An algorithm for integrating satellite precipitation ...

PUBLICATIONS Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE 10.1002/2014JD022788 Key Points: • A new algorithm for correcting biases in satellite precipitation estimates • A new algorithm for producing blended precipitation data on a pentad time scale • A high-quality blended pentad precipitation data set for Canada

Correspondence to: X. L. Wang, [email protected]

Citation: Wang, X. L., and A. Lin (2015), An algorithm for integrating satellite precipitation estimates with in situ precipitation data on a pentad time scale, J. Geophys. Res. Atmos., 120, doi:10.1002/2014JD022788. Received 30 OCT 2014 Accepted 4 APR 2015 Accepted article online 9 APR 2015

An algorithm for integrating satellite precipitation estimates with in situ precipitation data on a pentad time scale Xiaolan L. Wang1 and Achan Lin1 1

Climate Research Division, Science and Technology Branch, Environment Canada, Toronto, Ontario, Canada

Abstract This study proposes an algorithm for constructing pentad precipitation fields by integrating the popularly used Global Precipitation Climatology Project (GPCP) daily precipitation data set, GPCP1dd v1.2, with Canadian in situ daily precipitation data. This algorithm consists of two major steps. First, the GPCP data were adjusted to remove biases relative to the gauge data, with consideration of the differences between snowfall and rainfall, and of the gauge density. Then, a blended pentad precipitation field was constructed using the adjusted GPCP precipitation field and the differences between the gauge and adjusted GPCP precipitation fields (residual kriging). The skill of the algorithm is evaluated for three networks of sparse to medium gauge density, with the evaluation data set being much larger than the training data set. The results show that the algorithm produces better representation of pentad precipitation fields than the GPCP precipitation estimates or using the gauge data alone; it has smaller root-mean-square errors and higher correlation skill scores. This algorithm was used to produce the first blended pentad precipitation data set for the period of 1997–2007 for Canada (CanBP5dV1). It can be used for other regions around the world. 1. Introduction Precipitation is one of the key components of the hydrological climate system. It is of great societal importance, because it is closely related to freshwater supplies and extremes of potentially profound socioeconomic impacts such as flooding and droughts. It is essential to obtain high-quality estimates of the spatial distribution, amounts, and intensity of precipitation, which provide critical information on the hydrological cycle and water resources. A high-quality gridded precipitation data set is essential for global/regional climate model validation, for hydrological modeling and water resources management, for climate change and impact assessment studies, etc. Precipitation is highly variable over space and noncontinuous in time, which makes the observation and quantification of precipitation challenging. Gauge measurement of precipitation amount in an in situ network of gauge stations is the traditional way to obtain precipitation information, providing the most reliable point observations of precipitation. However, the gauge networks are often inadequate to capture all scales of precipitation over land, and the land-based observation gives little information over the ocean or waters. Satellites have been used to monitor land, ocean, and the atmosphere for more than 30 years, providing rich data pools. Satellite precipitation estimates (SPEs) provide better representation of the spatial variation of precipitation than in situ gauge data, especially for regions with sparsely distributed gauge stations. Combining SPEs with gauge data is a natural and economic choice to provide more realistic representation of the spatial pattern of precipitation. Thus, a number of merged (blended) precipitation data sets have been generated. A comprehensive list of precipitation data set information has been prepared by National Center for Atmospheric Research Staff [2014] and can be found at https:// climatedataguide.ucar.edu/climate-data/precipitation-data-sets-overview-comparison-table.

©2015. Her Majesty the Queen in Right of Canada. American Geophysical Union. Reproduced with the permission of the Minister of Environment. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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Canada has in situ observations of precipitation over the past 60 years or longer. However, the density of gauge stations is very sparse in northern Canada (north of 55°N), where the stations are typically 500–700 km apart. Such sparse gauge network makes it hardly possible to generate a reasonably representative gridded precipitation data set for Canada using in situ data alone, especially for higher temporal resolution. This motivated the study of Lin and Wang [2011], which developed an algorithm for integrating SPEs with gauge data on the monthly time scale and used it to produce a monthly blended precipitation data set for Canada (CanBPv0). They show that the resulting blended precipitation data set is more representative of the true monthly precipitation fields than the corresponding gridded precipitation data set generated from using the gauge data or the SPEs alone.

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In a northern country like Canada, both liquid and solid precipitation occurs. For both SPEs and gauge data, observational biases in rainfall and snowfall could be very different. However, such differences were not considered in Lin and Wang [2011], which focused on total precipitation only. In the present study, we aim to estimate and correct biases in the SPEs for rainfall and snowfall, separately, and to develop an algorithm for blending the bias-corrected SPEs with in situ gauge measurements of rainfall and snowfall on the pentad time scale to produce a high-quality pentad-blended precipitation data set for Canada. The rest of the article is structured as following. The data sets used in this study are described in section 2. The proposed algorithm is detailed in section 3; its performance is evaluated and discussed in section 4. Section 5 describes the characteristics of “biases” in the SPE rainfall and SPE snowfall data as decomposed from the version 1.2 Global Precipitation Climatology Project (GPCP) One-Degree Daily Data Set (GPCP1dd) [Huffman and Bolvin, 2013; Huffman et al., 2001, 2012], which is used as the original satellite precipitation estimates in this study. Section 6 compares our resulting blended analysis with the GPCP Pentad Data Set [Xie et al., 2003] and a Canadian gridded daily precipitation data set [Hutchinson et al., 2009]. Section 7 completes this study with concluding remarks.

2. Input Data Sets An in situ data set of daily rainfall and snowfall and a data set of daily SPEs are needed to carry out the research proposed in this study. The in situ gauge data itself are not necessarily the ground truth data. The observations often need to be corrected for systematic measuring errors, for example, wind-induced losses [Ungersböck et al., 2001]. Therefore, the in situ data set used in this study is the Canadian Adjusted Daily Rainfall and Snowfall Data Set version 2007, which is a carefully processed data set published on the Environment Canada Data Catalogue and the Canadian Government Open Data Portal (http://open.canada.ca/data/en/ dataset/d8616c52-a812-44ad-8754-7bcc0d8de305). As detailed in Xu [2012], the processing to produce this data set includes (i) conversion of snowfall to its water equivalent using the snow-water-equivalent ratio map for Canada developed by Mekis and Brown [2010]; (ii) corrections for gauge undercatch and evaporation due to wind effect, for gauge-specific wetting loss, and for trace precipitation amount using the procedure detailed in Mekis and Vincent [2011]; and (iii) treatment of flags (e.g., accumulation flags) following the procedure of Hutchinson et al. [2009]. This data set contains adjusted daily rainfall and snowfall data recorded at 2146 stations in Canada, with the record length varying from 3 to 167 years in the period of 1840–2007. The number of stations with data changes over time, with 302–924 stations in the period of 1950–1972, 1018–1408 stations in the period of 1973–1989, and 600–955 stations since 1998. As for SPE data, the Global Precipitation Climatology Project (GPCP), which was established by the World Climate Research Programme to quantify the distribution of precipitation around the globe over time, has developed/produced three combined precipitation data sets: the version 2 GPCP Monthly Satellite-Gauge Data Set [Adler et al., 2003], the GPCP Pentad Data Set [Xie et al., 2003], and the GPCP1dd [Huffman and Bolvin, 2013; Huffman et al., 2001, 2012]. The GPCP Pentad Data Set [Xie et al., 2003] is of a 2.5° resolution, although it covers the period since 1979. We need daily SPE data for the current study. Thus, we chose to use the GPCP1dd, which provides global 1° × 1° gridded fields of daily precipitation totals from October 1996 to near real time (updated with about 3 month delay) and is freely available online. The following five data sets were used to produce the GPCP1dd [Huffman and Bolvin, 2013]: 1. The GPROF (Goddard Profiling Algorithm) fractional occurrence of precipitation, retrieved from satellite-based passive microwave observations, the Special Sensor Microwave Imager, and Special Sensor Microwave Imager Sounder, using the multichannel physical approach GPROF. 2. The TIROS (Television Infrared Observation Satellite Program) Operational Vertical Sounder (TOVS) daily precipitation estimates of 1° spatial resolution. The data processing is described in Susskind and Pfaendtner [1989] and Susskind et al. [1997]. 3. The Atmospheric Infrared Sounder (AIRS) daily precipitation estimates of 1° spatial resolution, produced by the Satellite Research Team under the direction of J. Susskind located at NASA Goddard Space Flight Center’s Earth Sciences Division (Greenbelt, Maryland, USA).

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4. The GOES (Geosynchronous Operational Environmental Satellites) Precipitation Index (GPI) precipitation product, produced by the Geostationary Satellite Precipitation Data Centre of the GPCP under the direction of P. Xie located in the Climate Prediction Center, NOAA National Centers for Environmental Prediction (Washington D.C., USA). Since October 1996, the GPI data are accumulated on a 1° × 1° latitude-longitude grid for individual 3 hourly images. 5. The GPCP Version 2.2 Monthly Satellite-Gauge (SG) Combined Precipitation Data Set [Adler et al., 2003], which are monthly accumulations of precipitation on a 2.5° × 2.5° latitude-longitude grid, was used to calibrate the monthly values of the GPCP1dd values. In other words, the GPCP1dd values are calibrated to sum to the SG Combined Precipitation monthly values. There are large uncertainties in satellite precipitation estimates in high latitudes. First of all, passive microwave rainfall retrievals still have large biases over land. Second, Canada is entirely in the TOVS/AIRS domain in the GPCP1dd algorithm but is outside the boundaries of the recalibration of the TOVS/AIRS data to match the high-quality Threshold Matched Precipitation Index (TMPI) estimates. This implies larger errors in the TOVS/AIRS data over Canada. Despite being calibrated to monthly accumulations of precipitation derived using some gauge monthly data (as described above), the GPCP1dd data are referred to as the “original” satellite precipitation estimates in this study. Note that only data from a limited number of gauge stations (probably less than 300 stations) in Canada were used in producing the GPCP Monthly SG Data Set, because data from volunteer climate observing stations in Canada are not transmitted on the Global Telecommunication System and thus are not available internationally. A few studies on evaluation of the GPCP1dd for some regions have been published. For example, for the European Alps region, Rubel et al. [2002] showed that the GPCP1dd data have great accuracy on the monthly scale, but its daily precipitation values may still differ significantly from observations. For the United States, McPhee and Margulis [2005] reported that in general, there is good agreement between GPCP1dd and the North American Land Data System’s daily values (used as the realistic ground truth values), but the differences in the estimated precipitation for individual 1° cell can be significant. Bolvin et al. [2009] compared the GPCP SG and GPCP1dd with Finnish Meteorological Institute (FMI) gauge observations for the period of 1995–2007. They reported that the GPCP SG product agrees well with the FMI observations, while the GPCP1dd estimates compare reasonably well with the FMI gauge observations in summer but less so in winter. They also reported that the GPCP SG estimates are biased low by 6% when the same wind loss adjustment is applied to the FMI gauges as is used in the SG analysis [Bolvin et al., 2009]. Joshi et al. [2013] also pointed out that GPCP1dd is good enough in representing the spatial rainfall distribution over India but fails to capture the extreme rainfall in this region. Bearing this in mind, in this study, we will estimate and remove biases in the GPCP1dd using the adjusted daily rainfall and snowfall data recorded at 600–955 stations across Canada, prior to using the GPCP1dd to generate a blended pentad precipitation data set. For both the GPCP1dd and the gauge daily data, pentad mean rainfall (snowfall) rates are derived by simply averaging the total rainfall (snowfall) rates over the pentad period. For leap years, the extra day (i.e., 29 February) is included in the pentad extending from 25 February to 1 March. We denote the pentad data derived from the GPCP daily data as SPE0.

3. Algorithm In this section, we describe in detail the blending algorithm, including the bias correction algorithm. As summarized in Figure 1, there are three major steps. First, we separate the pentad SPEs into rain and snow amounts according to the ratio of rainfall and snowfall (liquid water equivalent) amounts in the corresponding gauge data. Then, we estimate and remove biases in the SPE rain and SPE snow data, separately, through validating the SPEs against the corresponding snowfall and rainfall gauge data. Finally, we propose and evaluate an algorithm for integrating the bias-corrected SPEs (i.e., SPE1) with the carefully processed gauge data to produce a pentad-blended precipitation data set. 3.1. Separation of the SPE0 (GPCP1dd) Precipitation Into Rainfall and Snowfall In a high-latitude country like Canada, there are different types of precipitation, such as rain, snow, and hail, which can be grouped into liquid and solid precipitation. The liquid precipitation comes from rainfall and solid precipitation, mainly from snowfall.

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Rainfall and snowfall are of different characteristics and are usually measured separately, although there are also measurements of total precipitation (rainfall, snowfall, and total precipitation have been archived as three different elements in the Environment Canada Archive). The measurement of rainfall is relatively direct, but the measurement of solid precipitation is more challenging. In Canada, the native snowfall measurement is solid accumulation on the ground, which is then converted to the liquid equivalent for archiving, using a universal fixed ratio of 10:1. As pointed out by Rasmussen et al. [2012], “The environment has a far greater impact on the accuracy of a snow measurement than on a rainfall measurement.” For example, the snowfall measurement accuracy is influenced much more by the local wind than is the rainfall measurement accuracy. And there is Figure 1. A flowchart showing how the different data sets are processed or still much to improve on converting merged. Here VOL standards stand for virtual observation locations and 5d the snowfall measurements to their for 5 days (pentad). See the text for other acronyms. water equivalents [Mekis and Brown, 2010; König et al., 2001; Walker and Goodison, 1993; Goodison, 1978]. These are some of the reasons for the development of the Canadian Adjusted Daily Snowfall and Rainfall Data Set (which is used in this study). To account for the different characteristics of rainfall and snowfall, we estimate and remove biases in the SPE rainfall and SPE snowfall data separately. To this end, for each pentad, we take two steps to separate the SPE0 precipitation into SPE0 rainfall and SPE0 snowfall for each grid cell. First, we use the gauge data to derive a 1° × 1° gridded map of rainfall and of snowfall, separately, for each pentad in the period of analysis (Step 0 in Figure 1). Since there are many valid zeros in each of these maps, which make some interpolation methods (i.e., kriging) handle poorly, we use the simple but effective inverse-distance-weighted interpolation [Shepard, 1968] to derive the maps of pentad rainfall and snowfall. We realize that it could be better if the interpolation included direction as well, which we will explore in future studies. The rainfall (snowfall) value for each grid point in the 1° × 1° grid is obtained as the inversedistance-weighted average of rainfall (snowfall) amounts recorded at the nearest 4 to 16 gauge stations found by the following procedure. Let k be the number of stations within 75 km radius from the target grid point. Here the 75 km radius was determined considering the pentad time scale and the gauge density in Canada. When k > 16 (extremely rare for Canada), only the nearest 16 stations are used in the averaging. When 4 ≤ k ≤ 16, all these stations are used. When k ≤ 4, we enlarge the search radius until we find 4 stations to do the averaging. Second, we separate the SPE0 precipitation into SPE0 rainfall and SPE0 snowfall, using the proportion of the rainfall and snowfall amounts in each grid cell in the corresponding maps of gauge rainfall and gauge snowfall derived above (see Step I in Figure 1). It is possible that the gauge precipitation amount for a certain grid cell is zero, which means that both the rainfall and snowfall amounts in that grid cell are zero. In this case, we use the climatological (1997–2007) mean proportion of the rainfall and snowfall amounts in that grid cell for that pentad to separate the SPE0 precipitation into SPE0 rainfall and SPE0 snowfall. Note that this situation does not happen often. In the 822 pentads (from October 1996 to end of 2007) we

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analyzed in this study, 73.5% of the pentads have less than 100 grid cells (out of 5000 grid cells) with zero gauge precipitation (both rain and snow) amount but nonzero SPE0; only 8 pentads (less than 1%) have more than 500 grid cells with zero gauge precipitation (both rain and snow) but nonzero SPE0, and most of these grid cells are located in very high altitudes (around 85°N–90°N). 3.2. Correction of Biases in the SPE0 Rainfall and the SPE0 Snowfall Lin and Wang [2011] developed a method for removing biases in the SPE0 precipitation for Canada, which considers the characteristics of the gauge network in Canada (sparse in the north and much denser in the south). In this study, we adapt the method to remove the biases in the SPE0 rainfall and the SPE0 snowfall separately. The actual procedure is as follows: 1. For each target grid point, average the SPE0 rainfall (snowfall) over the region within 150 km radius (determined after using several trial radius values) from the target grid point to obtain the average value Sr (Ss). Similarly, the regional average value of gauge rainfall (snowfall), Gr (Gs) is obtained from the gauge rainfall (snowfall) map constructed in section 3.1. Then, similar to Lin and Wang [2011], we define the correction factor for rainfall and snowfall, respectively, as

C rainfall

8 > > 0:1 > > > > > > > < Gr ¼ Cr ¼ > Sr > > > > > > > > : 4

if

Gr ≤ 0:1 Sr

if 0:1 < if

Gr ≤ 4 ; C snowfall Sr

Gr > 4 Sr

8 > > 0:1 > > > > > > > < Gs ¼ Cs ¼ > Ss > > > > > > > > : 4

if

Gs ≤ 0:1 Ss

if 0:1 < if

Gs ≤4 Ss

(1)

Gs > 4 Ss

We further modified Cr and Cs so that min [SPE0r ,Gs] ≤ Cr SPE0r ≤ max [SPE0r,Gr] and min [SPE0s,Gs] ≤ Cs SPE0s ≤ max [SPE0s,Gs], where Gr, Gs, SPE0r, and SPE0s are values obtained in Steps 0 and I of the algorithm (see Figure 1 and section 3.1). Further, considering the resolution of the designated 1° × 1° latitude-longitude grid (about 100 km resolution at midlatitudes) and the pentad time scale, we let m be the number of gauge stations within 250 km radius from the target grid point and define  m=8 if m < 8 λ¼ (2) 1 elsewhere Then, we correct biases in the SPE0 rainfall (SPE0r) and SPE0 snowfall (SPE0s) as follows: SPE1r ¼ ð1  λÞSPE0r þ λC r SPE0r ¼ ð1  λ þ λC r ÞSPE0r

(3)

SPE1s ¼ ð1  λÞSPE0s þ λC s SPE0s ¼ ð1  λ þ λC s ÞSPE0s

(4)

SPE1 ¼ SPE1r þ SPE1s

(5)

Here SPE1r, SPE1s, and SPE1 are the bias correction versions of the SPE0r, SPE0s, and SPE0, respectively (see Step II in Figure 1). Here the gauge station density is reflected by the coefficient λ (0 ≤ λ ≤ 1). When there is no gauge station within 250 km radius from the target grid point, λ = 0, so that SPE0r and SPE0s are unadjusted; thus, SPE1 = SPE0, with the exception of the truncations when the gauge-to-SPE ratio is outside the interval (0.1, 4.0) as described in equation (1) above. When there are 8 or more gauge stations within the 250 km radius, λ = 1; we use only the correction factors Cr and Cs to adjust the SPE0r and SPE0s, respectively, trusting in the gauge rainfall and snowfall fields to the maximum extent. When the gauge density is in between, SPE1r (SPE1s) is a weighted combination of SPE0r (SPE0s) and gauge rainfall (snowfall), with more weight (higher λ value) being given to the gauge value when there are more stations in the neighborhood. 3.3. Combining Gauge Data With Bias-Corrected Satellite Precipitation Estimates As in Lin and Wang [2011], here we also refer to a 1° × 1° grid point as a virtual observation location (VOL) if there is at least one gauge station with valid (not missing) precipitation value in the 1° × 1° grid box. A virtual observation value is obtained as the inverse-distance-weighted average of precipitation amounts recorded at the nearest 4 to 16 gauge stations found by the procedure described earlier in section 3.1 (paragraph 4).

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Figure 2. (a) The 678 gauge stations that have daily precipitation observations for the 36th pentad of 2004 and (b–d) the three gauge station densities used as the training data set in this study.

The procedure we use in this study to obtain a blended pentad precipitation data set is similar to the one developed by Lin and Wang [2011] to produce the version 0 of the blended monthly precipitation data set (i.e., CanBPv0). For each pentad in the period of analysis, the blended pentad precipitation value, BP5d, is obtained by combining the bias-corrected satellite precipitation estimates, SPE1, with kriging (optimal interpolation) of the residual field as follows: BP5d ¼ SPE1 þλK ½GVOLs  SPE1VOLs ;

(6)

where λ is as defined in equation (2) and XVOLs denotes the X value at the virtual observation locations (VOLs); the residual field, K[GVOLs  SPE1VOLs], is obtained by interpolation (through ordinary kriging) of the differences between the gauge and SPE1 values at all virtual observation locations (i.e., GVOLs and SPE1VOLs, respectively) for the pentad in question. This algorithm is different from that developed by Lin and Wang [2011], because it considers the gauge density effect in an earlier stage, when correcting for biases in the SPE0 (see section 3.2), and in the final blending stage. The bias correction method here is also different because it estimates and corrects biases in rainfall and snowfall, separately (see Figure 1 and sections 3.1 and 3.2). All available gauge stations (about 600–1000 stations during the period of 1997–2006; see Figure 2a for the 36th pentad of 2004) are used in equation (6) to obtain to the final blended pentad precipitation data set (CanBP5dV1). For evaluation of the blending algorithm performance, we only use a very small training set of gauge stations (details in the next section) to obtain the blended analysis.

4. Performance of the Blending Algorithm In order to assess the performance of the blending algorithm described in section 3 above, we use an evaluation approach similar to that of Lin and Wang [2011]. Here the evaluation period is 1997–2003 (inclusive), during which the total number of gauge stations range from 748 to 1009. As shown in Figures 2b–2d, we choose three small sets of gauge stations that are well distributed over southwestern Canada

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(90°W–140°W, 48°N–62°N) as the training sets representing the sparse, medium, and dense gauge networks, respectively. The sparse (S) training set is similar to (slightly better than) the gauge density in North Canada (north of 55°N); the dense (D) training set is dense in a relative sense (relative to the sparse and medium densities), not really an ideal dense gauge network (much denser gauge networks exist in South Canada and many European countries). The average distance between a station to its nearest neighboring station is about 295 km (130–740 km), 190 km (100–400 km), and 110 km (40–400 km) in the sparse, medium, and dense gauge training sets, respectively (the distance range given in parentheses). Each station in a training set has no missing observations during the evaluation period. Thus, each of the three training sets contains the same set of stations for all pentads in the evaluation period, like in Lin and Wang [2011]. For each pentad, we use all valid gauge stations (with no missing observations) that are not in the training set to form the evaluation set. Thus, the training and evaluation sets do not contain any common station; the size and composition of the evaluation set may change from one pentad to another (due to possible missing observations at some stations or station closures/openings). Note that each of the training sets is very small (24 to 96 stations); its corresponding evaluation sets are always much larger (652 to 985 stations) and hence well represent the actual spatial distribution of precipitation (i.e., precipitation field). Thus, the evaluation is very stringent. For each pentad in the evaluation period, using one of the three training sets, first, we perform a kriging analysis of the virtual observation values derived from the corresponding evaluation set of gauge precipitation data, obtaining a gauge-only precipitation field to represent the “true” precipitation field. Then, we feed the SPE1 field and the gauge precipitation field of the training set being used in equation (6) to obtain the blended precipitation field for the pentad in question. Then, for all pentads in the period of 1997–2003, the blended precipitation fields are evaluated against the true precipitation fields obtained above to assess the performance of the blending algorithm. For comparison, both the SPE0 (satellite-only product) and SPE1 fields, and the kriging fields of the training set gauge precipitation data (a gauge-only product, denoted as kriging), are also evaluated against the true precipitation fields. It is anticipated that the performance of the blended analysis (BP5d) would be similar to that of the gauge-only product in a dense gauge network but to that of the satellite-only product in a sparse gauge network. First, we calculate the mean “errors” (MEs), the root-mean-square errors (RMSEs), as well as the correlations between the true precipitation fields and the data product being evaluated (BP5d or SPE0 or SPE1 or kriging). (Here the errors are differences between the data sets; they are errors relative to the assumed truth and thus in quotes.) For each of the three training sets, the MEs are shown in Figure 3; the seasonal means of RMSEs and of the correlations are shown in Figures 4 and 5 for each season; the pseudomonthly time series of RMSEs and correlations are also shown in Figures 6 and 7 (each pseudomonth contains 6 pentads except that the eighth month contains 9 pentads). As shown in Figure 3, the uncorrected satellite-only product (SPE0) has the largest MEs (largest box height— largest range between the first and third quartiles), and the MEs of the other three data sets decrease in absolute value as the gauge density increases. In terms of MEs, the blended analysis (BP5d) is the best for the sparse gauge network and is comparable to the gauge-only product (kriging) for the medium-dense gauge networks; it is better than the bias-corrected satellite product (SPE1) for all three gauge densities. Clearly, the blended analysis (BP5d) has the smallest RMSEs and highest correlation skill scores in all seasons throughout the evaluation period, when using the sparse and medium-density training sets of gauge stations (Figures 4–7). As expected, in a dense gauge network, the performance of the blended analysis is comparable to that of the gauge-only product (kriging) but much better than that of the uncorrected satellite-only product (SPE0); the bias-corrected satellite product (SPE1) is nearly as good as the blended analysis (Figures 4 and 5). In a sparse network, the gauge-only product (kriging) has the poorest performance among the four data sets. The blended analysis (BP5d) is almost always the best in terms of RMSEs (Figure 6). Further, we divide the observed precipitation rates into K = 10 categories (0–1, 1–2 …, 11–15, >15 mm/d) and calculate the hit rate, the overestimate rate, and the underestimate rate for each category to show the performance of the blending algorithm in representing precipitation events of different intensities (Figure 8). A hit is counted when a forecast F falls within 90% to 110% of the corresponding observation O (namely, |F  O| < 0.1 × O, also called 10% tolerance). Note that the absolute value of the 10% tolerance increases as precipitation rate increases (from 1.5 mm/d for Category 10).

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We group a hit in the category in which the corresponding observation falls, regardless of the forecast category (for an observation that is near the category boundary, the forecast may be a hit but falls in the neighboring category; e.g., a 4.2 forecast for a 3.9 observation is a hit but not within the observation category of 3–4). We define the hit rate as the number of hits divided by the total number of observations in a category. Accordingly, an overestimate (underestimate) is counted when a forecast is over 110% (under 90%) of the corresponding observation (i.e., F > 1.1 × O or F < 0.9 × O). The overestimate (underestimate) rate is the number of overestimates (underestimates) divided by the total number of observations in a category. For comparison, we also calculated the hit rates with 25% tolerance (Figures 8a–8c). As shown in Figure 8, the hit rate is generally higher in the dense (D) network than in the sparse (S) network, and the blended analysis (BP5d) always has higher hit rates than the satellite-only product (SPE0) regardless of precipitation intensity. The bias-corrected satellite product (SPE1) is similar to the blended analysis and thus will not be discussed further. The comparison with the gauge-only product (kriging) depends on the precipitation intensity. For light-moderate precipitation events Figure 3. The box-and-whisker plots of the mean errors (mm/d) in the SPE0, (with pentad mean precipitation SPE1, and the indicated analysis (BP5d and kriging of training set gauge precipitation) based on (a) the 24-station training set (S), (b) 48-station rate < 5 mm/d), the gauge-only kriging training set (M), and (c) the 96-station training set (D) of gauge stations. Here analysis has the highest hit rates, and the mean errors refer to the differences between the spatial means of the satellite-only product SPE0 has the indicated analysis and of the corresponding virtual observation values of the evaluation set for each pentad; the spatial mean refers to the average over all lowest hit rates in all three gauge densities (Figures 8a–8f). For intense virtual observations locations of the evaluation set. The evaluation period is 1997–2003 (there are 7 × 73 mean errors in each box-and-whisker plot). precipitation events (with pentad mean precipitation rate > 5 mm/d), the blended analysis has the highest hit rates; the gauge-only kriging analysis has the lowest hit rates and is much worse than the satellite-only product SPE0 for the medium and sparse gauge densities (Figures 8a–8f). All the four products in comparison tend to overestimate light-moderate precipitation and underestimate intense precipitation, as can be seen from the overestimate (underestimate) rates that decrease (increase) with increasing precipitation intensity (Figures 8g–8l). The gauge-only kriging analysis is the worst in this

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Figure 4. The 7 year (1997–2003) mean root-mean-square errors (RMSEs) of the SPE0, SPE1, and the indicated analysis (BP5d and kriging of training set gauge precipitation) using the 96-station training set (D), 48-station training set (M), and the 24-station training set (S) of gauge stations for each season.

regard. Its overestimate (underestimate) rates are much higher than the other three analyses when the pentad mean precipitation rate < 3 mm/d (>4 mm/d). The above evaluation results clearly show that the blending algorithm described in section 3 above produces a precipitation data set that is better than using the gauge data alone or using the satellite data alone. This algorithm has been used to produce the first blended pentad precipitation data set (CanBP5dV1) for the period of 1997–2007, which will be updated to cover the recent years once the Adjusted Daily Rainfall and Snowfall Data Set is updated to cover this recent period.

5. Characteristics of Biases in the SPE0 Data Set As described in section 3.1, the GPCP1dd precipitation data were decomposed into rainfall and snowfall amounts using the rainfall/snowfall ratio derived from in situ observations. Figure 9 shows the differences between the regional mean monthly mean SPE0 rainfall and snowfall and the corresponding SPE1 values (i.e., the bias-corrected version) for each month, for South Canada, North Canada, and the whole Canada, respectively. A positive value in this figure indicates an overestimate of the SPE0 data and a negative value, an underestimate.

Figure 5. The 7 year (1997–2003) mean correlations between the true field and the indicated analysis (SPE0, SPE1, BP5d, and kriging of training set gauge precipitation) using the 96-station training set (D), the 48-station training set (M), and the 24-station training set (S) of gauge stations for each season. The true field is an ordinary kriging analysis of the evaluation set gauge precipitation.

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Figure 6. The pseudomonthly (each pseudomonth contains 6 pentads except that the eighth month contains 7 pentads) time series of root-mean square errors (RMSEs) of the indicated analysis (SPE0, SPE1, BP5d, and kriging of the training set gauge precipitation) using (a) the 96-station training set (D), (b) 48-station training set (M), and (c) the 24-station training set (S) of gauge stations. The evaluation period is 1997–2003.

The biases in the SPE0 data are characterized as follows. Averaged over southern Canada (south of 55°N), the SPE0 data set overestimates rainfall in April–September but underestimates rainfall in the other months; while it underestimates snowfall in all seasons (Figure 9a). Averaged over northern Canada (north of 55°N), the SPE0 data set overestimates snowfall in October–March but slightly underestimates snowfall in the other months; while it overestimates rainfall in all seasons (Figure 9b). In the warm season, the SPE0 overestimates of rainfall are larger in southern Canada than in northern Canada; in the cold season, the SPE0 snowfall biases in southern Canada and northern Canada are of the opposite signs (Figures 9a and 9b). Averaged across Canada, the SPE0 overestimates rainfall in almost all months (except January and November), while the averaged snowfall biases are small (Figures 9a and 9c). Note that the GPCP1dd values are calibrated to sum to the GPCP SG monthly values. As stated in Adler et al. [2003], the GPCP SG product uses monthly rain gauge data that are bias corrected using long-term mean monthly correction factors after Legates [1987], which are based on data from the 1960s and 1970s. In comparison with daily rain gauge data from high-resolution networks of the Baltic Sea Experiment (BALTEX) that have been bias corrected “on event” using information about precipitation type and wind speed from the individual daily synoptic data, the area mean of the GPCP SG monthly precipitation climatology (over Sweden and Poland) mostly lies between the corrected and uncorrected BALTEX gauge analyses; but it is slightly biased high in winter (December to February) in Poland (see Figure 16 in Adler et al. [2003]).

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Figure 7. The pseudomonthly time series of correlations between the true field and the indicated analysis (SPE0, SPE1, BP5d, and kriging of the training set gauge precipitation) using (a) the 96-station training set (D), (b) 48-station training set (M), and (c) the 24-station training set (S) of gauge stations. The evaluation period is 1997–2003. The true field is a kriging analysis of the evaluation set gauge precipitation.

Also, note that Canada is entirely in the TOVS/AIRS domain in the 1DD algorithm (i.e., north of 40°N), in which the TOVS and AIRS data are extensively recalibrated to match the higher-quality Threshold Matched Precipitation Index (TMPI) estimates at the boundaries of the latitude band 40°N–40°S. This implies larger errors in the TOVS/AIRS data over Canada. Further, there is a time mismatch in the climatological day definition between the Canadian gauge data and the GPCP1dd data. Gauge data from both synoptic and ordinary stations in Canada are used in this study. For the first-order stations (synoptic stations) in Canada, the time of observation for daily precipitation is 06:00 Z since 1 July 1961 [Allsopp, 2004]. For ordinary stations (including volunteer stations) in Canada, the time of observation for daily precipitation is 08:00 local standard time (13:00 Z in Ontario and Quebec) since 1 January 1933 [Allsopp, 2004]. However, the GPCP1dd product uses eight estimates at the synoptic times in a UTC day, so its climatological day starts from 00:00 Z. The above time mismatches very likely contribute to the differences between SPE0 and SPE1 (or the gridded gauge data used to produce SPE1) on the pentad time scale, although there is little we can do about it.

6. Comparison of CanBP5dV1 With Other Pentad Precipitation Data Sets In this section, we briefly compare the first blended pentad precipitation data set (CanBP5dV1) with the GPCP Pentad Data Set (GPCP_Pen) [Xie et al., 2003] and the pentad precipitation data derived from the Canadian

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Figure 8. (a–l) The 7 year (1997–2003) mean hit rates (with 25% or 10% tolerance) and the mean rates of overestimate and underestimate (by at least 10%) of the indicated analysis (SPE0, SPE1, BP5d, and kriging of the training set gauge precipitation) using (Figures 8a, 8d, 8g, and 8j) the dense training set (D), (Figures 8b, 8e, 8h, and 8k) the medium training set (M), and (Figures 8c, 8f, 8i, and 8l) the sparse training set (S). See section 4 for the definition of these rates.

gridded daily precipitation data set ANUSPLIN [Hutchinson et al., 2009] for their common period of 1997–2006. The ANUSPLIN daily data set [Hutchinson et al., 2009] was produced using trivariate thin-plate smoothing splines to interpolate daily total precipitation (not snowfall and rainfall) data, after the daily precipitation data being treated for flags, but not being adjusted for any other known biases, unlike the adjusted daily snowfall and rainfall data used in this study. The comparison was done using the box-and-whisker plots of the

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Figure 9. The differences (mm/d) between the spatial mean monthly mean SPE0 and the corresponding SPE1 (i.e., the bias-corrected SPE0) for each month. The regional mean is average over (a) southern Canada, (b) northern Canada, and (c) Canada.

regional averages and spatial standard deviations, and the pattern correlations between CanBP5dV1 and GPCP_Pen or ANUSPLIN pseudomonthly values, for northern and southern Canada, respectively (Figure 10). As an example to show the differences in the monthly mean fields, the maps of the rainfall, snowfall, and total precipitation for March and September 2003 are also shown in Figure 11, including the GPCP SG monthly precipitation fields [Adler et al., 2003]. As shown in Figure 10, the regional averaged pentad precipitation rate is highest in CanBP5dV1, and lowest in ANUSPLIN, especially for northern Canada (Figure 10, top). This is largely due to the fact that CanBP5dV1 is based on the adjusted daily rainfall and snowfall data, which have been corrected for gauge undercatch and evaporation due to wind effect, for gauge-specific wetting loss, and for trace precipitation amount, after a more realistic snow-water-equivalent ratio map being used to convert snowfall to total precipitation (see section 1). The total precipitation data used in the ANUSPLIN were not corrected for any of these biases and were obtained using the default 10:1 snow-water-equivalent ratio. The spatial variability (standard deviation) is smallest in ANUSPLIN, while CanBP5dV1 is comparable to the GPCP_Pen (Figure 10, second row). In general, GPCP_Pen has much higher pattern correlations with CanBP5dV1 than does ANUSPLIN (Figure 10, bottom). This is in part due to the fact that both GPCP_Pen and CanBP5dV1 used satellite precipitation estimates, while ANUSPLIN is a gauge-only product and the gauge data used in ANUSPLIN are uncorrected, different from those used in CanBP5dV1. We have shown in Lin and Wang [2011] and in this study that a gridded precipitation data set produced by interpolation of gauge precipitation data alone is less reliable in the sparse gauge network in Canada even on monthly and pentad time scales.

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Figure 10. Comparison of the blended analysis CanBP5dV1 with the GPCP Pentad Data Set (GPCP_Pen) [Xie et al., 2003] and ANUSPLIN data set [Hutchinson et al., 2009], in terms of box-and-whisker plots of the regional averages and spatial standard deviations, and the pattern correlations between CanBP5dv1 and GPCP_Pen (solid line) or ANUSPLIN (dashed line) pseudomonthly values. The unit for the averages and standard deviations is mm/d. The period for comparison is 1997–2006 (10 years).

For comparison of the spatial distribution of precipitation, the monthly mean precipitation fields as derived from the GPCP1dd, the SPE1 (bias-corrected GCPC1dd), the blended analysis (CanBP5dV1), the GPCP_Pen, the GPCP SG, and the ANUSPLIN are shown in Figure 11 for March and September 2003. The rainfall and snowfall maps for March 2003 are also shown for the SPE0 (the rainfall-snowfall-decomposed version of

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Figure 11. (a–o) An example of the GPCP1dd (SPE0) and bias-corrected satellite precipitation estimates (SPE1) fields, in comparison with the blended pentad precipitation analysis (CanBP5dV1), the GPCP Pentad Data Set (GPCP_Pen) [Xie et al., 2003], and the GPCP Monthly Satellite-Gauge analysis (GPCP SG) [Adler et al., 2003] (for March and September 2003). The total precipitation amount was split into rainfall and snowfall liquid equivalent amounts using the gauge rainfall/snowfall ratio (see section 3.1). Here the month of September as derived from the pentad data covers the period from 3 September to 2 October inclusive, except for the monthly product CanBPv0 (for which September is the calendar month).

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the GPCP1dd) and the SPE1 (Figures 11b, 11c, 11e, and 11f). Comparing SPE0 with SPE1 for March 2003 reveals that SPE0 underestimates snowfall, especially in Newfoundland and southern Alberta (Figures 11c and 11f), and overestimates rainfall over the Canadian Rocky Mountain area (Figures 11b and 11e). In March, the blended analysis shows more precipitation in northwestern Ontario but less precipitation in southern Ontario than do all the other data sets (Figures 11a, 11d, 11g, and 11j). In September (Figures 11k–11o), all the CanBP5dV1 show more precipitation in the region from southern Manitoba to northwestern Ontario, and less precipitation in the west coast, than the three GPCP data sets; the ANUSPLIN shows much less precipitation in the west coast than the other data sets and less precipitation in Manitoba-Ontario than the GPCP SG, GPCP1dd, and CanBP5dV1. As shown in Figure 11, the GPCP_Pen and GPCP SG show much less spatial variability of precipitation than the CanBP5dV1 (and SPE1 and GPCP1dd) in March and to a lesser degree in September; the ANUPLIN shows a little more spatial variability than the GPCP_Pen and the GPCP SG but still less than the CanBP5dV1.

7. Concluding Remarks In this study, we have developed an algorithm for constructing pentad precipitation fields by integrating the popularly used GPCP daily precipitation data set, GPCP1dd v1.2, with Canadian in situ daily precipitation data —the adjusted daily rainfall and snowfall data. This algorithm includes a bias correction procedure that considers the differences between snowfall and rainfall, as well as the gauge density (e.g., no correction if there is no gauge data within 250 km radius). Then, a blended pentad precipitation field was obtained by combining the bias-corrected GPCP precipitation field with an ordinary kriging analysis of the differences between the gauge and bias-corrected GPCP precipitation field at virtual observation locations (i.e., kriging of residuals). We have evaluated the skill of the algorithm for gauge networks of three densities (sparse, medium, and relatively dense), with the evaluation data set being much larger than the training data set (652–985 stations versus 24–96 stations). The results show that the algorithm produces better representation of pentad precipitation fields than the GPCP1dd precipitation estimates or than using the gauge data alone; it has smaller root-mean-square errors and higher correlation skill scores. Although evaluated using Canadian precipitation data, this algorithm can be used for other regions around the world. We have used it to produce the first blended pentad precipitation data set for the period of 1997–2007 for Canada (CanBP5dV1). This CanBP5dV1 data set will be updated to cover the recent period once the Canadian Adjusted Daily Rainfall and Snowfall Data Set is updated to cover this period (ongoing now).

Acknowledgments The authors are grateful to Ewa Milewska for her helpful internal review comments on an earlier version of this manuscript, to the GPCP data producers for making the their data products available online free of charge, and to the GPCP data archive at the NASA Goddard Space Flight Center (http://precip.gsfc.nasa.gov/) where we downloaded the GPCP data sets. The Canadian gauge precipitation data will be available free of charge by contacting the corresponding author. For the Canadian ANUSPLIN data, contact Ewa Milewska ([email protected]) or M.F. Hutchinson ([email protected]). Achan Lin is an independent contractor who had a contract with Environment Canada to work, under Dr. X. L. Wang’s direction, on this research project, which was proposed and designed by X. L. Wang (the scientific authority of the contract).

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Further, we have found that, averaged over southern Canada (south of 55°N), the SPE0 rainfall and snowfall data set, as decomposed from the GPCP1dd, overestimates (underestimates) rainfall in April–September (in the other months), while it underestimates snowfall in all seasons. Averaged over northern Canada, the SPE0 data set overestimates (underestimates) snowfall in October–March (in the other months), while it overestimates rainfall in all seasons. Some of these differences on the pentad time scale very likely arise from the time mismatch in the climatological day definition between the Canadian gauge data and the GPCP1dd data (see section 5).

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