1. Introduction
Recent climate analysis has indicated that Minnesota is part of a large area in the Northern Hemisphere where increases in heavy rainfall are anticipated for the future (Runkle et al. 2022). The same analysis also indicated that since 1990, total annual precipitation has been above the long-term (1895–2020) average of 670.6 mm (26.4 in.) (Fig. 4 in Runkle et al. 2022). Additionally, for the 5-yr periods occurring since 1980, all but one (2005–09) have had 5-yr annual averages exceeding the long-term (1900–2020) average for the annual number of extreme precipitation days with at least 50.8 mm (2 in.) of precipitation. (Fig. 2d in Runkle et al. 2022). Increases in precipitation and heavy rainfall events can have substantial impacts on flood threat and damage (Pielke and Downton 2000; Villarini et al. 2013; Harding and Snyder 2015; Mallakpour and Villarini 2016), agriculture (Gornall et al. 2010), as well as water quality and ecosystems (Cooney et al. 2018). Because these concerns are significant for Minnesota, and to help meet the needs of climate forecasters, researchers, and planning teams, our study adds to precipitation information available from other sources through the analysis of hourly precipitation data covering the entire state at 4-km resolution to identify precipitation and heavy rain event patterns. Prior work has indicated that improvements are needed in warm season rainfall prediction and quantitative precipitation forecasting (Fritsch and Carbone 2004; Stevenson and Schumacher 2014). With a monthly perspective that can be of interest to forecasters and modelers, especially in comparisons with climatologies underlying operational forecasting models, this study offers both spatial and temporal analysis of the distribution and variability of all rain events and heavy rain events during the warm season of May–September in Minnesota during the 17 years of 2004–20.
According to Runkle et al. (2022), Minnesota is in a transition zone in the United States between the eastern humid climate region and the semiarid region to the west. A primary source of precipitation in summer is warm, moist air that originates near the Gulf of Mexico. Average annual precipitation varies substantially from more than 889 mm (∼35 in.) in southeastern Minnesota to approximately 584 mm (∼23 in.) in far northwestern Minnesota. Almost two-thirds of Minnesota’s annual precipitation occurs during May–September. In addition, according to the Minnesota Department of Natural Resources (DNR), Minnesota can experience “mega-rain events,” which are events that feature 6 in. (152 mm) of rain across more than 1000 mi2 (>2590 km2) in 24 h or less, and at least 8 in. (∼203 mm) of rain somewhere in that area. These mega-rain events have occurred 16 times between 1973 and 2020, with 11 of these events developing after 2000 (Minnesota Department of Natural Resources 2022a,b). Overall, heavy rainfall has led to flooding events that have been deadly (Czuba et al. 2012) and resulted in extensive damage to homes, businesses, and infrastructure (Czuba et al. 2012; Cooney et al. 2018). Such a major event occurred in northeastern Minnesota on 19–20 June 2012, when extensive flooding triggered by wet antecedent conditions (2–4 in. of rain delivered in the weeks prior to the event) and heavy rains delivered by waves of thunderstorms resulted in the most damaging flood event in Duluth’s history (Czuba et al. 2012). The June 2012 rainfall impacted three major watersheds (the Mississippi Headwaters, the St. Croix in the Mississippi drainage area, and Western Lake Superior) and led to a disaster declaration for nine counties. The situation caused evacuations, water rescues, transportation disruptions, and major damage amounting to >$100 million (U.S. dollars).
Other areas of concern related to heavy rainfall include reduced water quality and potential impacts to habitat. Storm runoff can be a major source of water quality degradation because contaminants and sediment can be collected along the flow path (Moss et al. 2017). Regarding habitat, Minnesota’s world-renowned 4000 km2 Boundary Waters Canoe Area Wilderness (BWCAW), is a sensitive habitat for boreal forest species near their biome boundaries, and scientists are concerned about possible vulnerability to changes in precipitation (Frelich and Reich 2009).
Previous research about precipitation distribution and extremes in Minnesota has been limited. Early research used precipitation data from 91 stations to explore the seasonality of precipitation across nine climatological regions within Minnesota (Baker and Kuehnast 1978), whereas a later study defined four rain event types for Minnesota and examined their corresponding circulation patterns in order to develop synoptic analogs for use in forecasting (Winkler 1988). Other precipitation-related studies for Minnesota have focused on specialty topics affecting only portions of the state, such as climate in the Laurentian mixed forest region of Minnesota (Handler et al. 2014) and streamflow analyses in a subset of major Minnesota river basins (Novotny and Stefan 2007).
Since daily precipitation data frequently have relatively long periods of record over multiple decades, daily data can be used to explore temporal precipitation variability over long periods of time. One study used daily data from more than 600 stations in the contiguous United States with ≥80 years of data from 1895 to 2002 to explore total precipitation and the contribution from intense precipitation (Pryor et al. 2009). Results showed that some of the largest precipitation trends occurred in the northwestern Midwest. This analysis was consistent with Villarini et al. (2013), which used daily data from 447 rain gauge stations with ≥50 years of data and found increasing trends in heavy rainfall in the north-central United States. Another study focused on the eastern two-thirds of the United States, including Minnesota, to analyze extreme rain event frequency, seasonality, and diurnal cycle with 5 years of data based on the National Weather Service (NWS) cooperative high-resolution 24-h rain gauge network (Schumacher and Johnson 2006). They found that in the northern part of the United States, extreme rain events occur primarily in the warm season and that most in the northern region are caused by mesoscale convective systems (MCSs).
Finer temporal resolution is available with hourly precipitation data over varied spatial resolutions. For instance, the Hourly Precipitation Dataset (HPD) from the National Centers for Environmental Information (NCEI) during 1948–93 was used to study heavy rain events of ≤3 h across the contiguous United States (Brooks and Stensrud 2000). Their results showed a heavy precipitation peak around July. However, they noted that the HPD was inadequate to capture extreme precipitation events due to large station spacing of approximately 50 km. Hitchens et al. (2010) also used hourly data from 48 widely spaced Midwest rain gauges and found that most precipitation in an extreme precipitation event occurs within a 1–2-h time period during the event. Another study used HPD to investigate durations and intensities of heavy precipitation and found substantial changes over the central United States during prior decades (Groisman et al. 2012). Other research utilized NCEP Stage-IV hourly precipitation data regridded to 8.33-km spacing and found that heavy rainfall was characterized by a diurnal cycle across the contiguous United States, with afternoon maxima and morning minima during spring, summer, and autumn (Hitchens et al. 2013). Another analysis provided precipitation-related statistics based on NCEP Stage-IV hourly data with a grid spacing of ∼8.25 km for the central and eastern United States (Stevenson and Schumacher 2014). While these studies provide interesting insights into heavy rain patterns and their spatiotemporal variability, the results lack spatiotemporal resolution optimal for use by stakeholders and decision makers in Minnesota.
This study provides finer spatiotemporal resolution than was applied in the previously discussed research. We addressed the current gap concerning the analysis of heavy rain in Minnesota by using Stage-IV hourly, 4-km resolution precipitation data for May–September 2004–20. The goal of the analysis is to identify both rain events and heavy rain events and to generate region-based and event-based statistics to characterize events. The study examined event frequency, intensity, duration, and accumulation during warm season months. The use of hourly data enabled identification of rain events that could occur within or across daily boundaries so that events could be evaluated in their entirety. The forthcoming analysis establishes a baseline for past and future analyses of precipitation patterns in Minnesota, as well as builds a foundation for future research into weather patterns that lead to heavy precipitation.
2. Data and methods
a. Domain and dataset
The National Weather Service National Centers for Environmental Prediction (NCEP) Stage-IV hourly precipitation data (Du 2011) over the continental United States provided the basis for the analyses performed in this study. The Stage-IV data are a national mosaic, multisensor radar-gauge product that is based on WSR-88D NEXRAD radar data (Fulton et al. 1998) and merged with precipitation gauge data from the River Forecast Centers (RFCs) (Seo and Breidenbach 2002). The data are organized in the National Weather Prediction Hydrologic Rainfall Analysis Project (HRAP) polar stereographic projection (true at 60°N/105°W), which has a spatial resolution of 4.7 km at 60°N (Li et al. 2021).
In this study, we used Stage-IV data from a spatial domain that encompasses the state of Minnesota (Fig. 1). Latitude–longitude bounding coordinates for Minnesota are as follows: (west bounding: −97.5° longitude), (east bounding: −89.00° longitude), (north bounding: 49.5° latitude), and (south bounding: 43.0° latitude) (Minnesota IT Services Geospatial Information Office MnGeo 2022). Operational WSR-88D weather radars covering Minnesota include Grand Forks, North Dakota; Sioux Falls, South Dakota; Duluth, Minnesota; Minneapolis, Minnesota; and La Crosse, Wisconsin (Fig. 1). Hourly data for the months of May–September were examined for the years 2004–20. It should be noted that although precipitation during the May–September warm season typically occurs in the form of rainfall, it is possible for snowfall to occur rarely during May and September. For the sake of simplicity in this analysis, no distinction has been made in precipitation type.
Topography map and county borders of Minnesota. Geographic features discussed on the text are highlighted. Location of the operational radars are highlighted by purple circles with the 150-km range centered around the radar location. (Sources: Minnesota Pollution Control Agency, Minnesota map, stormwater.pca.state.mn.us/images/b/bc/Minnesota_land_surface_elevation.jpg; Nations Online Project, U.S. map, https://www.nationsonline.org/oneworld/usa_map_small.htm.)
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
Although the RFCs perform some manual quality control for the Stage-IV data, advantages and limitations of the data, as outlined by Nelson et al. (2016), need to be considered for this analysis. Stage-IV precipitation estimates perform well at high rain rates and are useful for analyses that require the high spatial resolution provided by the approximately 4-km grid point spacing. They found, however, that Stage-IV data have limitations related to radar operational processing and data merging from RFCs that use varied precipitation processing algorithms. Radar precipitation estimation includes challenges such as hot and cold biases, bright banding, and the cone of silence (e.g., Smith et al. 1996; Young et al. 1999; Krajewski and Vignal 2001; Nelson et al. 2010). Another limitation is that precipitation coverage close to the surface (<3 km AGL) is limited by the WSR-88D radar scanning geometry (National Oceanic and Atmospheric Administration 2022). Precipitation estimates are also challenging at distances > ∼100 km from WSR-88D radars due to the elevation of the radar beam that occurs with increasing distance. Indeed, Hunter (1996) indicates that WSR-88D radar beams that overshoot precipitation cores are likely the primary source of precipitation estimation errors from the radar, and usually lead to underestimates of precipitation. Furthermore, previous studies have indicated the influence of radar range effects on Stage-IV data within the Minnesota region (Chang et al. 2016; Smalley et al. 2014). This is a major challenge for precipitation study in Minnesota as there is a noticeable gap in coverage outside the ranges of the radars located in Grand Forks, North Dakota; Duluth, Minnesota; and Minneapolis, Minnesota (Fig. 1). The spatial mapping of precipitation in our study demonstrated apparent radar range effects in some areas, with lower precipitation values at distances beyond ∼100-km range from a radar. Additionally, open-access Stage-IV hourly data contain numerous spurious data artifacts (Stevenson and Schumacher 2014; Nelson et al. 2016) that need to be addressed in quality-control postprocessing, which is described in the next section.
b. Quality control
To address the challenge of spurious data, which was more noticeable in the early years of data for this study, we established a set of quality control steps. In the initial quality control process, we generated spatial precipitation maps based on the Stage-IV hourly data and flagged time steps with rainfall rates > 75 mm h−1 for further quality control. A common pattern of unrealistic data (>75 mm h−1) was a bull’s-eye pattern (Figs. 2a,b; also discussed in Stevenson and Schumacher 2014; Nelson et al. 2016). This pattern either occurred without surrounding precipitation (Figs. 2a,b) or was embedded in precipitation (Fig. 2c), which could be a result of invalid data not addressed by RFC quality control. In addition, we found irregular speckled patterns with unrealistically high values (>75 mm h−1; Fig. 2d). Both patterns skew the maximum intensity and precipitation values at a grid point and signal a need for quality control data adjustments.
Quality control steps identified types of possibly spurious rainfall intensity cell patterns as shown here. (a) A bull’s-eye pattern without nearby precipitation indicates likely invalid data. (b) A partial bull’s-eye pattern without nearby precipitation indicates likely invalid data. (c) An irregular rainfall intensity pattern with some bull’s-eye effect needs further examination to determine if some portion of the pattern is unrealistic and likely invalid. (d) An irregular rainfall intensity pattern with a high intensity spike needs further examination to determine if some portion of the pattern is unrealistic and likely invalid.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
To remove the spurious data patterns, we followed the three step process shown in Fig. 3. In the first step we used a high-pass filter identifying all spatiotemporal grid points with high-intensity hourly rain rates > 75 mm h−1 (step 1 in Fig. 3). The high-pass filtering process identified a relatively low percentage (<0.003%) of the spatiotemporal points during all months between 2004 and 2012 as having a high-intensity rain rate > 75 mm h−1. Then we visually inspected the spatial patterns around the high-intensity spatiotemporal grid points and decided if the filtered high-intensity rain rates were likely associated with actual precipitation or with unrealistic patterns (steps 2–3 in Fig. 3). This approach enabled us to separate bull’s-eye patterns and other spurious data from actual precipitation. The bull’s-eye patterns exhibit a maximum at their center with interpolated values decreasing outward from the local maximum. When there was no apparent precipitation connected to the bull’s-eye, the pattern was considered invalid. When such a bull’s-eye was identified, we placed a 2D box around the bull’s-eye pattern that enclosed the maximum in the center and extended to the outer edges of the bull’s-eye. The values within the 2D box were then replaced by NaN values. NaN denotes “not a number” and can be used in Python data processing to represent data values that are missing, uncertain, or invalid. A function, such as mean, standard deviation, or percentile, that has been constructed for use with data containing NaN values, is designed to ignore NaN values and to not include them in the count of data points being processed by the NaN function. Occasionally, the bull’s-eyes occurred within a broader area of precipitation and featured radial rings of reduced values that decreased outward from the local maxima (Fig. 2c). It is important to note that some bull’s-eye patterns within a precipitation pattern might be considered valid as the result of the processes used to generate Stage-IV data. Consequently, visual inspection was used to evaluate ambiguous bull’s-eye patterns embedded within areas of precipitation and to classify them as valid or invalid. Those deemed invalid were replaced by NaN values. Figure 4 shows an example of total rainfall accumulation in the month of June 2006 before and after quality control adjustments have been applied to a bull’s-eye pattern.
Schematic of the preprocessing steps used to identify and correct invalid high-intensity data patterns. This example demonstrates the process for a spatiotemporal grid point in June 2006.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
Minnesota region monthly rain event accumulation for June 2006 (a) before and (b) after data quality processing to eliminate invalid bull’s-eye pattern.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
Non-bull’s-eye, irregularly speckled patterns occurred as single isolated pixels without precipitation (Fig. 2d) or were embedded within precipitation. Single isolated pixels with rainfall rates > 75 mm h−1 were simply removed. If speckled patterns were observed within a broader area of precipitation, one of two actions was taken depending on the values of local maxima and their neighboring grid points. In particular, if a local maximum was between 75 and 110 mm h−1, we retained the values in the analysis. Most points in this range appeared to be part of valid precipitation patterns. We considered any grid points greater than 110 mm h−1 to be unrealistic and replaced them by NaN values. The 110 mm h−1 threshold was based on the Rainfall Frequency Atlas of the Midwest (Huff and Angel 1992). Namely, rainfall frequency data for a 100-yr 1-h event in the Atlas indicated a maximum contour of a little more than 100 mm within the nine-state Midwest region that includes Minnesota, and we decided to cap valid values slightly higher at 110 mm h−1.
c. Analysis methods
In this study, we used the gridded hourly Stage-IV data to quantify rain hours and rain events at each grid point. This data does not differentiate between liquid and solid phases of precipitation. Because this study was conducted for the warm season months, May–September, an assumption was made that the precipitation would be predominantly rainfall. We subsequently established definitions for key terms that would be used in the analysis. A rain hour was an hour for which the rain rate exceeded 2.5 mm h−1, which is the threshold between light and moderate rainfall based on the Glossary of Meteorology from the American Meteorological Society (2021). A heavy rain hour was defined in this study as a rain hour for which the precipitation intensity was >16 mm h−1, which is the mean value of the 95th percentile of rain hour rain rates across Minnesota during May–September 2004–20. A rain event was defined as a sequence of hours with an hourly rain rate > 2.5 mm h−1 and <3 h of interruption. A rain event can be as short as one hour or considerably longer, depending on when the rain event hour sequence is interrupted by a non-rain hour interval of at least 3 h between events. This definition implies that total accumulation of a rain event will be greater than 2.5 mm. The 3-h gap threshold resulted from analyzing the time gaps between rain hours. Namely, we found that a 1–2-h gap between rain hours was not uncommon within synoptic systems that could be considered one event. A rain event hour was an hour within a rain event. It should be noted that based on the definition of a rain event, a rain event hour might experience rainfall or be part of a short dry interval within the rain event. Due to our research focus on heavy rainfall, we also defined a subset of rain events as heavy rain events. A heavy rain event was a rain event with an accumulation > 36 mm, which represents the mean value of the 95th percentile of rain event total accumulations in the Minnesota domain during 2004–20. The 95th percentile threshold of 36 mm was consistent with the types of thresholds found in other literature, such as “the upper 5% of events” in Groisman et al. (2005), or a heavy rainfall definition using a 95th percent threshold for the events defined in Villarini et al. (2013).
To create rainfall statistics, we analyzed rain hours and rain events in two ways: (i) a region-based analysis which examined rain characteristics on a point-by-point basis across Minnesota to indicate spatial and seasonal variability and (ii) an event-based analysis regardless of location to demonstrate event characteristics, seasonal variability, and 2004–20 year-to-year changes.
For the region-based analysis, we performed the steps described here for each warm season month (May–September) during 2004–20. First, we identified all rain events and heavy rain events occurring at each grid point across Minnesota during each month. From this data, we subsequently determined the monthly event frequency (events/month), the monthly total accumulation from events (mm), and the monthly total rain event hours (h) for all rain events and heavy rain events at each grid point. Then, we calculated the mean monthly values of these variables at each grid point by averaging the monthly values over the 17-yr period, 2004–20. These mean monthly values at each grid point were used to generate the spatial maps shown in Fig. 5 (and later in Figs. 7 and 8). In addition, regional percentiles were calculated based on the mean monthly values across all grid points in Minnesota. Median values (50th percentiles) are discussed at length in the results section, and complete percentile curves are plotted in Fig. 6 (and later in Fig. 9), enabling comparison of the months May–September for a range of percentile values.
(top) Frequency of rain events, (middle) monthly total rain event accumulation, and (bottom) monthly number of rain event hours for (a),(f),(k) May; (b),(g),(l) June; (c),(h),(m) July; (d),(i),(n) August; and (e),(j),(o) September averaged over 17 years (2004–20) based on Stage-IV precipitation data. Black lines indicate state borders. Numbers in the lower-left corner are median values over the domain. Numbers in the lower-right corner are mean (in bold font) and standard deviation (in normal font) over the Minnesota regional domain. Note that radar range effects are strongly evident for the months of May, June, and September and to a lesser degree for July and August.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
Percentile curves for all rain events based on data shown in Fig. 5 for monthly mean (a) event frequency, (b) rain event accumulations, and (c) rain event hours for each month May–September (color coded) during 2004–20.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
For the event-based analysis, we utilized the list of all rain events and heavy rain events that were identified as part of the region-based analysis and their monthly classification (May–September). For all rain events and heavy rain events, we determined event accumulation (mm), event duration (h), event mean intensity (rainfall rate) (mm h−1), and event maximum intensity (rainfall rate) (mm h−1) for each event. It should be noted that for the event-based analysis, the locations of events are disregarded, in contrast to the region-based analysis described above.
For each month (May–September), we combined the 17 years (2004–20) of event variable data for all rain events and for heavy rain events. Percentiles for each of the variables were then calculated for each month (May–September) based on all the events occurring during the 17-yr period for that month. We then constructed frequency distribution graphs (see Fig. 10) as a function of each month and variable for all rain events and for heavy rain events, as well as a two-dimensional histogram that represents the relationship between event accumulation and event duration for heavy rain events (see Fig. 11).
Using the calculated 95th percentile values for event accumulation, event duration, and event mean intensity, we also generated, as a function of month, the year-to-year time series plots (see Fig. 12). The time series plots enabled investigation of year-to-year changes for all rain events and heavy rain events during 2004–20. Although there were not enough years of data available for long term trend detection, we did apply a Mann–Kendall test at a 5% statistical significance level to the 17-yr time series to look for possible shorter-term trends during our study period. Mann–Kendall is a nonparametric test that can be used for trend detection in time series of data that are not normally distributed, such as precipitation (Ahmad et al. 2015).
3. Results
a. Region-based monthly rainfall characteristics for all rain events
On average in a year between 2004 and 2020, Minnesota experienced a median monthly frequency of at least four rain events per month between May through September (Figs. 5a–e). The median monthly total rain accumulation (Figs. 5f–j) and number of rain event hours (Figs. 5k–o) generally mirrored the rain event frequency (Figs. 5a–e) showing the highest values in areas with the highest median monthly frequency values. June had the maximum median monthly frequency of 6.5 events with median values of 75.1-mm accumulation and 12.9 rain event hours per month, followed by July (5.4 events, 70.6-mm accumulation, 10.5 rain event hours) and August (5.0 events, 64.4-mm accumulation, 10.2 rain event hours). May and September experienced lower median monthly frequencies of 4.7 and 4.5 events, 44.3- and 55.8-mm accumulation, and 9.4 and 9.9 rain event hours, respectively. Generally, northwest Minnesota had lower median event frequencies, lower accumulations, and lower numbers of rain event hours than the rest of the state. Largest values were observed in the southeastern portion of the state.
In May, the highest mean monthly frequency of rain events occurred in the southeast corner of the state with >7 rain events, >75-mm monthly accumulation, and >18 monthly rain event hours (Figs. 5a,f,k). The event frequency, monthly accumulation, and monthly number of rain event hours decreased gradually from the southeast toward the northwest. A zone of ∼50–75-mm monthly accumulation and ∼10–15 monthly rain event hours was encountered in east central and southwestern Minnesota. Toward the northwest, accumulation was mainly <50 mm and rain event hours < 12 h.
In June, average monthly values of ∼6–8 events were observed in the southern part of the state with ∼75–125-mm accumulation and ∼14–20 rain event hours (Figs. 5b,g,l). The northern two-thirds of the state commonly experienced ∼4–7 events, ∼50–100 mm of rainfall, and ∼10–15 rain event hours. June experienced the highest rain event frequency, accumulation, and rain event hours compared to the other months (Figs. 5b,g,l).
In July, mean monthly values of ∼6–7 rain events and ∼50–75-mm accumulation were distributed across the state (Figs. 5c,h). Local maxima of ∼7–8 events with ∼100–125-mm accumulation and >10 rain event hours were observed in the central region and in a narrow band along the northeastern border with Canada.
In August, the northern third of the state, especially the far northwest, showed lower mean monthly values with an estimated rain event frequency of ∼3–6 events, ∼25–75-mm accumulation, and ∼5–11 rain event hours (Figs. 5d,i,n). Event frequencies of ∼6–7 events, ∼50–100-mm accumulation, and ∼8–16 rain event hours were focused in the east central and southern areas.
In September, mean monthly rain event frequencies >6 events disappeared for the most part (Fig. 5e). The northwest generally demonstrated mean monthly values of ∼2–5 events, ∼25–75-mm accumulation, and ∼7–11 rain event hours over a broad area while the remainder of the state experienced ∼4–6 events, up to approximately 100-mm accumulation, and ∼10–16 rain event hours (Figs. 5e,j,o).
In addition to the spatial distribution of rain event characteristics, percentile curves that enable a monthly comparison of the distribution of mean monthly rain event characteristics across all Minnesota grid points have been plotted (Figs. 6a–c). For example, a comparison of the 95th percentile (P95) monthly rain event frequency values, as determined from all grid points across the state and averaged over 2004–20, revealed 6.9 events for May, 7.5 for June, 6.4 for July, 6.2 for August, and 5.2 for September (Fig. 6a). In general, Fig. 6 illustrates similarities and differences between monthly frequency distributions. Interestingly, the curves for the month of May reveal notably different frequency distribution shapes than those for the other warm season months June–September.
b. Region-based monthly rainfall characteristics for heavy rain events
Heavy rain event patterns demonstrated some similarity to the patterns for all rain events. For May, June, and September, the mean monthly heavy rain event frequency was relatively high in the southeastern Minnesota in comparison with other areas in the state (Figs. 7a–e). In addition, July and August had relatively high event frequencies of >0.8 events per month in the central portion of the state (Figs. 7c,d). Maxima in event frequencies, accumulations, and event hours for May–June, and to some degree in August–September, occurred in banded patterns oriented from southwest to northeast (Fig. 7). July and August were the peak months for the regional median mean monthly heavy rain event frequency (0.3 events per month). July was the peak month for accumulation (15.9 mm), while September, June, and July featured the largest regional median mean monthly heavy rain event hours (1.5 h) (Fig. 7). These heavy rain event observations stand in contrast to those for all rain events, which feature June as the peak month for all three variables (Fig. 5). Notably, for heavy rain events, the month of May had the lowest values, while September experienced values similar to those of June–August (Fig. 7). September was also the peak month for heavy rain accumulation as a percent (23.7%) of all rain event accumulation, followed by July (22.7%), August (21.7%), June (18.3%), and May (14.2%) (Figs. 8a–e).
As in Fig. 5, but for heavy rain events. Note that radar range effects are less evident for the heavy rain events in this figure than for all rain events in Fig. 5.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
Mean monthly heavy rain event hour accumulation as percent of mean monthly accumulation for all rain event hours, where accumulations were averaged over 17 years (2004–20) based on Stage-IV precipitation data. Numbers in the lower-left corner are median percentage values over the domain.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
In May, higher frequencies of heavy rain events (>0.2 events) were observed in south-central, southeast, and portions of northwest Minnesota. Heavy rain event accumulation and event hours generally ranged from as much as 24 mm and ∼1–4 h in the southern areas to generally <16 mm and ∼0–2 h in the northwest (Figs. 7a,f,k).
In June, heavy rain events became more widespread with frequencies increasing up to ∼1.1 events per month (Fig. 7b). Most events occurred in the southeastern part of the state with some extension northward. The highest monthly heavy rain event accumulations were observed in the southeastern third of the state and in isolated areas in the central region, with values > 40 mm (Fig. 7g). In general, the state remained partitioned into larger accumulations (∼28–50 mm) in the southeast and lower accumulations (<24 mm) in the northwest. Heavy rain event hours were ∼2–4 h in the southeast, ∼0–3 h in central Minnesota, and ∼0–2 h in the northwest (Fig. 7l).
In July, heavy rain event frequency (>0.7) was highest along a northwest–southeast-oriented area stretching from west central to southeastern Minnesota (Fig. 7c). The largest accumulations (>28 mm) were observed along a northwest–southeast-oriented band ranging from south-central to southeast Minnesota and a second west–east-oriented band located in central Minnesota (Fig. 7h). Embedded in these bands of enhanced accumulations were values > 28 mm across large areas. In July, heavy rain event hours > 3 h were observed along the aforementioned west–east and northwest–southeast-oriented bands of enhanced accumulation (Fig. 7m).
In August, the area with heavy rain event frequencies > 0.3 events per month decreased while isolated areas of enhanced frequency (>0.7 events) persisted in central and southern Minnesota (Fig. 7d). Large accumulations slightly decreased spatially and in magnitude compared to July, with most of the larger accumulations (>28 mm) focused in central and southern Minnesota (Fig. 7i). The distribution of heavy rain event hours during August was similar to July with ranges of ∼1–4 h in central areas, <3 h in the southwest, and ∼0–1 h in the northern areas (Fig. 7n).
In September, the frequency of heavy rain events was reduced further from prior months with widespread frequencies > 0.4 events per month limited to the southern quarter of Minnesota and isolated areas in the northwest part of the state (Fig. 7e). September accumulations resembled August patterns with accumulation maxima > 28 mm moving farther south and the largest heavy rain event hours of ∼3–6 h occurring in the southern quarter of the state, followed by ∼0–3 h in the northwest, and ∼0–2 h in central Minnesota (Figs. 7j,o).
As in the discussion for all rain events, heavy rain event percentile curves were produced to enable monthly comparison of frequency distributions among the warm season months May–September (Figs. 9a–c). Notably, for all three variables, the May curves demonstrated a slightly different shape and markedly lower percentile values than those of the other months.
Percentile curves for heavy rain events based on data shown in Fig. 7 for monthly mean (a) heavy rain event frequency, (b) heavy rain event accumulations, and (c) heavy rain event hours for each month May–September during 2004–20.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
c. Event-based rainfall characteristics
While we focused on the spatial distribution of rain characteristics between May–September in the previous sections, here we used data from 2004 to 2020 to characterize rain events and heavy rain events regardless of where they occurred in Minnesota. The forthcoming analysis examines frequency distributions by month for event frequency, event accumulation, event duration, event mean rainfall intensity, and event maximum rainfall intensity.
For all rain events the most commonly occurring event frequencies at a grid point were 4 events in May (at 14.0% of grid points), 6 in June (15.6%), 5 in July (16.5%), 5 in August (16.1%), and 3 in September (13.8%) (Fig. 10a). The frequency distribution for heavy rain events indicated that most grid points (>70%) experienced no heavy rain events during a month (Fig. 10f). Typically, between 10% and 25% of the grid points experienced exactly one heavy rain event per month, and less than 5% experienced more than one.
Event-based frequency distribution graphs for the following rain event characteristics: (a) monthly rain event frequency at a point, (b) rain accumulation per event (mm), (c) event duration (h), (d) mean intensity (mm h−1), and (e) maximum intensity (mm h−1). Event-based frequency distribution graphs for the following heavy rain event characteristics: (f) monthly rain event frequency at a point, (g) rain accumulation per event (mm), (h) event duration (h), (i) mean intensity (mm h−1), and (j) maximum intensity (mm h−1). Data are based on Stage-IV rainfall between 2004 and 2020. Median values are shown at top of plots. In addition, P95 values are shown on accumulation plots in (b) and (g).
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
For all months, greater than 45% of rain events showed event accumulation < 8 mm, and greater than 35% of heavy rain events experienced event accumulations between 36 and 44 mm (Figs. 10b,g). July (September) had the maximum median event accumulation of 8.9 mm (48.0 mm) for all (heavy) rain events. At the high end of the accumulation frequency distribution, the month of September had the maximum P95 accumulation of 38.8 mm (102.2 mm) for all (heavy) rain events.
For all rain events, event duration frequency distributions were very similar for each month during May through September (Fig. 10c). Approximately 50%–55% of the events were only one hour in duration, ∼20%–25% of the events had durations of 2 h, approximately 10% of the events had durations of 3 h, and <20% had 4 or more hours of duration. For heavy rain events, the most common event durations were 7 h in September, followed by 6 h in May, and 3–4 h in June–August (Fig. 10h). The longest heavy rainfall event was found to be 28 h and occurred in the month of September.
Mean intensities for all rain events were higher in June–August than in May and September (Fig. 10d). Mean intensity median values ranged from 4.6 to 5.3 mm h−1 in the summer and were 4.0 and 4.5 mm h−1 for May and September, respectively. For all warm season months, more than 70% of all rain events had mean intensities < 8 mm h−1, with May, June, and September values in the 80%–90% range. For heavy rain events, median values of mean intensities also were higher during the summer months (ranging from 9.7 to 11.6 mm h−1) than in May (7.4 mm h−1) and September (8.2 mm h−1) (Fig. 10i). In June–August, the most commonly occurring mean intensity for heavy rain events occurred in the 8 to 16 mm h−1 category, with 46%–49% of summertime heavy rain events falling in that range. Smaller percentages, from 24% to 36%, had mean intensities < 8 mm h−1. Additionally, 14%–21% of heavy rain events experienced mean intensities in the 16–24 mm h−1 range during those three months. During May and September, 47%–58% of heavy rain events had mean intensities < 8 mm h−1, and 34%–41% of heavy rain events experienced mean intensity in the 8–16 mm h−1 range. For all rain events and heavy rain events, the median intensity values peaked in July (Figs. 10d,i). Examination of both mean intensities and event durations shows that heavy rain events in June–August experienced generally higher intensities and shorter durations than heavy rain events in the transition months, May and September (Figs. 10c,d,h,i).
Analysis of event maximum intensity rates provided information about the role of heavy rain hours (>16 mm h−1) during rain events (Figs. 10e,j). We found that the approximate percentages of all rain events without any heavy rain hours were 96.4% for May, 91.9% for June, 87.4% for July, 89.5% for August, and 92.3% for September (Fig. 10e). The approximate percentages of heavy rain events with at least one heavy rain hour were 45.3% for May, 72.5% for June, 81.8% for July, 75.5% for August, and 60.8% for September (Fig. 10j).
The relationship between total accumulation and duration for each individual heavy rain event between May–September (Fig. 11) showed that August (Fig. 11d) had by far the longest (15–25 h) events with the largest accumulations (200–350 mm). June and September were characterized by events < 250 mm, that also lasted up to 25 h (Figs. 11b,e). Interestingly, heavy rain events in July frequently were <20 h in duration with 100–250 mm in total event accumulation (Fig. 11c). Heavy rain events in May were generally <25 h in duration with event accumulations not exceeding 200 mm (Fig. 11a).
Histograms of number of heavy rain events as a function of event accumulation and duration for heavy rain events that occurred in the study domain between 2004 and 2020. Event accumulation and duration combinations are binned for frequency analysis. A heavy rain event, regardless of its location, is included in the count of the bin associated with its accumulation and duration. The color-coded mapping indicates the relative frequency of occurrence for each bin.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
d. Event-based annual rainfall characteristics, 2004–20
To investigate changes in rainfall characteristics between 2004 and 2020, we plotted time series using 95th percentile (P95) values for all rain events and heavy rain events during each year (Fig. 12). Although the 17-yr study period is not sufficient to establish long term trends, the variable time series are plotted with their fitted trend lines to provide a snapshot in time of the year-to-year changes between 2004 and 2020. Event accumulation, duration, and mean intensity trend lines between 2004 and 2020 increased in May–September for all rain events, except for accumulation and duration in September and mean intensity in May (Figs. 12a–c). For heavy rain events between 2004 and 2020, event accumulation and duration trend lines increased in June–July and mean intensity trend lines increased in August and September (Figs. 12d–f). The largest trend line increases in heavy rain event accumulation occurred in June and July, whereas the largest trend line increases in event duration and mean intensity occurred in July and September, respectively.
Event-based 95th percentile of (a),(d) rain accumulation; (b),(e) duration; and (c),(f) mean intensity for (top) all rain events and (bottom) heavy rain events between 2004 and 2020 (dashed lines). Thick lines indicate trend lines. The differences in trend line values between 2004 and 2020 are shown at top of plots for each trend line. Asterisks indicate trend lines that demonstrate statistical significance at the 95% confidence level using the Mann–Kendall method.
Citation: Weather and Forecasting 38, 1; 10.1175/WAF-D-21-0186.1
The event accumulation trend lines for rain events exhibited an increase of 8.6 mm for June and 15.7 mm for July between 2004 and 2020, while accumulation trend lines changed slightly (from −2.1 to +2.1 mm) for May, August, and September (Fig. 12a). For heavy rain events, June and July trend lines increased by 17.4 and 30.0 mm, respectively (Fig. 12d). The trend line for August accumulations showed a decrease of −4.0 mm, while May and September demonstrated substantial decreasing trend line changes of −10.0 and −22.6 mm, respectively (Fig. 12d).
Event duration trend lines increased in May–August for all rain events, with the largest increase of +2.0 h in July, followed by +1.3 h in May and +1.0 h in June (Fig. 12b). The duration trend line for September showed a decrease of −0.6 h (Fig. 12b). For heavy rain events, only May–July displayed trend line increases, ranging from +0.1 h in June to +2.1 h in July (Fig. 12e). August and September displayed heavy rain event duration trend line decreases of −1.5 and −2.9 h, respectively.
For all rain events, June–September experienced increasing trend lines in rain event mean intensity between 2004 and 2020 (Fig. 12c). July featured the largest trend line increase of 3.6 mm h−1 over the study period (Fig. 12c), while September had a trend line increase of 3.2 mm h−1. May, however, demonstrated a mean intensity trend line decrease of −2.4 mm h−1 over the study period. For heavy rain events, September showed the largest mean intensity trend line increase of 4.3 mm h−1 over the study period, while August showed a lesser increase of +1.6 mm h−1 (Fig. 12f). May exhibited the largest trend line decrease of −6.5 mm h−1 with especially noteworthy underlying low rainfall rates (<10.0 mm h−1) between 2019 and 2020 (Fig. 12f).
4. Discussion
The results of this study have laid a foundation for future investigation of the meteorological drivers of heavy rainfall in Minnesota. Anticipated research has been informed by the results of prior studies. In particular, previous research has demonstrated linkage between large-scale meteorological patterns (LSMPs) and extreme precipitation events in North America (Barlow et al. 2019). Their work emphasized the importance of fronts and synoptic-scale cyclones in heavy precipitation events and indicated that extreme precipitation is frequently the result of mesoscale processes that have been influenced by an LSMP. Additionally, Carbone et al. (2002) explored the occurrence of compound events consisting of coherent sequences of convective systems. A later study further explored the importance of diurnal cycles and found that the majority of rainfall in the central United States is nocturnal and linked to factors such as the propagation of westerly rainfall systems originating near the Continental Divide, ascent over the plains region, and the transport of moisture by the Great Plains low-level jet (Carbone and Tuttle 2008). Other research has attributed extreme rainfall events in the central and eastern United States to mesoscale convective systems (MCS), synoptic-scale systems, and/or tropical systems (Stevenson and Schumacher 2014). A predecessor rain event (PRE), which occurs ahead of a recurving tropical cyclone, is another mechanism that can lead to extreme precipitation events. Minnesota received large rainfall amounts and experienced historic flooding resulting from a slow-moving MCS associated with a PRE in August 2007 (Schumacher et al. 2011). Planned future research of Minnesota heavy rainfall will consider the synoptic-scale and mesoscale drivers discussed in this section.
In our study, regional and seasonal analysis was conducted to develop precipitation statistics for Minnesota. Our research found that the highest Minnesota regional median value of mean monthly accumulation for heavy rain events occurred in July, with elevated values also occurring in June and August (Figs. 7g–i). The July peak was consistent with previous findings of a July peak in heavy precipitation in the contiguous United States (Brooks and Stensrud 2000) and in the eastern two-thirds of the United States (Schumacher and Johnson 2006). Heavy rain event precipitation accumulation peaks occurred in the southern part of Minnesota in June and generally increased northward as the warm season evolved, with July peaks found mainly in the central and south-central areas of the state (Figs. 7g–i). Monthly averages of precipitation variables from heavy rain events in May, June, and September feature bands with a southwest–northeast orientation for heavy rain event variables, while July averages displayed west–east-oriented bands, and both July and August averages featured northwest–southeast-oriented bands (Fig. 7). Future analysis of meteorological drivers and individual storms might investigate possible alignment of these results with heavy rain event types defined for Minnesota by Winkler (1988), where a Type I event required a southwest–northeast orientation of its rain cells that appeared to result from rain cell formation along a surface temperature discontinuity or a squall line. A Type II classification in the same study required a west–east or northwest–southeast rain cell orientation. Seasonal analysis of other precipitation variables showed that regional median event frequency of Minnesota heavy rain events (0.3 events per month) peaked in July and August (Figs. 7c,d). Of the warm season months, May generally had the lowest values for regional heavy rain event variables (Figs. 7a,f,k). Interestingly, although our study did find the regional monthly accumulation peak in July, the monthly number of heavy rain event hours peaked in June, July, and September (1.5 h) (Figs. 7l,m,o). In addition, as noted previously, the contribution of heavy rain event accumulation as a percentage of all rain event accumulation peaked in September (23.7%), followed in order by July (22.7%), August (21.7%), June (18.3%), and May (14.2%) (Figs. 8a–e).
In addition, previous studies have indicated an increase in annual heavy rainfall in the northwestern Midwest based on daily gauge station data of varied record lengths between 1890 and 2002 (Pryor et al. 2009) and in the northern part of the central United States based on ≥50-yr records of daily station data between about 1900–2010 (Villarini et al. 2013). In our study, multiyear temporal analysis of heavy rain events between 2004 and 2020 revealed a mix of increasing and decreasing changes for a variety of precipitation variables (Fig. 12). For example, our findings showed increasing trend lines for heavy rain event accumulation in June and July while May and September demonstrated decreasing trend lines. Because summertime (June–July) extreme rain events in the upper Midwest are largely associated with mesoscale convective systems (MCSs) (Schumacher and Johnson 2006), future research might investigate possible changes in MCSs during the study period for the Minnesota region. Similarly, synoptic systems have a greater association with extreme rain events outside of the summertime in May and September (Schumacher and Johnson 2006), and it seems likely that the longer event durations found for May and September are linked to the greater influence of synoptic systems during those months. Consequently, changes to synoptic drivers of precipitation might be responsible for the decreasing trend lines observed in May and September. Future research might also examine relationships between changes in mesoscale and synoptic systems alongside heavy rain event durations and mean intensity. It must be noted, however, that the 17-yr time period of this study is relatively short and not sufficient to establish long term trends. Nevertheless, this study provides a look into what has been happening in recent years and can help identify areas of potential interest for future study.
5. Conclusions
We used hourly Stage-IV precipitation data at 4-km resolution between 2004 and 2020 to study rainfall characteristics between May and September in Minnesota. We quantified total event accumulation, duration, and intensity during rain events and heavy rain events using region-based and event-based analyses. Main findings of this study can be summarized as:
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Region-based analyses showed that for all rain events, the highest median monthly rain event frequency occurred in June (greater than 6 events per month) and the lowest in September (at 4.5 events per month) (Figs. 5a–e). Median monthly accumulations were largest in summer, led by June and followed by July and August (Figs. 5f–j). Monthly rain event hours peaked at about 20 h in southeastern Minnesota during the warm season (Figs. 5k–o).
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Region-based median values of heavy rain event monthly frequency at grid points peaked in July and August, while monthly accumulation peaked in July (Figs. 7c,d,h). Peak median values for the monthly number of heavy rain event hours were reached in June, July, and September (Figs. 7l,m,o). During much of the warm season, heavy rain events were relatively impactful in approximately the southern third of the state with an especially strong presence in the southeast (Figs. 7a–o). Additionally, during July and August, heavy rain events demonstrated a strong presence in a central area of the state (Figs. 7c,d,h,i,m,n).
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Region-based analyses indicated that the contribution of heavy rain event accumulation peaked in September at 23.7% of all rain event accumulation. This was the maximum percentage of any month in the warm season (Fig. 8).
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Frequency distribution curves for all rain events showed that the most common monthly event frequency at grid points was 4 events in May, 6 in June, 5 in July, 5 in August, and 3 in September (Fig. 10a). Heavy rain events were relatively infrequent with most grid points experiencing no heavy rain events in any one month (Fig. 10f). Typically, exactly one heavy rain event per month occurred at 10%–25% of points and more than one event at fewer than 5% of points.
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Event-based analyses for all rain events during May–September 2004–20, demonstrated that 1) smaller event accumulations were much more frequent than larger event accumulations (Fig. 10b); 2) event duration frequency distributions showed that more than half of events had only 1-h duration, 20%–25% had 2-h duration, and approximately 10% had 3-h duration (Fig. 10c); 3) most events had mean intensity rates in the lowest intensity category of <8 mm h−1 (Fig. 10d).
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Event-based analyses for heavy rain events found that 1) accumulations for heavy rain events are largely concentrated at the low end of their accumulation ranges (>36 mm for heavy rain events) (Fig. 10g), 2) heavy rain event durations most commonly range from 3 to 4 h in summer months (June–August) and range from 6 to 7 h in transition months (May, September) (Fig. 10h), and 3) most heavy rain events experience mean intensities < 16 mm h−1, with the greatest monthly variability in the lowest category of <8 mm h−1 (Fig. 10i).
Because the hourly precipitation data in this study spanned a limited period of only 17 years due to data availability, it will be necessary to continue to monitor observations over time to establish longer term trends and to assess impacts of possible changes in climate conditions. The results of this study in their current form, while not directly applicable to operational forecasting, do establish a foundation for planned follow-on research. Future study of the relationship between meteorological drivers and heavy rainfall is intended to help identify patterns leading to heavy rain events and to enhance predictability of such events in climate modeling for operational forecasting during Minnesota’s warm season.
Acknowledgments.
The authors are grateful to the NCAR/UCAR–Earth Observing Laboratory for making available the NCEP/EMC 4KM Gridded Data (GRIB) Stage-IV precipitation data used in this analysis. The authors thank the Cloud and Precipitation Research Group, University of Colorado Atmospheric and Oceanic Sciences Department, for their helpful comments. The authors also thank three reviewers for their constructive feedback and suggestions.
Data availability statement.
The NCEP/EMC 4KM Gridded Data (GRIB) Stage-IV Data, version 1.0 (Du 2011) is available at https://doi.org/10.5065/D6PG1QDD. This analysis used the hourly datasets for May–September for each year during 2004–20.
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