1. Introduction
Rainfall processes occur in response to both synoptic and mesoscale forcing on preexisting conditions within the atmospheric column. However, the relationship between these atmospheric conditions and extreme precipitation is not well understood, especially on a regional basis. Several studies have recently examined the dependence of rainfall on ambient atmospheric variables (Berg et al. 2009; DeGaetano 2009; Groisman et al. 2005; Haerter and Berg 2009; Lenderink and Van Meijgaard 2008; Lenderink and van Meijgaard 2009; Shaw et al. 2011; Utsumi et al. 2011), primarily focusing on the dependence of precipitation intensity on near-surface temperature. These analyses were driven by the question of whether rainfall intensity and extremes will increase at the Clausius–Clapeyron (CC) rate of ~7% K−1 as the climate warms.
The CC rate, however, is not expected to represent the regional precipitation response to warming everywhere. In regions with appreciable access to moisture, such as the tropics or continental margins, the total rainfall will likely increase at approximately the CC rate. In certain areas, extreme rainfall intensity, especially for short-duration intense rainfall events, can increase at a higher rate, often referred to as a super-CC rate. One possible explanation for the super-CC rate of extreme rainfall is that a greater release of latent heat in a warmer climate may produce more intense updrafts (Lenderink and Van Meijgaard 2008). Another interpretation is that the fraction of convective precipitation increases with higher surface temperatures (Haerter and Berg 2009). The influence of a warmer climate on extreme rainfall intensity appears to be more complex over moisture-limited regions or those where advective processes are important (Lepore et al. 2015).
Comparatively little attention has been given in the literature to the dependence of precipitation on nonthermodynamic atmospheric variables or regional characteristics. Several authors have explored the relationships of daily and seasonal rainfall properties with atmospheric states including sea level pressure, geopotential heights, RH, wind components, and CAPE (Molini et al. 2011; Myoung and Nielsen-Gammon 2010; Hertig and Jacobeit 2013), and a few other analyses have looked at both dynamic and thermodynamic predictors of vertical structure in precipitation (Rudolph and Friedrich 2014). In an analysis of eastern U.S. hourly rainfall intensities, Lepore et al. (2015) examined dependencies on both dynamic and thermodynamic predictors, such as temperature, dewpoint temperature, and CAPE, finding that higher quantiles of precipitation (p > 0.75) are highly dependent on CAPE. These findings suggest the need to investigate the relationship of rainfall extremes with a wider spectrum of atmospheric variables. Interestingly, Lepore et al. (2015) found that rainfall intensity is better correlated with CAPE from reanalysis than with CAPE computed from atmospheric soundings. This result can be explained by considering the relative proximity of a reanalysis vertical sounding profile compared to observed sounding data. Radiosonde observations are unevenly spaced, typically taken twice daily, and can potentially fail. In contrast, reanalysis data are a model assimilation of available observations and are sampled on a 6- or 3-hourly gridded basis, meaning the environment is often more proximal, both in time and space, to the rainfall measurements (Brooks et al. 2003; Allen and Karoly 2014; Gensini et al. 2014). However, during reanalysis, topographically induced processes, as well as synoptic and mesoscale boundaries, can be temporally and spatially displaced, meaning that small-scale features are not as well represented as in a local sounding profile. Despite these limitations, the greater availability of reliable proximity profiles and evaluations compared to soundings has suggested that quantities such as CAPE, convective inhibition (CIN), and wind vectors are representative in reanalysis data, especially within the context of the analysis presented here, and that they can provide useful atmospheric profiles prior to and during rainy hours.
The concept of relating extremes to environmental descriptors, often referred to as an “ingredients based” approach, has been extensively used in short-range forecasting. A seminal work by Doswell et al. (1996) applied this methodology to flash flood prediction. Other authors have extended similar approaches to establish the effect of the large-scale environment on the seasonal and annual numbers of tropical cyclones (Camargo et al. 2007; Vecchi et al. 2011; Tippett et al. 2011) and to make projections under climate change scenarios (Camargo et al. 2014). For continental convection, a similar approach has been used to understand the influence of climate variations on severe thunderstorms (Brooks et al. 2003; Trapp et al. 2007; Diffenbaugh et al. 2013), tornadoes (Tippett et al. 2012, 2014), and hail (Allen et al. 2015a). Finally, this approach is also valuable for connecting severe weather events with large-scale climate variations (e.g., Allen et al. 2015b).
The motivation behind this work is to establish relationships between the environment and the rainfall intensity process. A deeper understanding of these links can be used for a variety of scientific applications, for example, to develop new models for the assessment of hydrological hazards. In fact, simple statistical models, such as linear regressions based on these relationships, can provide a way to overcome the spatial limitations of gauge networks and to quantify extreme precipitation risk where there are no gauges.
Here, we link the distribution of hourly rainfall rates with environmental variables (sections 2a and 2b) through the use of univariate and multivariate quantile regressions and conditional distributions (section 3). In particular, we focus on the extremes of the hourly rainfall rate distribution corresponding to percentiles equal or higher than the 75th percentile. The atmospheric variables included in our analysis describe moisture availability (i.e., dewpoint temperature, specific humidity, and RH), vertical instability (i.e., CAPE, CIN, and vertical wind shear), and advective processes (i.e., surface and higher winds). Some of these variables (e.g., CAPE and wind shear) are commonly used in the description of environments favorable to severe weather, and have been used to establish the contribution of convection and severe convection to rainfall extremes (Hitchens et al. 2013). Here, they allow us to gain some understanding of the role of nonconvective, convective, and severe convective processes in the precipitation process as a whole for the entire CONUS (section 4a). We use covariate relationships (section 4a) to discriminate between typically nonconvective, convective, and severe weather environments.
The results (sections 4b–d) compile a wide catalog of rainfall-atmospheric variable dependencies and explore how these dependencies vary regionally and seasonally. This set of results represents a necessary first step toward the development of statistical models that link extreme rainfall to atmospheric variables, which is key to the assessment of hydrologic hazards within a nonstationary framework.
2. Data
a. Hourly gauge data
Hourly precipitation intensity values (denoted I) are taken from the NCDC gauge network (available online at http://www.ncdc.noaa.gov/cdo-web/). The data used here cover the period 1979–2012. There are stations in all 50 states, and the number of recording stations varies in time, with recent increases taking the gauge network to almost 5000 sites (Groisman et al. 2012). Eliminating stations with missing or replaced values as in Lepore et al. (2015) results in the 278 stations that are used here and whose locations are shown in Fig. 1. The number of years of complete data available at each station ranges from 1 to 31 with half of the stations having at least 29 years of data. Station data are pooled over the eight regions shown in Fig. 1, to allow more robust estimates of higher quantiles. The region definitions take into account the spatial distribution of available stations and the similarity of rainfall characteristics (Lepore et al. 2015). Data are analyzed on a calendar year and seasonal basis. The four seasons considered are NH winter [December–February (DJF)], spring [March–May (MAM)], summer [June–August (JJA)], and fall [September–November (SON)].
Locations of the 278 stations (colored circles) with complete records during 1979–2012 and the eight regions. The color coding indicates the annual mean frequency of rainy hours (%).
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
b. North American Regional Reanalysis
Environmental parameters are taken from the North American Regional Reanalysis (NARR Mesinger et al. 2006) over the contiguous United States (CONUS). The NARR data have a native horizontal grid spacing of 32 km, 45 vertical layers, and a temporal resolution of 3 h. Here, the NARR data are first interpolated onto a 1° × 1° grid centered on each NCDC station. The 3-hourly data are taken to be piece-wise constant from one analysis time to the next for association with the hourly gauge data; for instance, the 1800 UTC reanalysis values are associated with hourly rainfall rates at 1800, 1900, and 2000 UTC. Interpolation of the reanalysis data onto the 1° × 1° grid captures large-scale atmospheric features from the reanalysis in the vicinity of the observed rainfall and removes some of the smallest-scale features. Table 1 lists the NARR variables used. They include variables representative of moisture availability (i.e., surface temperature 
List of variables and their units included in the analysis.
Several issues influence the quality of NARR atmospheric profiles positively and negatively (Tippett et al. 2014; Allen et al. 2015a). Gensini et al. (2014) and Baldwin et al. (2002) identified moisture biases in the midlayers, particularly over the western Great Plains associated with mixing from the shallow convective scheme. West et al. (2007) identified areas of overly moist surface profiles. On the other hand, wind profiles from reanalysis above the boundary layer are considered to be equivalent with rawinsonde profiles (Allen and Karoly 2014; Gensini et al. 2014), and the assimilation of observed rainfall as latent heat profiles may contribute to an improved product. This quality has been illustrated in examination of convective variables and other common parameters that suggest thermodynamic atmospheric properties are generally well represented (Mesinger et al. 2006; Gensini et al. 2014). Finally, by matching the NARR products with rainfall gauge data, rather than rainfall reanalysis products, we make use of a ground-observed and more reliable rainfall measurement (Bukovsky and Karoly 2007).
3. Methods
Calculation of conditional distributions and their analysis
We define rainy hours at each station as those hours when the station precipitation and the reanalysis surface temperature are both positive, and restrict our analysis to rainy hour precipitation intensity, where by intensity we mean hourly rainfall rate. There is no analysis of rainfall amounts accumulated from one hour to the next. Requiring positive surface temperature restricts the analysis almost exclusively to surface liquid precipitation. We abbreviate the condition 
4. Results
a. Frequency of rainy hours and convective rainy hours
The annual frequency of rainy hours in Fig. 1 shows that rainy hours are most frequent in the northern part of the West region along with the East and Northeast regions. Figure 2 shows the annual and seasonal frequency of rainy hours for the eight regions. The annual CONUS frequency of rainy hours is ~6%, with regional values ranging from a low of 2% for the Southwest to a high of 9% for the Northeast. Seasonality is strongest in the coastal and eastern regions (Northeast, West, and East), with the most rainy hours in winter and the fewest in summer. The frequency of rainy hours in the Central, Midwest, South, and Southwest regions shows substantially less seasonality. Spring and fall values in each region are generally similar to the annual values.
Annual (Y; circles) and seasonal (MAM–DJF; lines) regional frequencies of rainy hours (%). Regions are indicated by the color given in the legend.
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
The simplest characterization of rainfall type used here is 
Annual (Y; circles) and seasonal (MAM–DJF; lines) fractions of convective rainy hours as defined by (a) CAPE > 1 and discriminants (b) d1, (c) d2, and (d) d3. Regions are indicated by the color given in the legend.
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
We consider also three multivariate characterizations of rainfall type that have been applied in the literature to convective or severe convective storms (Table 2). Allen et al. (2011) used linear discriminant analysis to separate between severe convective storms [defined as those producing 2 cm+ diameter hail, 50 kt or greater winds (where 1 kt = 0.51 m s−1), or any tornado] and nonsevere convective storms, while other discriminants have sought to identify “significant” severe convection [responsible for 5 cm+ diameter hail, 65 kt or greater winds, and F2+ tornadoes; Brooks et al. (2003); Allen et al. (2011)]. The product of CAPE and S06 or S06 raised to a power greater than one is common to many of these severe thunderstorm discriminants (Marsh et al. 2007; Trapp et al. 2007). The first discriminant, denoted d1, depends on the product of CAPE, S06, and 
The three multivariate discriminants of convectivity.
The annual and seasonal fractions of rainy hours satisfying d1–d3 are shown in Figs. 3b–d. The three discriminants give a mostly consistent ordering of the annual fraction of convective rainy hours with the highest values in the South and Central regions; followed by the Midwest, East and Northeast regions; and finally the Southwest, Rockies and West regions. The highest fraction of convective rainy hours occurs in summer for all discriminants and regions except the South. Convective rainy hours in the South region are most frequent in summer according to 
b. Univariate dependence of rainy hour rainfall intensity on environment
The distribution of rainy hour rainfall rates conditional on the surrounding environment is characterized by the dependence of the conditional percentiles 
Percentiles of the regional distribution of rainy hour rainfall intensity conditional on reanalysis variables. Each row corresponds to a reanalysis variable (labeled on the left), and each column to a region (labeled at the top). The natural logarithms of the conditional percentiles 
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
The vertical axis reports the slope values [sp in Eq. (1)] of the linear regression calculated on the quantile plots presented in Fig. 4. The horizontal axis is for percentile levels; the titles indicate the variables considered in the panel. The black horizontal lines in 
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
The percentile plots for dewpoint temperature 
Percentiles of rainy hour intensities conditional on CAPE (Fig. 4, third row) show threshold behavior with 
In all regions east of the Rockies, rainy hour precipitation intensity has a clear overall negative relationship with S06 (Fig. 4, fifth row), a quantity that appears in the linear discriminants d1–d3 for convective and severe convective storms. The conditional percentiles show either little sensitivity or positive sensitivity (Midwest and Northeast regions) to S06 when its values are less than about 10 m s−1. There is a linear regime for values of S06 between 10 and 45 m s−1 where the Rockies region shows no clear slope, the West region shows a positive slope, and all other regions show a negative relation between rainfall percentiles and S06. An explanation for this behavior is that increased S06 can reflect an increased 6-km wind velocity, which has the consequence of a faster cloud or storm motion, which would reduce the residence time over a gauge of any rain-bearing cloud. Another possible explanation is that convection with insufficient 
The sensitivities of rainy hour rainfall intensity to boundary layer specific humidity 
Finally, the relationship between the wind direction ϕ and hourly rainfall intensities (Fig. 4, eighth row) is used to highlight the preferential wind direction, or the lack of wind (0 wind identifies no wind), for more intense rainfall occurrences in each region. Because of the shape of these relationships, slope values were not calculated for this quantity. The synoptic flow patterns associated with prefrontal warm-air advection and postfrontal wind regimes from the west or south are preferential for rainfall in most regions. Regional variations can also reflect the climatological wind direction of higher moisture content, favoring southerly flow in the central plains, South, and Midwest for intense rainfall, or southeasterly flow (Northeast and East).
Overall, hourly rainfall intensity in the West region displays different sensitivities compared to the other regions. Rainfall percentiles over the West region do show clear sensitivity to dewpoint temperature 
Repeating these analyses at the seasonal time scale reveals that the relationships to atmospheric variables in fall (SON) and spring (MAM) are very similar to the results found when using the entire year. In contrast, winter (DJF) and summer (JJA) show considerable differences, with the rainy hour rainfall rate being insensitive to 
c. Bivariate dependence of rainy hour rainfall intensity on environment
We first consider the bivariate distributions of atmospheric variables 
The bivariate distribution of environments 
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
In addition to parameters typically related to convection, rainfall processes can be also related to the advection of moisture at various levels in the atmosphere. These can be visualized by considering variables describing moisture (i.e., RH and 
At 70 hPa above ground (Fig. 6, row 4), the majority of the rainfall is linked to the southwesterly-to-westerly wind direction, associated with the large-scale flow patterns. For the West, Southwest, and Rockies, the wide distribution over both RH and ϕ values suggests that the rainfall process is less likely to originate from a single preferential flow pattern, perhaps reflecting a reduced dependence on synoptic-scale systems, in contrast with the behavior over the Central, South, East, and Northeast, and to a lesser extent the Midwest, where rainfall occurrence strongly responds to increasing RH values and prevailing SW-to-W winds, suggesting a strong synoptic contribution.
The 
Finally, we examine the joint behavior of 
This set of figures confirms the strong differences in rainfall properties between the eastern United States and the western part of the continent, in contrast with a more moderate regionality of precipitations over the eastern United States. An equivalent analysis performed using rainy hours with 
Seasonality is also of interest in precipitation processes, and the joint distributions of environments for rainy hours with 
As in Fig. 6, but for seasonal results: (a),(c),(e),(g) DJF and (b),(d),(f),(h) JJA. In (a) and (b), the dashed lines show the two discriminants d2 (black) and d3 (red). In the (c)–(f), the dashed line identifies the southerly direction. In (g) and (h), the solid line identifies the convective discriminant d1 and the dashed line corresponds to d2.
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
Overall, winter precipitation occurrence appears to have a reduced dependence on the local atmospheric state, with Figs. 7a,g displaying less preferential rainfall areas compared to the whole-year analysis in Fig. 6. There is instead a pronounced dependence on the wind direction and moisture, with very distinct blue areas in the plots of Figs. 7c,e, reflecting the prevalence of frontal storms during this season. Summer precipitation occurrence, however, is well described using the local atmospheric conditions and thermodynamic parameters Figs. 7b,h. For the 
The previous figures explore how atmospheric variables are distributed during rainy hours with 
The expected rainfall occurrence conditioned to a specific atmospheric state, 
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
d. Multivariate conditional percentiles
We extend the univariate results presented in Figs. 4 and 5, showing the dependence of rainy hour rainfall-rate percentiles on the environment to the multivariate setting and compute the conditional percentiles 
Natural logarithms (colors) of the rainy hour rainfall rate percentiles with 
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
Starting from the first set in Fig. 9 [
The South displays overall higher intensity values (darker blue) than the other regions, while the West shows a negligible gradient, suggesting little dependence on the set of variables. The results shown in this last set of panels further suggest moderate regional dependence for the conditional intensity distribution, outside of the West region outlier, and to some degree the South.
The first set of Fig. 9 [S06–
We evaluate the coefficients of the multivariate regression in Eq. (2) to quantify the best set of regressors and their relative efficiency in describing the intensity process. The results of various variable combinations are presented in Fig. 10. We first inspect the coefficients for 
The first two columns show the coefficients of the regressions between log-intensity percentiles, 
Citation: Journal of Climate 29, 9; 10.1175/JCLI-D-15-0331.1
These regressions represent two pathways through which changes in atmospheric temperature can affect the rainfall process; while very relevant to the process, they exclude other types of processes not strictly related to the local temperature (i.e., S06, U, and V), which may be relevant to the description of the regional rainfall process. To analyze the contributions of other factors, we consider alternatives (Fig. 10, rows 3 and 4) that match one of the previous variables, 
Finally, we compare the %ESS for these four models and include two other trivariate regressions: 
In summary, we confirm the importance of including both a thermodynamic and a dynamic variable in the description of the rainfall intensity process, for most of the regions in the United States. For the West, the best results are given by considering percentiles conditional on 
5. Conclusions
We have analyzed the dependence of high percentiles of hourly rainfall rate (intensity) on relevant atmospheric variables, using hourly gauge rainfall data and atmospheric quantities from reanalyses. This investigation extends the approach of relating the rainfall process and intensity to the environment by including a wider range of thermodynamic and meteorological variables, providing additional insight into the large- and regional-scale atmospheric contributions to the rainfall process. In addition, the consideration of common variables has allowed validation of previous results obtained using an alternative reanalysis over a more limited region, further supporting the statistical robustness of those findings (Lepore et al. 2015).
Two sets of analyses were considered: (i) the relationships of the hourly rainfall intensity conditioned on atmospheric drivers and (ii) how these drivers modulate the occurrence of the rainfall process. The thermodynamic variables 
The regional variability of the relationships between rainfall intensity and atmospheric drivers is moderate east of the Rocky Mountains, while the western United States has relatively unique features. In this analysis, we find no strong relation in the West of local thermodynamic and dynamic properties with rainfall intensity, whereas moisture advection plays a dominant role. In contrast, the occurrence of rainfall has a strong regional signature. The differences observed in Figs. 6 and 7 can be used to extrapolate the major drivers of the regional properties of the precipitation process in the CONUS. These results suggest the possibility of consolidating the eight regions in three macroregional behaviors. The first macroregion encompasses the eastern regions (Midwest, Northeast, Central, East, and South), which show similar seasonal convective climatology, with the South displaying the highest values. The second region includes the Southwest and Rockies, which have very similar seasonality and are found in the middle of the regional range. Finally, the West appears to form a macroregion of its own at the other tail of the distribution.
These findings indicate some of the challenges in constructing global or even CONUS-wide statistical rainfall models. A single approach is not appropriate for describing these processes when exploring the relationships to the climate system, particularly for the West Coast of the United States.
Our approach reveals the utility of combining a variety of information in a simple image that encapsulates the rainfall process, as seen in Figs. 6–9. Furthermore, we couple this analysis with established linear discriminants to identify the contributions of specific weather states (i.e., nonconvective, convective, and severe convective) to the yearly and seasonal rainfall regimes for the whole CONUS. Our approach represents a novel and compact methodology for looking at the rainfall process and its generation throughout the United States at the annual and seasonal scales. The analysis also catalogs a wide range of regional and seasonal rainfall-atmospheric variables dependencies, which provide the basis for future comparison and improved understanding of how both natural and anthropogenic climate variability will affect the properties of the regional rainfall process.
Acknowledgments
CL was partially supported by the National Science Foundation (AGS1243204), the Lamont-Doherty Earth Observatory, and Columbia’s Department of Earth and Environmental Sciences. CL, JTA, and MKT acknowledge funding from the Office of Naval Research (N00014-12-1-0911). We are grateful to Tanvir Ahmed and Seonkyoo Yoon for the processing and quality control of the rainfall gauge data.
REFERENCES
Allen, J. T., and D. J. Karoly, 2014: A climatology of Australian severe thunderstorm environments 1979–2011: Inter-annual variability and ENSO influence. Int. J. Climatol., 34, 81–97, doi:10.1002/joc.3667.
Allen, J. T., D. J. Karoly, and G. A. Mills, 2011: A severe thunderstorm climatology for Australia and associated thunderstorm environments. Aust. Meteor. Oceanogr. J., 61, 143–158.
Allen, J. T., M. K. Tippett, and A. H. Sobel, 2015a: An empirical model relating U.S. monthly hail occurrence to large-scale meteorological environment. J. Adv. Model. Earth Syst., 7, 226–243, doi:10.1002/2014MS000397.
Allen, J. T., M. K. Tippett, and A. H. Sobel, 2015b: Influence of the El Nino/Southern Oscillation on tornado and hail frequency in the United States. Nat. Geosci., 8, 278–283, doi:10.1038/ngeo2385.
Baldwin, M. E., J. S. Kain, and M. P. Kay, 2002: Properties of the convection scheme in NCEP’s Eta Model that affect forecast sounding interpretation. Wea. Forecasting, 17, 1063–1079, doi:10.1175/1520-0434(2002)017<1063:POTCSI>2.0.CO;2.
Berg, P., J. Haerter, P. Thejll, C. Piani, S. Hagemann, and J. Christensen, 2009: Seasonal characteristics of the relationship between daily precipitation intensity and surface temperature. J. Geophys. Res., 114, D18102, doi:10.1029/2009JD012008.
Brooks, H. E., J. W. Lee, and J. P. Craven, 2003: The spatial distribution of severe thunderstorm and tornado environments from global reanalysis data. Atmos. Res., 67–68, 73–94, doi:10.1016/S0169-8095(03)00045-0.
Bukovsky, M. S., and D. J. Karoly, 2007: A brief evaluation of precipitation from the North American Regional Reanalysis. J. Hydrometeor., 8, 837–846, doi:10.1175/JHM595.1.
Camargo, S. J., K. A. Emanuel, and A. H. Sobel, 2007: Use of a genesis potential index to diagnose ENSO effects on tropical cyclone genesis. J. Climate, 20, 4819–4834, doi:10.1175/JCLI4282.1.
Camargo, S. J., M. Tippett, A. Sobel, G. Vecchi, and M. Zhao, 2014: Testing the performance of tropical cyclone genesis indices in future climates using the HIRAM model. J. Climate, 27, 9171–9196, doi:10.1175/JCLI-D-13-00505.1.
DeGaetano, A. T., 2009: Time-dependent changes in extreme-precipitation return-period amounts in the continental United States. J. Appl. Meteor. Climatol., 48, 2086–2099, doi:10.1175/2009JAMC2179.1.
Diffenbaugh, N. S., M. Scherer, and R. J. Trapp, 2013: Robust increases in severe thunderstorm environments in response to greenhouse forcing. Proc. Natl. Acad. Sci. USA, 110, 16 361–16 366, doi:10.1073/pnas.1307758110.
Doswell, C. A., III, H. E. Brooks, and R. A. Maddox, 1996: Flash flood forecasting: An ingredients-based methodology. Wea. Forecasting, 11, 560–581, doi:10.1175/1520-0434(1996)011<0560:FFFAIB>2.0.CO;2.
Gensini, V. A., T. L. Mote, and H. E. Brooks, 2014: Severe-thunderstorm reanalysis environments and collocated radiosonde observations. J. Appl. Meteor. Climatol., 53, 742–751, doi:10.1175/JAMC-D-13-0263.1.
Groisman, P. Ya., R. W. Knight, D. R. Easterling, T. R. Karl, G. C. Hegerl, and V. N. Razuvaev, 2005: Trends in intense precipitation in the climate record. J. Climate, 18, 1326–1350, doi:10.1175/JCLI3339.1.
Groisman, P. Ya., R. W. Knight, and T. R. Karl, 2012: Changes in intense precipitation over the central United States. J. Hydrometeor., 13, 47–66, doi:10.1175/JHM-D-11-039.1.
Haerter, J. O., and P. Berg, 2009: Unexpected rise in extreme precipitation caused by a shift in rain type? Nat. Geosci., 2, 372–373, doi:10.1038/ngeo523.
Hertig, E., and J. Jacobeit, 2013: A novel approach to statistical downscaling considering nonstationarities: Application to daily precipitation in the Mediterranean area. J. Geophys. Res. Atmos., 118, 520–533, doi:10.1002/jgrd.50112.
Hitchens, N. M., H. E. Brooks, and R. S. Schumacher, 2013: Spatial and temporal characteristics of heavy hourly rainfall in the United States. Mon. Wea. Rev., 141, 4564–4575, doi:10.1175/MWR-D-12-00297.1.
Lenderink, G., and E. Van Meijgaard, 2008: Increase in hourly precipitation extremes beyond expectations from temperature changes. Nat. Geosci., 1, 511–514, doi:10.1038/ngeo262.
Lenderink, G., and E. Van Meijgaard, 2009: Unexpected rise in extreme precipitation caused by a shift in rain type? Nat. Geosci., 2, 373–373, doi:10.1038/ngeo524.
Lepore, C., D. Veneziano, and A. Molini, 2015: Temperature and CAPE dependence of rainfall extremes in the eastern United States. Geophys. Res. Lett., 42, 74–83, doi:10.1002/2014GL062247.
Li, H., and B. A. Colle, 2014: Multidecadal changes in the frequency and ambient conditions of warm season convective storms over the northeastern United States. J. Climate, 27, 7285–7300, doi:10.1175/JCLI-D-13-00785.1.
Marsh, P. T., H. E. Brooks, and D. J. Karoly, 2007: Assessment of the severe weather environment in North America simulated by a global climate model. Atmos. Sci. Lett., 8, 100–106, doi:10.1002/asl.159.
Mesinger, F., and Coauthors, 2006: North American Regional Reanalysis. Bull. Amer. Meteor. Soc., 87, 343–360, doi:10.1175/BAMS-87-3-343.
Molini, L., A. Parodi, N. Rebora, and G. C. Craig, 2011: Classifying severe rainfall events over Italy by hydrometeorological and dynamical criteria. Quart. J. Roy. Meteor. Soc., 137, 148–154, doi:10.1002/qj.741.
Myoung, B., and J. W. Nielsen-Gammon, 2010: Sensitivity of monthly convective precipitation to environmental conditions. J. Climate, 23, 166–188, doi:10.1175/2009JCLI2792.1.
Ralph, F. M., and Coauthors, 2005: Improving short-term (0–48 h) cool-season quantitative precipitation forecasting: Recommendations from a USWRP workshop. Bull. Amer. Meteor. Soc., 86, 1619–1632, doi:10.1175/BAMS-86-11-1619.
Ralph, F. M., P. J. Neiman, G. A. Wick, S. I. Gutman, M. D. Dettinger, D. R. Cayan, and A. B. White, 2006: Flooding on California’s Russian River: Role of atmospheric rivers. Geophys. Res. Lett., 33, L13801, doi:10.1029/2006GL026689.
Rudolph, J. V., and K. Friedrich, 2014: Dynamic and thermodynamic predictors of vertical structure in radar-observed regional precipitation. J. Climate, 27, 2143–2158, doi:10.1175/JCLI-D-13-00239.1.
Shaw, S. B., A. A. Royem, and S. J. Riha, 2011: The relationship between extreme hourly precipitation and surface temperature in different hydroclimatic regions of the United States. J. Hydrometeor., 12, 319–325, doi:10.1175/2011JHM1364.1.
Singh, M. S., and P. A. O’Gorman, 2014: Influence of microphysics on the scaling of precipitation extremes with temperature. Geophys. Res. Lett., 41, 6037–6044, doi:10.1002/2014GL061222.
Smith, B. L., S. E. Yuter, P. J. Neiman, and D. Kingsmill, 2010: Water vapor fluxes and orographic precipitation over northern California associated with a landfalling atmospheric river. Mon. Wea. Rev., 138, 74–100, doi:10.1175/2009MWR2939.1.
Steinschneider, S., and U. Lall, 2015: A hierarchical Bayesian regional model for nonstationary precipitation extremes in northern California conditioned on tropical moisture exports. Water Resour. Res., 51, 1472–1492, doi:10.1002/2014WR016664.
Tippett, M. K., S. J. Camargo, and A. H. Sobel, 2011: A Poisson regression index for tropical cyclone genesis and the role of large-scale vorticity in genesis. J. Climate, 24, 2335–2357, doi:10.1175/2010JCLI3811.1.
Tippett, M. K., A. H. Sobel, and S. J. Camargo, 2012: Association of U.S. tornado occurrence with monthly environmental parameters. Geophys. Res. Lett., 39, L02801, doi:10.1029/2011GL050368.
Tippett, M. K., A. H. Sobel, S. J. Camargo, and J. T. Allen, 2014: An empirical relation between U.S. tornado activity and monthly environmental parameters. J. Climate, 27, 2983–2999, doi:10.1175/JCLI-D-13-00345.1.
Trapp, R. J., N. S. Diffenbaugh, H. E. Brooks, M. E. Baldwin, E. D. Robinson, and J. S. Pal, 2007: Changes in severe thunderstorm environment frequency during the 21st century caused by anthropogenically enhanced global radiative forcing. Proc. Natl. Acad. Sci. USA, 104, 19 719–19 723, doi:10.1073/pnas.0705494104.
Utsumi, N., S. Seto, S. Kanae, E. E. Maeda, and T. Oki, 2011: Does higher surface temperature intensify extreme precipitation? Geophys. Res. Lett., 38, L16708, doi:10.1029/2011GL048426.
Vecchi, G. A., M. Zhao, H. Wang, G. Villarini, A. Rosati, A. Kumar, I. M. Held, and R. Gudgel, 2011: Statistical–dynamical predictions of seasonal North Atlantic hurricane activity. Mon. Wea. Rev., 139, 1070–1082, doi:10.1175/2010MWR3499.1.
West, G. L., W. J. Steenburgh, and W. Y. Cheng, 2007: Spurious grid-scale precipitation in the North American Regional Reanalysis. Mon. Wea. Rev., 135, 2168–2184, doi:10.1175/MWR3375.1.
