Effect of data coverage on the estimation of mean and variability of precipitation at global and regional scales

JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 534 546, doi:10.1002/jgrd.50118, 2013 Effect of data coverage on the estimation of mean and variability of precipitation at global and regional scales Hui Wan, 1 Xuebin Zhang, 1 Francis W. Zwiers, 2 and Hideo Shiogama 3 Received 30 July 2012; revised 6 November 2012; accepted 16 December 2012; published 30 January 2013. [1] We use monthly precipitation simulated by a high-resolution global climate model (the MIROC4h) to examine the effects of spatial and temporal coverage on the estimation of mean, trend, and variability of precipitation for large land regions and the global land area. We consider spatial and temporal coverage typical of publicly available precipitation data sets of in situ station observations. We find that the spatial coverage of these data sets is not sufficient for the estimation of total precipitation for the global and hemispheric land areas and for some large regions considered. Estimates of global and hemispheric total land precipitation tend to be biased to higher values due to undersampling in low precipitation regions. The existing station coverage may nevertheless provide reasonable estimates for the magnitude of trend and variability in global to regional land area mean precipitation. However, the incomplete spatial coverage of the observational records results in larger sampling errors in trend estimates, making it harder to detect statistically significant trends. Publicly available gridded precipitation data that are based on larger collection of stations (all of which are not publicly available) may provide a better alternative for the time being. Citation: Wan, H., X. Zhang, F. W. Zwiers, and H. Shiogama (2013), Effect of data coverage on the estimation of mean and variability of precipitation at global and regional scales, J. Geophys. Res. Atmos., 118, 534 546, doi:10.1002/jgrd.50118. 1. Introduction [2] Precipitation plays a vital role in both human and natural systems. Too much or too little precipitation both cause adverse impacts. Quantification of the amount of precipitation is essential for understanding the hydrological cycle. In addition, it is important to know how precipitation amount has changed and how it will change in the future. Yet, it is difficult to accurately quantify precipitation amount at global and hemispheric scales, and sometimes even at regional scales, due to high precipitation variability in both time and space and due to the limited availability of precipitation observations. [3] Station measurements of precipitation have been made for more than a century in some countries. The availability of observed precipitation data is not uniform in space or in time and is very sparse over much of the global land area. The Global Historical Climatology Network-Monthly (GHCN-M) data set [Peterson and Vose, 1997] is the only publicly available in situ precipitation data set that has global coverage. This data set contains observation records for >20,000 stations. Records for many stations are very 1 Climate Research Division, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada. 2 Pacific Climate Impacts Consortium, University of Victoria, Victoria, British Columbia, Canada. 3 National Institute for Environmental Studies, Tsukuba, Japan. Corresponding author: X. Zhang, Climate Research Division, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada. (Xuebin.Zhang@ec.gc.ca) 2013. American Geophysical Union. All Rights Reserved. 2169-897X/13/jgrd.50118 short, with only about a third of stations having records longer than 30 years. There has been a substantial change in station densityinbothspaceandtime.thenumberofstationsis largest in the 1970s and is lower in the early part of the 20 th century and in recent decades. The number of available stations has been sharply reduced since the 1990s because of reductions in the number of observing stations, the lack of real-time exchange of station data through the Global Telecommunication System (GTS), and the long-time delay in submitting data to global data centers for inclusion in the global data sets. [4] Two types of precipitation analysis products have been produced based on station observations. One type of products uses as large a number of stations as possible and sometimes also includes data from stations that are not publically available to provide maximum spatial coverage. These include the Global Precipitation Climatology Project (GPCP) [Adler et al., 2003], NOAA s Climate Prediction Center precipitation analyses [e.g., Xie and Arkin, 1997], and the more recent Global Precipitation Climatology Centre (GPCC) Full Data Reanalysis Data set that used GHCN-M stations and many additional stations that the GPCC collected [Becker et al., 2012]. [5] Another type of product uses only long-term station data, with the aim that the products would be more suitable for trend analysis. These include the gridded data sets by Willmott et al. [1994], Hulme et al. [1998], Beck et al. [2005], and Zhang et al. [2007]. A typical gridding approach involves several steps including the following: (1) Selecting stations with at least 20 25 years of data during a common base period (i.e., 1961 1990) as long-term stations; 534

(2) Computing monthly precipitation climatologies for these long-term stations for the base period; (3) Subtracting the climatologies from the station data; and (4) Gridding the resulting anomalies using various spatial interpolation methods. [6] The Climate Research Unit of the University of East Anglia produced gridded monthly precipitation anomalies on a 5 5 latitude and longitude grid using an earlier version of GHCN data as input [Hulme et al., 1998]. They used Thiessen polygon weights to average gauge data within each grid box. Where a monthly station value was missing, an estimate was obtained by interpolation of data from surrounding stations if there were at least two stations within a 600-km radius with valid data. Zhang et al. [2007] also produced a gridded monthly precipitation anomalies data set on the same 5 5 grid. They used a simple interpolation scheme that averaged monthly precipitation anomalies from all available long-term GHCN stations within the grid box. NOAA s National Climate Data Center (NCDC) used a similar approach to produce their gridded monthly precipitation data set, also on a 5 5 grid. The main difference between the Zhang et al. [2007] and NCDC data set is in the number of missing values allowed in the base period. Zhang et al. [2007] included stations that had at least 25 years of data in the 30-year base period, whereas NCDC has a more relaxed rule, requiring only 20 years of data during the 30-year base period. Because similar GHCN data sets have been used and because a minimum number of years of data within a common base period is required for a station to be included in the calculation of gridded data products, the Hulme et al. [1998], Zhang et al. [2007], and NCDC data products are all based on similar long-term station records. As a result, the differences between these data sets are small. [7] The GPCC also produced a gridded data set, VASClimO [Beck et al., 2005], for trend analysis. This data set is based on 9343 long-term stations from the GHCN data set and from GPCC s own collection. The data set consists of gridded monthly precipitation anomalies at the 0.5 0.5 to 2.5 2.5 resolutions from 1951 to 2000. To reduce inhomogeneity caused by changes in station coverage, the criteria for the inclusion of a station in their analysis were quite strict: only those stations with <10% missing values during 1951 2000 and that did not have an obvious inhomogeneity were used in the production of VASClimO. The resulting station density for Germany, France, and the United States is very high, but it is sparse in other parts of the world. It has been hoped that these gridded data sets would be suitable for regional and global trend analysis. However, the question of how suitable they are for this purpose analysis remains. In particular, the impact of incomplete data coverage in both space and time on trend estimates at different spatial scales is unclear. [8] The effect of changes in observational coverage on temperature trend estimates has been carefully assessed using observational data alone [e.g., Jones et al., 1986a, 1986b, 2012; Hansen and Lebedeff, 1987; Brohan et al., 2006] and by using climate model output in combination with observations [e.g., Karl et al., 1994; Jones et al., 1997; Duffy et al., 2001]. An advantage of using climate model simulations is that the effect of imperfect spatiotemporal data coverage can be assessed against fields with full spatial and temporal coverage. For example, Madden et al. [1993] used simulations produced with an early version of the National Center for Atmospheric Research Community Climate Model to empirically determine the impact of imperfect spatial and temporal sampling on global mean surface air temperature estimates. Karl et al. [1994] assessed uncertainties in global and hemispheric temperature trends resulting from inadequate spatial sampling. They found that the uncertainty in calculating historical temperature trends is dependent on the pattern of temperature change, the method of treating the effect of nonrandom spatial sampling, and the time and length over which the trend is estimated. They also found that estimates of historical temperature trends are relatively insensitive to the random errors associated with estimating grid-scale temperature anomalies. Jones et al. [1997] also investigated sampling errors in large-scale temperature averages. They considered the spatial density of the observations (the number of sites within a grid box) and their statistical properties (correlation among data records and temporal variability of station data). Duffy et al. [2001] estimated possible bias in estimates of the Earth s surface temperature change in the 20 th century due to large changes in the coverage of surface temperature measurements. All of these studies used climate model simulations to compare spatial averages from complete fields with spatial averages from fields masked by the spatial and temporal coverage of the observed data. Similar studies for precipitation, that is, the effect of spatial sampling on precipitation trend, are lacking. [9] For temperature, there has also been systematic study of the spatial representativeness (i.e., spatial covariance structure) of temperature observations that have been timeaveraged over periods of different lengths [e.g., North et al., 2011] and consequently the observational density required to well estimate temporal variations in time-averaged regional means [North et al., 1992]. A key finding from this work is that longer time averages (e.g., decadal means vs. annual means or monthly means) have stronger spatial covariance and therefore that a global or regional mean decadal temperature anomaly can be reliably estimated with fewer stations than a corresponding global or regional mean annual or monthly temperature anomaly. A similar understanding of the reliability of estimates of precipitation anomalies on different space and time scales is limited. For example, Hofstra and New [2009] and Osborn and Hulme [1997] examined the correlation decay distance of daily precipitation, and Dai et al. [1997] considered this question for monthly precipitation. However, substantially more should be done to fully explore the spatial variability of precipitation correlation decay lengths from data with different amounts of time averaging. [10] The main objective of this study is to examine how the coverage of the publicly available in situ precipitation data affects the estimation of various aspects of precipitation, including regional and global total precipitation, spatial correlation length as a function of time averaging, and trend estimates. For this purpose, we will use precipitation simulated by a high-resolution global climate model (GCM) as a proxy for spatially and temporally complete observations. The remainder of the article is organized as follows: 535

Sections 2 and 3 describe the data sets and methods we use. Section 4 reports our results followed by conclusions and discussion in Section 5. 2. Data [11] This study uses two types of precipitation data sets. One consists of long-term simulations of precipitation conducted by a GCM as a proxy for spatially and temporally complete observations. For this purpose, the spatial resolution of the GCM should be as high as possible so that the model simulated variability in both space and time are comparable to that in the observations. Another is a data set of precipitation measurements that represents publicly available in situ historical precipitation data. These data sets are described in the following two subsections. 2.1. High-Resolution Precipitation Simulated by a GCM [12] The Atmosphere and Ocean Research Institute of the University of Tokyo, the National Institute for Environmental Studies (NIES), and the Japan Agency for Marine-Earth Science and Technology have jointly developed a new high-resolution GCM, the MIROC4h [Sakamoto et al., 2012]. The atmospheric component of this model has a horizontal resolution of ~60 km (T213) with 56 vertical levels (the model top is at ~40 km). The ocean component has a horizontal resolution of 0.28125 zonally and 0.1875 meridionally, with 47 vertical levels. [13] The MIROC4h model has been used to produce a three-member ensemble of historical simulations for 1950 2005. These simulations are forced with the effects of estimated historical changes in greenhouse gases, sulfate aerosols, black and organic carbon aerosols, tropospheric and stratospheric ozone, land use, and also natural external forcing, including volcanic aerosols and solar irradiance change. The model also has a 100-year preindustrial control simulation run under 1850 conditions to mimic the preindustrial era climate. The model shows virtually no drift in global mean surface temperature [Figure 2a of Sakamoto et al., 2012], but top-of-the-atmosphere outgoing radiation flux is negative [Figure 2b of Sakamoto et al., 2012], which contributes to a warming drift in the deep ocean [Sakamoto et al., 2012]. [14] The high atmospheric resolution allows the model to reproduce the main features of the global precipitation climate reasonably well [Sakamoto et al., 2012]. In particular, the global geographical distribution of heavy rain (>50 mm/day) frequency is well simulated [Figure 12 of Sakamoto et al., 2012]. Also, in the East Asian regions, the frequency distributions of daily precipitation events are in good agreement with GPCP from weak to heavy rainfall events [Figure 13 of Sakamoto et al., 2012]. Figure 1 shows Figure 1. Daily precipitation amounts averaged from in situ station observations and from the third MIROC4h historical simulation over regions centered on Vancouver, British Columbia, Canada that are ~1 grid box, 3 3 grid boxes, 5 5 grid boxes, and 7 7 grid boxes in size for the period 1973 1974. See text for details. 536

daily precipitation amount averaged from in situ station observations and from MIROC4h simulations over regions centered on Vancouver, British Columbia, Canada, which are 1 grid box, 3 3 grid boxes, 5 5 grid boxes, and 7 7 grid boxes in size for the period 1973 1974 during which the observational density is the greatest. The average number of stations in the nested regions is 40, 133, 160, and 196, respectively. It appears that MIROC4h oversimulates the magnitude of daily extremes a bit. This is consistent with Wehner et al. [2010], who showed that, at the 60-km resolution, an atmosphere-ocean GCM was able to simulate extreme rainfall that was at least as intense as observations on the same mesh over the relatively densely observed continental United States. Note also that the model seems to be able to simulate multiday dry sequences without any precipitation that are similar to those seen in observations. Additional analysis comparing model simulated and observed precipitation variability is reported below. However, it does appear that the model simulated precipitation is suitable for our application, at least in midlatitudes. 2.2. Historical Data [15] The GHCN-M data set contains historical temperature, precipitation, and pressure data for thousands of land stations worldwide. The GHCN-M precipitation data set consists of raw and homogeneity-adjusted global monthly total precipitation observations for more than 20,000 stations, with some stations having data for more than a century [Peterson and Vose, 1997]. The data are collected and maintained at the NOAA s National Climatic Data Center (NCDC). It is the main source of publicly available in situ precipitation measurements over the global land area. It is used operationally by NCDC to monitor long-term trends in precipitation and has been employed directly or indirectly in several international climate change assessments. Subsets of long-term station data have also been used in detection and attribution number of grid boxes 10000 9000 8000 7000 6000 5000 4000 3000 2000 1000 All Masked Long-term Masked 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 year Figure 2. Number of MIROC4h grid boxes in each year that contain monthly reports from at least one GHCN-M station (black; All ), at least one GHCN-M station that has at least 25-year data in the 1961 1990 base period (blue; Masked ), and at least one GHCN-M Masked station before 1950 (red; Long-term Masked ). studies [e.g., Zhang et al., 2007; Noake et al., 2012; Polson et al., 2012]. The number of stations available in the data set varies substantially depending on the year of interest. Other global precipitation data sets such as that compiled by the GPCC have similar changes in the number of stations over time. [16] Figure 2 shows annual time series of the number of the MIROC4h land grid boxes that contain at least one GHCN-M station from 1901 to 2010. The number of the grid boxes varies from year to year. It, starts at ~3500 boxes in the 1900s and increases to slightly over 9000 boxes in 1970 before declining with two sharp decreases in the early 1990s and in 2006. The changes in the number of available stations mainly reflect reductions in observational data. The recent reductions are primarily due to switching from the use of world climate records that are published every decade to the use of the data exchanged through the GTS [Peterson and Vose, 1997]. The number of stations used in other global precipitation data sets, such as the GPCC Full Data Reanalysis Version 6 [Becker et al., 2012], has similar changes over time, although the number of available stations is much higher. Changes in the number of long-term stations (defined as stations with at least 25-year data in the 1961 1990 base period) are slightly more muted; there were ~3500 grid boxes from the 1930s to 1990s, although the availability of data records from those long-term station has also been much reduced in recent years due to the reduction in network density and to the lack of timely exchange of the station observations. [17] Observational coverage over space also has a large variation. Figure 3 displays the model grid boxes within which there was at least one annual value from a station. Relatively dense coverage was available only over the United States, Europe, and parts of Asia and Australia in the 1900s. Spatial coverage was much improved in the mid-1970s, although there was still a lack of spatial coverage over large regions such as part of North Africa. Since 2005, spatial coverage has been poorer than in the 1900s over many parts of the world. For example, there are only 30 50 Canadian stations after 2005 largely because the GHCN-M has not captured data from all available Canadian stations. In this study, we use the publicly available adjusted Canadian precipitation data [Mekis and Vincent, 2011] to replace those in the GHCN-M to improve coverage over Canada, but we have not been able to similarly augment coverage elsewhere. [18] We use the GHCN-M data combined with the Adjusted Canadian Precipitation Data to produce two monthly masks, indicating the availability of observational data for the model grids for 1901 2010: (1) Masked represents all available long-term observational data: In this case, a given month and given grid box is marked as having an observation if one or more monthly means from long-term stations were available for that month in that grid box. (2) Long-term Masked represents long-term stations that also have some records in the early half of the 20 th century: A given month in the Masked data set is set to missing if there was no observation (i.e., a report of monthly mean) in the grid box in that month between 1926 and1950. 537

1901 1975 2005 Figure 3. Spatial distribution of 60-km grid boxes within which long-term GHCN-M precipitation stations are available in years 1901, 1975, and 2005. [19] Some grid boxes may have more than 50 stations (e.g., a grid box in Costa Rica), but the majority of grid boxes have very few stations. For example, of all grid boxes that have observations, 69.5% have only one station, whereas only 14.0% and 6% have two and three stations, respectively. An implicit assumption we make is that monthly mean precipitation from available observations within a grid box is representative of the grid box scale. This does not seem to be a problem for grid boxes with multiple stations. As we will see later, in many model grid boxes, the standard deviation of annual precipitation is generally comparable between the simulations and the observations. Nevertheless, the observations tend to have higher variability overall. This means that trend estimates based on observations would have higher uncertainty than the trend uncertainties reported in this article, which are based on MIROC4h observational proxies. 3. Methods 3.1. Area Mean and Spatial Correlation [20] We use the 100-year preindustrial control simulation to assess whether the available spatial coverage of station observations is sufficient for the estimation of global or regional total precipitation for water budget analysis. For this purpose, we first average annual total precipitation amounts across the globe (or a region) for all GCM land grid boxes using area weighting. We then use the observations to mask the control simulation by matching the series such that retained coverage of the first year of the control simulation corresponds to that of the observations in 1901; model values are set to missing in grid boxes in which there were no observations. This is repeated for each year such that grid boxes are missing where observations are unavailable in each year. This masked data set is then averaged across space for all nonmissing grid boxes, again using area weighting, for every year. [21] We also compute the correlation in the seasonal and annual total precipitation between a pair of model grid boxes within each 10 latitude band. Additionally, following North et al., 2011 for temperature, we also compute correlations on time averages with 2-, 5- and 10-year moving windows to investigate if longer time averages (e.g., decadal means vs. annual means or monthly means) have stronger spatial covariance and therefore if global or regional average decadal mean precipitation anomalies can be reliably estimated with fewer stations than a corresponding global or regional average annual mean or monthly mean precipitation anomaly. 3.2. Uncertainty in Trend Estimate [22] The effect of changes in spatial coverage on trend estimation is quantified by comparing estimated linear trends based on the Thiel-Sen method [Zhang et al., 2000] from the data sets that have perfect spatial and temporal coverage with those from data sets that have the coverage of the observations. For this purpose, we combine MIROC4h simulated responses to historical forcing and preindustrial simulations to generate multiple realizations of precipitation data with known trend. The trend was specified to be the trend that was estimated from the ensemble mean of the historical climate simulations. The sequence of steps used to assess uncertainty in trend estimates is as follows: (1) Monthly values of the ensemble mean of the three historical simulations are calculated for every grid box. A linear trend is then estimated from these monthly values using the Thiel-Sen method for every grid box and for every month of the year; these estimated trends are used to represent the simulated precipitation response to external forcing. As the ensemble mean has smaller natural variability, trends estimated from the ensemble mean have smaller uncertainty. (2) Linear trend that may be present in the monthly values of the 100-year preindustrial control simulation is removed for every grid box, and the residual is used to represent model simulated variability in monthly mean precipitation. Trends are only removed as a precaution because, as noted previously, MIROC4h has very little drift in its surface climate. (3) The detrended preindustrial control simulation is divided into 20 nonoverlapping 5-year blocks. We then draw twenty-two 5-year blocks (with replacement) to form 110-year data records to cover the period 1901 2010 of the historical data. A substantial fraction of model produced interannual variability on subdecadal 538

time scales is maintained in this randomized series, including variability on the El Niño Southern Oscillation timescale, which the model simulates quite well [Sakamoto et al., 2012]. (4) The model simulated linear trends estimated from step (1) are extrapolated to cover 110 years and are then added to the noise data from step (3) to produce a 110-year data set with complete spatial and temporal coverage and externally forced trend. We refer this as the Perfect data set. Steps (3) and (4) are repeated for 1000 times to produce 1000 realizations of the data set. (5) For each realization, two additional data sets are produced to mimic the availability of station observations by setting the monthly grid box values as missing according to the Masked and Long-term Masked data masks described in Subsection 2.1. (6) The Perfect, Masked, and Long-term Masked data sets are interpolated onto the 5 5 latitude-longitude observational grid by averaging monthly precipitation anomalies relative to 1961 1990 mean values. (7) Time series for the area averages of annual precipitation anomalies are computed from each data set for the global land area, the Northern Hemisphere and the Southern Hemisphere land areas, 21 Giorgi-type regions [Giorgi and Francisco, 2000] as defined in Zwiers et al. [2011], and eleven 10 latitudinal bands from 40 Sto 70 N over land based on the 5 5 grid box values. Linear trends based on the nonparametric Thiel-Sen slope estimator [Zhang et al., 2000] are computed for those regional mean time series for the 100-, 75-, and 50-year periods ending in 2000. Trends were also computed for the 110- and 60-year periods ending in 2010 to examine how the additional data from the first decade of 21 st century, for which spatial coverage is very poor, would affect trend estimation at century and half-century scales. 4. Results 4.1. Regional and Global Mean [23] Figure 4 shows global and hemispheric averages of annual precipitation amount and annual precipitation anomalies relative to the model year 1961-1990 mean in the control simulation. It is clear that averages of annual precipitation for land areas over the globe and the Northern Hemisphere and Southern Hemisphere estimated from the grid boxes with observational coverage are too large. This means that estimates of total precipitation amount over the global and hemispheric land areas obtained by area weighted averages of in situ station observations would be biased too high. More sophisticated spatial averaging methods could improve the results, but the improvement would still be limited by the information available from the data set. Additionally, the time variation of the average series from full coverage ( Perfect ) and from only partial coverage ( Masked or Long-term Masked ) can be very different, suggesting that time series obtained by simply averaging the total amount of precipitation from available stations would reflect precipitation variations and, to a larger extent, temporal changes in spatial coverage of observations as well. Thus, such a series would not be suitable for the estimation of trends and variability. Similar behavior was found for surface Globe Northern Hemisphere Southern Hemisphere Figure 4. Global and hemispheric averages of annual mean precipitation and annual mean precipitation anomalies from the 100-year preindustrial control simulation. Red, average of total precipitation with full spatial and temporal coverage (the Perfect data set); gray, average of total precipitation from grid boxes that have at least one observation (the Masked data set); green, average of total precipitation only from grid boxes that have long-term observations (the Long-term Masked data set); blue, average of annual precipitation anomalies relative to 1961 1990 mean with full spatial coverage; purple, average of annual precipitation anomalies based on the Masked data set. temperature observations [Jones et al., 1982]. On the other hand, the anomaly series averaged from data with full coverage are not much different from those averaged only from the areas with observations. This means that, at the global and hemispheric scales, anomaly series may provide reasonable estimates of trend and variability. [24] Results for the Giorgi regions and for 10 latitudinal bands are listed in Table 1. The bias from imperfect observational coverage is relatively small in many regions, indicating that existing observations could provide reasonable estimates of total precipitation in these regions. 539

However, the variance of the regional series computed from averaged total precipitation is too high if there is less than full spatial coverage. Correlations between series derived from full and partial coverage are often small. This means that simply averaging total precipitation from observations will produce time series influenced by the availability of observations even in regions with sufficient data to make reasonable estimates of total precipitation. From the lower southern latitudes to lower-middle northern latitudes where both very wet and very dry climates are found, the use of existing observations to estimate regional total precipitation would result in fairly large biases. However, even in these regions, the anomaly series are little affected by changes in spatial coverage and therefore can still be used to estimate precipitation variability. Similar results were found for temperature [e.g., Jones et al., 1986a, 1986b]. 4.2. Correlation Decay Lengths [25] Figure 5 displays the correlation coefficients of annual or seasonal precipitation as a function of distance between land-only grid boxes within 10 latitudinal bands. The curves are plotted through the median correlation values obtained for pairs of grid boxes with separations that fall within 20-km intervals and the correlation decay length is defined as the distance where the curve has a correlation of 1/e [Hofstra and New, 2009]. It appears that correlation distances are larger in middle to high latitudes and lower in the low latitudes, similar to those reported in Dai et al. [1997] for the observations. Correlation distance is also higher for the Northern or Austral winters than for the annual mean or other seasons, which reflects the large-scale nature of winter circulation. The difference in the correlation decay lengths between the tropics and extra-tropics is of similar magnitude to the difference between those of warm and cold seasons. Note that, in contrast to temperature [e.g., North et al., 2011] for which longer time averages have greater correlation decay length, time averaging produces little impact on the correlation decay lengths for precipitation. This means that, in the event of incomplete spatial coverage, estimates of global or regional mean decadal precipitation anomalies may not be any more reliable than corresponding annual or monthly mean precipitation anomalies. Table 1. Comparison of the Mean and Variance and the Correlation Coefficients Computed From Series With Full Coverage and From Series With the Observational Coverage a Mean Variance Correlation All Mask All Mask Region 100 yr 100 yr 30 yr 30 yr All Mask Ano All Mask Ano GLB 18 14 17 15 6.28 3.61 0.88 0.23 0.31 0.85 NH 14 14 10 11 14.35 7.47 1.10 0.05 0.19 0.89 SH 30 21 36 29 5.44 6.71 1.01 0.45 0.35 0.90 ALA 12 19 5 8 2.24 2.97 0.89 0.40 0.32 0.90 CGI 35 35 28 27 7.60 9.38 1.10 0.21 0.13 0.62 WNA 4 4 1 1 1.76 2.00 1.07 0.76 0.73 0.97 CAN 2 3 0 0 1.26 1.37 1.08 0.94 0.92 0.99 ENA 3 4 2 2 1.37 1.32 1.10 0.91 0.89 0.98 CAM 6 3 7 4 1.56 1.40 1.15 0.82 0.80 0.91 AMZ 2 0 3 1 1.29 2.89 0.67 0.76 0.47 0.86 SSA 1 0 3 5 2.03 2.23 0.92 0.49 0.47 0.81 NEU 2 1 2 1 1.03 1.04 1.09 0.99 0.99 1.00 SEU 3 8 6 9 1.60 1.33 1.12 0.88 0.91 0.97 SAR 16 10 11 4 1.83 0.87 0.39 0.65 0.52 0.78 WAF 1 0 0 0 3.95 3.17 0.98 0.53 0.52 0.89 EAF 16 16 16 16 2.25 2.36 0.87 0.65 0.63 0.91 SAF 2 2 3 2 1.53 1.34 1.26 0.88 0.89 0.95 NAS 3 4 4 5 1.71 1.70 1.15 0.80 0.77 0.89 CAS 10 11 5 6 1.95 1.78 0.86 0.67 0.69 0.91 TIB 13 10 4 3 7.39 6.32 1.68 0.39 0.43 0.76 EAS 6 7 1 1 3.32 3.61 1.10 0.61 0.59 0.90 SAS 0 0-1 -1 1.81 2.06 1.30 0.76 0.66 0.87 SEA 5-2 10 3 3.33 3.16 0.54 0.58 0.52 0.79 AUS 3 3 3 3 0.95 0.93 0.94 0.98 0.98 0.99 40S -2-3 2 3 1.76 2.20 1.20 0.81 0.69 0.96 30S 1-2 2 0 1.27 1.30 1.09 0.85 0.85 0.93 20S 0-1 2 0 1.71 1.35 1.00 0.79 0.83 0.92 10S 4-4 8 3 2.84 3.38 0.65 0.45 0.26 0.75 0N 3 5 3 4 2.00 3.37 0.89 0.66 0.55 0.81 10N 16 10 10 8 6.30 4.00 1.30 0.24 0.34 0.87 20N 28 39 24 32 11.46 7.49 1.35 0.32 0.36 0.86 30N 10 15 7 10 2.00 2.46 1.12 0.77 0.73 0.93 40N 9 8 2 1 5.88 5.63 1.09 0.45 0.45 0.96 50N 0 0 0 0 1.81 1.63 1.06 0.86 0.89 0.95 60N 7 8 3 3 3.19 3.58 1.03 0.26 0.24 0.84 a The mean is expressed as the percentage difference relative to complete spatial coverage, whereas the variance is expressed as a ratio to the variance of complete coverage. All, all available records are used; Mask, only the Masked data set is used; Ano, anomaly relative to 1961 1990 base period mean. 100 yr and 30 yr indicate long-term averages are computed from 100 and 30 years of data, respectively. 540

(a) 60-70 N (b) 40-50 N (c) 20-30 N (d) 0-10 N (e) 20S -10 S (f) 40-30 S Figure 5. Correlation between pairs of grid boxes in the MIROC4h control run as a function of separation distance. Curves are plotted through the median of correlation values obtained for pairs of grid boxes with separations that fall within 20-km intervals. Blue, 10-year moving average; purple, 5-year moving average; green, annual; red, DJF; orange, MAM; cyan, JJA; yellow, SON. 4.3. Variability in MIROC4h Simulations and Observations [26] Figure 6a shows the standard deviation in annual total precipitation at MIROC4h land grid boxes over North America for 1901 2010 computed from the observations and from the Masked pseudo-observations constructed from MIROC4h. The interannual variability in the model simulations and in the observations is in general comparable, although observed variability appears to be stronger, with the upper tail being more poorly represented. This does not necessarily mean that the MIROC4h simulated variability in its native grid is smaller than that in the real-world precipitation at the model resolution. Rather, it may be an indication that monthly precipitation observed at one station may not represent the grid box mean well because many model grid boxes contain only one station. MIROC4h simulated variability is somewhat more comparable with observations if the comparison is restricted to grid boxes that contain more than one station (Figure 6b). The lack of station density in other regions can be even more problematic. Figure 6c displays the standard deviation in annual total precipitation for the global land area at 5 5 resolution. The GCM generally reproduces the broad values of interannual variability in the observations. However, there is a tendency for model simulated variability to be too low which may be due, at least in part, to insufficient observational density. An implication of this undersimulation of observed variability is that the signal-to-noise ratio for externally forced signals would be lower in the observations than in the model simulated data if model precipitation sensitivity to warming Figure 6. Standard deviation of annual precipitation computed from GHCN-M and from the 1000 sets of pseudo-observations over (a) North America 60-km grid, (b) North America 60-km grid but where there are at least two stations within each grid box, and (c) global land on 5 5 grid. 541

is similar to that in the real world. As a result, trend estimates in the observations could be less robust than inferred from model based pseudo-observations as used in this article. WAN ET AL.: PRECIPITATION DATA SAMPLING 4.4. Precipitation Trends [27] Figure 7a displays box plots of trends in the annual precipitation anomalies averaged over global land areas from the Perfect, Masked, and Long-term Masked pseudo-observations constructed from MIROC4h over 100-, 75-, and 50-year periods. The median values of the trends are slightly smaller in the Perfect data than in the Masked or Long-term Masked data for the 100-year trend, suggesting that the estimates of global land precipitation changes based on existing observational data set may have a small but not significant bias. There is almost no difference in the median trends for the Masked and the Long-term Masked data. The interquantile ranges (difference between the 75 th and the 25 th percentiles) of trends from three data sets overlap, but the range is larger in the Masked and Long-term Masked data. This suggests that, although the bias in the trend estimate from existing observational data is small when compared with sampling error as represented by the difference between the 95 th and the 5 th percentile trends, uncertainty in trend estimates is larger due to reduced data coverage. The interquantile range also becomes larger with decreases in the length of the record used to estimate trends indicating larger sampling errors in trend estimates for shorter periods as expected. Results for the Northern Hemisphere and Southern Hemisphere land areas are shown in Figures 7b and 7c, respectively. The conclusion for global land precipitation trends hold for the hemispheric land precipitation. This includes higher median trends and larger interquantile ranges in the Masked and the Long-term Masked data. Note that the Southern Hemisphere land areas show much larger sampling errors due to smaller land areas. [28] Box plots of regional trends in the annual precipitation anomalies computed from the Perfect, Masked, and Long-term Masked pseudo-observations over 100-, 75-, and 50-year periods are displayed in Figure 8. For the 100-year period, the median trends from the Perfect data are different than those from the Masked or Long-term Masked data for several regions. This is especially the case for Alaska (ALA), where the 95 th percentile trend in the Perfect data lies below the 5 th percentile trend in the Masked and Long-term Masked data, and in the Sahara (SAR), where the 5 th percentile trend in the Perfect data lies above the 95 th percentile trend in the Masked and Longterm Masked data. These results suggest that trend estimates based on existing observations may not be representative of true precipitation trends in some regions. The bias for many other regions is small. For example, median trends for Eastern North America (ENA), Southern South America (SSA), Northern Europe (NEU), Western Africa (WFA), Northern Asia (NAS), Eastern Asia (EAS), Southeast Asia (SEA), and Australia (AUS) in the Perfect data are almost identical to those in the Masked and the Long-term Masked data. The 5 th and 95 th percentile trends do not include zero over many regions including ALA, Eastern Canada and Greenland (CGI), Central North America (CAN), ENA, NEU, NAS, CAS, Tibet (TIB), SEA, and AUS, suggesting that there is very high certainty about the direction of trends in these Figure 7. Box plots of trends in area-averaged annual precipitation anomalies over 100-, 75-, and 50-year periods for the globe (a), Northern Hemisphere (b), and Southern Hemisphere (c) land areas. Trends are estimated from the 1000 pseudo-observations with different spatial masking for data availability. The upper and lower ends of each box are drawn at the 75 th and the 25 th quantiles, the bar through each box is drawn at the median, and the whiskers are drawn at the 5 th and the 95 th quantiles. regions. Sampling errors are smaller in the Perfect data as well. The uncertainty in the trend estimates becomes increasingly large with the decrease in the length of periods. In the 75-year period, there is one less region in which the 5 th and the 95 th percentile trends do not include zero. In the 50-year period, the 5 th and the 95 th percentile trends exclude zero in only four regions (ALA, CGI, ENA, and NAS). This suggests that existing data sets may provide 542

Trend (mm/yr) a) 100-yr 3 2 1 0-1 Perfect -2 Masked Long-term Masked -3 ALA CGI WNA CNA ENA CAM AMZ SSA NEU SEU SAR WAF EAF SAF NAS CAS TIB EAS SAS SEA AUS Trend (mm/yr) Trend (mm/yr) b) 75-yr 3 2 1 0-1 Perfect -2 Masked Long-term Masked -3 ALA CGI WNA CNA ENA CAM AMZ SSA NEU SEU SAR WAF EAF SAF NAS CAS TIB EAS SAS SEA AUS c) 50-yr 3 2 1 0-1 Perfect -2 Masked Long-term Masked -3 ALA CGI WNA CNA ENA CAM AMZ SSA NEU SEU SAR WAF EAF SAF NAS CAS TIB EAS SAS SEA AUS Figure 8. Same as Figure 7, except for the Giorgi regions. reasonable estimates for the magnitude of long-term trends for large regions (although 100-year trends in ALA and SAR could be substantially biased) but that the possibility of detecting a significant trend is much reduced due to larger sampling errors associated with incomplete data coverage. [29] Figure 9 shows results for the trends in 10 zonal means. Overall, significant positive trend can be detected over northern high latitudes (50 N and higher) with 50 years of data, but the domain in which trends can be detected expands further south with a longer period. Drying in the northern tropics becomes more significant in the 75- and 100-year data sets. It appears that trends can be most consistently detected in regions in the high northern latitudes. Min et al. [2008] found that anthropogenic influence may have contributed to the moistening in this region. [30] Results for the two hemispheres, the regions, and the 10 zonal bands indicate that precipitation trends have strong regional characteristics and that positive and negative trends in different regions tend to cancel each other, resulting in a very small trend for the land precipitation as awhole(figure7a). [31] The root mean square error (RMSE) between the trends calculated from data sets of full spatial and temporal coverage and from data sets that mimic observational coverage from the 1000 bootstrap samples provides some measure of impact of the (lack of) data coverage on trend estimates. Figure 10 shows the RMSE in units of the standard deviation of 50-year trends estimated from the series with complete spatial and temporal coverage. Results indicate that (1) The ratios are typically <1 (with the exception of a couple of regions), suggesting that errors due to changes in spatial coverage in the trend estimate are, in general, smaller than sampling error due to 50-year time-scale natural variability. (2) The ratios for the longer-term 100-year period are generally smaller than that for the 50-year period (except for Central America and Mexico, and SSA), indicating that longer records, even with poorer spatial coverage, may still provide a better chance to detect change than shorter-term records with better spatial coverage. In Central America and Mexico, the SSA, additional years of data do not compensate for the effects of the reduction in the spatial coverage. (3) The additional data from the first decade of the 21 st century improve trend estimates in general despite reductions in coverage, although the improvement is small. This suggests again that longer data records seem to do better even if spatial coverage of the data is poorer. Thus, it seems to be useful to update trend analyses with more recent data. [32] The results for trends in zonal mean precipitation tell a similar story: errors in the trend estimates due to incomplete spatial coverage are smaller than sampling error, and trend estimates from longer records generally have slightly smaller 543

100-yr 75-yr 50-yr Figure 9. Same as Figure 8, but for trends in zonal mean annual precipitation anomalies. a. Masked and Long-term Masked data b. Masked Data ending in 2000 and in 2010 Figure 10. RMSEs of precipitation trends for different periods and spatial coverage expressed in the units of standard deviation of the 50-year precipitation trends calculated from 1000 sets of perfect pseudo-observations. RMSEs compare trend estimates from masked data sets with estimates from corresponding perfect data sets. Century and half-century periods of record are considered, and the influence of adding the most recent decade to both is also considered. errors than estimates from shorter periods (Figure 11). Observational data with space and time coverage better than GHCN-M would have smaller errors in trend estimates. Consequently, detection and attribution results [e.g., Zhang et al., 2007; Noake et al., 2012] could have been more robust if better data coverage were available. 544

a. Masked and Long-term Masked data b. Masked data ending in 2000 and in 2010 Figure 11. Same as Figure 10 but for zonal mean precipitation trends. 5. Conclusions and Discussion [33] The Japan NIES has produced high-resolution 20 th century simulations based on MIROC4h. These simulations reproduce the main climatological features of precipitation reasonably well [Sakamoto et al., 2012]. We use MIROC4h simulated monthly precipitation to examine the impacts of spatial and temporal coverage changes in publicly available in situ precipitation data sets on the estimation of mean, variance, and trend. We found that the existing publically available global station precipitation data set GHCN-M does not likely provide sufficient spatial coverage for the estimation of total precipitation over the global and hemispheric land areas and over some large regions. The data, if carefully averaged, may provide reasonable estimates for the magnitude of regional precipitation trends, although sampling uncertainty range becomes larger. Except in a few regions, including ALA, CGI, NEU, and NAS, a trend in regional mean precipitation series similar to that specified in our pseudo-observations would be difficult to detect over a 50-year period. The prospects of detecting a significant trend increase with longer periods, provided that the trend persists through the whole period as constructed in our pseudo-observations, and this appears to be the case even if the spatial coverage of data may have been reduced. The uncertainty ranges of 75- or 100-year trends are smaller than for the 50-year trends despite reduced spatial coverage of data. It is thus advisable to use as long data record as possible. [34] In many places of the world, monthly precipitation observed at a station may not be a reliable estimate of grid-cell average precipitation as simulated by MIROC4h. Additionally, MIROC4h has a relatively high temperature sensitivity. This means that the signal-to-noise ratio in MIROC4h simulated precipitation could potentially be higher than that in observations, although recent detection and attribution studies of observed changes in mean and extreme precipitation suggest the models simulate smaller than observed changes in response to historical external forcing [e.g., Zhang et al., 2007; Min et al., 2008, 2011]. Additionally, issues in the observational data such as those related to data homogeneity (e.g., the effects of changes in station locations or instruments) and/or measurement errors (e.g., undercatch of solid precipitation or changes in undercatch due to warming) [Mekis and Vincent, 2011] would hinder trend estimation as well. Therefore, uncertainty in trends estimate in the real world could be higher than reported here based on MIROC4h simulation. [35] It should be mentioned that our finding that global total precipitation estimate may have positive bias based on GHCN-M data due to undersampling in drier regions may be specific to this data set. The new data products from GPCC [Becker et al., 2012] that use additional station data that are not publically available should improve regional and global total precipitation estimates. As GPCC data product uses data from many more stations, one would expect better estimates of trends and variability from those data products, although this remains to be confirmed. [36] Acknowledgments. Comments from two anonymous reviewers helped improve the earlier version of this article. Assistance provided by Basil Veerman is also much appreciated. References Adler, R. F., et al. (2003), The version-2 global precipitation climatology project (GPCP) monthly precipitation analysis (1979-present), J. Hydrometeorol., 4, 1147 1167. Beck, C., J. Grieser, and B. Rudolf (2005), A New Monthly Precipitation Climatology for the Global Land Areas for the Period 1951 to 2000, in Climate Status Report 2004, pp. 181 190, German Weather Service, Offenbach, Germany. Becker, A., P. Finger, A. Meyer-Christoffer, B. Rudolf, K. Schamm, U. Schneider, and M. Ziese (2012), A description of the global land-surface precipitation data products of the Global Precipitation Climatology Centre with sample applications including centennial (trend) analysis from 1901-present, Earth Syst. Sci. Data Discuss., 5, 921 998. Brohan, P., J. J. Kennedy, I. Harris, S. F. B. Tett, and P. D. Jones (2006), Uncertainty estimates in regional and global observed temperature changes: a new dataset from 1850, J. Geophys. Res., 111, D12106, doi:10.1029/2005jd006548. Dai, A., I. Y. Fung, and A. D. Del Genio (1997), Surface observed global land precipitation variation during 1900-88, J. Climate, 10, 2943 2962. Duffy, P. B., C. Doutriaux, I. K. Fodor, and B. D. Santer (2001), Effect of missing data on estimates of near-surface temperature change since 1900, J. Climate, 14, 2809 2814. 545