Theoretical and Applied Climatology

, Volume 104, Issue 3–4, pp 415–421 | Cite as

Spatial analysis of variations in precipitation intensity in the USA

  • Robert C. BallingJr.
  • Gregory B. Goodrich
Original Paper


In this study, we used various spatial analytical methods to examine variations and trends in precipitation intensity in the conterminous USA. We found that three different measures of precipitation intensity were highly correlated; intensity increased in a spatially coherent fashion in the northeastern quarter of the USA and generally decreased in the center portion of the western USA. Evidence is presented that spatial and temporal patterns in the trends of precipitation intensity are related to the Atlantic multidecadal oscillation. Our results are generally in agreement with others who are reporting an upward trend in precipitation intensity during a period when the planet appears to have warmed.


Pacific Decadal Oscillation Precipitation Intensity Standardize Regression Coefficient Anthropogenic Climate Change Extreme Precipitation Event 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1 Introduction

The United Nations Intergovernmental Panel on Climate Change (IPCC 2007) notes that extreme precipitation events may be increasing in frequency and intensity as a result of the ongoing anthropogenic emission of greenhouse gases. The conceptual foundation for changes in precipitation intensity has been detailed by Allen and Ingram (2002), among many others, and indeed numerical climate models generally predict an increase in extreme precipitation events as the planet warms. In simplest terms, warming increases potential evapotranspiration rates, a warmer atmosphere has the ability to hold more water, the higher atmospheric moisture levels and temperatures tend to destabilize the lower troposphere, and an increase occurs in the intensity of precipitation.

Given the prediction of increasing precipitation intensity, climatologists have examined records from throughout the world in an attempt to identify trends in extreme rainfall events during the period of historical records. Based largely on the global-scale review and analysis of Alexander et al. (2006), and on dozens of regional-scale analyses, the IPCC (2007) reports that extreme precipitation events have increased on average by approximately 0.21% per decade over the last half century. However, the trends in precipitation intensity levels show a relatively high degree of spatial entropy (a measure of spatial disorder) with stations near one another often revealing highly varying (even opposite) trends. Furthermore, as revealed by Sen Roy and Balling (2009) and Peralta-Hernandez et al. (2009), trend results can vary significantly for the same location and study period depending on the index used to define extreme precipitation.

Over the past decade, many researchers have focused attention on trends in extreme precipitation events for the USA. Kunkel et al. (1999) examined short-duration events (1–7 days) with a recurrence interval of 1 year or longer and found a national trend upward of 3% decade−1 for the period 1931 to 1996. Several years later, Kunkel (2003a) examined events over the period 1951 to 1997 and found that time varying sea-surface temperatures in a numerical model could force an upward trend in extreme precipitation events across the USA by increasing atmospheric water vapor content over the country. In an article with a longer period of study, Kunkel (2003b) found that the USA had experienced an upward trend in extreme precipitation events since the 1920s and 1930s, but during the late 1800s, extreme events were as frequent as in the 1980s and 1990s. He concluded that the natural variability of climate could be the “cause” of the observed increase of the past century, although the anthropogenic forcing due to increasing greenhouse gas concentrations could not be discounted as a contributor. Using a newly generated set of daily precipitation observations from 1895 to 2000, Kunkel et al. (2003) also found that irrespective of realistic decisions regarding event duration and/or selected return interval, heavy precipitation events were high in the late nineteenth and early twentieth centuries, low in the 1920s and 1930s, followed by a general increase into the 1990s. Pryor et al. (2009) found that most stations showed evidence of an upward trend in events above the 95th percentile, with the upward trend focused in the central Plains and northwestern Midwest.

In this investigation, we focus on trends in extreme precipitation for the conterminous USA; we use spatial analytical methods to better identify the nature of geographic dimensions that underlie variations and/or trends in the data. Our results should identify overall trends in precipitation intensity, geographic dimensions associated with those trends, and possible causes of the variations and trends in intensity that have been observed in recent decades.

2 GHCN daily data and intensity indices

We selected the stations in the conterminous USA that are included in the popular and widely used Global Historical Climatology Network (GHCN)—Daily database provided to us by scientists at the National Climate Data Center (NCDC) (Durre et al. 2008; Menne 2010). The GHCN-D is the world’s largest collection of daily climatological data and is considered well-suited for monitoring and assessment activities related to the frequency and magnitude of extremes. The data have undergone considerable quality assurance, the data are updated frequently, and all data are downloadable from the NCDC website and no cost to investigators. There are 1,218 stations in the conterminous USA included in the GHCN-D dataset.

Almost any starting date can be selected and defended, but in this study, we began in 1975 to capture 35 years of data during which the planet warmed; while some areas of the earth many have cooled during this period, this does not appear to be the case for the USA (IPCC 2007). For the entire network of 1,218 stations, we found that 6.82% of the daily precipitation data were missing; we eliminated any station with more than 5% missing data over the 1975 to 2009 study leaving a total of 807 stations (Fig. 1); those remaining stations had only 1.51% of missing data. The nearest neighbor statistic (Clark and Evans 1954) for the remaining network is 1.13 indicating a desirable “dispersed” spatial pattern. We calculated the linear trend in the total annual precipitation (simple regression with precipitation total as the dependent variable and year of record as the independent variable); universal kriging of the standardized regression coefficients reveals a relatively smooth underlying interpolated surface explaining 41.04% of the spatial variance in the trends. The map (Fig. 1) reveals a reduction in precipitation in the western USA (particularly in the American Southwest) and a general increase in the central and northeastern portions of the country. On a percentage basis, the linear change in precipitation for the entire study area was near zero, but in some cases, stations experience an increase or decrease of over 30% during the 1975–2009 period.
Fig. 1

Distribution of 807 stations and linear trend in total annual precipitation as indicated by standardized regression coefficient

We selected three different indices to depict temporal variance in precipitation intensity levels. The first intensity measure, abbreviated as “INTNS”, is simply the annual total precipitation divided by the frequency of precipitation days. The second indicator is the number of days with 50 mm of total precipitation (N 50). The third is a bit more sophisticated and involves determining over the 35 year time period the daily total below which contributed 90% of all the precipitation events that fell at that station over the entire time period. This threshold varies considerably from place to place (Fig. 2) and is generally largest in areas with the greatest total precipitation. The intensity time series for this threshold is the number of events in a given year at or above the threshold value (NP ≥ 90%). Based on Sen Roy and Balling (2009) and Peralta-Hernandez et al. (2009), we expected the three different precipitation indices to be relatively highly correlated through time.
Fig. 2

Precipitation threshold for large events that contribute 10% of the total precipitation

3 Analyses of intensity levels

For each station, we developed annual time series for the three primary indices of precipitation intensity (NP ≥ 90%, N50, INTNS). Each time series was converted to z-scores (transformed with a mean of 0.00 and a standard deviation of 1.00), and the z-scores were averaged across the entire network. This produced three highly correlated time series (the three intercorrelation coefficients ranged from +0.84 to +0.94) that should capture variations and trends in precipitation intensity for the entire conterminous USA. All three time series showed an upward trend, and the trends were statistically significant (p < 0.05) for the NP ≥ 90% and N50 indices. Given the high intercorrelations, we used principal components and found one component that explained 91.97% of the variance in the three variables with all three loadings >0.94. The component scores (Fig. 3) show considerable variability from year-to-year and a statistically significant (p = 0.05) upward linear trend. At the spatial scale of the continental USA, there is strong evidence that precipitation intensity has increased over the most recent 3.5 decades.
Fig. 3

Component scores for precipitation intensity (black line) for the conterminous USA with the Atlantic multidecadal oscillation (red dashed line)

The overall trend upward results from a complicated spatial pattern revealed in Fig. 4 for the NP ≥ 90% intensity variable. The standardized regression coefficients average +0.06, reinforcing the overall upward trend seen in Fig. 3. The map shows that precipitation intensity has increased in the central and northeastern portions of the country and generally in areas where total precipitation has increased overall; the map pattern correlation coefficient between Figs. 1 and 4 is +0.52 and is highly significant (p < 0.01). The complexity of the pattern is revealed by four different quantitative measures:
  1. (1)

    Spatial entropy (Shannon 1948) is a measure of disorder or dissimilarity in the pattern and is calculated as—Σ(p i log2 p i ) where p i is proportion of stations (station of interest and four surrounding stations selected with the criterion that the stations are closest to the station of interest) that are assigned to each class based on five classes for all data using a natural grouping of precipitation intensity trend values. Entropy for each station ranges from 0.0 where all five stations are in the same class to 2.32 when all five classes are represented in the five stations. With five classes and four surrounding stations, there are only seven possible spatial entropy values including 0.00, 0.71, 0.97, 1.37, 1.52, 1.92, and 2.32. The pattern seen in Fig. 4 has a mean entropy value of 1.64 indicating a relatively high level of spatial disorder.

  2. (2)

    We used universal kriging to produce an interpolated surface of the standardized regression coefficients in Fig. 4; the resultant surface explained only 10.44% of the spatial variance in the regression coefficients. This indicates that some relatively smooth underlying interpolated spatial pattern does not explain much variance in the standardized regression coefficients across the USA.

  3. (3)

    Spatial autocorrelation at the global scale (or in this case, the continental scale) can be calculated as the Moran’s I statistic (Moran 1950) as:

    $$ I = \frac{n}{{{S_O}}}\frac{{\sum\nolimits_{{i = 1}}^n {\sum\nolimits_{{j = 1}}^n {{w_{{i,j}}}{z_{{_i}}}{z_j}} } }}{{\sum\nolimits_{{i = 1}}^n {z_i^2} }} $$
    where z i and zj are deviations from the global mean at locations i and j, w i ,j is the spatial weight between location i and j that is inversely related the distance between the two locations, n is the total number of locations with valid data, and S0 is the aggregate of all spatial weights calculated as:
    $$ {S_0} = \sum\limits_{{i = 1}}^n {\sum\limits_{{j = 1}}^n {{w_{{i,j}}}} } $$
    The value of the Moran’s I statistic varies from near +1 indicating clustering of the z values to near -1 indicating spatial dispersion in the z values. In order to assess the statistical significance of the Moran’s I statistic, a standardized value, z I , is determined as:
    $$ {z_I} = \frac{{I - E\left[ I \right]}}{{\sqrt {{V\left[ I \right]}} }} $$
    where E[I] is the expected value of I assuming spatial randomization which simplifies to:
    $$ E\left[ I \right] = \frac{{ - 1}}{{\left( {n - 1} \right)}} $$
    and V[I] is the expected variance of the I values. The values in Fig. 4 have a Moran’s I of +0.15 indicating a statistically significant clustering (z = 11.81, p < 0.01), but overall, a relatively low level of spatial autocorrelation.
  1. (4)

    The Anselin Local Moran’s I (Anselin 1995) is a decomposition of the global Moran’s I and is basically determined as:

    $$ {I_i} = \frac{{{x_i} - \bar{X}}}{{S_i^2}}\sum\limits_{{j = 1,j \ne 1}}^n {{w_{{i,j}}}\left( {{x_i} - \bar{X}} \right)} $$
    where x i is the value of an attribute at point i, \( \bar{X} \) is the global mean of the x i values, w i,j is a spatial weight between location i and j, and \( S_i^2 \) is calculated as:
    $$ S_i^2 = \frac{{\sum\nolimits_{{j = 1,j \ne 1}}^n {{w_{{i,j}}}} }}{{}} - {\bar{X}^2} $$
    Just as with the global Moran’s I statistic, the Anselin Local Moran’s I may be standardized and expressed as a z-score, \( {z_{{{I_i}}}} \), computed as:
    $$ {z_{{{I_i}}}} = \frac{{{I_i} - E\left[ {{I_i}} \right]}}{{\sqrt {{V\left[ {{I_i}} \right]}} }} $$
    where E[I i ] and V[I i ] are the expected value of I i and the variance of I, respectively. We selected 1.65 as a threshold for the \( {z_{{{I_i}}}} \) values, and as seen in Fig. 5, only 182 of the 1,218 stations had significantly high levels of local spatial autocorrelation; of these 182 stations, 141 had a positive value indicating an increase in precipitation intensity. The pattern in Fig. 5 clearly shows that the precipitation intensity increase is strongest in the northeastern quarter of the country and intensity appears to have decreased in the central portion of the western USA.
Fig. 4

Standardized regression coefficients showing trends in precipitation intensity: 1975–2009

Fig. 5

Same as Fig. 4 except only for stations with strong local spatial autocorrelation

4 Teleconnections

Fluctuations of many facets of precipitation, including intensity, have been linked to several modes of low-frequency climate variability known as teleconnections (Trenberth et al. 2003). These teleconnections impact rainfall patterns through the changing of planetary wave structure on various time scales which in turn creates a shift in storm tracks. Higgins et al. (2007) found that interannual fluctuations in daily precipitation intensity are linked to ENSO while decadal fluctuations in intensity are caused by the Pacific decadal oscillation (PDO) in the western USA and to a lesser extent by the Arctic oscillation (AO) in the eastern USA. Other investigators have found relationships between precipitation intensity and additional teleconnections in seasonal and/or regional analyses. Griffiths and Bradley (2007) focused their analysis of precipitation intensity on the Northeast USA and found links to the Pacific/North American pattern in addition to ENSO and the AO, while Durkee et al. (2008) found that the phases of the North Atlantic Oscillation were related to precipitation extremes during winter in the eastern USA. Curtis (2008) suggested a link between the phases of the Atlantic multidecadal oscillation (AMO) and precipitation intensity during hurricane season in the mid-Atlantic and Southeast USA.

To determine if the temporal variation of component scores of precipitation intensity (Fig. 3) was related to any of the leading sources of interannual or interdecadal climate variability, the time series of component scores was correlated with the atmospheric and oceanic teleconnections mentioned above with known links to precipitation intensity (Table 1). While the 35-year time scale of the autocorrelation dataset is roughly half the period of the PDO and AMO, these teleconnections were included in the analysis since they both feature a modest level of interannual variability. All teleconnection data were downloaded from the CPC website except for the PDO (Joint Institute for the Study of the Atmosphere and Ocean) and AMO (NOAA’s Earth System Research Lab).
Table 1

Atmospheric and oceanic teleconnections linked to precipitation intensity or extremes






Durkee et al. (2008)



Griffiths and Bradley (2007)



Higgins et al. (2007)



Higgins et al. (2007)



Higgins et al. (2007)



Curtis (2008)



Higgins et al. (2007)

NAO North Atlantic oscillation, PNA Pacific North American, SOI Southern oscillation, PDO Pacific decadal oscillation, AMO Atlantic multidecadal oscillation, AO Arctic oscillation

Bold values show significance (α < 0.05)

Since the component scores displayed a significant upward trend over the 35-year period of record, we were skeptical that any of the interannual teleconnections would have a significant relationship to changes in precipitation intensity since interannual teleconnections have little to no trend over such a long time scale. Our analysis (Table 1) bears this out as only the AMO, which also has a significant upward trend during the period (p < 0.01), is significantly correlated with the time series of component scores (r = 0.44; p = 0.01). As the AMO moved from a cold phase in the 1970s and 1980s to a warm phase beginning in 1995, precipitation intensity has generally increased in the USA (Fig. 3). The link between the AMO and precipitation intensity has been established for the mid-Atlantic and Southeast regions during hurricane season but not thus far for all seasons. As discussed above in section three, precipitation intensity has generally increased in locations where precipitation itself has increased (Figs. 1, 4, and 5). This links well with the AMO which is positively correlated with precipitation in the Northeast and Southeast where precipitation intensity has increased and is negatively correlated with precipitation in the western USA where precipitation intensity has decreased (Enfield et al. 2001). This fits the physical model of the positive AMO suggested by Curtis (2008) where synoptic-scale changes in circulation over the Atlantic along with increased low-level moisture flux, potential instability, and the elevated topography of the Appalachians combine to improve the chances of intense rainfall over the mid-Atlantic and Southeast. This AMO relationship breaks down in the central USA, where precipitation is negatively correlated with AMO but still has shown increases in precipitation intensity. It must be noted that most stations in the central USA displayed weak local spatial autocorrelation. This lack of a coherent spatial signal with respect to precipitation intensity suggests that other more local-scale forcings may be responsible.

The linkage of the AMO to increases in precipitation intensity must be viewed with caution as only one cycle of the AMO was used in the analysis. There is also an open question regarding the dynamics of the AMO and the relationship between warming North Atlantic SSTs and anthropogenic climate change (Trenberth and Shea 2006). While reconstructions of tree-ring data suggest the AMO cycle has been present for at least five centuries (Gray et al. 2004), others have suggested anthropogenic warming is at least partially responsible for recent changes in the Atlantic basin (Ting et al. 2009). Thus it is possible that the positive relationship between the AMO and precipitation intensity observed since 1975 may be secondary to changes in the climate system caused by anthropogenic climate change. To test this, we detrended both the time series of precipitation intensity time series and the AMO in order to separate influences from climate change. The analysis between the detrended times series produced a correlation of r = 0.31 (p = 0.07), which is less than the correlation of the raw time series (r = 0.44, p = 0.01). The variance explained by the AMO from the detrended time series of AMO (R 2 = 0.096) is roughly half of the raw time series of AMO (R 2 = 0.194), which suggests that the variance explained in precipitation intensity since 1975 is roughly split between the AMO and warming SSTs from anthropogenic climate change.

5 Conclusions

Our analyses of daily precipitation records from the conterminous USA reveal that during a time the Earth warmed (1975–2009), precipitation intensity appears to have increased at a continental scale. The spatial pattern of the trends is one of relatively high entropy (disorder), but generally, the greatest increase occurred in the northeastern quarter of the country while a decrease occurred in the central portion of the West. Areas where total precipitation increased (decreased) are generally the areas where the precipitation intensity increased (decreased). We found some evidence that spatial and temporal variations and trends in precipitation intensity are related to the Atlantic multidecadal oscillation, although the AMO itself is conflated with anthropogenic climate change. Given the complexity of the spatial patterns in precipitation intensity trends along with a significant link to AMO, making any direct link between anthropogenic changes in atmospheric composition and increases in precipitation intensity must be done with caution.



This material is based upon a work supported by the National Science Foundation (NSF) under Grant No. SES-0345945 Decision Center for a Desert City (DCDC) and NSF Grant No. 0751790. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors thank R.S. Vose and others at the National Climatic Data Center who supplied the HCN data for this study.


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of Geographical Sciences and Urban PlanningArizona State UniversityTempeUSA
  2. 2.Department of Geography and GeologyWestern Kentucky UniversityBowling GreenUSA

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