Statistical Characteristics of Daily Precipitation - Climate and ...

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JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

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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;

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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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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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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

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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. REFERENCES Buishand, T. A., 1989: Statistics of extremes in climatology. Stat. Neerl., 43, 1–30. Chen, M., P. Xie, J. E. Janowiak, and P. A. Arkin, 2002: Global

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