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  • View in gallery

    Observations from the Dane County Regional Airport in Madison, WI, from 1981 to 2000 showing the frequency distribution of annual precipitation (bars). Lines represent the average number of events that reach or exceed the specific threshold expressed as a percent of the annual total.

  • View in gallery

    Frequency distribution of average precipitation (bars) in NARR during 1981–2000 (grid point closest to Madison, WI). Lines express the percentage of events that occur during each month within a given threshold (including wet and dry days).

  • View in gallery

    Simulated frequency distribution of average monthly precipitation for the CMIP3 multimodel mean during the late twentieth and late twenty-first centuries.

  • View in gallery

    Frequency distribution of Madison’s wettest (a),(d) 10%, (b),(e) 5%, and (c),(f) 1% of all days for the (a)–(c) late twentieth and (d)–(f) late twenty-first centuries. Individual curves are shown for each CMIP3 model. The multimodel average is the thick black line.

  • View in gallery

    Average monthly 925-hPa specific humidity (g kg−1) simulated during the late twentieth and late twenty-first centuries among the CMIP3 models.

  • View in gallery

    Spatial composite of SLP (hPa; contours) and average precipitation (mm day−1; shaded) during (a) the wettest 1% of days (N = 73 days), (b) cold-season months of the wettest 1% of days (N = 14), and (c) warm-season months of the wettest 1% of days (N = 59) in Madison, WI, in NARR from 1981 to 2000.

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    Late twentieth-century (1981–2000) spatial composites of daily precipitation (mm day−1) and SLP (hPa; contoured every 2 hPa) during the wettest 1% of days for models listed in Table 1.

  • View in gallery

    NARR composite of vertically integrated MFC (mm day−1) during Madison’s wettest 1% of days during 1981–2000.

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    Spatial composites of the mean vertically integrated MFC −[ · (Vq)] (shaded; mm day−1) and vertically integrated moisture flux (vectors; kgw m−1 s−1) for Madison’s wettest 1% of days in CMIP3 simulations of the twentieth century.

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    Scatterplot showing the relationship between the average change in precipitation and the average change in (top) MFC and (bottom) specific humidity, during Madison’s wettest 1% of precipitation events. Each dot represents a different model.

  • View in gallery

    Breakdown of the multimodel average MFC term as simulated by each of the CMIP3 models during (left) the late twentieth and (right) late twenty-first centuries. Total MFC increases by 53% between the two periods.

  • View in gallery

    Spatial composites of the average vertically integrated moisture convergence term {−[q · V]; mm day−1} for Madison’s wettest 1% of days in CMIP3 simulations during the late twentieth century.

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Understanding Simulated Extreme Precipitation Events in Madison, Wisconsin, and the Role of Moisture Flux Convergence during the Late Twentieth and Twenty-First Centuries

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  • 1 Nelson Institute Center for Climatic Research, and Department of Atmospheric and Oceanic Sciences, University of Wisconsin—Madison, Madison, Wisconsin
  • | 2 Nelson Institute Center for Climatic Research, University of Wisconsin—Madison, Madison, Wisconsin
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Abstract

Understanding extreme precipitation events in the current and future climate system is an important aspect of climate change for adaptation and mitigation purposes. The current study investigates extreme precipitation events over Madison, Wisconsin, during the late twentieth and late twenty-first centuries using 18 coupled ocean–atmosphere general circulation models that participated in the Coupled Model Intercomparison Project (CMIP3). An increase of ~10% is found in the multimodel average of annual precipitation received in Madison by the end of the twenty-first century, with the largest increases projected to occur during winter [December–February (DJF)] and spring [March–May (MAM)]. It is also found that the observed seasonal cycle of precipitation in Madison is not accurately captured by the models. The multimodel average shows a strong seasonal peak in May, whereas observations peak during midsummer. Model simulations also do not accurately capture the annual cycle of extreme precipitation events in Madison, which also peak in summer. Instead, the timing of model-simulated extreme events exhibits a bimodal distribution that peaks during spring and fall. However, spatial composites of average daily precipitation simulated by GCMs during Madison’s wettest 1% of precipitation events during the twentieth century strongly resemble the spatial pattern produced in observations. The role of specific humidity and vertically integrated moisture flux convergence (MFC) during extreme precipitation events in Madison is investigated in twentieth- and twenty-first-century simulations. Spatial composites of MFC during the wettest 1% of days during the twentieth-century simulations agree well with results from the North American Regional Reanalysis dataset (NARR), suggesting that synoptic-scale dynamics are vital to extreme precipitation events.

Nelson Institute Center for Climatic Research Publication Number 1067.

Corresponding author address: Kathleen Holman, Center for Climatic Research, University of Wisconsin—Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: kdholman@wisc.edu

Abstract

Understanding extreme precipitation events in the current and future climate system is an important aspect of climate change for adaptation and mitigation purposes. The current study investigates extreme precipitation events over Madison, Wisconsin, during the late twentieth and late twenty-first centuries using 18 coupled ocean–atmosphere general circulation models that participated in the Coupled Model Intercomparison Project (CMIP3). An increase of ~10% is found in the multimodel average of annual precipitation received in Madison by the end of the twenty-first century, with the largest increases projected to occur during winter [December–February (DJF)] and spring [March–May (MAM)]. It is also found that the observed seasonal cycle of precipitation in Madison is not accurately captured by the models. The multimodel average shows a strong seasonal peak in May, whereas observations peak during midsummer. Model simulations also do not accurately capture the annual cycle of extreme precipitation events in Madison, which also peak in summer. Instead, the timing of model-simulated extreme events exhibits a bimodal distribution that peaks during spring and fall. However, spatial composites of average daily precipitation simulated by GCMs during Madison’s wettest 1% of precipitation events during the twentieth century strongly resemble the spatial pattern produced in observations. The role of specific humidity and vertically integrated moisture flux convergence (MFC) during extreme precipitation events in Madison is investigated in twentieth- and twenty-first-century simulations. Spatial composites of MFC during the wettest 1% of days during the twentieth-century simulations agree well with results from the North American Regional Reanalysis dataset (NARR), suggesting that synoptic-scale dynamics are vital to extreme precipitation events.

Nelson Institute Center for Climatic Research Publication Number 1067.

Corresponding author address: Kathleen Holman, Center for Climatic Research, University of Wisconsin—Madison, 1225 W. Dayton St., Madison, WI 53706. E-mail: kdholman@wisc.edu

1. Introduction

Empirical evidence from observational networks across the United States has shown an increase in the number of days with precipitation and an increase in the intensity of extremely heavy events over the last century (Karl and Knight 1998; Kunkel et al. 1999; Small and Islam 2009; Alexander et al. 2006; Pryor et al. 2008; Groisman et al. 2004). The Midwest, which is an agriculturally important region, has experienced an increase in extreme precipitation events in agreement with these large-scale trends (Kling et al. 2003). According to Karl and Knight (1998), the largest increases in annual precipitation are occurring in the upper 5% (95th percentile) of all the daily precipitation amounts. The observed trends and implications for agriculture, transportation, and ecosystems have led to multiple investigations of how extreme precipitation events may change under future climate projections (Trenberth et al. 2003; Wehner 2005; Emori and Brown 2005; Vavrus and Van Dorn 2010). Model simulations under a moderate future greenhouse emissions scenario suggest that annual precipitation in the Midwest will increase slightly (Solomon et al. 2007), with an increase in frequency of heavy precipitation events during spring and fall (Cook et al. 2008). For example, the Chicago, Illinois, area is projected to experience an increase in the number of precipitation events at or exceeding 2.5 in. (63.5 mm) in a given 24-h period—a threshold that has been previously associated with flooding (Wuebbles et al. 2010).

In an attempt to understand previous flooding events in the Midwest, observational studies have investigated the origin of the rich supply of moisture that feeds these rainfalls. An analysis by Trenberth and Guillemot (1996) documented an atmospheric river of moisture from the Gulf of Mexico into the central United States during the upper-Mississippi basin flood of 1993. Dirmeyer and Kinter (2010) found that late spring and early summer (May–June) flooding events in the Midwest are enhanced by moisture from the Caribbean Sea. The authors contend that the available moisture is the result of enhanced evaporation in lower latitudes that is transported northward and merges with the Great Plains low-level jet (GPLLJ). According to Wang et al. (2007), there exists a low-level (~925 hPa) easterly wind maximum in the Caribbean during the summer months, referred to as the Caribbean low-level jet (CLLJ), which splits into two branches—one of which travels northward and connects with the GPLLJ. Future climate projections based on 18 coupled atmosphere–ocean general circulation models (GCMs) suggest an intensification of the GPLLJ during April–June associated with an enhanced Bermuda high (Cook et al. 2008). These studies suggest that remote moisture sources are important for the hydrologic budget in the Midwest and may continue to play a vital role in extreme precipitation events during the twenty-first century.

The primary purpose of the current study is to investigate the physical mechanisms responsible for producing extreme precipitation events in Madison, Wisconsin (WI), in model simulations of the twentieth and twenty-first centuries. This dynamical analysis, which includes a breakdown of model-simulated vertically integrated moisture flux convergence (MFC), is intended to improve our understanding of the underlying processes of extreme precipitation events in the Midwest and to assess models’ reliability and projections. The analysis of MFC is motivated by previous hydrological analyses using observational data and model simulations. Roads et al. (1994) performed an analysis on the United States’ hydrologic cycle and found a strong correlation between precipitation anomalies and MFC anomalies, particularly over the eastern half of the country. Ruiz-Barradas and Nigam (2006) concluded that Great Plains precipitation anomalies present in the North American Regional Reanalysis dataset (NARR) are mostly the result of convergence of remote moisture fluxes and, to a lesser extent, local evaporation of precipitation. Cook et al. (2008) investigated projected changes in precipitation across the United States using four GCMs and found that increases in precipitation were closely associated with atmospheric moisture convergence increases.

Well-cited studies such as Karl and Knight (1998) and Groisman et al. (2004) have approached the topic of future changes in extreme precipitation events from more of a statistical standpoint, while other studies such as Meehl et al. (2005) and O’Gorman and Schneider (2009) have focused on the physical basis for increasing extreme precipitation. The investigation by Cook et al. (2008) focused on projected changes in monthly precipitation and the relationship with moisture convergence. However, none has focused on the relationship between extreme precipitation events and MFC. Here, we use a combination of reanalysis data and model simulations of the twentieth and twenty-first centuries to understand extreme precipitation events in Madison, WI. Madison is chosen as the point of interest because of its location in the Midwest region and extended observational record.

2. Data and methods

a. Data

The data used in the current investigation include station observations, a reanalysis product that encompasses the United States, and output from 18 general circulation models. NARR, from the National Centers for Environmental Prediction (NCEP), is used to complement an observed precipitation time series from the Dane County Regional Airport [43.08°N, 89.21°W, and 264 m (866 ft) above sea level] in Madison, WI, and to expand the spatial domain of observations for data comparison. The reanalysis product combines observations and data assimilation, and is therefore considered an estimate of the real atmosphere. A frozen version of NCEP’s mesoscale Eta forecast model is used in NARR, while precipitation observations are assimilated as latent heating profiles (Lin et al. 1999). The assimilation of observed precipitation ensures that the hydrological cycle is not entirely based on model forecasts, therefore resulting in a more realistic product (Mesinger et al. 2006). NARR also includes the Noah land surface model (Ek et al. 2003), which allows for two-way interactions between the atmosphere and land surface. NARR data are available from October 1978 to December 2003 at a relatively high spatial and temporal resolution: 32 km horizontal, 45 vertical layers, and 3-h time intervals. Although available for 30 yr, we extracted 20 yr of data from the end of the twentieth century (1981–2000) to ensure that comparisons made with GCM simulations covered the same time interval.

Studies investigating the accuracy and usefulness of NARR’s representation of the hydrological cycle have been published since its distribution. Bukovsky and Karoly (2007) deem NARR precipitation fields superior to those represented in the NCEP–Department of Energy (DOE) Atmospheric Model Intercomparison Project II (AMIP-II) global reanalysis (NCEP–DOE) and the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40). The authors contend that NARR correctly captures the summertime maximum in the annual precipitation cycle over the eastern half of the United States, while extreme precipitation events are also considered well reproduced. For example, NARR was able to reproduce a flooding event that took place in Las Vegas, Nevada, during the summer of 1999, capturing the intensity and spatial pattern of the precipitation (Bukovsky and Karoly 2007).

Daily model output is analyzed from 18 different coupled ocean–atmosphere GCMs that participated in the World Climate Research Programme’s (WCRP) Coupled Model Intercomparison Project phase 3 (CMIP3) (Meehl et al. 2007) used in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) (Table 1). The grid spacing expressed in Table 1 is different from the effective resolution, which is usually four times larger than the grid spacing (Walters 2000). Three model-simulated time periods are available: late twentieth century (1981–2000), mid-twenty-first century (2046–65), and late twenty-first century (2081–2100). Future climate simulations used throughout the analysis were forced using the Special Report on Emissions Scenarios (SRES) A1B emissions scenario—a moderate emissions projection in which atmospheric carbon dioxide concentrations reach 717 ppm (ppm) by the year 2100 (Nakicenovic and Steward 2000). The current analysis exclusively uses the late twenty-first-century data to maximize the climate change signal. Model simulations and reanalysis data were left on their native grids to prevent any degradation from spatial interpolation.

Table 1.

Listing of CMIP3 GCMs used in this study (* indicates models used in the MFC analysis).

Table 1.

b. Methods

The analysis begins by identifying the seasonal cycle of average precipitation and extreme precipitation in Madison, WI. We define extreme precipitation events as the wettest 5% (95th percentile) and wettest 1% (99th percentile) of all days in the time series (including both wet and dry days, therefore about 18 and 4 days per year, respectively). Model results from the twentieth-century simulations are compared with observations from the Dane County Regional Airport, NARR, and late twenty-first-century simulations.

The days on which extreme precipitation events occurred in the reanalysis and CMIP3 simulations were used as the basis for composite analysis. Spatial composites of NARR and GCMs focus on average accumulated precipitation, sea level pressure, and vertically integrated MFC and its components. Daily specific humidity was a limiting factor in the analysis of model-simulated vertically integrated MFC: out of 18 GCMs, only 13 provided daily specific humidity data (Table 1).

An analysis of the vertically integrated MFC is used to identify the physical mechanism responsible for producing extreme precipitation events in reanalysis data and model simulations. The moisture flux convergence term from NARR is a provided product that is vertically integrated throughout the depth of the atmosphere (1000–100 hPa). However, the analysis of GCM-simulated moisture flux convergence involved vertically integrating the mathematical expression shown in Eq. (1), where is the gradient operator, V is the horizontal wind vector, and q is the specific humidity (brackets indicate vertically integrated):
e1

The first term on the right-hand side of Eq. (1) represents the convergent component of the MFC, which represents the product of the convergent component of the wind with specific humidity. The second term on the right-hand side of Eq. (1) represents the advective component, which describes the horizontal advection of specific humidity (Banacos and Schultz 2005). Equation (1) was vertically integrated from 1000 to 300 hPa, which is consistent with the approach in Ruiz-Barradas and Nigam (2006). We chose a lower bound of 1000 hPa to ensure data near the surface were included in the integration. The upper bound of 300 hPa was chosen because most of the water vapor in the atmosphere resides in the lower-to-middle troposphere. The second term on the right-hand side of Eq. (1), the advective component, was computed as a residual because of potential errors associated with taking the gradient of specific humidity in areas of missing data. The left-hand side and first term on the right-hand side of Eq. (1) were calculated by using either spherical harmonics or centered finite differencing, depending on the configuration of the GCM.

3. Results

a. Seasonal precipitation

Madison, WI, is characterized by a warm-season peak in average monthly precipitation indicated by observations recorded at the Dane County Regional Airport between 1981 and 2000 (Fig. 1). Over this time period, June receives the largest amount of monthly precipitation, followed by July and then August, while heavy precipitation events are even more concentrated in summer (Fig. 1). For example, daily precipitation events of 2 in. or more (50.8 mm) occur most frequently during June–August (JJA) (~68% of the time), although there exists a minimum in the contribution from July events. The frequency distribution of 0.5 in. (12.7 mm) or greater and 1 in. (25.4 mm) or greater precipitation events also show a summer peak, which is consistent with the timing of mean precipitation.

Fig. 1.
Fig. 1.

Observations from the Dane County Regional Airport in Madison, WI, from 1981 to 2000 showing the frequency distribution of annual precipitation (bars). Lines represent the average number of events that reach or exceed the specific threshold expressed as a percent of the annual total.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

Observations from the Dane County Regional Airport are not directly comparable to output from model simulations because the observational data represent a single point in space, while the results from a CMIP3 model simulation represent a gridbox average that is typically 3° latitude × 3° longitude, or 330 × 240 km2 in the vicinity of Wisconsin. Therefore, we use the precipitation fields produced by NARR as a first step in bridging the spatial differences between observations and model simulations. NARR is an appropriate choice because the grid spacing is larger than a point observation, yet still high resolution relative to model simulations.

Results for NARR (Fig. 2) indicate that the seasonal cycle of Madison precipitation is well captured at a 32-km horizontal resolution. The frequency distributions for extreme events—which are defined as the wettest 10%, 5%, and 1% of all days in the time series—show general agreement with data from the airport, except at the uppermost limit of events defined here. The frequency distribution of the wettest 1% of events from NARR is characterized by peaks in June and August, with September following in third. The airport distribution of 2-in.-or-greater events also shows peaks during June and August (although with larger contributions), with May falling in third. The differences at this threshold most likely result from a mismatch of scales, and agreement between airport data and NARR may not occur at more extreme thresholds. An alternative explanation for the discrepancy between NARR simulations and airport observations during the heaviest events may be differences in the magnitudes of the wettest 1% of events. The magnitude of average daily accumulated precipitation in the wettest 1% events from the Dane County Regional Airport is 49.78 mm, whereas the same category of events in NARR is 34.19 mm.

Fig. 2.
Fig. 2.

Frequency distribution of average precipitation (bars) in NARR during 1981–2000 (grid point closest to Madison, WI). Lines express the percentage of events that occur during each month within a given threshold (including wet and dry days).

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

To better understand the effect of resolution differences on precipitation timing and magnitude in NARR, we generated four time series of daily precipitation between 1981 and 2000 (not shown), averaged over various clusters of NARR’s 32-km grid boxes (3 × 3, 5 × 5, 7 × 7, and 9 × 9), centered on Madison, WI (the area ranged from 96 × 96 km2 to 288 × 288 km2). Results showed that the frequency distributions of average monthly precipitation and the wettest 10%, 5%, and 1% of days showed a warm-season peak (JJA), and were not affected by the size of the averaging domain. The frequency distributions of the wettest 0.05% and 0.01% of days did show some variability; however, the number of events was so small for each category (N = 35 and N = 7 for the 0.05% and 0.01% categories, respectively) that a definitive statement cannot be made. Although each time series calculated was significantly correlated with the original time series for Madison, WI, above the 95% confidence interval, the magnitude of precipitation during the wettest 1% was reduced from 34.19 to 26.67 mm day−1 (−22%) as the spatial area increased. However, the focus of the current study is not on the magnitude of extreme events but the timing, which does not appear to be significantly impacted by increasing the averaging domain.

In addition to the extended spatial analysis using NARR, we included an analysis of precipitation throughout Wisconsin and the upper Midwest. We calculated a time series (not shown) of daily precipitation averaged over eight stations around the state of Wisconsin from 1950 to 2007 that are all part of the Historical Climatology Network (HCN) (Peterson and Vose 1997). These stations were specifically chosen because they cover a large spatial domain within Wisconsin and are generally first-order stations. The area-averaged monthly precipitation and frequency distributions from the generated time series strongly resemble results from the point observations recorded at the Dane County Regional Airport (Fig. 1). The annual cycle in monthly precipitation and frequency distribution of the wettest 10% and wettest 5% events exhibit a warm-season peak, while the frequency distribution for the wettest 1% of days also peaks during summer months with a slight drop in the number of July events. After examining precipitation around Wisconsin, we investigated the annual cycle of precipitation in four other cities in the upper Midwest using the National Oceanic and Atmospheric Administration’s (NOAA) Climate Prediction Center (CPC) United States Unified Precipitation data (available at http://www.esrl.noaa.gov/psd/; Higgins et al. 2000). The cities included Sioux City, Iowa; Springfield, Illinois; Des Moines, Iowa; and St. Paul, Minnesota. Each location exhibits a warm-season peak (predominantly JJA) in average monthly precipitation, while the wettest 10% and 5% distributions show a peak during March–May (MAM). The frequency distributions for the wettest 1% of events show a strong preference for May–August. This finding suggests that the JJA peak in the wettest 10% and 5% of events occurring in Madison may be a local response rather than regional. However, the agreement in the average monthly precipitation and wettest 1% of events among stations suggests that this is a typical feature of the Midwest climate.

The agreement among data sources (airport data, reanalysis, and HCN data) in capturing a midsummer peak (JJA) in average monthly precipitation and the timing of extreme precipitation events suggests that this feature is typical of the region’s climate. GCMs that accurately capture large-scale atmospheric features and accurately partition precipitation throughout the year should capture a summer peak in monthly precipitation.

Figure 3 shows the late twentieth-century (1981–2000) and late twenty-first-century (2081–2100) multimodel mean of average monthly precipitation for the grid box covering Madison, calculated using each GCM listed in Table 1. The twentieth-century multimodel average in precipitation maximizes in May, with June a close second and April third. These results do not agree with those from the Dane County Regional Airport (Fig. 1) and NARR (Fig. 2)—both of which exhibit a summertime peak. However, these results are consistent with previous findings from Ruiz-Barradas and Nigam (2006), which showed that some GCMs have difficulty simulating the summer maxima in precipitation in the central United States. During the late twenty-first century, the multimodel average peaks again in May, with April second and June third. The difference between the multimodel means indicates that average monthly precipitation in Madison increases in most months during the late twenty-first century. This finding is consistent with some of the previous research done on statewide averages of precipitation (Lorenz et al. 2009).

Fig. 3.
Fig. 3.

Simulated frequency distribution of average monthly precipitation for the CMIP3 multimodel mean during the late twentieth and late twenty-first centuries.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

The frequency distributions of twentieth- and twenty-first-century model-simulated extreme events—defined as the wettest 10%, 5%, and 1% of all days produced by each model—are displayed in Fig. 4. Distributions of the wettest 10% of events during both periods show a clear preference for late spring and early summer. As the intensity of the events increases, the distributions become dominated by spring and, secondarily, autumn occurrences. These results show that the timing of the heaviest precipitation events, as simulated by climate models for the late twentieth and twenty-first centuries, are not accurately captured either on an individual model basis or as a multimodel average. Similar frequency distributions of twentieth-century model-simulated extreme events were generated for the same upper-Midwest cities previously mentioned to check the robustness of Fig. 4. Results (not shown) indicate a bimodal distribution in the timing of the wettest 5% and 1% of events at each location, whereas the frequency distributions of the wettest 10% of events consistently show a peak during AMJ that is similar to the Madison grid cell (Fig. 4).

Fig. 4.
Fig. 4.

Frequency distribution of Madison’s wettest (a),(d) 10%, (b),(e) 5%, and (c),(f) 1% of all days for the (a)–(c) late twentieth and (d)–(f) late twenty-first centuries. Individual curves are shown for each CMIP3 model. The multimodel average is the thick black line.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

The twentieth- and twenty-first-century representations of the seasonal cycle of precipitation peak too early (spring), while the frequency distributions of extreme events show a bimodal distribution with a preference for spring and autumn. These findings led to an investigation of model-simulated atmospheric moisture content. Because the seasonal cycle of specific humidity is driven predominantly by temperature, large-scale models should be capable of capturing this feature. We perform an analysis of surface specific humidity to determine whether the models can accurately capture the seasonal cycle of moisture. If the seasonal cycle of simulated specific humidity peaks during the summer months as observed, the analysis suggests that model dynamics rather than (moist) thermodynamics are forcing the extreme events at the wrong time of year compared to observations. Alternatively, if the seasonal cycle of specific humidity exhibits a bimodal distribution that is similar to the distribution of extreme precipitation events, then models are probably utilizing the available moisture and thus moist thermodynamics are driving the simulated extreme events.

Figure 5 shows the late twentieth-century multimodel mean of average monthly 925-hPa specific humidity that exhibits a seasonal cycle that is remarkably similar to the seasonality of the 2-m specific humidity from NARR (not shown). The multimodel average exhibits a warm-season peak with values that are similar to those represented in NARR, although about 25% lower because 925 hPa is approximately 600–700 m above the surface during the summer. Average 925-hPa specific humidity from the twenty-first century also shows a distinct seasonal cycle with a noticeable increase in the magnitude during each month relative to the twentieth-century simulations (Fig. 5). The difference in the multimodel average of monthly specific humidity between the two time periods (twenty-first century − twentieth century) is also characterized by a seasonal cycle with a warm-season peak that can be explained by the Clausius–Clapeyron (CC) equation. Because of increased air temperatures and only slight changes in relative humidity that arise under future climate projections using the SRES A1B scenario, the greatest change in absolute specific humidity is expected to occur during the warmest season (Lorenz and DeWeaver 2007). However, the largest relative changes in 925-hPa specific humidity occur during January, December, and April. The accurate seasonality of simulated 925-hPa specific humidity and inaccurate seasonality of extreme precipitation events in Madison suggest that model dynamics, rather than thermodynamics, are forcing the extreme precipitation events during the wrong time of year.

Fig. 5.
Fig. 5.

Average monthly 925-hPa specific humidity (g kg−1) simulated during the late twentieth and late twenty-first centuries among the CMIP3 models.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

b. Precipitation composites

One of the major results so far is that the seasonal timing of late twentieth-century precipitation (both average and extreme) is not being accurately captured in model simulations, even though 925-hPa specific humidity is well simulated. In the current section, we employ a second method to evaluate model simulations of extreme precipitation events beyond the seasonal timing. We use spatial composites averaged over the wettest 1% of days in Madison in order to highlight the synoptic structure present in reanalysis data and compare this with results from model simulations.

Before looking at spatial composites of precipitation from a model perspective, we begin by identifying the important features found in the reanalysis output. A spatial composite of accumulated precipitation and sea level pressure (SLP) for Madison’s wettest 1% of days (Fig. 6a) produced by NARR (including warm and cold seasons) shows a localized bull’s eye of precipitation over Madison (34.19 mm day−1) and southern Wisconsin, which includes an area of precipitation that spreads over a large portion of the Midwest. The lobe of lighter precipitation (~10 mm day−1 and less) that extends from the central Iowa–Missouri border to the Oklahoma–Arkansas border resembles a precipitation pattern that may be associated with a frontal boundary. A weak low-pressure center (1009 hPa) is located to the southwest of the precipitation maximum with higher pressures off the east coast (potential westward extension of the Bermuda high). The SLP contours extending northeast from the low-pressure center combined with the precipitation structure extending eastward from the precipitation maximum also resemble a frontal boundary—probably a warm front or stationary front. The SLP contours over the eastern half of the United States imply southerly flow from the Gulf of Mexico region, which is typically characterized by high moisture content. The distinct synoptic pattern in Fig. 6a suggests that a combination of dynamic and thermodynamic processes is required for extreme precipitation events.

Fig. 6.
Fig. 6.

Spatial composite of SLP (hPa; contours) and average precipitation (mm day−1; shaded) during (a) the wettest 1% of days (N = 73 days), (b) cold-season months of the wettest 1% of days (N = 14), and (c) warm-season months of the wettest 1% of days (N = 59) in Madison, WI, in NARR from 1981 to 2000.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

Individual analyses of the cold-season (October–March) and warm-season (April–September) events highlight subtle differences in the atmospheric conditions occurring during Madison’s wettest 1% of events. On average, the cold-season events (Fig. 6b) have a slightly lower central minimum pressure (1007 hPa versus 1009 hPa for the warm-season events). In addition, the spatial distribution of precipitation includes a much larger domain: Madison and southern Wisconsin are still characterized by a large maximum in precipitation that also extends southward to the Gulf of Mexico, near the Texas–Louisiana border. The SLP structure present during the cold-season events shows dominant flow into the Madison area from the Gulf of Mexico, similar to Fig. 6a, although the Bermuda high is not present in the cold-season composites. Higher pressure located to the east and north of the low in the cold-season composite induces southerly flow into the region. The warm-season composite of precipitation and SLP (Fig. 6c) looks remarkably similar to the average composite because 80% of the wettest 1% events occur during the warm season.

Twentieth-century spatial composites of accumulated precipitation and SLP for Madison’s wettest 1% of days for each GCM are shown in Fig. 7. Twentieth-century simulations capture the precipitation maximum over Madison, with a large area of precipitation occurring in adjacent states and the general Midwest area. The sea level pressure composites look remarkably similar to the structure in NARR, with a weak low-pressure center positioned to the southwest of the precipitation maximum in nearly every model. However, mk3_0, ingv_echam4, and ccsm3_0 place the low-pressure center directly over the precipitation maximum while mk3_5 produces the weak low-pressure slightly to the southeast of the precipitation maximum. The implied surface flow over the eastern United States is characterized by a southerly component in each model, with the Gulf of Mexico being the source region (similar to NARR).

Fig. 7.
Fig. 7.

Late twentieth-century (1981–2000) spatial composites of daily precipitation (mm day−1) and SLP (hPa; contoured every 2 hPa) during the wettest 1% of days for models listed in Table 1.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

The spatial composites of twentieth-century accumulated precipitation and SLP were separated into cold- and warm-season events for each model (similar to NARR), which highlighted certain differences between the seasons. The cold-season composites of precipitation showed a larger spatial extent of precipitation that extended southward from the Midwest to the Gulf of Mexico. Conversely, the warm-season composites showed a smaller area of accumulated precipitation that remained centered over Madison. The warm-season composites of SLP showed a westward extension of the Bermuda high more consistently; however, all composites showed southerly flow into the Midwest region originating in the Gulf of Mexico. The multimodel average SLP pressure during the cold-season events is 1006.9 hPa, which is slightly lower than the warm-season average of 1007.8 hPa.

Accumulated precipitation and SLP composites for the wettest 1% of days in the late twenty-first century look very similar to those for the twentieth century and are therefore not shown. However, there do exist subtle differences between the two periods. The magnitude of precipitation occurring over Madison during the wettest 1% of precipitation events increases during the late twenty-first century in every model except bccr_bcm2_0, with an increase in the multimodel mean of ~15% (Table 2). A second difference between the two time periods is an increase in size of the spatial area receiving precipitation during the late twenty-first-century extreme events.

Table 2.

The average precipitation and vertically integrated MFC (mm day−1) calculated over Madison for wettest 1% of precipitation events from reanalysis and model simulations.

Table 2.

c. MFC composites

Vertically integrated MFC is an important variable related to precipitation extremes (Roads et al. 1994; Becker et al. 2009). Becker et al. (2009) suggest a link between strong MFC and precipitation extremes in NARR. In addition, Cook et al. (2008) found that increases in Midwest precipitation were coincident with increases in MFC in future climate change scenarios. Thus, previous findings give sufficient evidence to support an investigation of the relationship between precipitation and MFC more thoroughly in the analysis of Madison’s extreme events during the late twentieth and late twenty-first centuries.

The spatial composite of MFC for the wettest 1% of days in NARR is shown in Fig. 8. There is a region of strong moisture convergence occurring directly over the region of maximum extreme precipitation (Fig. 6), while weak divergence is occurring to the west, in the Great Plains region. During the wettest 1% of days in NARR, the magnitude of MFC (Fig. 8) is comparable to the average amount of precipitation that falls in all such events, regardless of whether they occur during the cold season or warm season (Fig. 6).

Fig. 8.
Fig. 8.

NARR composite of vertically integrated MFC (mm day−1) during Madison’s wettest 1% of days during 1981–2000.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

Model simulations of MFC on very wet days for the late twentieth century are shown in Fig. 9 (the output of 13 models included daily specific humidity). There is a great deal of variety among models, with clear differences in model resolution, yet there still exist common features. All models produce a maximum in MFC directly over or immediately surrounding Madison. These models produce a large zonally oriented region of convergence around the precipitation maximum, covering some of the neighboring states such as eastern Michigan, northeastern Illinois, and northwestern Indiana. The strong region of convergence over the Madison area is associated with weak divergence to the southwest of the convergence region in every model except inmcm3_0, which produces two areas of weak divergence to the north and to the west. The magnitude of maximum convergence greatly exceeds the magnitude of maximum divergence, albeit over a smaller spatial region. There are two models, mpi_echam5 and miroc_medres, that produce a large spatial area of weak divergence across almost the entire United States, similar to what is captured in NARR, while the remaining models capture areas of weak convergence occurring at various locations around the United States (Fig. 9).

Fig. 9.
Fig. 9.

Spatial composites of the mean vertically integrated MFC −[ · (Vq)] (shaded; mm day−1) and vertically integrated moisture flux (vectors; kgw m−1 s−1) for Madison’s wettest 1% of days in CMIP3 simulations of the twentieth century.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

The spatial structure of vertically integrated moisture flux [Vq] highlights the dominant direction of moisture transport and identifies the likely moisture source region for heavy precipitation in Madison (assuming local evaporation is small relative to the moisture transport). All models in Fig. 9 capture the anticyclonic flow pattern of the Bermuda high off the eastern coast of the United States. In all models except inmcm3_0, the flux of moisture into the Midwest originates in the Gulf of Mexico. The magnitude of the moisture flux into the region of positive MFC varies among models from 20 to over 120 kgw m−1 s−1. Interestingly, in inmcm3_0, the moisture source appears to be the central United States and the Pacific Ocean.

The spatial composites of MFC and vertically integrated moisture flux for Madison’s wettest 1% of days during the twenty-first century (not shown) resemble those for the twentieth century. The twenty-first-century simulations capture the large maximum in moisture flux convergence occurring over the Madison area, with a similar region of convergence that covers neighboring states in the same manner as the twentieth century. However, twenty-first-century results show a substantial increase in the magnitude of MFC occurring over Madison and the neighboring states (Table 2). In addition, twenty-first-century vertically integrated moisture flux vectors are larger in magnitude than twentieth-century counterparts.

Table 2 shows the magnitude of average precipitation and MFC calculated over the wettest 1% of days from reanalysis and model simulations for the Madison grid box, along with the difference between the simulated results. The magnitude of simulated precipitation occurring on the wettest 1% of days increases for all except one model (bccr_bcm2_0), while the magnitude of MFC increases for every model (a 53% increase in the multimodel mean). The correlation between the change in precipitation and the change in MFC (0.78) among all models is much greater than the correlation between the change in precipitation and the change in surface specific humidity (0.33), underscoring the dominant role of MFC in regulating Madison’s heavy precipitation (Fig. 10).

Fig. 10.
Fig. 10.

Scatterplot showing the relationship between the average change in precipitation and the average change in (top) MFC and (bottom) specific humidity, during Madison’s wettest 1% of precipitation events. Each dot represents a different model.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

As shown in Eq. (1), the MFC term can be decomposed into two components referred to as the convergence term −[q · V] and the advective term −[V · q]. We utilize the mathematical breakdown to quantify the dominant component during the twentieth and twenty-first centuries and also to address any changes in the magnitude of these terms under a future climate regime. The decomposition is performed on the same GCM data that was used in the MFC analysis. The contribution of each term to the total MFC during the late twentieth and twenty-first centuries is shown in Fig. 11. Both terms increase in magnitude during the late twenty-first centuries, as indicated by an increase in diameter in Fig. 11. The advective component shows the largest absolute and relative increase of 8.3 mm day−1 and 201%, respectively. The convergence term also shows an absolute and relative increase of 5.1 mm day−1 and 24%, respectively.

Fig. 11.
Fig. 11.

Breakdown of the multimodel average MFC term as simulated by each of the CMIP3 models during (left) the late twentieth and (right) late twenty-first centuries. Total MFC increases by 53% between the two periods.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

d. Moisture convergence composites

The breakdown of MFC for Madison indicated that although the projected change in the advective component during the late twenty-first century actually exceeds the projected change in the convergent component, the convergence term is the dominant component of the total MFC during simulations of both the late twentieth and late twenty-first centuries (Fig. 11). This result led to a further investigation of the convergence term {Eq. (1); −[q · V]}, which quantifies the product of specific humidity and the convergent component of the horizontal wind to identify any changes in the spatial features between the two periods. Here, we analyze spatial composites of moisture convergence during the wettest 1% of days for Madison simulated by the same models used in the MFC analysis.

Spatial composites of moisture convergence during Madison’s wettest 1% of days simulated by GCMs for the late twentieth century are shown in Fig. 12. The spatial composites of moisture convergence bear a strong resemblance to the spatial composites of MFC (Fig. 9) and, consequently, to the spatial composites of precipitation as well. Each model in Fig. 12 captures a strong region of moisture convergence occurring in the general vicinity of the Midwest and neighboring states. The spatial extent of moisture convergence for each model appears to be somewhat larger than the region of MFC shown in the corresponding model plot of Fig. 9, which implies that not all of the converging moisture is actually falling as precipitation. The corresponding model results for late twenty-first-century simulations strongly resemble the spatial structure of MFC for the same time period (not shown), except with larger magnitudes of convergence.

Fig. 12.
Fig. 12.

Spatial composites of the average vertically integrated moisture convergence term {−[q · V]; mm day−1} for Madison’s wettest 1% of days in CMIP3 simulations during the late twentieth century.

Citation: Journal of Hydrometeorology 13, 3; 10.1175/JHM-D-11-052.1

4. Discussion

The current investigation has improved our understanding of extreme precipitation events in climate simulations and highlighted potential areas of future research. Along the way, however, a few important features of this study have evolved and need to be addressed more thoroughly.

All but one model used in analyzing the MFC term show an increase in the magnitude of precipitation occurring during Madison’s wettest 1% of days during the twenty-first century. However, differences in the magnitude of precipitation and MFC exist among models. The five models with the highest resolution yielded 31% and 46% more precipitation on the heaviest events than the remaining eight lower-resolution models during the twentieth and twenty-first centuries, respectively. Similar numbers were found for the magnitude of MFC: during the twentieth (twenty first) century, higher-resolution models produced MFC values that were 40% (41%) higher than the remaining lower-resolution models. These simple calculations suggest that model resolution is important for capturing the magnitude of precipitation and MFC during the most extreme precipitation events.

Surface specific humidity was also shown to increase for every model used in the analysis of MFC between the twentieth and twenty-first centuries. The increase in multimodel average annual specific humidity between the two time periods is 1.31 g kg−1 (an increase of 25%), which is the same percentage change as the multimodel average increase in surface specific humidity during the most extreme events (5.45 g kg−1). This result suggests that changes in surface specific humidity during extreme events are reflected in changes in the mean specific humidity, even though the average specific humidity during Madison’s wettest 1% of days in the twentieth century is slightly more than four times larger than the climatological mean.

The spatial composite of precipitation for the wettest 1% of days in the reanalysis data captured some common synoptic features that appear during Madison’s extreme events, and are also captured in model simulations. The agreement between NARR and model simulations in the current analysis increases our confidence in the ability of GCMs to capture the average synoptic conditions that are a signature of extremely wet days in Madison. NARR captures a large swath of precipitation that is maximized for the Madison grid box and extends into neighboring states, suggesting that the extreme precipitation events are not strictly a local feature but rather part of a coherent synoptic-scale pattern. On extremely wet days in Madison, NARR produces a strong sea level pressure gradient that is found in the northeastern portion of the precipitation maximum and oriented in a southwest-to-northeast manner, which suggests the presence of a frontal boundary. This frontal boundary also appears in model simulations for both centuries, indicating a particular synoptic feature that is common to extreme precipitation events. Vavrus and Van Dorn (2010) identified a similar warm-front feature on Chicago’s extremely wet days in an analysis using gfdl_cm2_1 and PCM models.

The spatial composites of MFC on Madison’s wettest 1% of days in model simulations show that the source region of moisture is the Gulf of Mexico and Caribbean in nearly every model, implying that extreme precipitation events in Madison are directly affected by a remote source region. The analysis also shows that there exists a dynamical feature common to the extreme precipitation events captured by the models. The changes in the mean simulated circulation patterns in the twenty-first century relative to the twentieth century suggest an enhanced flux of moisture from the Gulf of Mexico during the springtime, which coincides with the largest increases in average monthly precipitation and extreme precipitation events (Fig. 3).

The breakdown of MFC [Eq. (1)] includes two components that represent very different physical processes occurring in the atmosphere. The advective component is important on a large scale and represents a transport of specific humidity by the wind in the presence of a horizontal gradient. An increase in the horizontal gradient of specific humidity with no change in the horizontal wind would lead to an increase in MFC. The convergent component, which is important on a local scale, describes the magnitude of horizontal mass convergence, including water vapor (specific humidity). The role of moisture advection is projected to increase in the future, which may be related to large-scale atmospheric circulation patterns and a moister atmosphere. Although the advective and convergent terms are projected to increase by the end of the twenty-first century, the contribution of the advective component in Eq. (1) to the total MFC is projected to double. Increases in the horizontal gradient of specific humidity throughout the atmosphere between the tropics and extratropics may be the leading cause of the increase in the advective term.

5. Conclusions

Increases in extreme precipitation events under future scenarios of global warming are a robust finding and have many important implications for our society and natural environment. The current study is focused on gaining a better understanding of the character of extreme precipitation events in observations, reanalysis data, and model simulations of the late twentieth and late twenty-first centuries at one location (Madison, WI). Our analysis of observations was used to evaluate how well the CMIP3 GCMs performed at capturing the seasonal cycle of extreme events. An examination of the vertically integrated moisture flux convergence term (MFC) and its components highlighted this physical mechanism as being largely responsible for producing extreme precipitation events.

Based on our findings, GCMs do not accurately capture the seasonal timing of mean and extreme precipitation events around Madison. The multimodel mean of monthly precipitation during the late twentieth and late twenty-first centuries peaks during the spring, which is earlier than the summertime maximum found in the observational record. Observed summertime precipitation is more likely to be convective (compared with winter precipitation, which is likely to be forced via large-scale disturbances), and hence heavily parameterized in model simulations. The timing of simulated extreme precipitation events exhibits a bimodal distribution that peaks during the spring and autumn and becomes more pronounced as the intensity increases. The bimodal peaks are apparent in simulations from both time periods and are consistent with seasonal shifts in the Northern Hemisphere jet stream over southern Wisconsin.

Conversely, models do accurately represent the seasonal cycle of surface specific humidity during the twentieth century. Surface specific humidity increases in every month during the late twenty-first century. The largest increases are projected to occur during the summer months, when the Clausius–Clapeyron equation dictates a larger change in moisture content for a given increase in temperature. Average monthly precipitation also increases in the multimodel mean during the twenty-first century for all months except July–September, which is consistent with previous findings that suggest little to slightly negative changes in summer precipitation around Wisconsin. However, models show the greatest disagreement among summer precipitation projections (Lorenz et al. 2009).

In general, the spatial composites of MFC simulated in models on Madison’s wettest 1% of days closely resemble the structure occurring in NARR, and they also look remarkably similar to the spatial composites of simulated precipitation. Another finding from the current study is that the convergence term in the MFC equation dominates over the advective component during both centuries, and the spatial composites of the convergence term mirror those of the MFC. However, the advective component becomes much more important in the future climate scenario, essentially doubling by the end of the twenty-first century. Results show that the change in extreme precipitation is more highly correlated with the change in MFC than the change near surface specific humidity—a relationship that has been supported by others as well (Roads et al. 1994; Ruiz-Barradas and Nigam 2006; Becker et al. 2009).

Analysis of the vertically integrated moisture flux vectors during extreme precipitation events reveals the moisture source region is likely the Gulf of Mexico and the Caribbean in the late twentieth and twenty-first centuries. This finding has significant implications for future climate change studies because it highlights the importance of a remote region to the climate impacts at a local scale. Projected multimodel average changes in precipitation minus evaporation (P − E) over the greater Caribbean region from the CMIP3 models suggest a large increase in net evaporation and 925-hPa specific humidity in this region that may be important for Madison’s twenty-first-century climate.

Previous studies have suggested that extreme precipitation events should increase proportionally with atmospheric water vapor (Allen and Ingram 2002; Pall et al. 2007). Here, changes in extreme precipitation events are compared with changes in the average global surface temperature and changes in the average surface temperature in Madison between the two centuries. The magnitude of the most extreme precipitation events (wettest 1%) increased by 15%. According to the Clausius–Clapeyron (CC) equation, the rise in surface temperature between the late twentieth and late twenty-first centuries of 3.24 K (global) and 4.19 K (Madison) would suggest an increase in extreme precipitation of 23% (28%). Hence, the magnitude of extreme precipitation events is not increasing at the rate suggested by the CC equation, but rather by a smaller amount consistent with O’Gorman and Schneider (2009). However, the change in absolute specific humidity on an annual basis and during the most extreme precipitation events (25%) is increasing at a rate compatible with the CC equation.

A great deal of questions related to projections of extreme precipitation events and MFC remain unanswered. For example, what other types of synoptic patterns and MFC structures are common among extreme precipitation events? Also, if a similar analysis of MFC is performed using other reanalysis datasets, will the same structure arise? Alternative analyses such as empirical orthogonal functions (EOFs) and self-organizing maps (SOMs) (Cavazos 2000) could be used to investigate the variety of synoptic patterns that occur during extremely wet days that are not captured by the compositing method presented here. This type of categorizing could be useful for relating projected changes in circulation patterns to changes in the frequency and intensity of extreme precipitation events.

A useful data source for future work is the recently released high-resolution model output from the North American Regional Climate Change Assessment Program (NARCCAP) (Mearns et al. 2009). These dynamically downscaled model results would be a great complementary source of data for investigating some of these ideas, including the structure and seasonal variability of MFC. Finally, the statistically downscaled precipitation data provided by the Wisconsin Initiative on Climate Change Impacts (WICCI) (Notaro et al. 2011) could be compared with raw GCM output, as well as with NARCCAP data.

Acknowledgments

This research was supported in part by the Environmental Protection Agency Star Grant (RD-83275001) and the Wisconsin Focus on Energy Grant (3104-01-08). CPC U.S. Unified Precipitation data was provided by the NOAA/OAR/ESRL PSD in Boulder, Colorado, from their website at http://www.esrl.noaa.gov/psd/. The authors would like to acknowledge the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modeling (WGCM) for their roles in making available the WCRP CMIP3 multimodel dataset. Support of this dataset is provided by the Office of Science, U.S. Department of Energy. The authors would also like to acknowledge Daniel Vimont for his contribution to this research and the reviewers for their valuable comments.

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