1. Introduction
In the northeastern United States (the Northeast), the most severe historical rainfall extremes and floods are linked to Atlantic hurricanes (Liu et al. 2017; Su and Smith 2021; Henny et al. 2022; Smith et al. 2023). The extratropical stage of Hurricane Ida (2021) is a recent example of an impactful extreme rainfall event associated with a hurricane’s extratropical transition but stood out from prior storms due to the observed intensity of hourly scale rainfall. After rapid intensification in the Gulf of Mexico, Ida made landfall in Louisiana as a category 4 hurricane on 29 August (Beven et al. 2022, Figs. 1b,d). Subsequently, Ida underwent extratropical transition while moving across the eastern United States. Ida reached the Northeast on Wednesday, 1 September, with 24-h precipitation accumulations exceeding 200 mm across a heavily populated swath of the region (Fig. 1c). Several locations within this region experienced record flooding and 1–3-h rainfall (Fig. 1e). Smith et al. (2023) demonstrate that record flood peaks at USGS stream gauging stations coincided in space and time with intense mesoscale convection, in particular supercell thunderstorms and clusters of supercells. Localized short-duration rainfall rates exceeded standard 1000-yr return interval magnitudes from NOAA’s precipitation frequency atlas (Bonnin et al. 2006). Tornadoes touched down in New Jersey, Pennsylvania, and Maryland; the strongest was an EF3 tornado in Mullica Hill, New Jersey (Smith et al. 2023; Beven et al. 2022).
Observed precipitation along Ida’s trajectory. (a) Track of Hurricane Ida, from HURDAT. Red boxes surround landfalling TC-centered and Northeast domains. (b) TC-centered domain: 24-h MRMS system observed precipitation accumulation from 1200 UTC 29 to 30 Aug 2021. (c) Northeast domain: 24-h precipitation accumulation from 1200 UTC 1 to 2 Sep 2021 (mm). Note that (b) and (c) use different color bar scales. (d) Maximum 1-h precipitation (mm) from the same 24-h period used in (b). (e) Maximum 1-h precipitation (mm) from the same 24-h period as used in (c).
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
The National Weather Service had issued warnings of heavy rainfall and flooding 2 days in advance, disseminating forecasts that appropriately predicted heavy rainfall accumulations over a 6-h period. However, members of the public and government officials were unprepared for the heavy hourly scale rainfall that flooded buildings and overwhelmed stormwater management infrastructure (Olivas 2022). Ida’s extratropical stage caused at least 55 deaths in New York, New Jersey, and Pennsylvania. Most deaths were related to flash flooding: victims were trapped in cars, swept away by floodwaters, or drowned in flooded homes and apartments (Hanchey et al. 2021; Beven et al. 2022).
The predictability (also called “practical predictability”) of an event is the extent to which its outcome is knowable in advance based on available information such as the quality and quantity of observational data for initial conditions and given available modeling tools. Atmospheric processes are subject to deterministic chaos, with the time range of “intrinsic predictability” generally decreasing with the spatial scale of the phenomenon in question (Robinson 1967; Lorenz 1969; Tribbia and Baumhefner 2004; Rotunno and Snyder 2008). Predictability also depends on our ability to accurately model relevant physical processes. A model’s representation of an event, the quality of which we refer to as “model skill,” is probabilistic in nature because of limits on intrinsic predictability. Characterizing predictability is therefore necessary for a statistically robust understanding of the localized rainfall extremes in Ida’s extratropical stage.
Describing the statistics and dynamics of extreme events is important for disaster preparedness and adaptation, and extreme rainfall after extratropical transition has not previously been investigated with convection-permitting ensemble hindcasts. We present a case study examining extreme rainfall in the northeastern United States in the extratropical stage of Hurricane Ida. We perform perturbed initial condition ensemble hindcasts of the event using a version of the Geophysical Fluid Dynamics Laboratory (GFDL) system for High-resolution prediction on Earth-to-Local Domains (SHiELD) model configured with a convection-permitting nest over the tropical Atlantic version of GFDL’s SHiELD (T-SHiELD). We evaluate predictability in forecasts of Ida’s extratropical stage: could the highly localized impacts have been forecasted and communicated in advance? Then, we show how the mechanisms responsible for extreme rainfall in the extratropical stage of the storm affect the character and predictability of hazards.
2. Methods
a. Observations
1) Tropical cyclone tracks
The National Hurricane Center (NHC) maintains an official record of the track, intensity, and central pressure of tropical cyclones (TCs) and subtropical cyclones. These data are included in the hurricane database (HURDAT). The “best tracks” of tropical cyclones in the HURDAT are based on poststorm analyses of multiple data sources, reviewed and smoothed by NHC experts (Landsea and Franklin 2013). To represent the observed TC track, we use information pertaining to Hurricane Ida from the HURDAT2 database (https://www.aoml.noaa.gov/hrd/hurdat/hurdat2.html).
2) Precipitation observations
For comparison with simulated rain rates, we use two observational datasets: the Multi-Radar Multi-Sensor (MRMS) system data from NOAA’s National Severe Storms Laboratory and the National Centers for Environmental Prediction (NCEP) stage IV precipitation reconstruction. These datasets were chosen because they have a spatial grid size comparable to or finer than that of T-SHiELD’s nested domain and are available at hourly resolution.
Quantitative precipitation estimates from the MRMS dataset are derived from three-dimensional volume scan data from WSR-88D radars and hourly numerical weather prediction model analyses. Rainfall rates are calculated using empirical rain rate–radar reflectivity (R–Z) relationships for three classes of hydrometeor types: warm and cold stratiform rain, convective rain and hail, and snow. The rain rate field is calculated every 2 min (Zhang et al. 2016), and these 2-min estimates are combined to create fields on longer time intervals. MRMS estimates as of October 2020 use specific differential phase shift (KDP) measurements from dual-polarization radar to estimate precipitation rates in scenarios where hail is present. MRMS data are available at high spatial resolution: 0.01° latitude/longitude. We use the variable for radar-based 1-h precipitation accumulations, “RadarOnly_QPE_01H.”
NCEP stage IV precipitation estimates (Du 2011; Lin and Mitchell 2005) are based on multisensor rainfall estimates produced from rain gauge–corrected radar observations at each of 12 River Forecast Centers (RFCs; the area analyzed in this study includes part of the mid-Atlantic and Northeast RFCs) in the continental United States. These fields are sent to the NCEP, where manual quality control is performed and analyses from different regions are combined to produce a national mosaic. A more thorough description and assessment of NCEP stage IV precipitation estimates can be found in Nelson et al. (2016). NCEP stage IV analyses have a grid spacing of 4 km × 4 km.
We chose to use radar-based precipitation reconstructions because they are better suited for the analysis of convective precipitation than lower-resolution datasets such as satellite-based products. These reconstructions are subject to biases inherent to radar-based measurements, such as beam blockage, anomalous propagation, and range-dependent measurements. Additional uncertainty stems from quality control methods and postprocessing algorithms. Both datasets are based on similar raw data, so by comparing the two, we sample some of the uncertainty introduced during the transformation of radar observations into spatially and temporally complete estimates of rainfall.
b. Numerical simulations
We perform a series of simulations using the 2021 version of T-SHiELD (Gao et al. 2021), a configuration of GFDL’s SHiELD (Harris et al. 2020b) optimized for medium-range Atlantic tropical cyclone and hurricane prediction. SHiELD uses the GFDL nonhydrostatic, finite-volume cubed-sphere (FV3) dynamical core, which solves the fully compressible Euler equations with a Lagrangian vertical coordinate (Harris et al. 2020a, 2021). Microphysics parameterizations are tightly coupled to the dynamical core; for example, SHiELD explicitly represents the effects of water vapor and condensate on the density and specific heat capacity of air (Zhou et al. 2019; L. Zhou et al. 2022; Harris et al. 2021).
T-SHiELD uses two-way nesting over the tropical North Atlantic (Harris and Lin 2013), which has been shown to improve general circulation model (GCM) skill in the simulation of structure, intensity, intensification rate, and climatology of major hurricanes and to improve representation of the TC inner core and convective-scale features important for storm evolution (Gao et al. 2019a,b). T-SHiELD is configured with a 13-km grid global domain, with a two-way nest refined by a factor of 4 over the tropical North Atlantic for a nested grid spacing of ∼3 km.
Physical parameterizations are adapted from the operational Global Forecast System (GFS) version 14 parameterizations, with further testing and modifications at GFDL to improve TC track and intensity forecasts. We use NCEP’s GFS deep and shallow scale-aware cumulus convection scheme (Han et al. 2017) to parameterize convection; the parameterization of deep convection in the high-resolution nest, where the resolution is sufficient to explicitly represent deep convection, is turned off (i.e., Prein et al. 2015). Additional physical parameterizations include GFDL’s single-moment five-phase cloud microphysics scheme (Zhou et al. 2019), the Yonsei University planetary boundary layer scheme (Zhou et al. 2019), the Rapid Radiative Transfer Model for GCMs (Iacono et al. 2008), and a simple mixed-layer ocean model (Pollard et al. 1973) to account for atmosphere–ocean interactions, including turbulent fluxes at the ocean surface.
Ensemble forecasts are generated with initial conditions derived from NCEP’s Global Ensemble Forecast System (GEFS). GEFS initial conditions are 31-member ensembles—a baseline and 30 perturbed ensemble members—with 25-km horizontal grid spacing. Initial condition fields are produced using a nonhydrostatic, FV3-based model, and perturbations are generated using an ensemble Kalman filter, without TC relocation (X. Zhou et al. 2022). GEFS initial conditions are regridded from their original resolution to the T-SHiELD grids. No TC-specific data assimilation techniques are used.
In each set of ensemble forecasts, the baseline is labeled “c00,” and the 30 perturbed ensemble members are labeled “p01,” “p02,” and so on. Each simulation is run for 7 days, with output saved out at an hourly frequency. Initialization times are 0000 UTC 26–31 August 2021. Hereafter, the six sets of ensemble forecasts will be labeled by initialization date as 26–31 August.
Tropical cyclone tracking is performed using the GFDL quick tracker (https://github.com/lharris4/GFDL_quick_tracks), which tracks tropical cyclones based on sea level pressure, 10-m winds, and the 500–300-mb (1 mb = 1 hPa) temperature difference. The tracking method is described in the appendix of Harris et al. (2016). In our application, the number of required closed sea level pressure contours is 1, and the contour interval is 4 mb. The tracker is applied to hourly data, only at times during which Ida was a tropical storm with a well-defined warm-core structure.
3. Results
a. Predictability and skill
We characterize the predictability of rainfall within a probabilistic framework that considers limits to intrinsic predictability alongside model skill. Ensemble members differ from one another in their initial conditions only; no changes are made to the model itself. We therefore expect ensemble spread to be inversely related to intrinsic predictability of the quantity in question. Model skill is distinct from intrinsic predictability: irrespective of ensemble spread, we would expect the distribution of outcomes simulated by a higher skill model to be closer to the observed outcome, while the outcomes simulated by a lower skill model would be further from the observed outcome and show more “systematic bias.” Systematic bias pertains to the location of the simulated distribution, while intrinsic predictability pertains to the spread.
Before analyzing the extratropical stage, we briefly discuss the tropical portion of Ida, whose representation is important for setting the trajectory of extratropical transition. In Ida’s tropical stage, ensemble simulations initialized multiple days before landfall demonstrates systematic biases compared to the observed TC track (Fig. 2). Accordingly, the 24-h accumulated rainfall between 1200 UTC 29 and 30 August 2021 in a fixed domain is consistently centered to the south and west of the observed TC rainfall (comparing Fig. 3 to Fig. 1). In contrast to ensembles 26–28 August, ensembles 29–31 August do not have an obvious westward bias compared to Ida’s observed track after landfall (Fig. 2, Figs. S1–S3 in the online supplemental material).
Track forecast error increases with lead time. (a) Ensemble hourly TC tracks from initialization time to 1800 UTC 31 Aug 2021. The HURDAT track is shown in black. (b) Track forecast error at 1200 UTC 30 Aug 2021 [starred location in (a)]. Horizontal line at mean of ensemble members.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
Ensemble variation in tropical-stage rainfall. Accumulated rainfall between 1200 UTC 29 and 30 Aug 2021 for the 27 Aug ensemble. The domain is fixed around the observed TC center at 0000 UTC 30 Aug. MRMS QPE and NCEP stage IV observations are shown in the last two panels.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
We consider rainfall from Ida’s extratropical phase in a rectangular domain from 279° to 288°E and from 37° to 41.4°N (red box in Fig. 1). This domain was chosen to encompass the areas with the highest observed storm total rainfall. Results related to the most extreme values of rainfall within the domain do not qualitatively change with an expansion or contraction of domain size. Results regarding the pattern of precipitation are relatively more sensitive to domain placement, but analyses with modest changes in domain size yield qualitatively similar results; for example, see Fig. S29. The relevant 24-h period is between 1200 UTC 1 and 2 September.
We first compare the simulated and observed patterns of rainfall accumulations across the region. In the 30 August ensemble—which has a lead time of 60 h to the beginning of this temporal window, a time scale typical for forecasting and hazard warnings—the large-scale patterns of rainfall are qualitatively consistent across all ensemble members, with swaths of rainfall over 100 mm day−1 in southeastern Pennsylvania and parts of New Jersey. Areas of extreme rainfall exceeding 150 mm day−1 are diverse in their locations and sizes across the ensemble. The size of areas exceeding 200 mm of rainfall in the ensemble (Fig. 4) is visibly smaller than observed (Fig. 1). We highlight here the 30 August ensemble for parsimony, but the same remarks apply to the 29 and 31 August ensembles, as evident in Figs. S6 and S7.
Ensemble variation in extratropical-stage rainfall. Accumulated rainfall between 1200 UTC 1 and 2 Sep 2021 for the 30 Aug ensemble. MRMS QPE and NCEP stage IV observations are shown in the last two panels.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
We analyze pattern correlations to characterize the lead time dependence of predictability and skill for simulated extratropical precipitation. For each ensemble, a matrix of the Pearson product-moment correlation coefficients (r values) between observations and each ensemble member and between each unique pair of ensemble members is computed from data regridded to a uniform 0.25° × 0.25° grid (changing this resolution does not significantly alter the results). The pattern correlation measures the similarity between the spatial pattern, but not the magnitude or scale, of rainfall in each pair. Variations in pattern correlations arise from the chaotic effects of initial condition perturbations. Because distributions of r values are skewed for values close to −1 or 1, making it difficult to perform statistical tests, we use Fisher’s z transformation (z; Fisher 1921) to normalize the r distributions. Correlation matrices of both z and r are shown in Fig. S8. Higher average pattern correlations indicate that the average discrepancy between ensemble members is lower and that the spatial pattern of 24-h precipitation has a higher intrinsic predictability.
The means μ of the distributions of ensemble–ensemble r values (red solid lines in Fig. 5a) and of observation–ensemble z values (gray solid lines in Fig. 5a) increase with decreasing lead time, consistent with the expectation that forecast precision decreases with increasing time from initialization. The differences between means of ensemble–ensemble and observation–ensemble r (red dashed line) and z (gray dashed line) values tend to decrease with decreasing lead time, indicating that the model ensemble also becomes more accurate at shorter lead times. This can be understood visually in Fig. S8; Fig. 5a uses means of the distributions plotted in Figs. S8f–j. For a model with perfect skill within constraints of intrinsic predictability, the ensemble simulations would be statistically indistinguishable from the observed phenomenon, and the ensemble–ensemble and observation–ensemble z values would be effectively drawn from the same underlying distribution. In Fig. 5b, p is the probability that the null hypothesis—that the distribution of z values from ensemble–ensemble correlations and observation–ensemble correlations (green and blue PDFs in Fig. S8) are generated by sampling a distribution with the same mean—is true. The logarithm of p is plotted against initialization time; higher p values correspond to higher skill.
Lead time dependence of extratropical-stage rainfall pattern predictability. (a) Solid lines: mean μ of z (gray lines) or of r (red lines) values for ensemble–ensemble pattern correlations (as in Figs. S5f–j) by ensemble initialization date. Dashed lines show respective differences in means between the ensemble–ensemble distributions and observation-ensemble distributions of z or r. (b) The p value from the Student’s t test is applied to the ensemble–ensemble and observation–ensemble distributions of z for each ensemble initialization date, where the null hypothesis is that the two distributions have the same mean. The time interval is the same as Figs. 1 and 4. Data have been regridded to a uniform 0.25° × 0.25° grid.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
The 27 August ensemble has a very poor skill for the pattern of accumulated rainfall in this domain, as is also evident visually in Fig. S4. Only a handful of ensemble members in the 27 August ensemble produces significant extratropical rainfall in the Northeast domain (Fig. S4), suggesting that the process and impacts of extratropical transition were not well captured in this ensemble. This is likely related to the prominent systematic bias in the TC track for the 27 August ensemble compared to observations (Fig. 2), as errors in the phasing of the TC and extratropical system are known to be a reason for forecast error (Keller et al. 2019).
The 29–31 August ensembles have p values exceeding 0.03, representing the large-scale rainfall pattern more skillfully than the two ensembles with earlier initialization times. We note, however, that the increase in p with decreasing lead time from 27 to 31 August is nonmonotonic. On the one hand, systematic errors within the ensemble are amplified with increasing lead time and have a negative influence on the p value. On the other hand, the inherent predictability of an event is higher with decreasing lead time, and this decreased variability among ensemble members can draw the p value down: observations will stand out more from a slightly biased ensemble if there is less variability within that ensemble. Thus, the nonmonotonicity of p with changing lead times reflects the competing influences of changes in systematic errors and intraensemble spread.
Still, the 29–31 August ensembles have relatively higher skill than earlier initialization times. Can these three ensembles, which reasonably simulate the large-scale pattern of rainfall, capture the scale and magnitude of observed rainfall extremes? Hour by hour, the distributions of exceedance probabilities versus rainfall rates mostly span a space that includes corresponding values from the two observational datasets (Fig. 6). The ensembles have large variations in simulated maximum hourly intensity and sample the most intense observed rainfall rates. In the most heavily precipitating hours from 2300 UTC 1 September to 0100 UTC 2 September, the maximum simulated rainfall rates in a single ensemble differ by factors of 2.5–3.9. The shapes of simulated precipitation distributions are most apparently biased in the hours shortly after the maximum observed rainfall. At 0200 and 0300 UTC 2 September, simulated exceedance probabilities diverge for hourly rainfall values above the 99th percentile before meeting again at their respective maximum values. The area over which these very high hourly rainfall rates are reconstructed in observations exceeds the area over which these rates are simulated in the ensemble.
Simulated and observed hourly precipitation in the Northeast. Probability of exceedance (%) vs magnitude of hourly precipitation, by hour, within Northeast domain. Black lines represent the observations, with the dotted line representing MRMS quantitative precipitation estimates and the dashed line representing NCEP stage IV data. Orange, green, and blue lines represent the model ensembles initialized on 29, 30, and 31 Aug, respectively. All data have been regridded to a ∼3-km grid.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
The distribution of 24-h rainfall accumulations (Fig. 7) integrates over biases in the hourly rainfall distributions. Simulated and observed exceedance probabilities are similar for rainfall accumulations less than approximately 150 mm, or the 95th percentile of observed rainfall values. A bias in the spatial extent of heavy rainfall values is clear between the 95th and 99.9th percentiles of rainfall accumulations (marked with gray dashed lines), indicating that the ensembles underestimate the spatial extent of heavy rainfall accumulation. The value of the maximum 24-h rainfall (regridded to a uniform ∼3-km grid) diverges between the MRMS and NCEP datasets, with MRMS recording accumulations up to 300 mm and NCEP recording accumulations up to 259 mm. The 29–31 August ensembles simulate rainfall accumulations up to 289, 301, and 326 mm, respectively. The simulated maxima in 24-h rainfall accumulations differ by a factor of 2 or more in each ensemble. The maximum observed rainfall accumulation, whether based on MRMS or NCEP reconstructions, falls at the upper end of the distribution spanned by the three ensembles.
Simulated and observed 24-h precipitation accumulations in the Northeast. Probability of exceedance (%) vs magnitude of accumulated 24-h precipitation (mm) within Northeast domain. Black lines represent the observations as in Fig. 6. Orange, green, and blue lines represent the model ensembles initialized on 29, 30, and 31 Aug, respectively. All data have been regridded to a ∼3-km grid.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
The three ensembles show a significant spread in the magnitude and location of simulated rainfall maxima across the Northeast. Figure 8 summarizes the spread in maximum simulated daily (Fig. 8a) and hourly (Fig. 8b) rainfall rates for the 29–31 August ensembles. Colors correspond to the magnitude of maximum precipitation, and a star marks NCEP observations. For both daily and hourly rates, the locations of the observed extremes within the domain range from just adjacent (14 km away) to the observed maximum to the southern edge of the domain over 400 km away from the observed maximum.
Spread in geographic location and magnitude of precipitation maxima. (a) Markers at locations of 24-h precipitation maxima. The color indicates the magnitudes of maximum precipitation accumulations. Circles, triangles, and diamonds denote 29, 30, and 31 Aug initialization times, respectively. Star denotes observations. (b) As in (a), but for hourly precipitation within the same period.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
Most simulated 24-h rainfall maxima are lower than the NCEP maximum; only 4% of ensemble members have maximum precipitation values exceeding the observed maximum in NCEP (Fig. 8a). For hourly precipitation, however, 47% of ensemble members exceed the reconstructed hourly precipitation maximum, and simulated maxima reach up to 1.4 times that value. The ensemble reaches hourly rainfall rates well above the observed maxima in some individual hours (Figs. 6 and 8b) but underestimates the temporal coherence of these maxima and so underestimates maxima in accumulated 24-h rainfall.
b. Environmental covariates
Relationships between ensemble spread in precipitation rates and ensemble spread in environmental variables such as moisture, winds, and convective available potential energy (CAPE) may be examined for insight into the mechanisms driving extreme rainfall in Ida’s extratropical stage. In this section, we analyze environmental covariates to describe mechanisms governing different magnitudes and time scales of rainfall. To illustrate the particular character of extratropical hazards, we contrast impacts in the Northeast to the tropical portion of the storm.
Unsurprisingly, both tropical (Fig. 9a) and extratropical (Fig. 9b) domains show a strong positive linear relationship between average moisture flux convergence in the domain and average accumulated precipitation over a 24-h period. However, a significant contrast emerges between tropical and extratropical stages in the relationship between large-scale moisture convergence and grid-scale rainfall extremes. In Ida’s tropical stage, local hourly rainfall rates are well correlated to total domain moisture flux convergence—and accordingly to total precipitation—across nearly all intensities shown, including extreme values above the 95th percentile (Fig. 9e). By contrast, in Ida’s extratropical stage, interensemble spread in large-scale moisture flux convergence does not predict interensemble spread in the most extreme rainfall rates. For the Northeast domain (Fig. 9f), r begins to dip rapidly between the 90th and 95th percentiles of hourly rainfall. As r values decrease, p values rise to exceed 0.05: there is no longer a significant positive relationship between large-scale convergence and hourly precipitation magnitudes. In the 30 August ensemble, the relationship between large-scale convergence and hourly rainfall rates becomes significantly negative around the 97th percentile, suggesting that extreme hourly precipitation may depend on processes that are negatively correlated to moisture convergence. [The interpretation of Fig. 9e is insensitive to whether the domain is centered around individually tracked storms in each ensemble or around the observed storm center (Fig. S20). We do not perform a similar storm-centered analysis for the Northeast domain because by the time of the heavy rainfall there, the storm had transitioned to a cold-core, frontal system with relatively weaker and less compact pressure gradients.]
Relationship between moisture convergence and precipitation in tropical vs extratropical stages. (a),(b) Domains to be analyzed in each column: equal-area boxes around the observed TC center at 0000 UTC 30 Aug in (a) and Northeast domain in (b). (c),(d) Scatterplots of domain-average 24-h precipitation vs domain-average 24-h moisture convergence. The black line represents the linear regression of all data points. (e),(f) Solid lines show Pearson correlation coefficients r between domain-average 24-h moisture convergence and increasing percentiles of hourly rainfall rates. Dashed lines show corresponding p values. The 24-h period used for the TC-centered domain in (d) and (f) is 1200 UTC 29–30 Aug 2021. The 24-h period used for the Northeast domain is 1200 UTC 1–2 Sep 2021. Dots and lines in all panels are color-coded by ensemble initialization times as labeled.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
Figures S10–S12 visualize this phenomenon in another way. These figures are similar to Fig. 6, but with plots for each ensemble individually, color-coded by the rank of the maximum hourly precipitation during any of the 9 h shown. There is some coherence across time: ensembles that have high maximum hourly rainfall rates when a single maximum is chosen across all 9 h also tend to have high maximum hourly rainfall rates when a maximum is taken in each of these hours separately. However, the rank of the exceedance probabilities at very high rainfall thresholds bears no clear relationship to the rank of exceedance probabilities at lower rainfall thresholds.
A snapshot of CAPE and hourly precipitation accumulations at 0000 UTC 2 September (Fig. 10) illuminates mechanisms relevant to extreme short-duration rainfall during this event. Off the coast of the eastern United States, values of CAPE reach up to 3000 J kg−1, and extreme hourly rainfall accumulations tend to appear along gradients in surface-based CAPE. Gradients in CAPE coincide with the position of the surface front, whose intraensemble variability may be visually identified in 1000-mb temperatures in Figs. S23–S25. Mesoscale convective systems, organized systems of thunderstorms spanning thousands of square kilometers, often form in relation to synoptic features like extratropical fronts, which can act to lift unstable air past the level of free convection and initiate thunderstorm development (Moore et al. 2012; Schumacher and Rasmussen 2020). Contours of hourly precipitation rates exhibit lines and clusters characteristic of mesoscale convection, with a high degree of diversity in form across the ensemble. The highest rainfall rates are associated with organized mesoscale convective systems; for example, p29 in Fig. 10 is the ensemble member with the hourly point-maximum rainfall rate at this time. Other ensemble members with lower rainfall maxima lack these organized forms; for example, p02 in Fig. 10 is highlighted as the ensemble member with the lowest point maximum in rainfall. Those ensemble members with the highest maximum hourly rainfall rates are not necessarily those with the highest domain-average moisture convergence (Fig. 9) or the highest values of surface-based CAPE (Fig. 10).
Snapshot of ensemble variation in surface-based CAPE and extreme 1-h rainfall. Plots of surface-based CAPE (J kg−1; filled contours) and hourly precipitation accumulations (open white contours; interval 20 mm) at 0000 UTC 2 Sep 2021, in the 30 Aug ensemble. Ensemble members p29 and p02 have the highest and lowest hourly rainfall rates at this time, respectively. The hourly rainfall maximum in ensemble p04 is the closest in space to the observed maximum at this time; the location of the maximum hourly rainfall in NCEP observations is denoted by the pink star.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
In a convective cell, wind shear reduces the extent to which precipitation and downdrafts interfere with updrafts and supports the development of dynamic vertical pressure gradients (Markowski and Richardson 2010). Consequently, conditions of high CAPE and wind shear favor supercell formation. Such conditions are common, for example, in the central United States (Nielsen and Schumacher 2018, 2020; Ashley et al. 2023). The wind shear between the surface and 6-km height is often used to forecast storm type, with supercells associated with shear of over 20 m s−1 (Markowski and Richardson 2010). Across the 29–31 August ensembles, extreme hourly precipitation values are found in locations with relatively high low-level moisture and high wind shear (shown for 30 August in Fig. 11 and for the 29 and 31 August ensembles in Figs. S26 and S28, respectively). The highest hourly precipitation values are collocated with the strongest wind shear. High low-level moisture is necessary but insufficient to produce extreme hourly precipitation rates. The presence of this relationship suggests that T-SHiELD captures, with a nonhydrostatic configuration at ∼3-km grid spacing, some of the processes relevant to mesoscale convective organization.
Importance of wind shear for hourly precipitation extremes. Plot of low-level (850 mb) specific humidity vs 10 m–500-mb wind shear (similar to 0–6-km wind shear), with bins colored by the mean of hourly precipitation rates in each bin. Data are from the 30 Aug ensemble, Northeast region from 283°–287°E and 37°–41.5°N, and 24-h period from 1200:00 UTC 1–2 Sep 2021.
Citation: Journal of the Atmospheric Sciences 81, 7; 10.1175/JAS-D-23-0160.1
4. Summary
Ida’s extratropical stage was distinguished by extreme, highly localized rainfall. We investigated the predictability and character of this rainfall using several large ensembles of hindcasts from a global weather prediction model with a convection-permitting nest. Conclusions are summarized below:
-
Ensembles initialized up to ∼4 days before the most extreme rainfall in the Northeast (29–31 August ensembles) reproduce the observed pattern of rainfall, irrespective of rainfall magnitudes, with relatively higher skill than ensembles with earlier initialization times. For these more skillful ensembles, the distribution of pattern correlations between ensemble members is more difficult to statistically distinguish from the distribution of pattern correlations between ensemble members and observations. Ensembles initialized earlier than ∼4 days before the most extreme rainfall exhibit a systematic westward bias in TC track location around Ida’s landfall and fail to reasonably predict the pattern of precipitation in Ida’s extratropical stages.
-
The 29–31 August ensembles sample observed values of point-maximum hourly rainfall within the extratropical domain. These ensembles also marginally sample point-maximum 24-h rainfall accumulations in the extratropical domain: the observed values of maximum 24-h rainfall fall at the higher end, but not outside of, the modeled distribution.
-
The 29–31 August ensembles have a negative bias in the spatial extent of 24-h rainfall accumulations between the 95th and 99.9th percentile values of rainfall in the Northeast domain.
-
There is great diversity in the magnitude and location of both hourly rainfall maxima and 24-h maximum rainfall accumulations. The magnitude of the most extreme simulated extratropical rainfall rates is not well predicted by large-scale moisture convergence. Instead, these extreme accumulations are controlled by highly chaotic mesoscale processes.
5. Discussion
Dynamical models with convection-permitting grid spacings of approximately 4 km or finer have become more tractable in recent years, especially when configured with regional, stretched, or nested grids. Compared to coarser-resolution models, convection-permitting models improve representations of subdaily extreme precipitation; diurnal cycles of convection and precipitation; effects from surface heterogeneity, including orography and coastlines; mesoscale convective systems; and tropical cyclones (e.g., Prein et al. 2015; Kendon et al. 2021; L. Zhou et al. 2022). This study of Hurricane Ida’s extratropical stage with T-SHiELD demonstrates the advantages and limitations of forecasting an extreme precipitation-producing event with a convection-permitting model, highlights insights from an ensemble approach, and points to some areas for future inquiry.
At lead times for which the synoptic-scale pattern of rainfall is well represented, ensembles capture the most extreme observed hourly rainfall values, demonstrating an encouraging ability to simulate the magnitude of localized convection-driven precipitation extremes in a record-breaking event. However, there are biases in the spatial and temporal structure of extreme rainfall-producing processes. Hindcasts consistently underestimate the spatial extent of extreme 24-h rainfall accumulations even when they are able to capture observed point maxima. At ∼3-km grid spacing, T-SHiELD is capable of representing meso-β-scale (20–200-km scale) features such as mesoscale convective complexes and squall lines, which are shown by Smith et al. (2023) to be associated with some of the most extreme rainfall rates from Ida’s aftermath. T-SHiELD cannot resolve in detail processes on the meso-γ scale (2–20-km), including rotating mesocyclones within supercells and updraft/downdraft dynamics within thunderstorms (Markowski and Richardson 2010, chapter 9.1). Biases in the spatial extent of very extreme precipitation might be related to the model’s inability to adequately resolve, at ∼3 km-grid spacing, processes important for the structure and upscale growth of mesoscale convective systems.
Could increasing resolution mitigate bias? Prior work supports the notion that models with grid sizes of a few kilometers can partially represent, but not fully resolve, mesoscale convection (Prein et al. 2015; Neumann et al. 2019; Kendon et al. 2021). Decreasing grid size to ∼2 km or less has in previous studies caused marked changes in the size and spacing of convection (Miyamoto et al. 2013; Prein et al. 2015). This indicates that mitigating biases in the statistics of extreme rainfall from mesoscale convective systems may at least partially be a matter of increasing model resolution. Further development of scale-aware parameterization schemes could also help to improve the simulation of convective rainfall at convective-permitting resolutions (Han et al. 2017; Park et al. 2022; Tomassini et al. 2023).
Systematic biases in the representation of Ida’s track at landfall are a synoptic-scale limiting factor on the predictability of extratropical rainfall. Our ensembles were not treated with any TC-specific vortex initialization, but such techniques have been shown in previous work to improve track forecast skill (e.g., Liu et al. 2020) and are used in operational forecasts. Ensemble hindcasts initialized with TC vortices based on assimilated observational data could be used to more faithfully investigate the predictability of extratropical transition—which is sensitive to small differences in the position of tropical and/or extratropical features (Evans et al. 2017; Scheck et al. 2011) and which has been associated with decreased forecast skill in downstream regions (Aiyyer 2015; Anwender et al. 2008)—from a probabilistic perspective. Further investigation into the predictability of extratropical transition events at longer lead times, for ensembles initialized earlier on in the storm’s lifetime, is warranted.
Variability within the ensemble provides information about the statistics of extreme precipitation risk. An ensemble generated with perturbed initial conditions and constant model physics represents an array of counterfactual scenarios, which are each as plausible as the next. In contrast to Ida’s tropical stage, postextratropical transition impacts are governed by convective processes that are likely best conceptualized as fundamentally probabilistic on these forecasting time scales. Localized individual extremes arise from chaotic processes that determine location and intensity such that risks are spread over a wide geographic area. A single high-resolution forecast does not contain useful information about the specific locations or magnitudes of the most severe extremes, but the distribution of outcomes provided by an ensemble offers a useful probabilistic picture of the spread of potential hazards and the range of places at risk. Placing too much emphasis on the extreme precipitation projection from a single forecast could result in raising disproportionate alarm in, and overallocating resources to, one particular area at the expense of others in the region. The tendency to anchor (in the sense of Tversky and Kahneman 1974) future expectations to past experience does not account for the highly contingent nature of the outcome we happened to experience.
The heuristic that moisture convergence determines rainfall accumulations in extreme events does not apply to local and hourly scales in the extratropical stages of Hurricane Ida, nor—we posit—in other similar events. This is important to note in considerations of probable maximum precipitation (WMO 1973), where events in a “storm catalog” of previously observed extreme precipitation accumulations are taken to represent the mechanisms capable of bringing the most extreme precipitation possible to a given location. These events are scaled to represent the most extreme manifestation of analogous storms, often through moisture maximization techniques, which typically assume a linear relationship between precipitation and vertically integrated water vapor (IWV; WMO 2009). In line with previous studies that find a nonlinear relationship between IWV and precipitation from mesoscale convective storms (Zhao et al. 1997; Abbs 1999; Yang and Smith 2018), our results suggest that such an assumption would not apply well to small-scale rainfall extremes in this scenario. We recommend that efforts to attribute localized rainfall and consequent flooding to global warming avoid assuming a priori linear relationships between atmospheric moisture and small-scale extreme precipitation.
Topography and land surface cover are possible additional influences on the magnitude and pattern of rainfall in Ida’s extratropical stage. Topography may serve as a lifting mechanism for mesoscale convection (i.e., Schumacher and Rasmussen 2020), and the northeastern United States has somewhat more topographic variation than the Gulf states where Ida made landfall. Enhancement of precipitation downwind of urban areas is observed on climatological time scales (Liu and Niyogi 2019), and urbanization was shown to exacerbate rainfall and flooding in hindcasts of Hurricane Harvey (Zhang et al. 2018). The heaviest simulated 24-h rainfall accumulations occur around the Chesapeake Bay, downwind of Baltimore and Washington, D.C. (Fig. 8a). Was this region truly predisposed to a higher risk of extreme precipitation? Future targeted experiments altering topography and land cover type could test the extent to which these characteristics played a role in the spatial patterns of the likelihood of extreme rainfall.
Finally, this study has implications for forecasting and communication of hurricane hazards after extratropical transition. Evidence suggests that people tend to underestimate risks from extratropical transition events (Meyer et al. 2014; Evans et al. 2017; Masson 2014). This appears to have been true in the case of Ida’s extratropical stage (Olivas 2022; see also McKinley et al. 2021a,b,c), which brought, in addition to extreme rainfall, tornado hazards highly unusual for the northeastern United States [a concurrent and collocated tornado and flash flood (“TORFF”) event as discussed in Nielsen et al. 2015]. Evidence from digital footprint data suggests a corresponding lack of preparedness for Ida in New Jersey and New York, compared to Louisiana (Li et al. 2023). A communication strategy specific to extratropical impacts could emphasize the widespread risks and unpredictable outcomes of such events and convey the hazards of extreme short-duration rainfall rates in addition to storm total accumulations. Given appropriate infrastructure, ensemble forecasting with convection-permitting resolution could play a useful role in forecasting and communicating the magnitude and geographical spread of possible impacts in advance of extreme rainfall events.
Acknowledgments.
The simulations in this study were performed on the Stellar computing cluster at Princeton University. David Luet led the initial installation of T-SHiELD on stellar and helped to design the computational workflow for ensemble simulations. Lucas Harris wrote the “GFDL quick tracks” TC tracker. Princeton Research Computing staff provided technical support. The FV3 team at the GFDL developed the FV3 dynamical core and SHiELD Unified Forecast System. We thank them for making T-SHiELD available and supporting its use for this research. We used FRE-NCtools, primarily written by members of GFDL’s Modeling Systems Group, to postprocess T-SHiELD output. The xESMF (https://doi.org/10.5281/zenodo.7447707) Python package was used for regridding.
Data availability statement.
T-SHiELD output used to create figures in this manuscript may be accessed through Princeton Data Commons at https://doi.org/10.34770/2kwv-8r43.
REFERENCES
Abbs, D. J., 1999: A numerical modeling study to investigate the assumptions used in the calculation of probable maximum precipitation. Water Resour. Res., 35, 785–796, https://doi.org/10.1029/1998WR900013.
Aiyyer, A., 2015: Recurving western North Pacific tropical cyclones and midlatitude predictability. Geophys. Res. Lett., 42, 7799–7807, https://doi.org/10.1002/2015GL065082.
Anwender, D., P. A. Harr, and S. C. Jones, 2008: Predictability associated with the downstream impacts of the extratropical transition of tropical cyclones: Case studies. Mon. Wea. Rev., 136, 3226–3247, https://doi.org/10.1175/2008MWR2249.1.
Ashley, W. S., A. M. Haberlie, and V. A. Gensini, 2023: The future of supercells in the United States. Bull. Amer. Meteor. Soc., 104, E1–E21, https://doi.org/10.1175/BAMS-D-22-0027.1.
Beven, J. L., II, A. Hagen, and R. Berg, 2022: Tropical cyclone report: Hurricane Ida (AL092021). NHC Tech. Rep., 163 pp., https://www.nhc.noaa.gov/data/tcr/AL092021_Ida.pdf.
Bonnin, G. M., D. Martin, B. Lin, T. Parzybok, M. Yekta, and D. Riley, 2006: NOAA Atlas 14: Precipitation-frequency atlas of the United States. Tech. Rep., 295 pp., https://www.weather.gov/media/owp/oh/hdsc/docs/Atlas14_Volume2.pdf.
Du, J., 2011: NCEP/EMC 4KM Gridded Data (GRIB) Stage IV data, version 1.0. UCAR/NCAR–Earth Observing Laboratory, accessed 3 May 2024, https://doi.org/10.5065/D6PG1QDD.
Evans, C., and Coauthors, 2017: The Extratropical transition of tropical cyclones. Part I: Cyclone evolution and direct impacts. Mon. Wea. Rev., 145, 4317–4344, https://doi.org/10.1175/MWR-D-17-0027.1.
Fisher, R. A., 1921: 14: On the “probable error” of a coefficient of correlation deduced from a small sample. Metron, 1, 3–32.
Gao, K., J.-H. Chen, L. Harris, Y. Sun, and S.-J. Lin, 2019a: Skillful prediction of monthly major hurricane activity in the North Atlantic with two-way nesting. Geophys. Res. Lett., 46, 9222–9230, https://doi.org/10.1029/2019GL083526.
Gao, K., L. Harris, J.-H. Chen, S.-J. Lin, and A. Hazelton, 2019b: Improving AGCM hurricane structure with two-way nesting. J. Adv. Model. Earth Syst., 11, 278–292, https://doi.org/10.1029/2018MS001359.
Gao, K., L. Harris, L. Zhou, M. Bender, and M. Morin, 2021: On the sensitivity of hurricane intensity and structure to horizontal tracer advection schemes in FV3. J. Atmos. Sci., 78, 3007–3021, https://doi.org/10.1175/JAS-D-20-0331.1.
Han, J., W. Wang, Y. C. Kwon, S.-Y. Hong, V. Tallapragada, and F. Yang, 2017: Updates in the NCEP GFS cumulus convection schemes with scale and aerosol awareness. Wea. Forecasting, 32, 2005–2017, https://doi.org/10.1175/WAF-D-17-0046.1.
Hanchey, A., and Coauthors, 2021: Notes from the field: Deaths related to Hurricane Ida reported by media—Nine states, August 29–September 9, 2021. Morb. Mortal. Wkly. Rep., 70, 1385–1386, https://doi.org/10.15585/mmwr.mm7039a3.
Harris, L., X. Chen, L. Zhou, and J.-H. Chen, 2020a: The nonhydrostatic solver of the GFDL finite-volume cubed-sphere dynamical core. NOAA Tech. Memo. OAR GFDL 2020-003, 7 pp., https://doi.org/10.25923/9wdt-4895.
Harris, L., and Coauthors, 2020b: GFDL SHiELD: A unified system for weather-to-seasonal prediction. J. Adv. Model. Earth Syst., 12, e2020MS002223, https://doi.org/10.1029/2020MS002223.
Harris, L., X. Chen, W. Putman, L. Zhou, and J.-H. Chen, 2021: A scientific description of the GFDL finite–volume cubed–sphere dynamical core. NOAA Tech. Memo. OAR GFDL 2021-001, 109 pp., https://repository.library.noaa.gov/view/noaa/30725.
Harris, L. M., and S.-J. Lin, 2013: A two-way nested global-regional dynamical core on the cubed-sphere grid. Mon. Wea. Rev., 141, 283–306, https://doi.org/10.1175/MWR-D-11-00201.1.
Harris, L. M., S.-J. Lin, and C. Tu, 2016: High-resolution climate simulations using GFDL HiRAM with a stretched global grid. J. Climate, 29, 4293–4314, https://doi.org/10.1175/JCLI-D-15-0389.1.
Henny, L., C. D. Thorncroft, and L. F. Bosart, 2022: Changes in large-scale fall extreme precipitation in the mid-Atlantic and northeast United States, 1979–2019. J. Climate, 35, 6647–6670, https://doi.org/10.1175/JCLI-D-21-0953.1.
Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, https://doi.org/10.1029/2008JD009944.
Keller, J. H., and Coauthors, 2019: The extratropical transition of tropical cyclones. Part II: Interaction with the midlatitude flow, downstream impacts, and implications for predictability. Mon. Wea. Rev., 147, 1077–1106, https://doi.org/10.1175/MWR-D-17-0329.1.
Kendon, E. J., A. F. Prein, C. A. Senior, and A. Stirling, 2021: Challenges and outlook for convection-permitting climate modelling. Philos. Trans. Roy. Soc., A379, 20190547, https://doi.org/10.1098/rsta.2019.0547.
Landsea, C. W., and J. L. Franklin, 2013: Atlantic hurricane database uncertainty and presentation of a new database format. Mon. Wea. Rev., 141, 3576–3592, https://doi.org/10.1175/MWR-D-12-00254.1.
Li, Q., A. Ramaswami, and N. Lin, 2023: Exploring income and racial inequality in preparedness for Hurricane Ida (2021): Insights from digital footprint data. Environ. Res. Lett., 18, 124021, https://doi.org/10.1088/1748-9326/ad08fa.
Lin, Y., and K. E. Mitchell, 2005: The NCEP stage II/IV hourly precipitation analyses: Development and applications. Preprints, 19th Conf. on Hydrology, San Diego, CA, Amer. Meteor. Soc., 1.2, https://ams.confex.com/ams/Annual2005/techprogram/paper_83847.htm.
Liu, J., and D. Niyogi, 2019: Meta-analysis of urbanization impact on rainfall modification. Sci. Rep., 9, 7301, https://doi.org/10.1038/s41598-019-42494-2.
Liu, M., G. A. Vecchi, J. A. Smith, and H. Murakami, 2017: The present-day simulation and twenty-first-century projection of the climatology of extratropical transition in the North Atlantic. J. Climate, 30, 2739–2756, https://doi.org/10.1175/JCLI-D-16-0352.1.
Liu, Q., and Coauthors, 2020: Vortex initialization in the NCEP operational hurricane models. Atmosphere, 11, 968, https://doi.org/10.3390/atmos11090968.
Lorenz, E. N., 1969: Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci., 26, 636–646, https://doi.org/10.1175/1520-0469(1969)26<636:APARBN>2.0.CO;2.
Markowski, P., and Y. Richardson, 2010: Mesoscale Meteorology in Midlatitudes. John Wiley & Sons, 432 pp.
Masson, A., 2014: The extratropical transition of Hurricane Igor and the impacts on Newfoundland. Nat. Hazards, 72, 617–632, https://doi.org/10.1007/s11069-013-1027-x.
McKinley, J., D. Rubinstein, and J. C. Mays, 2021a: The storm warnings were dire. Why couldn’t New York be protected? New York Times, 3 September, https://www.nytimes.com/2021/09/03/nyregion/nyc-ida.html.
McKinley, J., N. Schweber, A. Rosa, and C. R. Marcius, 2021b: Flooding from Ida kills dozens of people in four states. New York Times, 2 September, https://www.nytimes.com/live/2021/09/02/nyregion/nyc-storm.
McKinley, J., N. Schweber, A. Rosa, and C. R. Marcius, 2021c: New York flooding: Flooding from Ida kills dozens of people in four states. New York Times, 2 September, https://www.nytimes.com/live/2021/09/02/nyregion/nyc-storm.
Meyer, R. J., J. Baker, K. Broad, J. Czajkowski, and B. Orlove, 2014: The dynamics of hurricane risk perception: Real-time evidence from the 2012 Atlantic hurricane season. Bull. Amer. Meteor. Soc., 95, 1389–1404, https://doi.org/10.1175/BAMS-D-12-00218.1.
Miyamoto, Y., Y. Kajikawa, R. Yoshida, T. Yamaura, H. Yashiro, and H. Tomita, 2013: Deep moist atmospheric convection in a subkilometer global simulation. Geophys. Res. Lett., 40, 4922–4926, https://doi.org/10.1002/grl.50944.
Moore, B. J., P. J. Neiman, F. M. Ralph, and F. E. Barthold, 2012: Physical processes associated with heavy flooding rainfall in Nashville, Tennessee, and vicinity during 1–2 May 2010: The role of an atmospheric river and mesoscale convective systems. Mon. Wea. Rev., 140, 358–378, https://doi.org/10.1175/MWR-D-11-00126.1.
Nelson, B. R., O. P. Prat, D.-J. Seo, and E. Habib, 2016: Assessment and implications of NCEP stage IV quantitative precipitation estimates for product intercomparisons. Wea. Forecasting, 31, 371–394, https://doi.org/10.1175/WAF-D-14-00112.1.
Neumann, P., and Coauthors, 2019: Assessing the scales in numerical weather and climate predictions: Will exascale be the rescue? Philos. Trans. Roy. Soc., A377, 20180148, https://doi.org/10.1098/rsta.2018.0148.
Nielsen, E. R., and R. S. Schumacher, 2018: Dynamical insights into extreme short-term precipitation associated with supercells and mesovortices. J. Atmos. Sci., 75, 2983–3009, https://doi.org/10.1175/JAS-D-17-0385.1.
Nielsen, E. R., and R. S. Schumacher, 2020: Observations of extreme short-term precipitation associated with supercells and mesovortices. Mon. Wea. Rev., 148, 159–182, https://doi.org/10.1175/MWR-D-19-0146.1.
Nielsen, E. R., G. R. Herman, R. C. Tournay, J. M. Peters, and R. S. Schumacher, 2015: Double impact: When both tornadoes and flash floods threaten the same place at the same time. Wea. Forecasting, 30, 1673–1693, https://doi.org/10.1175/WAF-D-15-0084.1.
Olivas, S., 2022: Identifying public response and uncertainty to Hurricane Ida’s Remnants (2021) in the northeastern United States. Undergraduate thesis, University of Miami, 22 pp.
Park, H., G. Kim, D.-H. Cha, E.-C. Chang, J. Kim, S.-H. Park, and D.-K. Lee, 2022: Effect of a scale-aware convective parameterization scheme on the simulation of convective cells-related heavy rainfall in South Korea. J. Adv. Model. Earth Syst., 14, e2021MS002696, https://doi.org/10.1029/2021MS002696.
Pollard, R. T., P. B. Rhines, and R. O. R. Y. Thompson, 1973: The deepening of the wind-mixed layer. Geophys. Fluid Dyn., 4, 381–404, https://doi.org/10.1080/03091927208236105.
Prein, A. F., and Coauthors, 2015: A review on regional convection-permitting climate modeling: Demonstrations, prospects, and challenges. Rev. Geophys., 53, 323–361, https://doi.org/10.1002/2014RG000475.
Robinson, G. D., 1967: Some current projects for global meteorological observation and experiment. Quart. J. Roy. Meteor. Soc., 93, 409–418, https://doi.org/10.1002/qj.49709339802.
Rotunno, R., and C. Snyder, 2008: A generalization of Lorenz’s model for the predictability of flows with many scales of motion. J. Atmos. Sci., 65, 1063–1076, https://doi.org/10.1175/2007JAS2449.1.
Scheck, L., S. C. Jones, and M. Juckes, 2011: The resonant interaction of a tropical cyclone and a tropopause front in a barotropic model. Part I: Zonally oriented front. J. Atmos. Sci., 68, 405–419, https://doi.org/10.1175/2010JAS3482.1.
Schumacher, R. S., and K. L. Rasmussen, 2020: The formation, character and changing nature of mesoscale convective systems. Nat. Rev. Earth Environ., 1, 300–314, https://doi.org/10.1038/s43017-020-0057-7.
Smith, J. A., M. L. Baeck, Y. Su, M. Liu, and G. A. Vecchi, 2023: Strange storms: Rainfall extremes from the remnants of Hurricane Ida (2021) in the northeastern US. Water Resour. Res., 59, e2022WR033934, https://doi.org/10.1029/2022WR033934.
Su, Y., and J. A. Smith, 2021: An atmospheric water balance perspective on extreme rainfall potential for the contiguous US. Water Resour. Res., 57, e2020WR028387, https://doi.org/10.1029/2020WR028387.
Tomassini, L., and Coauthors, 2023: Confronting the convective gray zone in the global configuration of the Met Office Unified Model. J. Adv. Model. Earth Syst., 15, e2022MS003418, https://doi.org/10.1029/2022MS003418.
Tribbia, J. J., and D. P. Baumhefner, 2004: Scale interactions and atmospheric predictability: An updated perspective. Mon. Wea. Rev., 132, 703–713, https://doi.org/10.1175/1520-0493(2004)132<0703:SIAAPA>2.0.CO;2.
Tversky, A., and D. Kahneman, 1974: Judgment under uncertainty: Heuristics and biases. Science, 185, 1124–1131, https://doi.org/10.1126/science.185.4157.1124.
WMO, 1973: Manual for estimation of probable maximum precipitation. Secretariat of the World Meteorological Organization, 190 pp.
WMO, 2009: Manual on estimation of Probable Maximum Precipitation (PMP). WMO 1045, 291 pp., https://library.wmo.int/doc_num.php?explnum_id=7706.
Yang, L., and J. Smith, 2018: Sensitivity of extreme rainfall to atmospheric moisture content in the arid/semiarid southwestern United States: Implications for probable maximum precipitation estimates. J. Geophys. Res. Atmos., 123, 1638–1656, https://doi.org/10.1002/2017JD027850.
Zhang, J., and Coauthors, 2016: Multi-Radar Multi-Sensor (MRMS) quantitative precipitation estimation: Initial operating capabilities. Bull. Amer. Meteor. Soc., 97, 621–638, https://doi.org/10.1175/BAMS-D-14-00174.1.
Zhang, W., G. Villarini, G. A. Vecchi, and J. A. Smith, 2018: Urbanization exacerbated the rainfall and flooding caused by Hurricane Harvey in Houston. Nature, 563, 384–388, https://doi.org/10.1038/s41586-018-0676-z.
Zhao, W., J. A. Smith, and A. A. Bradley, 1997: Numerical simulation of a heavy rainfall event during the PRE-STORM experiment. Water Resour. Res., 33, 783–799, https://doi.org/10.1029/96WR03036.
Zhou, L., S.-J. Lin, J.-H. Chen, L. M. Harris, X. Chen, and S. L. Rees, 2019: Toward convective-scale prediction within the next generation global prediction system. Bull. Amer. Meteor. Soc., 100, 1225–1243, https://doi.org/10.1175/BAMS-D-17-0246.1.
Zhou, L., and Coauthors, 2022: Improving global weather prediction in GFDL SHiELD through an upgraded GFDL cloud microphysics scheme. J. Adv. Model. Earth Syst., 14, e2021MS002971, https://doi.org/10.1029/2021MS002971.
Zhou, X., and Coauthors, 2022: The development of the NCEP Global Ensemble Forecast System version 12. Wea. Forecasting, 37, 1069–1084, https://doi.org/10.1175/WAF-D-21-0112.1.
