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Statistical Characteristics of Daily Precipitation: Comparisons of Gridded and
Point Datasets
LESLIE A. ENSOR*
AND
SCOTT M. ROBESON
Atmospheric Science Program, Department of Geography, Indiana University, Bloomington, Indiana
(Manuscript received 12 April 2007, in final form 6 March 2008)
ABSTRACT
Gridding of daily precipitation data alleviates many of the limitations of data that are derived from point
observations, such as problems associated with missing data and the lack of spatial coverage. As a result,
gridded precipitation data can be valuable for applied climatological research and monitoring, but they too
have limitations. To understand the limitations of gridded data more fully (especially when they are used
as surrogates for station data), annual precipitation total, rain-day frequency, and annual maxima are
calculated and compared for five Midwestern grid points from the Climate Prediction Center’s Unified Rain
Gauge Dataset (URD) and those of its nearest (rain gauge) station. To further examine differences between
the two datasets, return periods of daily precipitation were calculated over a region encompassing Illinois
and Indiana. These analyses reveal that the gridding process used to create the URD produced nearly the
same annual totals as the rain gauge data; however, the gridding significantly increased the frequency of
low-precipitation events while greatly reducing the frequency of heavy-precipitation events. Extreme precipitation values also were greatly reduced in the gridded precipitation data. While smoothing nearly always
occurs when data are gridded, the gridding of discrete variables such as daily precipitation can produce
datasets with statistical characteristics that are very different from those of the original observations.
1. Introduction
Gridded precipitation datasets are useful for many
types of climate research, including the analysis of climatic change and variability (Dai et al. 1997; Sen and
Habib 2000; Sen Roy and Balling 2004). Gridded
datasets are developed and used because they provide a
more spatial representation of precipitation. In comparison, networks of weather-observation sites typically
are irregularly distributed throughout space and frequently have periods of missing data. In addition, high
elevations, oceans, and areas with low population are
generally not well represented in precipitation datasets
composed of station networks (Daly et al. 1994). Grid-
* Current affiliation: Illinois State Water Survey, Champaign,
Illinois.
Corresponding author address: Scott M. Robeson, Atmospheric
Science Program, Department of Geography, Indiana University,
Bloomington, IN 47405.
E-mail: [email protected]
DOI: 10.1175/2008JAMC1757.1
© 2008 American Meteorological Society
ded precipitation datasets can offer a solution—albeit
an imperfect one—to the problems of missing data and
spatial bias that result from uneven and unrepresentative spatial sampling (i.e., bias toward populated areas,
mountain valleys, etc.; Liebmann and Allured 2005;
Robeson and Ensor 2006).
Precipitation becomes more spatially continuous
over longer time periods, making temporal averages
more amenable to spatial analysis. As a consequence,
monthly datasets are typically used in climate studies
(Legates and Willmott 1990; New et al. 2002; Xie and
Arkin 1997). The availability of (digital) monthly precipitation data also influences the choice of time scale.
Comparisons between monthly gridded precipitation
datasets and point (rain gauge) observations have
shown that the two types of data have produced similar
trends during the twentieth century (Klein Tank et al.
2002). Interpolated climatological datasets also show a
close relationship with monthly data derived from satellite observations (Krajewski et al. 2000). Few studies,
however, have compared daily gridded precipitation
datasets with station data (Hewitson and Crane 2005;
SEPTEMBER 2008
NOTES AND CORRESPONDENCE
Higgins et al. 2007; Silva et al. 2007). One reason for
this is that gridded precipitation data are not widely
available at a daily resolution (Liebmann and Allured
2005). The few daily precipitation datasets that have
been created often are used to initialize climatic, ecological, or hydrological models (Kittel et al. 2004; Jolly
et al. 2005). Gridded daily precipitation datasets on a
fine spatial scale are especially useful because they provide uniform spatial coverage of events that are climatologically, ecologically, and hydrologically important.
Just as the order of spatial and temporal averaging
can affect the characteristics of daily precipitation
(Kursinski and Zeng 2006), the spatial interpolation
method used to grid the daily precipitation values can
introduce bias into a gridded dataset (Daly 2006; Chen
et al. 2002; Robeson and Ensor 2006). To understand
the characteristics and limitations of daily gridded precipitation datasets, a comparison of a gridded daily precipitation dataset, the National Oceanic and Atmospheric Administration Climate Prediction Center
(CPC) unified rain gauge dataset (URD), with station
(point) observations is performed. The station observations used here are included in the URD (this situation
is unavoidable, because all reliable rain gauge data are
included in the URD), and, therefore, our results
should be viewed as conservative estimates of the differences between the two data sources. In addition, our
analysis is not intended to be an independent evaluation of the accuracy of the URD. Our goal is to demonstrate the differences between the URD and nearby
rain gauge data and to make clear the implications of
these differences for research in applied climatology.
Because gridded data are convenient and are sometimes used interchangeably with rain gauge data, this
research demonstrates some of the limitations of using
(smoothed) gridded data as if they were equivalent to
point representations.
2. Data
a. Unified rain gauge dataset
The gridded precipitation dataset used here is the
unified rain gauge dataset from the CPC. The URD
contains daily precipitation values on a 0.25° latitude by
0.25° longitude grid covering the continental United
States for the time period of 1948 onward (updated
daily; Higgins et al. 2000, 2007). Between 13 000 and
15 000 daily observing sites from the CPC’s daily cooperative dataset, the National Climatic Data Center’s
cooperative dataset (TD-3200), and an hourly gridded
precipitation dataset (Higgins et al. 1996) from across
the United States are used in the calculation of the
gridded values. Precipitation data from these stations
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are interpolated to the grid using a modified Cressman
(1959) scheme. Although iterative, the Cressman
scheme is fundamentally a distance-weighting method,
meaning that the primary determination of the gridpoint precipitation value is the distance between the
grid point and its local stations. The Cressman method
produces smooth output, but its output is an estimated
value at each grid point that frequently is evaluated
using nearby station data (Higgins et al. 2007; Silva et
al. 2007).
Because it is a real-time dataset, the CPC has used
the URD frequently for monitoring precipitation, for
applied research projects such as the U.S. National
Threats Assessment and the U.S. Drought Assessment,
for Palmer drought severity index calculations, and for
soil-moisture forecasts (Higgins et al. 2000). Another
application of the URD is for verification of precipitation forecasts from numerical weather prediction models such as the operational Medium-Range Forecast
Model, the National Centers for Environmental Prediction Global Forecast System, and ensembles (Higgins
et al. 2000; Kingtse et al. 2005; Mo et al. 2005). This
dataset has also been used to force land surface models
(Cosgrove et al. 2003), to understand feedbacks within
the hydrological cycle (Koster et al. 2003), and to understand relationships between climatic phenomena
(e.g., ENSO, the Pacific decadal oscillation, and Gulf of
California moisture surges) and precipitation (Higgins
et al. 2004, 2007).
To reduce the effects of topography on the gridding
process, a Midwestern region encompassing Illinois and
Indiana is used (Fig. 1). This area also has a highquality network of precipitation-station records with
which to evaluate the gridded data. A total of 825 grid
points, centered on Illinois and Indiana, were extracted
for the analysis over the study area.
b. Station data
Daily Historical Climate Network (HCN/D) data are
used for comparison with the URD. The HCN/D is a
widely used, high-quality data archive (Easterling et al.
1999) that spans the same time period as the URD. This
set of stations was created with the express aim of having long, unbiased time series (that are mostly free of
inhomogeneities) for use in climatic-change studies
(Karl et al. 1990). Because many of the digital records
for precipitation began during 1948, our comparison
begins in January 1949. Over Illinois and Indiana, the
stations are densely located in comparison with other
areas of the United States. As a result, any URD grid
point has several nearby stations available for comparison. In total, 105 HCN/D stations are used (Fig. 1).
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ferences between the station and its nearest grid point,
a number of statistics–—annual total, annual maxima,
and precipitation frequency for low, medium, and high
values of precipitation—–were resampled using bootstrapping (Efron and Tibshirani 1993). The resampling
was performed 1000 times to simulate many of the possible combinations of precipitation characteristics. Error bars of the 95% confidence interval of the characteristics are used for each station–gridpoint pair, which
also allows the differences in characteristics between
the regions to be evaluated and compared.
b. Return-period analysis
FIG. 1. The Midwestern study area for this research is shown
with the 0.25° ⫻ 0.25° latitude/longitude grid. The dots indicate
the Historical Climate Network stations, with the largest dots
indicating the five stations used for more-detailed analysis.
3. Methods
a. Station–gridpoint comparison
Five stations (rain gauges) and their nearestneighboring grid points (Fig. 1; Table 1) were initially
chosen for comparison. These station–gridpoint pairs
are located throughout the Midwest and are representative of differing precipitation regimes within the study
area (wetter to the south; larger snowfall amounts in
the north). These sites also were chosen because 1) the
distance between the station and gridpoint pairs is small
(less than 8 km) and 2) the amount of missing data over
the 50-yr period is among the lowest of the HCN/D
stations (on average, less than 4 days yr⫺1 are missing at
these stations).
To evaluate the significance of the precipitation dif-
To reveal differences between extreme precipitation
at the grid points and stations, 5-, 10-, 25-, and 50-yr
return periods of daily precipitation were estimated at
each grid point and for each station within the study
region. Return-period calculations also can be used in
analyses of changing extreme events, but they are especially valuable when dealing with floodplain designations and engineering designs. For a number of reasons,
therefore, it is useful for gridded daily precipitation
datasets to represent extreme events accurately.
Two forms of the generalized extreme value (GEV)
distribution were fit to the annual precipitation maxima
for each grid point and station to determine the returnperiod values. The GEV has been found to produce
reliable estimates of extreme events (Coles et al. 2003;
Buishand 1989), and using the annual maxima assures
statistical independence within the sample. The Gumbel and Frèchet forms of the GEV were used and evaluated using a Kolmogorov–Smirnov (K-S) goodness-offit test (Legates 1991). Although both forms of the
GEV produced cumulative distribution functions that
fit both data types accurately, the Gumbel form produced slightly higher p values, with no grid point or
station showing a significant difference from the Gumbel distribution (␣ ⫽ 0.05). Although the Frèchet form
produced similar return-period values, a few of the grid
points showed significant differences (␣ ⫽ 0.05) between the observed and modeled distributions. As a
result, the Gumbel distribution is used for the returnperiod calculations.
TABLE 1. Stations and grid points used for trend analysis (missing days for entire period of record).
Region
Station No.
Station name
Missing days
Northwest
Northeast
Southwest
Southeast
Central
131635
201675
110187
127875
114198
Clinton, IA
Coldwater, MI
Anna, IL
Scottsburg, IN
Hoopeston, IL
9
199
12
47
33
Grid point
41.75°N,
42.00°N,
37.50°N,
38.75°N,
40.50°N,
90.25°W
85.00°W
89.25°W
85.75°W
87.75°W
Distance (km)
5.80
4.45
3.45
4.77
7.54
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NOTES AND CORRESPONDENCE
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FIG. 2. The mean and 95% confidence interval of the annual precipitation totals for the
five station–gridpoint pairs (see Fig. 1 for locations).
Because substantial differences in the distances between the gridpoints and their nearest-neighbor station
exist (from 1.1 to 90.7 km), it is not appropriate to
perform a one-to-one station–gridpoint comparison. As
a result, contour maps were created over the region to
show the spatial patterns and magnitude differences between the gridded and point datasets. To create the
contour maps, the return-period statistics (not the daily
precipitation values) were interpolated to the same grid
as the URD, similar to the kriging of trends seen in
Gallego et al. (2006). A Delaunay linear triangulation
interpolation method (Isaaks and Srivastava 1989) was
used because it is a conservative, nonsmoothing interpolator (Robeson 1997).
4. Results
a. Station–gridpoint comparison
To determine how well the URD represents precipitation characteristics, means and confidence intervals
of the characteristics were calculated at these highquality stations and their nearest neighboring grid
point. Annual totals are very similar, although every
region has a gridpoint mean value that is slightly
smaller than that of the paired station (Fig. 2). The 95%
confidence intervals clearly reveal that the annual totals
of the stations and their nearest grid point are not significantly different.
The frequency of precipitation for the three precipitation classes clearly demonstrates the differences between the gridpoint and rain gauge data: the gridpoint
data have much higher frequency of light precipitation,
approximately the same frequency of moderate precipitation, and lower frequency of heavy precipitation (Fig.
3). Even though the magnitude of the frequencies differs across the five regions, the pattern of precipitation
frequency is consistent. For instance, at the southeast
station (Scottsburg, Indiana), the mean frequency of
light (ⱕ10 mm) precipitation is 19% in the rain gauge
data and 36% in the gridded data, but all locations show
a significant difference. The highest frequencies of light
precipitation were observed in the northeastern section
of the region for both the grid point and the station. For
heavy (ⱖ30 mm) precipitation frequencies, the largest
difference between grid point and rain gauge was in the
northwest (Clinton, Iowa), with all regions having a
smaller frequency of heavy precipitation in the gridded
data. The small confidence intervals for precipitation
frequency for all precipitation classes indicate that the
number and type of rain days at the stations and grid
points did not vary much from year to year. The differences between the annual maxima are much less than
those shown for frequency, but the values are noticeably greater at the stations than at the grid points (Fig.
4). The annual precipitation maxima at the grid points
are typically 10–20 mm less than those at the nearby
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FIG. 3. The mean and 95% confidence intervals for the bootstrapped values of the annual
frequency of (a) light precipitation (ⱕ10 mm), (b) moderate precipitation (10–30 mm), and (c)
heavy precipitation (ⱖ30 mm) for the five station–gridpoint pairs.
stations. Although in not all cases are the differences
statistically significant, all cases have profound differences.
b. Return periods
When comparing the 5-yr return periods at the stations with those at the grid points for the Gumbel distribution, nontrivial differences were observed (Fig. 5).
For the stations, daily totals for the 5-yr return period
are generally between 60 and 100 mm, but the values
for the URD grid points are smaller and range from
approximately 50 to 80 mm. The largest discrepancies
occur in the southern portion of the study area where
the largest daily maxima occur. This reveals that the
highest daily precipitation totals, which are most important in design, are severely reduced within the gridded data.
Similar patterns are seen in the longer return periods.
The evaluation of the 50-yr values from the Gumbel
distribution revealed much larger differences between
the station (100–140 mm) and gridded data (60–100
mm) return-period values, although the spatial patterns
are similar (Fig. 6). The typical difference between the
50-yr return-period values for the stations and the grid
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NOTES AND CORRESPONDENCE
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FIG. 4. The mean and 95% confidence intervals for the annual maximum of daily
precipitation (mm) for each station–gridpoint pair.
FIG. 5. Contour maps showing the 5-yr return-period values for daily precipitation totals calculated using the Gumbel form of the
GEV. Even at this short recurrence interval, the totals for the (a) stations are noticeably larger than those for the (b) grid points.
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FIG. 6. Contour maps showing the 50-yr return-period values for daily precipitation totals using the Gumbel distribution.
points is approximately 50 mm, which is a much bigger
difference than what was observed for the 5-yr return
periods. All return periods from 5 to 50 yr (10 and 25 yr
were estimated but are not shown here) had higher
values for the station data than those of the URD, with
the differences increasing with increasing return-period
time frames. From the calculation of the return-period
values, it can be concluded that the gridding process
within the URD smoothed the precipitation values to
such an extent that the heavy and extreme daily precipitation totals became much lower, producing returnperiod totals that are far smaller than the rain gauge
data.
5. Summary and conclusions
The gridding of daily precipitation, especially by
means of a smoothing procedure, can tremendously influence the characteristics of precipitation such as precipitation frequency and extreme events (Robeson and
Ensor 2006). When compared with nearby rain gauge
data, the URD daily precipitation data, which were created using a modified Cressman scheme, illustrate the
changes that occur in the distribution of daily precipitation data. Although annual totals are similar between
station data and the URD grid points, the precipitation
frequencies for low-precipitation events—as well as ex-
treme values—are vastly different. The gridding procedure results in a precipitation probability distribution
that has precipitation on many more days, but those
days have less precipitation occurring. In comparison
with rain gauge data, the spatially variable and discontinuous nature of daily precipitation is obscured when
many stations are used in the calculation of a gridpoint
value. To some extent, this reduction in variability is a
natural outcome of the URD being more like an areally
averaged precipitation product than a point-precipitation product, but these changes can be especially critical if the URD is used for applications that require
accurate extreme values. For 50-yr return periods, the
extreme values within the URD were reduced by up to
50 mm from those seen in the station data.
The large distribution differences between the station and URD data are attributed to the use of multiple
stations and the inherent smoothing produced by the
method of spatial interpolation (Robeson and Ensor
2006). Other methods can be implemented that will
produce gridded daily precipitation data that are more
similar to daily station observations. One promising approach is indicator kriging (Isaaks and Srivastava 1989).
Indicator kriging is used to interpolate occurrence
(value of “1”) and nonoccurrence (value of “0”) across
the grid (Jolly et al. 2005). An interpolated value of
approximately 0.5 and above (although this number can
SEPTEMBER 2008
NOTES AND CORRESPONDENCE
vary) is considered a rain day. Only the grid points
designated as rain days have a precipitation total subsequently calculated for that day. This same technique
can be used with interpolation methods other than kriging (Thornton et al. 1997).
Several methods also have been proposed to reduce
the problem of decreased variability within the gridded
datasets—in particular, to solve the problem of reduced
maximum values. One of these methods, which also
reduces the high precipitation frequencies, is to change
the radius of influence based on the synoptic feature
producing that day’s precipitation (Hewitson and
Crane 2005). The synoptic types that produce localized
or heavier amounts are gridded using a smaller radius
of influence than the radius used for large-scale produced precipitation. For midlatitude areas, convective
(summer) precipitation would be gridded with a much
smaller radius than synoptic-scale systems that occur
more frequently in the winter. Although this approach
would still produce some smoothing, heavier, more localized events would not be reduced in magnitude to
the extent seen in the URD. Gridded daily precipitation datasets can benefit climate studies in many ways,
especially in the uniformity of their data coverage. It is
critical, however, to understand the differences that
spatial interpolation methods produce in gridded data.
Smoothing nearly always occurs when gridding precipitation fields, but excessive smoothing can result in precipitation characteristics that are very different from
the original observations. This is especially true during
seasons with highly localized precipitation events and
for grid points with numerous nearby stations. When
the number of stations near a grid point changes with
time, as they do with the URD, the degree of smoothing and resulting statistical distribution also can be time
varying. Although long-term totals (averages) are
shown to be similar in both station and gridded
datasets, the characteristics that compose the distribution of daily totals—such as frequency and extreme
events—are very different. When the differences between gridded and rain gauge data are known and understood, gridded datasets still can be useful tools for a
wide range of studies in applied climatology.
Acknowledgments. The authors are grateful to the
three anonymous reviewers and Dr. Art DeGaetano
for their constructive comments and suggestions.
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