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  • View in gallery

    Observed and NARR precipitation seasonal mean (left) amount, (middle) intensity, and (right) frequency for (top two) winter (DJF) and (bottom two) summer (JJA) over the contiguous United States. The threshold defining a day with precipitation is 1.0 mm day−1. The period of record is 1979–2005.

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    Area-averaged daily precipitation values from NARR (vertical axes) and gridded observations (horizontal axes) for northern California, Pacific Northwest, Southwest, Gulf of Mexico–South, Great Plains, and Mid-Atlantic for the 1979–2005 period of examination. The area averages were performed over 5° latitude × 5° longitude land-only boxes (see Fig. 4). The gray line indicates the line fit between NARR and observations.

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    The (left) 95th percentile for daily precipitation events, (middle) gamma distribution scale parameter, and (right) gamma distribution shape parameter for (top two) winter and (bottom two) summer over the contiguous United States. The scale parameter shows the contribution of extreme events to the seasonal total and the shape parameter indicates the contribution of lighter-to-moderate events. Areas where the chi-squared statistic indicated the gamma distribution did not adequately fit the PDF are masked from this figure.

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    Rank correlations between MFC and precipitation and between precipitable water and precipitation. (top) The results for winter for (left) MFC precipitation and (right) precipitable water precipitation over the United States. (bottom two) The area-averaged results for the six 5° latitude × 5° longitude boxes indicated: northern California, Pacific Northwest, Southwest, Gulf of Mexico–South, Great Plains, and Mid-Atlantic over each of the four seasons. The black bars show the precipitation rank correlation with precipitable water and the gray bars show MFC. All data are from NARR.

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    NARR precipitable water intensity and the gamma distribution scale and shape parameters for (top) winter and (bottom) summer over the United States for 1979–2005. The fit of the gamma distribution to the precipitable water PDF was evaluated using the chi-squared statistic, and areas where the fit was inadequate are masked.

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    As in Fig. 5, but for vertically integrated moisture flux convergence.

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    NARR winter (DJF) mean 200-hPa zonal wind for (left) El Niño and (right) La Niña that were examined for this study. The extended Pacific jet stream is characteristic of an El Niño winter while the right panel shows the weaker jet stream of La Niña.

  • View in gallery

    Winter El Niño (red) and La Niña (blue) precipitation histograms for four grid points in the Pacific Northwest, Ohio River Valley, Southern California, and Gulf of Mexico Coast regions. See Table 1 for mean precipitation amount and gamma distribution parameters corresponding to these histograms. Precipitation data are from NARR.

  • View in gallery

    (a) Winter difference and (b) summer difference between El Niño and La Niña precipitation intensity, frequency, scale, and shape parameters. Red shows areas where the quantity is greater during El Niño, and blue where it is greater during La Niña, expressed as the shift relative to the average of all El Niño and La Niña months. Areas where shifts are significant above the 95% confidence interval are indicated with hatching. Precipitation data are from NARR.

  • View in gallery

    Shifts between El Niño and La Niña (left) precipitable water intensity and (right) scale parameter for (top) winter and (bottom) summer. Red areas show where the quantity is greater during El Niño, and blue where it is greater during La Niña, expressed as the shift relative to the average of all El Niño and La Niña months. Areas where shifts are significant above the 95% confidence interval are indicated with hatching.

  • View in gallery

    As in Fig. 10, but for vertically integrated moisture flux convergence.

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Understanding the Characteristics of Daily Precipitation over the United States Using the North American Regional Reanalysis

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  • 1 Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland
  • | 2 Climate Prediction Center, NOAA/NWS/NCEP, Camp Springs, Maryland
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Abstract

This study examines the seasonal characteristics of daily precipitation over the United States using the North American Regional Reanalysis (NARR). To help understand the physical mechanisms that contribute to changes in the characteristics of daily precipitation, vertically integrated moisture flux convergence (MFC) and precipitable water were included in the study. First, an analysis of the NARR precipitation was carried out because while observed precipitation is indirectly assimilated in the system, differences exist. The NARR mean seasonal amount is very close to that of observations throughout the year, although NARR exhibits a slight systematic bias toward more-frequent, lighter precipitation. Particularly during summer, the precipitation intensity and the probability distribution function (PDF) indicate that NARR somewhat underestimates extremes and overestimates lighter events in the eastern half of the United States. The intensity and PDF of moisture flux convergence exhibit a strong similarity to those of precipitation, suggesting a link between strong MFC and precipitation extremes. On the other hand, the relationship between the precipitable water and precipitation PDFs is weaker, based on the lack of agreement of their gamma distribution parameters.

The dependence of the precipitation PDF on the lower-frequency modulation of ENSO was examined. During El Niño winters, the Southwest and central United States, Gulf of Mexico region, and southeastern coast have greater precipitation intensity and extremes than during La Niña, and the Ohio River and Red River basins have lower intensity and fewer extreme events. During summer, the northern Rocky Mountains receive higher intensity precipitation with more extreme events. Most areas where the change in the daily mean precipitation between ENSO phases is large have greater shifts in the extreme tail of the PDF. The ENSO-related response of moisture flux convergence is similar to that of precipitation. ENSO-related shifts in the precipitation PDF do not appear to have a strong relationship to the shifts in precipitable water.

Corresponding author address: E. H. Berbery, Department of Atmospheric and Oceanic Science/ESSIC, University of Maryland, College Park, 3427 Computer and Space Sciences Bldg., College Park, MD 20742-2425. Email: berbery@atmos.umd.edu

Abstract

This study examines the seasonal characteristics of daily precipitation over the United States using the North American Regional Reanalysis (NARR). To help understand the physical mechanisms that contribute to changes in the characteristics of daily precipitation, vertically integrated moisture flux convergence (MFC) and precipitable water were included in the study. First, an analysis of the NARR precipitation was carried out because while observed precipitation is indirectly assimilated in the system, differences exist. The NARR mean seasonal amount is very close to that of observations throughout the year, although NARR exhibits a slight systematic bias toward more-frequent, lighter precipitation. Particularly during summer, the precipitation intensity and the probability distribution function (PDF) indicate that NARR somewhat underestimates extremes and overestimates lighter events in the eastern half of the United States. The intensity and PDF of moisture flux convergence exhibit a strong similarity to those of precipitation, suggesting a link between strong MFC and precipitation extremes. On the other hand, the relationship between the precipitable water and precipitation PDFs is weaker, based on the lack of agreement of their gamma distribution parameters.

The dependence of the precipitation PDF on the lower-frequency modulation of ENSO was examined. During El Niño winters, the Southwest and central United States, Gulf of Mexico region, and southeastern coast have greater precipitation intensity and extremes than during La Niña, and the Ohio River and Red River basins have lower intensity and fewer extreme events. During summer, the northern Rocky Mountains receive higher intensity precipitation with more extreme events. Most areas where the change in the daily mean precipitation between ENSO phases is large have greater shifts in the extreme tail of the PDF. The ENSO-related response of moisture flux convergence is similar to that of precipitation. ENSO-related shifts in the precipitation PDF do not appear to have a strong relationship to the shifts in precipitable water.

Corresponding author address: E. H. Berbery, Department of Atmospheric and Oceanic Science/ESSIC, University of Maryland, College Park, 3427 Computer and Space Sciences Bldg., College Park, MD 20742-2425. Email: berbery@atmos.umd.edu

1. Introduction

Over the past two decades, several studies have discussed the sensitivity of the frequency distribution of daily precipitation to climate variability (e.g., Groisman et al. 1999; Trenberth et al. 2003; and references therein). Changes in the characteristics of precipitation, including the number and intensity of very heavy and extreme precipitation events, can occur independently from changes in the seasonal mean (Gershunov 1998). For example, a season with a total rainfall amount near the climatological mean could have a greater-than-average incidence of very heavy and extreme precipitation events and a reduced number of light and moderate rainfall events. More importantly, more extreme events, even within a season of average total precipitation amount, can lead to high streamflow and flooding (Groisman et al. 2001). Consequently, the variability of daily precipitation statistics, such as the frequency distribution and intensity of rainfall within a season, can be more informative than seasonal mean variability for many applications.

Many studies have focused on changes in extreme precipitation events, and have found sensitivity in the extreme tails of the probability distribution functions (PDFs) to climate modes such as ENSO (Gershunov and Barnett 1998; Cayan et al. 1999; Higgins et al. 2000a). Recent research has found that ENSO, which has significant effects on seasonal average precipitation and surface temperature in various regions of North America (e.g., Ropelewski and Halpert 1986, 1996; Kiladis and Diaz 1989; Mo and Higgins 1998), also affects the character of daily precipitation. According to Schubert et al. (2005), La Niña years tend to produce considerably fewer extreme storms than El Niño years along the Gulf and East Coasts. Higgins et al. (2007) found that during winter the Southwest averages up to 15% more days with measurable (>1 mm) precipitation per season during El Niño phases, compared to La Niña. On the other hand, the Pacific Northwest and Ohio Valley average up to 15% fewer wet days per winter season for El Niño than for La Niña. During summer, the northern United States averages up to 15% more wet days per season during El Niño, compared to La Niña (Higgins et al. 2007).

A better understanding of the characteristics of daily precipitation is relevant for studies of climate change, long-term trends, and predictability of the intraseasonal-to-interannual variability. Some previous modeling studies have suggested that climate change due to increased atmospheric CO2 may take the form of an El Niño–like response (Meehl and Washington 1996; Meehl et al. 2006). If this is the case, the proportion of heavy-to-extreme rainfall days to light-to-moderate days should be expected to change (Katz and Brown 1992; Wilby and Wigley 2002; Watterson and Dix 2003). In a study of global precipitation trends, Groisman et al. (2005) found that statistically significant changes in mean total rainy-season precipitation are accompanied by stronger changes in the heavy precipitation. In the United States, several studies have found a century-long precipitation increase, with a nationwide increase in mean total precipitation of 7%–15% (100 yr)−1 (Groisman et al. 2001, 2004), and a significantly greater increase in heavy and very heavy precipitation (Groisman et al. 2004; Higgins et al. 2007). In addition, the increases in heavy precipitation are well correlated to increased streamflow in the eastern two-thirds of the United States (Groisman et al. 2004). Predictability of the statistics of daily precipitation on both the shorter (2 weeks to several months) and longer time scales could be enhanced by a greater understanding of the response of daily precipitation to major climate modes (e.g., Gershunov and Cayan 2003; Higgins et al. 2007).

The primary objective of this study is to improve understanding of the characteristics and variability of daily precipitation over the United States. Two precipitation-related fields, moisture flux convergence and precipitable water, are employed to examine the atmospheric conditions related to daily precipitation. In this sense, the current study should help elucidate the physical mechanisms that contribute to changes in the characteristics of daily precipitation and so contribute to advances in climate prediction and projections.

The methods used in this study are discussed in section 2. Section 3 contains an assessment of the North American Regional Reanalysis (NARR) precipitation using gridded observed precipitation, and an examination of the seasonal mean patterns of daily precipitation and its PDF. Selected factors that govern the daily precipitation distribution are discussed in section 4. Section 5 investigates the ENSO modulation of the precipitation PDF and related factors. Conclusions and a brief summary are given in section 6.

2. Method

a. Frequency distribution of precipitation

The bulk of daily precipitation events are light events, with fewer heavy and extreme events, and so the PDF of daily precipitation is usually positively skewed. This pattern has been previously described using the gamma distribution, which is bounded on the left by zero and positively skewed (Wilks 1995). However, many other statistical distributions have been used to empirically approximate precipitation (e.g., Katz et al. 2002; Koutsoyiannis 2004; Wilson and Toumi 2005). Several earlier examinations of the precipitation PDF have found that there is no single distribution that fits for all geographical regions (Ananthakrishnan and Soman 1989; Panorska et al. 2007). Studies have provided evidence that, for many geographical regions, precipitation is “heavy tailed,” especially in areas with a wide variety of precipitation-producing systems (Katz et al. 2002; Panorska et al. 2007). This means the probability of precipitation events in the heavy-to-extreme end of the PDF decreases at a slower rate than that expressed by exponentially decreasing distributions. In several regions the gamma distribution, which is exponentially tailed, could substantially underestimate the return periods of extreme events (Panorska et al. 2007). For the purposes of predicting the probability of extreme events, the appropriate PDF should be chosen for each local area (Kozubowski et al. 2009).

For the current study, the focus is on the relative contributions of heavy-to-extreme daily events and light-to-moderate events to the seasonal total. Thus, the gamma distribution, with the sensitivity of its shape and scale parameters to shifts in the underlying histogram, is a helpful tool. The gamma distribution is a two-parameter frequency distribution given by
i1520-0442-22-23-6268-e21
where α is the shape parameter, β is the scale parameter, and Γ(α) is the gamma function, defined by the definite integral:
i1520-0442-22-23-6268-e22
The gamma function can be solved or estimated from tables; see Wilks (1995) for discussion.

The gamma distribution can be characterized by the two parameters, shape (α) and scale (β), which succinctly describe a wide variety of distributions (Wilks 1990). The shape parameter, α, describes the skewness of the gamma distribution. Low values of α (<1) give a distribution with the maximum of variable x occurring at x = 0. The “exponential distribution” is described by α = 1, and high values of the shape parameter (α > ∼20) mean a distribution approaching the Gaussian or normal distribution (Thom 1958). The parameter β scales the distribution by stretching or shrinking it along the x axis. Husak et al. (2007), looking at monthly rainfall in Africa, defined regions as “shape dominated” (large α, small β) or “scale dominated” (small α, large β). Shape-dominated regimes tend to define areas that typically received consistent rainfall accumulation in the historical record, and scale-dominated areas have large variance in comparison to the mean (Husak et al. 2007).

The shape and scale parameters need a statistical estimation. For this study, the maximum likelihood estimators (MLE) method of Thom (1958) was used. Thom’s MLE method defines the following:
i1520-0442-22-23-6268-e23a
i1520-0442-22-23-6268-e23b
i1520-0442-22-23-6268-e23c
where np is the number of nonzero values, x indicates the time mean, and α̂ and β̂ are the estimated parameters. Thom’s estimators have a slight bias, even for a large sample size, but this bias is generally of little importance for α > 0.1 (Shenton and Bowman 1970).
The shape and scale parameters cannot be computed for days with zero precipitation [see Eq. (2.3a)], thus they were estimated for the intensity of daily precipitation, (e.g., Watterson and Dix 2003; Husak et al. 2007). For this study, a threshold of 1.0 mm day−1 was used to define a day with precipitation. The definition of a third parameter, the precipitation frequency, complements the use of the gamma distribution. This parameter is defined as
i1520-0442-22-23-6268-e24
where n is the number of days with precipitation greater than 1.0 mm day−1 and N is the total number of days in the record. This parameter allows for the interpretation of the gamma distribution in the context of seasonal total precipitation.

As follows from Eq. (2.3c), the product of the shape and scale parameters is equal to the mean of the nonzero observations. Hence, if the mean remains constant and α decreases, β must increase, and vice versa. Daily precipitation distributions have a smaller shape parameter (i.e., are more strongly skewed) than the distribution of monthly values. However, the basic conceptual relationship between α and β remains the same. Husak et al. (2007) used this concept to locate areas of Africa where occasional drought may have an impact on agriculture, and possibly match crops and infrastructure to the precipitation regime. While agriculture and infrastructure in the United States are almost fully developed, the gamma parameters can identify areas sensitive to heavy and extreme precipitation. This technique can be applied to other variables related to the overall hydrologic cycle, including precipitable water and moisture flux convergence, to better relate the statistics of precipitation to the statistics of the hydrologic cycle terms.

3. Daily precipitation characteristics from NARR and gridded observations

In this section, the NARR daily precipitation is assessed by comparison to gridded observation data, and then the ability of the gamma distribution to represent the PDF of precipitation is examined. Regions where extreme precipitation dominates the mean seasonal total are identified, and some of the statistics of daily precipitation from NARR are compared to the observations.

a. Data

A gridded daily precipitation analysis obtained from the Climate Prediction Center [(CPC) at the National Oceanic and Atmospheric Administration/National Weather Service/National Centers for Environmental Prediction (NOAA/NWS/NCEP)] is employed to examine the mean amount, intensity, frequency, and PDF of daily precipitation. The gridded daily analysis (Higgins et al. 2000b) was produced using the CPC’s unified rain gauge database, which contains precipitation information from over 8000 stations across the United States. The station data was used to make a daily analysis, from 1200 to 1200 UTC, then gridded to a 0.25° × 0.25° latitude–longitude grid using a Cressman (1959) interpolation scheme, and several types of quality control were then applied (see Higgins et al. 2000b). Data for this study were obtained directly from the CPC.

In section 3b, the gridded observations are used to evaluate NARR, a long-term, dynamically consistent, high-resolution, high-frequency, atmospheric and land surface hydrology dataset for the North American domain (Mesinger et al. 2006). The regional reanalysis was developed with the 2003 version of the Eta model and its associated Eta Data Assimilation System (EDAS). The Eta model is coupled to the Noah land surface model (Ek et al. 2003) that simulates land surface temperature, the components of the surface energy balance and the surface water balance, and the evolution of soil temperature and soil moisture, both liquid and frozen. The NARR computational grid has a 32-km horizontal resolution, with 45 layers in the vertical (Mesinger et al. 2006).

The model does not assimilate precipitation directly but instead derives latent heating profiles from precipitation analyses and from this forcing produces the NARR precipitation (Lin et al. 1999). Over the continental United States, the daily analysis is disaggregated to hourly using temporal weights derived from a 2.5° × 2.5° analysis of hourly rain gauge data (see Shafran et al. 2004; Mesinger et al. 2006). A recent independent examination of NARR precipitation, including extremes, found it to be superior to global reanalysis over the contiguous United States (Bukowsky and Karoly 2007).

NARR was created at NCEP. [Data for this study was obtained from the NOAA/Office of Oceanic and Atmospheric Research/Earth System Research Laboratory (NOAA/OAR/ESRL) Physical Sciences Division (PSD), in Boulder, Colorado, from their Web site at http://www.cdc.noaa.gov.] As the CPC’s gridded daily precipitation analysis (hereafter “observations” in this paper) is created from 1200 to 1200 UTC, for the comparison section of this study NARR 3-hourly precipitation data was obtained and compiled into a matching 1200–1200 UTC daily dataset. For the remainder of the study, the daily NARR analysis, which is defined from 0000 to 0000 UTC, was obtained from the PSD.

b. Mean seasonal amount, intensity, and frequency

The mean seasonal precipitation amount, intensity (average for days with precipitation), and the frequency of days with >1.0 mm day−1 are shown in Fig. 1, for the NARR and the gridded observations. For brevity, winter [December–January–February (DJF)] and summer [June–July–August (JJA)], are shown. The winter mean precipitation amount (Fig. 1, first column) shows strong similarity between the observations (first row) and NARR (second row). The highest mean precipitation areas, along the West Coast and portions of the South, are similarly represented in both observations and the NARR. Examination of the intensity (second column) and frequency (third column) reveal a slightly lower intensity in the South in NARR than in the observations. The correspondence between observations and NARR in intensity and frequency along the West Coast and the Rocky Mountain range is good, as well as in the higher-intensity, lower-frequency Southwest.

In summer (Fig. 1, bottom half), for the most part the observations and NARR have good agreement in the mean daily amount (first column), with NARR showing a slightly higher mean throughout portions of the Midwest. More important differences between the two analyses are seen in the intensity and frequency fields. The center of the country has high precipitation intensity in the warmer months, likely due to the transport of moisture from the Gulf of Mexico by the Great Plains low-level jet (GPLLJ; Bonner 1968; Higgins et al. 1997). This area has a lower intensity in the NARR than the observations, as does much of the eastern half of the United States. This finding, and the higher frequency in NARR (third column), suggests that NARR has a higher occurrence of lighter rain days than the observations over this portion of the country during summer. The area of higher frequency through Arizona and New Mexico is very similar in both observations and the NARR, and is likely representative of the North American monsoon, which usually begins in July. The monsoon is characterized by a reversal in the surface winds along the Gulf of California (Badan-Dangon et al. 1991), and contributes increased precipitation in the form of consistent light and moderate rains to the Southwest United States (Douglas et al. 1993). The core monsoon is located in northwestern Mexico, but only its fringes affect the Southwest. Therefore, the U.S. part of the monsoon does not appear as a strong feature in the mean amount or intensity.

A direct comparison of the daily precipitation in observations and the NARR is presented in Fig. 2 for selected relevant regions of size 5° longitude × 5° latitude. For each of the six regions represented by figure, the land-only area average was calculated for each day in the 1979–2005 record for both the observations and NARR. Then, the observation value and the NARR value were plotted with the observation on the x axis and the NARR on the y axis. Hence, each panel has 9862 points, one for each day over the period 1979–2005. The gray line depicts the line fit between the observations and NARR. In all panels, the majority of points are clustered along the y = x line, meaning most daily values of NARR are close to the observations. The two western regions, northern California and the Pacific Northwest (top row), show the highest agreement between NARR and the observations. In the Southwest, Gulf Coast/south, Great Plains, and Mid-Atlantic regions, the precipitation from the gridded observations is generally slightly higher than from the NARR, especially along the Gulf Coast and Mid-Atlantic regions. A similar examination for each individual season found that the patterns shown in Fig. 2 are consistent throughout the year.

c. Precipitation gamma distribution

As stated in section 2, several theoretical distributions can be used to describe the precipitation PDF. Here, the fit of the gamma distribution to the PDF will be assessed. When the gamma distribution is applied to the precipitation PDF, the distribution can be described by the shape (α) and scale (β) parameters (see section 2). In general, shape-dominated areas (large shape, small scale) will have a higher contribution to the total seasonal amount from more-consistent rain with fewer extreme events, while scale-dominated areas (small shape, large scale) will receive more precipitation from extreme events. The fit of the gamma distribution to the underlying probability histogram has been tested using the chi-squared test (Wilks 1995). Locations where the fit is not good (below the 0.05 level) have been masked from the figures.

The scale parameter shows a strong relationship to the threshold for extreme rainfall events in both observations and NARR (Fig. 3, first and second columns). In other words, if an extreme daily event is defined as being above the 95th percentile of all daily values, areas where that threshold is high (e.g., larger than 45 mm day−1 in the Gulf Coast in winter) have high scale parameters. Likewise, the scale parameter is lower where the threshold is lower. This suggests that the scale parameter is a sensitive indicator of extreme events, and shifts in the scale parameter indicate shifts in the extremes. The relationship of the scale parameter to the shape (Fig. 3, second and third columns) reveals the relative contribution to the seasonal total from extremes and from light-to-moderate events.

Overall, winter precipitation patterns (Fig. 3, first and second row) are very similar to the scale parameter patterns (i.e., where the precipitation intensity is high; see Fig. 1, second column), there are more extreme events. For example, the average wet-day amount of precipitation in California and along the West Coast, which is high relative to most of the rest of the country, is dominated by heavy events (e.g., Cayan et al. 1999), and the pattern of the scale parameter reflects this. The Atlantic and Gulf of Mexico coasts are also scale-dominated regions where heavy precipitation from winter storms contributes to the higher mean. Another area of note is the Great Lakes region and western New York state. This area receives most or all winter precipitation as snow, and is shape dominated. In winter, the gamma parameters from both NARR and the observations are very similar, with NARR exhibiting a slightly lower-scale parameter along the Gulf Coast, similar to the intensity.

In summer (Fig. 3, third and fourth rows), the effect of the GPLLJ in transporting moisture away from the Gulf Coast into the central plains can be seen in the inland peak in intensity. In this region, variable rains and more extreme events provide the dominant contribution to the mean in summer (large scale, small shape). The southern Appalachian Mountains have a greater contribution to the mean from more-frequent lighter events, as indicated by the slightly larger shape parameter. While larger discrepancies between NARR and observation gamma parameters appear in summer—when the scale parameter in the observation data is higher than in NARR over the center of the country and the Gulf and Atlantic Coasts—NARR is still able to represent the relationship between the gamma parameters in these areas. For example, the center of the country is scale dominated, meaning a higher contribution to the mean from extreme events, in both NARR and the observed precipitation, and the relatively higher contribution of lighter events (higher shape) along the Appalachian range. The Florida peninsula, which is affected by highly volatile summer precipitation (e.g., Panorska et al. 2007), presents the largest difference between NARR and the observations: the shape parameter is disproportionately larger in NARR than in observations, and the scale parameter is smaller, indicating that NARR may be missing some extreme events, and overrepresenting the number of lighter precipitation events.

4. Precipitation-related factors

Precipitation is one key component of the hydrologic cycle, and it is influenced by the content of water in the atmospheric column (precipitable water) and the vertically integrated moisture flux convergence (Rasmusson 1968; Berbery et al. 1996). To better understand precipitation, the vertically integrated moisture flux convergence (MFC) and precipitable water from NARR have been examined for the same period as precipitation. Precipitation is governed by complex dynamic and thermodynamic properties, and several other precipitation-related factors could be considered, including convective available potential energy (CAPE), convective inhibition, soil moisture, or others. While outside of the scope of this manuscript, it is likely that these factors would reveal more about the characteristics of precipitation.

The rank correlations between precipitable water and precipitation, and between MFC and precipitation, were examined first (Fig. 4). The rank correlation is the correlation coefficient between two sets of data, computed using the rank of each value within its set. Each panel includes the area average of the rank correlations for the six locations shown in Fig. 4 (top). To understand the correlation between larger rain events and these two factors, the correlation was calculated using days with precipitation >10 mm, using NARR data. With the exception of northern California during winter, MFC has a stronger correlation with precipitation. As illustrated in the winter correlation maps for precipitable water and MFC (Fig. 4, top), the MFC–precipitation correlation in the West Coast region is highest in the areas with highest precipitation (see Fig. 1), and has a finer structure than the precipitable water. This relationship in these areas is obscured by the area averaging in Fig. 4.

For further comparison, a gamma distribution was fitted to MFC and precipitable water. The mean seasonal intensity and the gamma distribution scale and shape parameters of precipitable water are presented in Fig. 5. The fit of the gamma distribution has been tested using the chi-squared test, and areas where the fit was determined to be inadequate were masked out of the figure. During winter (Fig. 5, first row), the western half of the country has low precipitable water intensity. The eastern half features a roughly zonal pattern, with the maximum of around 30 mm day−1 occurring in southern Florida and Texas, and decreasing steadily northward. The gamma distribution is a poor fit to the precipitable water data over a portion of the western interior. Only in the northeast are daily values of precipitable water relatively variable, as illustrated by the higher-scale parameter in this area. Toward the north, the bulk of daily values are in the lighter range, and the PDF is positively skewed (smaller shape parameter), but the southern portions of the country have a large shape parameter, meaning the PDF is less skewed. Over Florida and farthest south Texas, the shape parameter is 20 or greater, indicating very little skew in the PDF. Although higher precipitable water is present in areas of higher precipitation (West Coast and Southeast), the spatial patterns do not have a strong resemblance. The areas with more variable and extreme precipitation (i.e., the scale-dominated precipitation areas; see Fig. 3), do not have a correspondingly high precipitable water–scale parameter. These differences imply that there is not a clear similarity between the precipitation PDF and the precipitable water PDF.

The overall winter patterns of vertically integrated MFC intensity and scale parameter (Fig. 6, first row) closely resemble those of precipitation (Figs. 1 and 3). Over the areas that receive the heaviest precipitation intensity—in California and along the West Coast and the central Gulf Coast—MFC is strongest (maximum ∼20 mm day−1), and the gradient between the strongest MFC (Southeast) and the weakest (northern plains) is similar to the precipitation gradient. As well, the southernmost areas of the country, south Florida and south Texas, have both lower mean precipitation and weaker MFC relative to the central Gulf Coast. Similar to precipitation, the gamma distribution is a better fit to MFC data in areas with higher intensity, including the West Coast and the east, and is not a good fit over areas of the northern United States. Areas of strong mean MFC are characterized by variable convergence with more daily values in the strong and extreme range, as illustrated by the similarity between the mean and the scale parameter. The map of MFC scale parameter is very similar to the precipitation scale parameter (Fig. 3), indicating a resemblance between the heavy-to-extreme tails of the MFC and precipitation PDFs. Similarities between the scale parameters of MFC and precipitation are stronger than between their shape parameters. This suggests the MFC and precipitation PDFs have more similarity along the heavy-to-extreme tails than on the lighter side of the spectrum.

In summer, the precipitable water intensity (Fig. 5, row 2) is much higher than in winter, especially in the eastern half of the country. The effect of the North American monsoon can be seen in the southern portions of Arizona; however, this area of high precipitable water extends farther west, into southern California, than does the enhanced precipitation signal of the NAMS (e.g., Douglas et al. 1993). The precipitable water PDF is not very skewed over most of the country during the summer, indicated by a high shape parameter, and hence is not well-described by a gamma distribution. This also indicates the mean precipitable water intensity is not dependent on high daily values. There is not a strong similarity between the precipitation PDF and that of precipitable water during the summer. This result is in agreement with the rank correlation (Fig. 4), which showed a weak relationship between precipitable water and precipitation in summer.

During summer the MFC intensity maxima occur in the northern Midwest and along the northeast Atlantic coast (Fig. 6, row 2). This pattern likely in part reflects the moisture transport from the Gulf of Mexico into the central United States by the GPLLJ (Higgins et al. 1997; Mo et al. 2005). The other area of relatively strong MFC is in southern Arizona, likely due to the North American monsoon (Berbery and Fox-Rabinovitz 2003; Becker and Berbery 2008). Like winter, the scale parameter of summer MFC corresponds well with the scale parameter of precipitation (Fig. 3). This finding and the higher rank correlation between MFC and precipitation (see Fig. 4) indicate a strong relationship between the extreme ends of the PDFs of precipitation and MFC.

5. ENSO modulations

To examine the changes in the seasonal distribution of daily precipitation due to low-frequency variability associated with ENSO, the oceanic Niño index (ONI), compiled by NOAA’s CPC, is employed. The index is computed from 3-month running values of SST departures from averages in the Niño-3.4 region. For the purposes of this study, El Niño is characterized by a positive ONI greater than or equal to +0.9°C, and La Niña is characterized by a negative ONI less than or equal to −0.8°C (because of the unequal number of events, the threshold was adjusted slightly between the two phases). (This index can be found on the CPC Web site at http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml.) The effects of ENSO are not limited to the warm and cold phase. Earlier studies (e.g., Gershunov 1998; Higgins et al. 2000b) have documented important differences between El Niño and the neutral phase as well as between La Niña and the neutral phase, and revealed nuances such as shifts in precipitation during neutral years immediately preceding the warm phase. The current study focuses on the shifts between El Niño and La Niña, but there are many interesting possibilities for further studies in this area.

To confirm that the El Niño and La Niña winter months used for the current analysis are representative of the typical atmospheric patterns of each phase, the NARR 200-hPa zonal wind was examined (Fig. 7). The strong Pacific jet stream of the warm phase is clearly visible in the left panel. The weaker jet stream of the cold phase, which is positioned farther north than during the warm phase, can be seen in the right panel. This is consistent with previous studies (Arkin 1982; Ropelewski and Halpert 1986, 1996) that show that the extended Pacific jet stream characteristic of the warm phase leads to wetter-than-average conditions in the south and warmer-than-average conditions in the north, while the weaker, farther-north Pacific jet stream of the cold phase tends to bring wetter-than-average conditions to the Northwest.

a. Precipitation

Composites of the daily precipitation and the gamma distribution parameters from NARR for the El Niño and La Niña phases were created and the differences between them were examined. A few examples for winter are shown in Fig. 8, to illustrate the shifts that occur in the PDFs between the two phases. Many grid points were examined, and the four presented in Fig. 8 are representative of the general structures observed. The red bars represent the winter El Niño probability histogram, and the blue bars the winter La Niña probability histogram. Table 1 contains the mean, scale, and shape parameters corresponding to these distributions. Three of these areas, the Pacific Northwest, southern California, and the Gulf Coast, have greater mean precipitation during El Niño compared to La Niña. Of these, nearly all of the heavier precipitation events occur during El Niño, and the PDF becomes more scale dominated, with a larger contribution to the mean from events on the heavy tail. The scale parameter is accordingly greater during El Niño and the shape is smaller. On the other hand, the Ohio River Valley has fewer extreme events during El Niño than during La Niña, and these account for a lower mean daily precipitation.

The differences between El Niño and La Niña winters for precipitation and its gamma parameters are presented in Fig. 9a; the values represent the percent change between the two phases. Significance of the results has been tested using permutation tests: for each test statistic (e.g., difference in scale parameter, etc.), the null hypothesis is that the two data batches (e.g., El Niño winters and La Niña winters) are equal with respect to the test statistic. To test this, the data batches are combined into one pool, and this pool is sampled into two batches 10 000 times without replacement. For each sample, the test statistic is computed, and confidence intervals are determined using the resulting distribution of test statistics (Wilks 1995). Statistics within the 95% confidence intervals have been indicated in Fig. 9 with hatching. While the results presented are from NARR, examination of the ENSO-related shifts using observations revealed very similar patterns and relationships to those in NARR, with shifts in the gamma distribution parameters that were of slightly higher magnitude than those seen in NARR. NARR’s underestimation of extremes in the eastern half of the United States during summer was discussed earlier (see discussion of Figs. 1 –3).

Using the CPC index, 19 winter El Niño months and 12 winter La Niña months in the 1979–2005 record were identified (Fig. 9a). For reference, the outlines of several river basins are drawn on the top-left panel of Fig. 9a. The southern United States has a higher precipitation intensity during El Niño than during La Niña; this increase is greater than 60% in some areas, particularly the Southeast and California. This is likely due to the extended Pacific jet stream and amplified storm track characteristic of an El Niño winter (Fig. 7; Kousky et al. 1984; Nakamura et al. 2004). Reduced precipitation during El Niño is found over the Ohio River and Arkansas–Red River basins. The top-right panel of Fig. 9a shows an increased wet-day frequency during El Niño over much of the South and Southwest, again, likely attributable to the extended Pacific jet stream. These results are in general spatial agreement with Dai and Wigley (2000, see their Fig. 2) and Higgins et al. (2007).

Several of the areas of changed daily precipitation intensity are accompanied by changes in the tails of the PDF (as represented by the scale parameter) of the same sign and greater magnitude (Fig. 9a, lower left). Shifts in the contribution of light-to-moderate daily events (shape parameter, Fig. 9a, lower right) are milder than those seen in the scale. Earlier studies have found that that the heavy-to-extreme range of daily precipitation magnitude is often more sensitive to ENSO phase than is the mean (Gershunov 1998; Cayan et al. 1999), and changes in overall climate affect the scale of the gamma distribution of precipitation more than the shape (Wilby and Wigley 2002; Watterson and Dix 2003). In the northern Ohio River basin region and the Arkansas–Red River basin (over Oklahoma and Kansas), there is a shift in the PDF toward fewer extreme events (lower scale, higher shape) during El Niño. On the other hand, California, the Gulf Coast, and western Washington state have an increase in extremes and a decrease in the contribution of light-to-moderate events, as represented by larger-scale parameters and decreased shape. The southern Appalachian Mountain region, which has little shift in the intensity, shows a change in the PDF toward a higher contribution from extremes (increase in the scale, decrease in the shape).

The sample size for ENSO events in summer during the 1979–2005 record (Fig. 9b) is smaller than that of winter, with 11 El Niño months and 7 La Niña months. Again, shifts within the 95% confidence interval are hatched. The northern Rocky Mountains region shows the largest increase in precipitation intensity in the country during summer (Fig. 9b, top left), and an increase in frequency (Fig. 9a, top right) similar to that found in Higgins et al. (2007). The increase in intensity in this region is accompanied by shifts in the PDF toward more extremes (higher scale, lower shape). On the other hand, North and South Dakota and Nebraska feature a smaller-scale parameter and larger shape, indicating a decrease in the contribution to the mean from the extremes. Similar to the effect seen in winter, the magnitude of shifts in the extreme range of the PDF is greater than shifts in the intensity in summer.

b. Precipitation-related factors

The mean precipitable water (Fig. 10, top row) exhibits very little change between El Niño and La Niña in winter. The most noticeable pattern is an increase in precipitable water over the northern half of the country and a small part of Maine. This area has about a 20% increase in mean precipitable water during El Niño compared to La Niña. There is a large shift in the precipitable water PDF in the northern center of the country, toward fewer events on the extreme tail of the PDF. Precipitable water is relatively low in this area during winter, and this shift in the PDF does not appear to have similarities with the precipitation PDF. However, in the Gulf Coast–Southeast region, where winter precipitation is high, the scale parameter of both the precipitable water and precipitation gamma distributions increase during El Niño compared to La Niña, suggesting that despite their lack of overall similarity (see discussion of Fig. 5), increases in precipitable water extremes may have some relationship with increases in precipitation extremes in these southernmost regions.

Unlike precipitable water, the winter pattern of change in MFC intensity between El Niño and La Niña (Fig. 11, top row) resembles that of precipitation intensity (Fig. 9a), although the magnitude of the change in MFC over most of the country is about half that in precipitation. For example, southern California, where the precipitation intensity increases more than 60% between the two ENSO phases, exhibits an increase in MFC of about 20%–40%. The change in MFC extremes (as represented by the scale parameter, Fig. 11a) is greater than the change in the mean, suggesting that the tail of the MFC distribution (i.e., strong and extreme convergence) is more sensitive than the mean to changes in climate, similar to precipitation. However, like the mean, the magnitude of the change in the MFC scale parameter is about half that of the precipitation scale, throughout the country.

In summer, precipitable water has a low correlation with precipitation (see discussion of Fig. 4), and few significant shifts are seen in the intensity or the tails of the PDF with ENSO phase (Fig. 10, second row). MFC, which has a stronger correlation with precipitation, has summer ENSO shifts that resemble those seen in precipitation. Specifically, the increased intensity and extremes (as represented by the scale parameter) seen in precipitation over the northern Rocky Mountains and the shifts of opposite sign over the northern Great Plains, are also present in the MFC field. The response of the scale parameter (representing the extremes of the PDF) is stronger than the response of the intensity, also similar to the effect seen in the precipitation. These findings imply that shifts in the PDF of moisture flux convergence are related to shifts in the precipitation during summer.

6. Summary and conclusions

Advances in climate prediction on seasonal time scales are highly dependent on improved understanding of the expected variability within the season. With this motivation, this study examined the seasonal characteristics of the PDF of daily precipitation over the United States, and its dependence on the lower-frequency modulation of ENSO, using the North American Regional Reanalysis (NARR) 1979–2005 daily data. The gamma distribution was used to represent the PDF, and the chi-squared statistic was used to measure the goodness-of-fit of the gamma distribution to the underlying data. The gamma distribution parameters, which can provide useful information about the contribution of light-to-moderate and heavy-to-extreme events to the total precipitation, were then examined. In addition to precipitation, two factors related to the hydrological cycle, precipitable water and moisture flux convergence, were also examined to help understand the physical mechanisms that contribute to changes in the characteristics of daily precipitation.

First, the patterns of daily precipitation in NARR were evaluated using gridded observations of precipitation. The NARR mean seasonal amount is very close to that of observations throughout the year, although NARR exhibits a slight systematic bias toward more-frequent, light precipitation events. The NARR precipitation gamma distribution has a slightly lower intensity and scale parameter and higher frequency than the observations over the eastern half of the United States during summer, which suggests that NARR underestimates extremes and overestimates lighter events during this season. However, this bias is systematic, and the relationship between the gamma distribution parameters is well represented in NARR. The greatest discrepancy between NARR and the observed precipitation is in Florida during the summer, when NARR does not capture all of the extreme events seen in observations. This suggests that NARR is not capturing the magnitude of precipitation from the convective storms that occur in this region during summer.

Spatial patterns of the MFC intensity and its gamma distribution parameters have strong similarity to those of precipitation, suggesting a relationship between the MFC and precipitation PDFs, in both summer and winter, and a corresponding link between strong MFC and precipitation extremes. The relationship between the precipitable water and precipitation PDFs is weaker, based on the lack of agreement of their gamma distribution parameters. The rank correlation of higher-magnitude precipitation with MFC and with precipitable water also shows that the stronger relationship is to MFC, especially during the summer.

During winter, many regions of the United States have a daily precipitation PDF that has a strong dependence on ENSO variability. The Southwest and central United States, Gulf of Mexico region, and southeastern coast show intensity increases on the order of 40%–60% during El Niño, compared to La Niña. On the other hand, reduced daily precipitation intensity during El Niño is found over the Ohio River and Red River basins. Most areas that see a large change in the daily mean precipitation between ENSO phases have greater shifts in the extreme tail of the PDF, as represented by an increase in the gamma distribution scale parameter. This is offset by a small decrease in contribution to the mean from lighter and moderate events, seen in the shape parameter. In summer, ENSO-related increases in precipitation extremes are found over the northern Rocky Mountains, and decreases are found in the northern plains. Similar to winter, the shifts in the tail of the PDF are greater than shifts in the intensity.

The pattern of change in mean MFC between El Niño and La Niña resembles that of mean precipitation, although the MFC does not change as much as precipitation. Similar to precipitation, the change in MFC extremes is greater than the change in the mean, suggesting that the frequency of strong convergence is more sensitive than the mean to changes in climate. The relationship of the variability of daily precipitation to the variability of precipitable water appears to be generally weak, based on the lack of similarity between shifts in the intensity and gamma distribution parameters, and on their weak correlation. However, in the Southeast during winter, similar shifts in the gamma distribution scale parameter indicate there may be a relationship between increases in precipitable water extremes and precipitation extremes.

While the PDF of daily precipitation can be determined from observations or reanalysis that assimilate precipitation, its reliability in a model’s seasonal forecasts is in doubt because of the model’s biases that are the product of uncertain parameterizations. Given that MFC has a lesser dependence than precipitation on parameterizations, it is speculated that its PDF is a good alternative to assess frequency distributions in the more biased-affected seasonal forecasts.

Acknowledgments

The authors would like to acknowledge the thoughtful comments of two anonymous reviewers, which helped to significantly improve the manuscript. NARR daily data were obtained from the Physical Sciences Division of NOAA (http://www.cdc.noaa.gov/cdc/data.narr.html). The assistance of the Cooperative Institute for Climate Studies (CICS) and Dr. Phil Arkin are appreciated. This work was supported by NOAA Grants NA17EC1483 and NA04OAR4310164.

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Fig. 1.
Fig. 1.

Observed and NARR precipitation seasonal mean (left) amount, (middle) intensity, and (right) frequency for (top two) winter (DJF) and (bottom two) summer (JJA) over the contiguous United States. The threshold defining a day with precipitation is 1.0 mm day−1. The period of record is 1979–2005.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 2.
Fig. 2.

Area-averaged daily precipitation values from NARR (vertical axes) and gridded observations (horizontal axes) for northern California, Pacific Northwest, Southwest, Gulf of Mexico–South, Great Plains, and Mid-Atlantic for the 1979–2005 period of examination. The area averages were performed over 5° latitude × 5° longitude land-only boxes (see Fig. 4). The gray line indicates the line fit between NARR and observations.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 3.
Fig. 3.

The (left) 95th percentile for daily precipitation events, (middle) gamma distribution scale parameter, and (right) gamma distribution shape parameter for (top two) winter and (bottom two) summer over the contiguous United States. The scale parameter shows the contribution of extreme events to the seasonal total and the shape parameter indicates the contribution of lighter-to-moderate events. Areas where the chi-squared statistic indicated the gamma distribution did not adequately fit the PDF are masked from this figure.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 4.
Fig. 4.

Rank correlations between MFC and precipitation and between precipitable water and precipitation. (top) The results for winter for (left) MFC precipitation and (right) precipitable water precipitation over the United States. (bottom two) The area-averaged results for the six 5° latitude × 5° longitude boxes indicated: northern California, Pacific Northwest, Southwest, Gulf of Mexico–South, Great Plains, and Mid-Atlantic over each of the four seasons. The black bars show the precipitation rank correlation with precipitable water and the gray bars show MFC. All data are from NARR.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 5.
Fig. 5.

NARR precipitable water intensity and the gamma distribution scale and shape parameters for (top) winter and (bottom) summer over the United States for 1979–2005. The fit of the gamma distribution to the precipitable water PDF was evaluated using the chi-squared statistic, and areas where the fit was inadequate are masked.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 6.
Fig. 6.

As in Fig. 5, but for vertically integrated moisture flux convergence.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 7.
Fig. 7.

NARR winter (DJF) mean 200-hPa zonal wind for (left) El Niño and (right) La Niña that were examined for this study. The extended Pacific jet stream is characteristic of an El Niño winter while the right panel shows the weaker jet stream of La Niña.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 8.
Fig. 8.

Winter El Niño (red) and La Niña (blue) precipitation histograms for four grid points in the Pacific Northwest, Ohio River Valley, Southern California, and Gulf of Mexico Coast regions. See Table 1 for mean precipitation amount and gamma distribution parameters corresponding to these histograms. Precipitation data are from NARR.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 9.
Fig. 9.

(a) Winter difference and (b) summer difference between El Niño and La Niña precipitation intensity, frequency, scale, and shape parameters. Red shows areas where the quantity is greater during El Niño, and blue where it is greater during La Niña, expressed as the shift relative to the average of all El Niño and La Niña months. Areas where shifts are significant above the 95% confidence interval are indicated with hatching. Precipitation data are from NARR.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 10.
Fig. 10.

Shifts between El Niño and La Niña (left) precipitable water intensity and (right) scale parameter for (top) winter and (bottom) summer. Red areas show where the quantity is greater during El Niño, and blue where it is greater during La Niña, expressed as the shift relative to the average of all El Niño and La Niña months. Areas where shifts are significant above the 95% confidence interval are indicated with hatching.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for vertically integrated moisture flux convergence.

Citation: Journal of Climate 22, 23; 10.1175/2009JCLI2838.1

Table 1.

Mean and gamma distribution scale and shape parameters corresponding to the histograms in Fig. 8.

Table 1.
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