatively less sensitive to SPPT and iSPPT perturbations. Comparing the hourly rainfall variability for SPPT and iSPPTMP experiments indicates that iSPPTMP experiments are consistently associated with greater ensemble mean rainfall rates, but the rainfall rate appears to be more sensitive to the stochastic pattern tuning parameters when using SPPT (Fig. 10). While the rainfall rate evolves similarly during the 18-h period for both types of experiments, iSPPTMP experiments are generally associated with a greater area-averaged mean rainfall rate and standard deviation, particularly during 1400–1500 UTC (Fig. 10).
As in Fig. 6, but for (a) SPPT and (b) iSPPTMP experiments during 0000–1800 UTC 16 Jun 2008 during SoWMEX-IOP8.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
c. Northern Taiwan mei-yu front event: 1800 UTC 1 June–1200 UTC 2 June 2017
The 1–2 June 2017 mei-yu front event is characterized by both the heaviest rainfall and largest ensemble standard deviation of the three cases. Each of the REF configuration experiments are associated with three band-like regions of large rainfall standard deviation exceeding 60 mm over northwestern Taiwan, with finer scale differences with respect to the areas of the largest standard deviation (Fig. 11). The SPPT experiment places the three band-like regions over northwestern Taiwan, with rainfall standard deviation exceeding 100 mm in the center band, while the iSPPTPBL experiment appears to be associated with a southward shift of these bands and a smaller region of standard deviation exceeding 100 mm (Figs. 11a,b). The iSPPTMP experiment is associated with the largest standard deviation of these four experiments, exceeding 120 mm over the central band (Fig. 11c). Similar to the preceding cases, iSPPTRad is associated with the smallest standard deviation, not exceeding 80 mm anywhere in the domain (Fig. 11d).
As in Fig. 4, but for 1800 UTC 1 Jun 2017–1200 UTC 2 Jun during the 2017 mei-yu front event. The box over northern Taiwan outlines the specific region of interest described for this event (25.6°–24.6°N, 120.0°–122.5°E).
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
As in the previous two cases, rainfall standard deviation during the 2017 mei-yu front event is particularly sensitive to the decorrelation time scale and perturbation amplitude scale. While the SPPT-REF and T21600s experiments (Figs. 12a,h) are associated with rainfall standard deviation up to 110 and 120 mm over northwestern Taiwan, respectively, the standard deviation during the T900s experiment does not exceed 90 mm (Fig. 12g). The A0.3 and A0.4 experiments are each associated with a small region of rainfall standard deviation exceeding 110 mm (Figs. 12c,d). Both L15km and L500km experiments appear to reduce the spatial extent of standard deviation greater than 80 mm compared to the REF configuration, similar to the two preceding cases (Figs. 12e,f).
As in Fig. 11, but using only SPPT with the (a) REF, (b) EEPS, (c) A0.3, (d) A0.4, (e) L15km, (f) L500km, (g) T900s, and (h) T21600s configurations.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
Similar to the TS Lee case, the area-averaged hourly ensemble mean rainfall rate and standard deviation during the 2017 mei-yu front experiments is particularly sensitive to microphysics tendency perturbations. Additionally, the standard deviation remains nearly constant while the mean rainfall rate decreases prior to 0400 UTC 2 June, potentially indicating uncertainty in the timing and evolution of the heavy rainfall during this period (Fig. 13). For all configurations, the area-averaged mean rainfall rate is up to 3 mm h−1 greater in iSPPTMP experiments than in SPPT experiments until approximately 0000 UTC 2 June (Fig. 13). Similarly, the area-averaged standard deviation is approximately 1–2 mm h−1 greater during iSPPTMP experiments than those using SPPT, with the T21600s and A0.4 configurations contributing the largest standard deviation (Fig. 13).
As in Fig. 6, but for (a) SPPT and (b) iSPPTMP experiments during 1800 UTC 1 Jun 2017–1200 UTC 2 Jun during the 2017 mei-yu front event with area averages restricted to northern Taiwan (25.6°–24.6°N, 120.0°–122.5°E).
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
The total rainfall standard deviation of the 2017 mei-yu front experiments is summarized in Fig. 7c. Similar to the TS Lee case, iSPPTMP is associated with the largest standard deviation when paired with the REF configuration (50.5 mm), followed by SPPT (44.8 mm), iSPPTPBL (41.9 mm), and iSPPTRad (33.9 mm). This ranking is consistent for all configurations except L15km and T900s, where iSPPTRad and iSPPTPBL, respectively, produce the second-largest ensemble standard deviations (Fig. 7c).
d. Verification metrics
In addition to the ensemble standard deviation, it is important to consider how rainfall forecast skill varies in response to the SPPT and iSPPT configurations used in this research, as the application of stochastic perturbations to nonlinear NWP models can alter the skill and biases of the ensemble mean forecast (Romine et al. 2014). Verification metrics are presented here on a case-by-case basis, as the small number of cases and use of different observational datasets limits the generalization of these results beyond individual cases. Despite these limitations, there are some notable similarities in how the stochastic perturbations affect the behavior of the accumulated rainfall forecast skill between the three cases, particularly in iSPPTMP experiments.
In the TS Lee case, the spatial orientation of the control forecast area of rainfall greater than 40 mm approximately matches ST4 observations (Fig. 14a; hereafter area40), but is nearly 28% smaller than the observed area, particularly related to an underrepresentation of rainfall over southeastern Pennsylvania (Fig. 14b). All configurations of iSPPTMP shift the ensemble area40 distribution toward greater areal coverage relative to the control forecast as well as increasing the range of coverages represented among the ensemble members (Fig. 14b). As such, ensemble mean forecasts which reduce the area40 error compared to the control forecast are also associated with an improvement of the FSS of the 40-mm rainfall threshold, with iSPPTMP associated with the highest FSSs for all configurations except T21600s and EEPS (Fig. 14c).
Accumulated rainfall verification metrics for the TS Lee event during 0000–1800 UTC 7 Sep 2011. (a) Control forecast rainfall (mm; shaded, black contour denotes 40 mm) and ST4 rainfall estimates (white dashed 40-mm contour), (b) box and whisker distribution of all ensemble members’ areal coverage of at least 40 mm of rainfall percent error compared to ST4, where the control forecast error is denoted by the dashed black line and the percent error of the ensemble mean forecasts are denoted by filled gray circles, and (c) the difference between the fractions skill score of the ensemble means and the control forecast using a rainfall threshold of 40 mm and a neighborhood length of 63 km.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
The positive shift associated with iSPPTMP during TS Lee experiments is also present at higher rainfall thresholds, such as area70, despite a positive bias in the control forecast at these greater thresholds (e.g., Figs. 3d and 14a). The iSPPTMP experiments are therefore associated with a degradation of the FSS using a 70-mm rainfall threshold (not shown). Moreover, iSPPTMP increases the ensemble mean accumulated rainfall at the 75th, 90th, 95th, and 99th percentiles by 10%–15% over the control forecast, while the control forecast rainfall at the 99th percentile (126.68 mm) is already 27.4% greater than the 99th percentile of observed rainfall (96.08 mm; not shown). Accumulated rainfall percentiles associated with other SPPT and individual iSPPT experiments of the TS Lee event are generally within approximately 5% of the control forecast (not shown).
The observed spatial extent of the area40 over southwestern Taiwan during SoWMEX-IOP8 is generally well represented by the control forecast, but this forecast is characterized by a positive bias in areal coverage which is made worse using SPPT and individual iSPPT schemes, particularly due to an erroneous rainband over the eastern side of the island. Alternatively, it is possible that a portion of this positive bias is influenced by relatively sparse rain gauge observations on the eastern slopes of the CMR compared to the majority of the island (e.g., Fig. 1a of Yang et al. 2014). Examining the heavy rainfall over southwestern Taiwan, total accumulation is generally underestimated by the control forecast (Figs. 3e and 15a), an error that is likely related to the position of the MCS cold pool in this simulation.
As in Fig. 14, but for 0000–1800 UTC 16 Jun 2008 during SoWMEX-IOP8 and using rain gauge observations. In (a), the discontinuous observed rainfall contour over southern Taiwan is a result of the classification of all observations offshore of Taiwan as “missing.”
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
Similar to the TS Lee case, SoWMEX-IOP8 iSPPTMP experiments are associated with a larger ensemble mean area40 than that of the control forecast as well as a shift of the area40 distribution toward larger areas (Fig. 15b). Conversely, non-iSPPTMP experiments are generally shifted toward reduced area40 values (Fig. 15b). Assuming that the available rain gauge observations sufficiently capture this event, all ensemble experiments degrade the FSS for a 40-mm rainfall threshold, with iSPPTMP characterized by the largest FSS decrease (Fig. 15c).
The 2017 mei-yu front control forecast overestimates the QPESUMS observed area40 by nearly 16%, which represents an areal coverage bias that is generally made worse when applying SPPT and iSPPT, particularly iSPPTMP (Fig. 16). Unlike the TS Lee case, however, the control forecast underestimates rainfall at higher thresholds, possibly as a result of errors in the simulated southward progression of the mei-yu front and errors in the representation of the low-level barrier jet. In this case, the control forecast rainfall at the 99th percentile (221.67 mm) is nearly 25% smaller than observed (283.56 mm; not shown). Therefore, the positive bias associated with iSPPTMP generally improves the forecast of the 99th percentile rainfall.
As in Fig. 14, but for 1800 UTC 1 Jun 2017–1200 UTC 2 Jun during the 2017 mei-yu front event and using QPESUMS observations.
Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0064.1
5. Discussion
The preceding section documents the effects of varying the stochastic pattern tuning parameters of SPPT and individual implementations of iSPPT on ensemble forecasts of three heavy rainfall events. While this small sample may limit the generalization of some of these results beyond their case-by-case interpretation, several aspects of these experiments appear to be consistent between the three cases. In particular, the response of the rainfall standard deviation to the stochastic pattern tuning parameters is similar between the three cases, while the relative contribution of individually perturbed parameterization schemes is less clear.
Accumulated rainfall standard deviation is generally most sensitive to the decorrelation time scale and amplitude scale for each heavy rainfall event. Examining all cases and experiments together in Fig. 7, increasing either parameter (T21600s and A0.4) with respect to the REF configuration generally yields greater ensemble variability. Conversely, decreasing these parameters tends to decrease the ensemble spread. For the T21600s experiment, it is likely that the application of a spatially consistent perturbation pattern over a longer period of time drives the solutions of individual ensemble members further apart from each other. The results of the A0.4 experiments are perhaps intuitive, as these experiments simply use numerically larger perturbations to achieve greater variability in the ensemble rainfall forecasts.
Perhaps one of the more surprising results of the tuning experiments is the response of the accumulated rainfall standard deviation to the perturbation length scale, as most L15km and L500km experiments decrease rainfall forecast variability as compared to the REF configuration (Fig. 7). It is possible that the rapid spatial decorrelation in the L15km experiments approximates spatially uncorrelated noise, which may result in strongly damped perturbations, while the large length scale used in the L500km and EEPS experiments may be more effective on slowly evolving meso–synoptic-scale features. Generalization of the results of various tuning experiments is more challenging for iSPPTRad experiments, which are less sensitive to the scaling of the tuning parameters, and iSPPTMP experiments, which exhibit more case-by-case variability.
In addition to being the least sensitive to the stochastic pattern tuning parameters, iSPPTRad experiments are also generally characterized by the smallest accumulated rainfall standard deviation (Fig. 7), likely due to the stochastic pattern directly perturbing the θ tendency, only (Table 2). The response of the accumulated rainfall standard deviation to different configurations of iSPPTRad is not consistent between the different cases nor is it consistent with other perturbed parameterization schemes. For example, in the TS Lee iSPPTRad experiments (Fig. 7a), the accumulated rainfall standard deviation responds similarly to the other non-iSPPTRad experiments. During SoWMEX-IOP8 experiments, however, all configurations of iSPPTRad except for EEPS yield reduced rainfall forecast variability with respect to the REF configuration (Fig. 7b). Similarly, all configurations of iSPPTRad during the 2017 mei-yu front experiments, except L500km, increase the standard deviation compared to the REF configuration (Fig. 7c).
While the response of the accumulated rainfall standard deviation to different tuning configurations of iSPPTMP is consistent between cases, the amount of variability relative to other SPPT and iSPPT experiments appears to depend more strongly on the meso–synoptic scale environment and the physical processes leading to heavy rainfall. Specifically, the TS Lee and 2017 mei-yu front events exhibit the greatest variability when using iSPPTMP (Figs. 7a,c), and are characterized by rainfall occurring along a synoptic-scale frontal zone associated with a large 925-hPa θe gradient and large-scale convergence (Figs. 3a,c). The SoWMEX-IOP8 event is primarily driven by the interaction of an MCS with the land breeze and southern CMR in Taiwan [Fig. 3b and Fig. 19 of Xu et al. (2012)] and is characterized by greater rainfall variability during SPPT experiments (Fig. 7b), indicating that the rainfall in this case may be more sensitive to perturbations to the parameterized momentum tendencies than the more frontally forced cases.
It is unlikely that the reduced sensitivity of the SoWMEX-IOP8 accumulated rainfall standard deviation to iSPPTMP is related to the choice of physical parameterization schemes, as both SoWMEX-IOP8 and the 2017 mei-yu front event use the Goddard microphysics scheme (Table 1). In this vein, it is noted that rainfall forecasts during the TS Lee and 2017 mei-yu front events are similarly sensitive to the use of iSPPTMP despite the use of different microphysics schemes (Table 1). Current research is ongoing to understand the physical processes by which direct perturbations to physical tendencies, such as those associated with the microphysics and boundary layer parameterization schemes, act to indirectly influence rainfall forecasts.
6. Summary and conclusions
Motivated by the limited understanding of stochastic model error schemes on meso–synoptic-scale heavy rainfall events, this paper examines the sensitivity of WRF-ensemble rainfall forecasts of three synoptically similar heavy rainfall events to the configuration of SPPT and various individual iSPPT schemes. Comparison of the rainfall standard deviation of thirty-two 20-member ensembles of 1) the remnants of TS Lee over the northeast United States in 2011, 2) SoWMEX-IOP8 over southern Taiwan in 2008, and 3) a mei-yu front event over northern Taiwan in 2017 indicates that high-amplitude, slowly evolving perturbations are generally associated with the largest rainfall forecast variability. Additionally, perturbations to microphysics tendencies are associated with the largest rainfall standard deviation during the TS Lee and mei-yu front events, while perturbations to sum of the parameterized nonmicrophysics tendencies are associated with the largest standard deviation during SoWMEX-IOP8. Finally, a preliminary examination of forecast skill from these individual cases indicates that microphysics tendency perturbations are generally characterized by the largest changes to the FSS as compared to the control forecast, while also increasing the spatial coverage of high rainfall totals.
The research described in this paper presents several potential avenues for future work, particularly in terms of verification studies and process-based experiments. The results of the limited verification study included in this research could be used as a starting point for future analyses, as there is some consistency in how select skill metrics respond to different configurations of SPPT and individual iSPPT schemes; however, a more robust analysis of forecast skill should be conducted over many cases with a fixed model configuration and verification dataset. Future verification studies should also include a representation of initial condition uncertainty in addition to using SPPT, while iSPPT experiments could additionally benefit from perturbing multiple parameterization schemes with independent stochastic patterns.
Examination of the physical processes by which SPPT and iSPPT schemes lead to rainfall forecast variability is the subject of ongoing research. Stochastic perturbations to the physical tendencies associated with the radiation, microphysics, and boundary layer schemes are likely to induce spread in ensemble rainfall forecasts by acting on considerably different processes, such as those associated with rainfall rate and duration (e.g., Doswell et al. 1996). It is expected that this type of analysis, as well as the tuning experiments included in this study, could provide insight on the interpretation of ensemble forecasts generated using stochastic perturbation schemes.
Acknowledgments
This research is supported by the National Science Foundation (NSF) through Grant OISE-1545917. High-performance computing support was provided by NCAR’s Computational and Information Systems Laboratory (Cheyenne; doi:10.5065/D6RX99HX), sponsored by the NSF. ST4 data were provided by NCAR/EOL (https://data.eol.ucar.edu/) under sponsorship of the NSF. QPESUMS rainfall data were made available by the Central Weather Bureau (CWB) in Taiwan, and rain gauge observations were also made available by the CWB and provided in gridded, hourly form by Hsiang-Wen Cheng (NCU). We would also like to thank Dr. Judith Berner (NCAR) for her assistance in implementing iSPPT into version 3.7.1 of the WRF Model, as well as Dr. Jeffrey Whitaker (NOAA-ESRL) and Dr. Ching-Sen Chen (NCU) for providing insightful discussion on SPPT and the 2 June 2017 mei-yu front event, respectively. Comments and suggestions from three anonymous reviewers were also beneficial to the clarity of this paper as well as the discussion of the results.
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Since the observational data may not be available over the entire model domain, the threshold areal coverage metrics are only computed for forecast rainfall at model grid points where the observational data are not missing. Missing data are also ignored when computing FSSs.
Negative water vapor mixing ratios are adjusted by subtracting these quantities from a neighboring grid point and setting the original grid point to zero. Supersaturated grid points following SPPT or nonmicrophysics iSPPT perturbations are handled by the microphysics scheme. Since iSPPTMP is applied after completion of the microphysics scheme, it is possible for supersaturated grid points to exist at the start of subsequent model time steps.