JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, D20113, doi: /2009jd011705, 2009

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2009jd011705, 2009 Changes in synoptic weather patterns and Greenland precipitation in the 20th and 21st centuries: 1. Evaluation of late 20th century simulations from IPCC models Keah C. Schuenemann 1 and John J. Cassano 2 Received 4 January 2009; revised 27 May 2009; accepted 16 July 2009; published 28 October [1] Using the self-organizing map (SOM) technique, the sea level pressure synoptic climatology and precipitation of 15 Intergovernmental Panel on Climate Change Fourth Assessment Report (IPCC AR4) models are compared to that of the ERA-40 reanalysis for the North Atlantic region for the period 1961 to Three of the models, the CCCMA-CGCM3.1(T63), the MIROC3.2(hires), and the MPI-ECHAM5, best reproduce the ERA-40 synoptic climatology and are chosen for further analysis of precipitation over Greenland. The MIROC3.2(hires) is the best single performing model, in that it best matches ERA-40. Although the three-model ensemble simulates the same mean annual precipitation over Greenland as ERA-40, the ensemble simulates the mean annual precipitation differently than ERA-40. A dry bias in the CCCMA-CGCM3.1(T63) and a wet bias from the MPI-ECHAM5 cancel in the ensemble average. The mean annual precipitation difference between the model ensemble, as well as each individual model, and ERA-40 is then attributed to differences in intrapattern variability and pattern frequency components in the models that make up the ensemble. Pattern frequency differences between the model and ERA-40 indicate a difference in the occurrence of synoptic weather patterns, while intrapattern variability differences denote differences in the amount of precipitation produced when a given synoptic weather pattern occurs. Intrapattern variability differences between the models and ERA-40 are predominantly responsible for Greenland precipitation differences, but pattern frequency (circulation) differences in the models also play a small role. Part 2 of this paper uses this three-model ensemble to analyze and attribute predicted increases in precipitation over the Greenland ice sheet for the 21st century. Citation: Schuenemann, K. C., and J. J. Cassano (2009), Changes in synoptic weather patterns and Greenland precipitation in the 20th and 21st centuries: 1. Evaluation of late 20th century simulations from IPCC models, J. Geophys. Res., 114,, doi: /2009jd Introduction [2] Precipitation over Greenland is the key input term to the mass balance equation for the Greenland ice sheet (GrIS). The GrIS consists of a volume of km 3 of ice [Bamber et al., 2001], which is equivalent to a potential global sea level rise of approximately 7.2 m [Church et al., 2001]. Information on the processes by which precipitation arrives on the GrIS, such as knowledge about the frequency of weather patterns producing precipitation there, facilitates predictions on how those processes might change in the future. Global warming may cause a shift in storm track as well as an amplification of the hydrologic cycle, both of 1 Laboratory for Atmospheric and Space Physics and Department of Atmospheric and Oceanic Sciences, University of Colorado at Boulder, Boulder, Colorado, USA. 2 Cooperative Institute for Research in Environmental Sciences and Department of Atmospheric and Oceanic Sciences, University of Colorado at Boulder, Boulder, Colorado, USA. Copyright 2009 by the American Geophysical Union /09/2009JD which could affect Greenland precipitation [Alley et al., 2007]. The magnitude of precipitation falling over Greenland during the future will be a major factor in determining whether precipitation will balance melt and ice sheet dynamics that would deplete the ice sheet in a warmer atmosphere. Sea level rise and changing weather patterns resulting from a withering ice sheet would have worldwide societal impacts and motivates further investigation of all components of the Greenland ice sheet mass balance, including precipitation. [3] Records of observed precipitation over the GrIS are sparse and inaccurate due to blowing snow and the desolate nature of the ice sheet. Accumulation from ice core records is not directly comparable to precipitation due to contributions from ablation, deposition, and blowing and drifting snow. Therefore, data sets from reanalyses and model simulations have been the primary source of data for Greenland precipitation analyses covering the whole ice sheet [Bromwich et al., 1993, 2001; Chen et al., 1997; Cassano et al., 2001; Box et al., 2004, 2006]. In preparation for the Intergovernmental Panel on Climate Change s Fourth Assessment Report (IPCC AR4), global climate modeling centers from around 1of20

2 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 1. Map of analysis domain with inset map showing domain location relative to the pan-arctic. Greenland ice sheet elevation is contoured every 500 m beginning with the 2000-m line in bold. A scale bar at bottom right shows a distance of 200 km, which is the EASE grid resolution that all data are interpolated to. the world performed simulations for the past using observed greenhouse gas concentrations, and for the 21st century using IPCC emissions scenarios. This study compares sea level pressure (SLP) patterns and precipitation in these model simulations to the ERA-40 reanalysis, assumed here to be the best representation of reality, from 1961 to 1999 over a North Atlantic domain (Figure 1). Schuenemann et al. [2009] found good agreement between ERA-40 precipitation and estimates of Greenland precipitation from other studies. The purpose of this paper is to find the models that best reproduce the ERA-40 synoptic climatology and precipitation over this domain, so that these models can be used for an analysis of future, predicted precipitation over the GrIS [Schuenemann and Cassano, 2009, hereafter part 2] and to make estimates of the future state of the GrIS based on model output from the best performing models. This study uses self-organizing maps (SOMs) as an analysis tool that allows a detailed look at what drives the differences between the reanalysis and model data on the synoptic scale. 2. Data and Methodology 2.1. Data [4] Daily SLP and precipitation data from fifteen IPCC AR4 Atmosphere-Ocean General Circulation Models (AOGCMs) (Table 1) 20th century simulations (20c3m) from 1961 through 1999, as well as Special Report on Emission Scenarios (SRES) A1B scenario output for years 2046 through 2065 and 2081 through 2100, in addition to data from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-40 reanalysis from 1961 to 1999, were used for this analysis. These dates were chosen based on the overlapping availability of daily data from all of the models as well as the reanalysis. IPCC AR4 model data were obtained from the World Climate Research Programme s (WCRP s) Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel data set. [5] The ERA-40 reanalysis [Uppala et al., 2005] is here considered the best approximation of the synoptic climatology in the North Atlantic domain, specifically its SLP and precipitation, from 1961 to 1999 as discussed by Schuenemann et al. [2009]. The National Center for Environmental Prediction/ National Center for Atmospheric Research (NCEP/NCAR) Reanalysis could have also been used for comparison, but the ERA-40 has been shown to perform better over the Arctic regions [Serreze et al., 2005] and the use of ERA-40 data is consistent with the study of Schuenemann et al. [2009]. Although ERA-40 Greenland precipitation does have its shortcomings, compared to ice core accumulation it performs best in southeastern Greenland, the region of highest precipitation [Hanna et al., 2006]. In previous work, Schuenemann et al. [2009] provided a detailed discussion of the ERA-40 synoptic climatology over this domain, including a discussion of the frequency of occurrence of synoptic patterns, storm tracks, and the synoptic forcing of precipitation over the GrIS. ERA-40 was found to reproduce known cyclone features, such as the blocking, splitting, and intensification of cyclones by the high elevations of the ice sheet [Chen et al., 1997; Doyle and Shapiro, 1999; Kristjansson and McInnes, 1999; Petersen et al., 2003; Doyle et al., 2005; Tsukernik et al., 2007] as well as the active North Atlantic storm track in the winter season and then the weakening of that storm track during the summer [Serreze and Barry, 2005]. It should be noted that because the analysis presented in this paper uses both ERA-40 and IPCC model output, the SOM from Schuenemann et al. [2009], which uses only ERA-40 data, is not the same as the master SOM presented here. [6] The IPCC AR4 20c3m experiments were run by global climate modeling centers around the world using observed greenhouse gas concentrations from the past, while the 21st century simulations use greenhouse gas concentrations as specified in the SRES A1B scenario [Alley et al., 2007]. This scenario describes a future with very rapid economic growth, population that peaks midcentury and then declines, and the rapid introduction of new and more efficient technologies. Technological change in the energy system includes a balance between fossil fuel and nonfossil fuel energy sources. This SRES scenario was chosen because it represents the middle of the road of future climate scenarios. [7] Daily SLP and precipitation data were used to ensure that the SOM algorithm captures the synoptic-scale systems that are responsible for the large precipitation events over Greenland. The ERA-40 data used in this study have a horizontal resolution of 2.5 degrees by 2.5 degrees, with 23 vertical levels while each IPCC AR4 model has its own 2of20

3 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Table 1. Fifteen IPCC AR4 Models, Their Country of Origin, Institution, Atmospheric Resolution, Vintage, and a Reference for More Information on the Model a Model Country Institution Atmospheric Resolution Vintage Reference CCCMA-CGCM 3.1 Canada Canadian Centre for Climate Modeling and Analysis T47 (2.8 by 2.8) L McFarlane et al. [1992] CCCMA-CGCM 3.1(T63) Canada Canadian Centre for Climate Modeling and Analysis T63 (1.9 by 1.9) L McFarlane et al. [1992] CSIRO-Mk3.0 Australia Commonwealth Scientific and Research Organization, Atmospheric Research GFDL-CM2.0 USA U.S. Dept. of Commerce/National Oceanic and Atmospheric Administration/Geophysical Fluid Dynamics Laboratory GFDL-CM2.1 USA U.S. Dept. of Commerce/National Oceanic and Atmospheric Administration/Geophysical Fluid Dynamics Laboratory GISS-AOM USA National Aeronautics and Space Administration/Goddard Institute for Space GISS-ER USA National Aeronautics and Space Administration/Goddard Institute for Space IAP-FGOALS-g.1.0 China Laboratory for Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics T63 (1.9 by 1.9) L Gordon et al. [2002] (2.0 by 2.5) L GFDL Global Atmospheric Model Development Team (GFDL GAMDT) [2004] (2.0 by 2.5) L GFDL GAMDT [2004] (3 by 4) L Russell et al. [1995] (4 by 5) L Schmidt et al. [2006] T42 (2.8 by 2.8) L Wang et al. [2004] IPSL-CM4 France Institut Pierre Simon Laplace (2.5 by 3.75) L Hourdin et al. [2006] MIROC3.2(hires) Japan Center for Climate System Research (University of Tokyo), T106 (1.1 by 1.1) L K-1 Model Developers [2004] National Institute for Environmental Studies, Frontier Research Center for Global Change (JAMSTEC) MIROC3.2(medres) Japan Center for Climate System Research (University of Tokyo), National Institute for Environmental Studies, Frontier Research Center for Global Change (JAMSTEC) MIUB-ECHO-G Germany/Korea University of Bonn and Korean Meteorological Administration T42 (2.8 by 2.8) L K-1 Model Developers [2004] T30 (3.9 by 3.9) L Roeckner et al. [1996] MPI-ECHAM5 Germany Max Plank Institute for Meteorology T63 (1.9 by 1.9) L Roeckner et al. [2003] MRI-CGCM2.3.2A Japan Meteorological Research Institute T42 (2.8 by 2.8) L Shibata et al. [1999] NCAR-CCSM3.0 USA National Center for Atmospheric Research T85 (1.4 by 1.4) L Collins et al. [2006] a Horizontal resolution is listed by triangular (T) spectral truncation with an approximation of degrees latitude by longitude in parentheses or only listed in degrees latitude by longitude in parentheses. Vertical resolution is indicated by the number of levels (L). Vintage is the year of the first publication of results from each model. 3of20

4 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 resolution, as listed in Table 1. More details on model resolution and features as well as references to further model specific information are given in the IPCC AR4 Working Group 1 Report [Randall et al., 2007, Table 8.1]. All data were interpolated to a 200 km Equal-Area Scalable Earth (EASE) grid over a North Atlantic domain to assure the equal weight of data at northern and southern latitudes in both the training of the SOM and in averaging over the domain or subsets of the domain [Armstrong and Brodzik, 1995]. Figure 1 shows the North Atlantic domain over which the EASE grid was created. Located in the bottom right corner of Figure 1 is a scale bar showing the 200 km grid spacing. SLP data directly over Greenland were removed due to the difficulty of properly adjusting surface pressure at high elevations to sea level [Streten, 1980]. Greenland elevation reaches 3208 m at Summit [Serreze and Barry, 2005], but the elevation gain is largest at the margins of the ice sheet, as shown by the close proximity of the 2000 m elevation contour to the Greenland coast in Figure 1. Prior to the SOM analysis described below, daily SLP anomalies were calculated by subtracting the daily, domain averaged SLP from the SLP at each grid point of the EASE grid. SLP anomaly data were then used as input data for the SOM algorithm, allowing the SOM algorithm to focus on the gradients that drive the circulation rather than the varying magnitudes of SLP from day to day among the models and reanalysis Description of the Self-Organizing Map Technique [8] Kohonen [2000] offers an explanation of the development and details of the SOM algorithm while Hewitson and Crane [2002] describe the use of SOMs in classifying synoptic patterns in climate data. Using SOMs to create a synoptic climatology is an accepted technique [Barry and Carleton, 2001] that has been widely used in recent years. Reusch et al. [2005, 2007] and Liu et al. [2006] have validated the use of SOMs in the field of climatology. Reusch et al. [2005] compared SOMs to principal component analysis and found that the SOM technique offered several advantages over the principal component analysis for identifying real synoptic patterns in the atmosphere, Liu et al. [2006] also found advantages of using SOM analysis over the empirical orthogonal function method. The analysis technique that uses SOMs to attribute precipitation differences to changes in circulation and within-pattern change in precipitation is based on techniques introduced in the work of Cassano et al. [2006, 2007]. This SOM analysis uses the SOM-PAK software, which is available for downloading at [Kohonen et al., 1996]. [9] The SOM algorithm is a neural network algorithm that is used here to stratify 80 years of daily SLP anomaly data from 16 different sources into the 35 patterns that best span the range of daily synoptic weather patterns in the training data. These patterns, also referred to as nodes, appear in an organized 2-D array known as a self-organizing map (SOM) (Figure 2). The training or creation of a SOM is an unsupervised iterative procedure where no assumptions regarding the resulting patterns are made by the user. The user input is limited to the choice of SOM dimensions and a few training parameters (learning rate, learning radius, and training length) [Kohonen, 2000]. [10] Using the daily SLP anomaly input data from the reanalysis for 1961 to 1999 and from all of the models for 1961 to 1999, 2046 to 2065, and 2081 to 2100, the SOM dimensions and training parameters were varied to create over 500 SOMs, all based on the same input data. The input data matrix was created by placing each day s SLP data in one row. Each column in the file, therefore contains SLP data for all days and models at a given spatial point on the domain. The first rows have reanalysis data, then the model data followed in later rows. By using all of the past and future SLP data as input to the SOM algorithm, the resulting SOMs represent both past and future circulation patterns in all of the models as well as the reanalysis, which will aid in our analysis in part 2. Each daily SLP anomaly in the input data best matches a synoptic pattern represented by a single node on the SOM. The best match node is chosen by finding the minimum mean squared difference between a day s SLP pattern and each node. [11] In choosing the master SOM which is the basis of this analysis, quantization errors were calculated and compared among all of the created SOMs. The quantization error is the sum of the mean squared differences between all of the daily input data and the nodes to which they best match. The error is used as a performance index that quantifies the difference between the input data and each SOM. Low quantization error SOMs would therefore indicate the SOMs that best fit the input data. SOMs with the lowest quantization errors for each set of SOM dimension were then explored further by comparing their Sammon maps, which shows the spatial organization of the nodes relative to each other by plotting the approximate Euclidean distance between each of the nodes [Sammon, 1969]. Several SOMs were then plotted, as in Figure 2, for visual inspection of the distinction between patterns and general organization. Once the low quantization error, Sammon map, intuitive organization of patterns, and distinction between patterns were taken into consideration, the SOM with dimensions 7X5, learning rate of 0.01, radius of 3, neighborhood function set to bubble, and running length of 12 million steps was chosen as the master SOM used for the basis of this analysis. Because all of the SOMs were trained using the same data set, results presented in this paper would be similar regardless of which SOM was chosen. Several different sized SOMs with varying parameters and low quantization errors were taken through the first part of this analysis to ensure that the three-model ensemble chosen was robust among different sized SOMs. 3. Results and Analysis 3.1. Master SOM [12] The master SOM (Figure 2) consists of 35 nodes, or distinct SLP synoptic patterns, that span the range of SLP patterns present in the training data. Positive (red shades and solid contours) and negative (blue shades and dashed contours) SLP anomalies indicative of high- and lowpressure systems, or anticyclones and cyclones, respectively, can be found in each node. The SOM in Figure 2 can be divided into six general patterns based on the SLP and precipitation patterns (precipitation will be discussed later in section 3.3 and Figure 6). Seven nodes in the top left corner of the SOM have synoptic patterns that include weak 4of20

5 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 2. Master SOM of SLP anomalies (hpa) trained from 20th and 21st century data from 15 IPCC AR4 AOGCMs as well as ERA-40 reanalysis data. Anomaly SLP contour interval is 2 hpa. Blue shades and dashed contours represent negative SLP anomalies, while red shades and solid contours represent positive SLP anomalies. Node group abbreviations stand for the following: W, weak; LC, Labrador cyclone; BB, Baffin Bay cyclone; ST, Southern Tip cyclone; NA, North Atlantic cyclone; IL, Icelandic Low cyclone. cyclones (W). Labrador cyclones (LC) are located in the top central portion of the SOM. These cyclones generate strong onshore flow over southern Greenland and are named for the Labrador Sea southwest of Greenland where the center of the cyclones lie. Cyclones with their centers west of Greenland are called Baffin Bay cyclones (BB). These four nodes are located in the upper right portion of the SOM and their weather patterns cause onshore flow over the west coast of Greenland. Nodes in the middle left portion of the SOM contain southern tip cyclones (ST) whose centers are located southwest, south, and southeast of the southern tip of Greenland, allowing for onshore flow onto the southeast coast of Greenland. Some cyclones are located too far from Greenland to produce a significant amount of onshore flow over the ice sheet and are given the name North Atlantic cyclones (NA). These NA nodes are located in the bottom left corner of the SOM. Icelandic Low cyclone (IL) patterns are represented by nodes in the bottom right of the SOM. IL cyclones have low-pressure centers near Iceland east of Greenland and create onshore flow in the middle to upper east coast of Greenland. [13] The master SOM (Figure 2) was created using data from the past as well as future predictions, however, for the remainder of this paper, analysis will focus only on past data from 1961 to 1999 and discussion of future data will be reserved for part 2 of this paper Frequency of Occurrence of Weather Patterns [14] The frequency of occurrence of each of the SOM nodes within the input data is represented as a percentage of 5of20

6 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 the total number of daily samples in the particular data set. Figure 3a shows the frequency of occurrence of each of the nodes in the daily ERA-40 data (1961 to 1999). The method for reading these types of plots is as follows, each number in Figure 3a represents the node in the same position in the master SOM (Figure 2). For convenience, node reference numbers are given along the left side and bottom of Figure 3a (also in Figures 3b 3g and Figures 8a 8f) that correspond to the labeled node numbers on the master SOM. For example, node (2,0) in Figure 2, a weak (W) circulation pattern, corresponds to the third column from the left side of the SOM, labeled 2 in Figure 3a, and the top row, labeled 0 in Figure 3a, and has a frequency of 5.49%. The same group boundaries shown by black lines on the master SOM (Figure 2) are indicated by black lines in Figure 3 (and Figure 8). This frequency value for node (2,0) is bold in Figure 3a, revealing that it is significantly different at a 95% confidence level from a value of 2.86%, or 1 divided by 35 nodes, should all of the nodes have occurred equally as frequent in the ERA-40 data. Bold, italic numbers indicate statistical significance below the 95% confidence interval. Assuming that the process is binomial, the 95% confidence limits are calculated by p 1:96 pð1 pþ 1 = 2; ð1þ n where p is the probability that any daily sample would map to any node and n is the number of daily samples. Note that there is no reason to expect each node to occur equally frequently, and this highlighting of the most and least frequent nodes is used solely to draw attention to the synoptic patterns that occur very frequently or infrequently. [15] Twelve nodes have frequencies significantly greater than the even distribution value of 2.86%, including three of seven W nodes, half of the IL nodes, and three of four BB nodes. Eighteen nodes have frequencies significantly less than the expected value, including most of the ST, NA, and LC nodes and the three of seven W nodes. A comparison between modeled 20th century and ERA-40 data shows a large range of variation in frequency of synoptic patterns among the models and between the models and ERA-40 (Figures 3b 3f). [16] Node frequencies from an ensemble of all 15 models is shown in Figure 3b. The difference between the 15-model ensemble and the ERA-40 reanalysis frequency is shown in Figure 3c. Statistically significant differences, at a 95% confidence level, are in bold or bold and italic print. The significance of the difference between model and ERA-40 node frequencies is evaluated using the test statistic in equation (2), ðp 1 p 2 Þ p 2ð1 p 2 Þ þ p 1ð1 p 1 Þ 1 = 2 n 2 ; ð2þ where for each node, p 1 is the ERA-40 frequency, p 2 is the node frequency for the model ensemble, n 1 is the number of samples in the ERA-40 data, and n 2 is the number of samples in the model data. If the test statistic is greater than 1.96, the node frequency is considered statistically different, at the 95% confidence level, from the ERA-40 frequency. Areas with dashed contours include nodes that are underrepresented by the 15-model ensemble and areas with solid contours show nodes that are overrepresented by the model ensemble. The dashed contours over the BB and IL nodes in the SOM, in addition to nodes (2,0) and (3,0), indicate that synoptic patterns with cyclones in the northern portion of the domain, east or west of Greenland, and high pressure over the Azores in the southeast corner of the domain are underrepresented by the 15-model ensemble, while NA cyclones are overrepresented by the 15-model ensemble. Thus, the 15-model ensemble produces a more southern storm track with more NA cyclones, which creates less onshore flow over Greenland and leaves less room for anticyclones over the Azores. [17] An ideal model or model ensemble would recreate the same synoptic patterns that take place in the real atmosphere, here represented by the ERA-40 reanalysis, and therefore, the same node frequencies as ERA-40. The performance of each model can be represented by a correlation between ERA-40 node frequency and each model s node frequency over the same time period [Cassano et al., 2007]. This correlation was done as an annual calculation and then for seasonal correlations (DJF, MAM, JJA, and SON), shown in Table 2, where correlations greater than 0.50 are in bold print. The correlations show that small errors within the seasons accumulate to larger errors on an annual basis, giving the annual performance generally lower correlations. The models were ranked from best correlation to ERA-40 to worst, for an annual and seasonal basis. These ranks were totaled and Table 2 is ordered from the best total rank to the worst total rank, which appears in the right column. A top three- and five-model ensemble were chosen based on this order. Three models that correlate very well with ERA-40 are MIROC3.2(hires), CCCMA- CGCM3.1(T63), and MPI-ECHAM5. There is a clear break between the sum of ranks for the third best model (31), MPI-ECHAM5, and the next model (45), GFDL-CM2.1. n 1 Figure 3. Frequency of occurrence (%) of each node on the master SOM for 1961 to 1999, where each number represents the node in the same position in the master SOM (Figure 2). Node frequencies below a statistically significant 95% confidence range are shown in italics, while frequencies above the range are bold. Positive values have solid contours, while negative values in difference plots are contoured with dashed lines. The darkest shades in all plots indicate the largest values and, in the difference plots, the largest absolute values. (a) Node frequency of ERA-40, (b) 15-model ensemble node frequency, (c) 15-model ensemble node frequency difference from ERA-40, (d) five-model ensemble node frequency, (e) five-model ensemble frequency difference from ERA-40, (f) three-model ensemble node frequency, and (g) three-model ensemble frequency difference from ERA-40. Figures 3a, 3b, 3d, and 3f share the same shading scheme and a contour interval of 0.5. Figures 3c, 3e, and 3g share the same shading scheme and a contour interval of of20

7 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 3 7of20

8 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Table 2. Correlations Between ERA-40 and Model Synoptic Pattern Frequencies for All 15 Models as Well as a Three-Model Ensemble, Five-Model Ensemble, and 15-Model Ensemble Using Data From 1961 to 1999 a Correlations Ranks Model Annual DJF MAM JJA SON Annual DJF MAM JJA SON Sum of Ranks Three-model ensemble b Five-model ensemble c model ensemble MIROC3.2(hires) b CCCMA-CGCM3.1(T63) b MPI-ECHAM5 b GFDL-CM2.1 c NCAR-CCSM3.0 c IPSL-CM MIROC3.2(medres) MIUB-ECHO-G CCCMA-CGCM MRI-CGCM2.3.2A IAP-FGOALS-g CSIRO-Mk GISS-ER GFDL-CM GISS-AOM a The models and ensembles are ordered by the sum of ranks column from best to worst performance over the Greenland region. Correlations greater than 0.50 are in boldface. b The models included in the three-model ensemble. c The models included in the five-model ensemble. When ordering the models by their performance on the annual time period, GFDL-CM2.1 model performs poorly, with a correlation of only 0.27, but each individual season has high correlations greater than 0.60, making it the fourth best model when ordering by the sum of ranks. The NCAR- CCSM3 has a poor MAM correlation, but performs well for all other seasons and annually. When ordered by rank, the NCAR-CCSM3 is the fifth best model. Although the threemodel ensemble is clearly superior, the low correlations in only one of the time periods provokes a more detailed look into these two American models beyond the top three. Therefore two ensembles were created for further analysis, a three-model ensemble (MIROC3.2(hires), CCCMA- CGCM3.1(T63), and MPI-ECHAM5) and a five-model ensemble (includes the same models in the three-model ensemble as well as GFDL-CM2.1 and NCAR-CCSM3). These models will now be referred to as MIROC, CCCMA, ECHAM, GFDL, and NCAR in the remainder of the paper. These five models are the same top models that appear in literature analyzing the Mackenzie River Basin (Canada) [Finnis et al., 2008] and four of the five top models are the same that were analyzed for the Arctic region (the MIR- OC3.2(hires) was not included) [Cassano et al., 2007]. While the top models in these studies are all similar, some differences are noted, and should be expected given that not all models will perform equally well in all regions. This highlights the importance of evaluating a model, or models, for the region of interest. It is evident from Table 2 that the three- and five-model ensembles, and even the 15-model ensemble perform better than any individual model. The three-model ensemble performs best, the five-model ensemble second best, and the 15-model ensemble third best when ordered by either rank or annual correlations. The higher correlations among the ensembles than any individual model motivates the use of ensemble forecasting. [18] A visual inspection of the node frequency of ERA-40 and each of the ensembles, Figures 3a and 3b (15-model ensemble), 3d (five-model ensemble), and 3f (three-model ensemble), show general similarities of greater values along the edges of the SOM and smaller values in the center of the SOM, a common occurrence in SOMs. Ideally, no node frequencies would be significantly different than ERA-40 frequencies. The difference between the three-model ensemble and ERA-40 (Figure 3g) shows that only 20 of the 35 nodes are significantly different than ERA-40, compared to 24 nodes in the five-model ensemble (Figure 3e), and 26 nodes when using the 15-model ensemble (Figure 3c). This supports the conclusion from Table 2 that the three-model ensemble correlates best to ERA-40, then the five-model ensemble, and then the 15-model ensemble. Therefore, the remainder of the paper will use this three-model ensemble to analyze precipitation, but the two American models and the five-model ensemble will also be discussed in section [19] Separating node frequencies into seasons (DJF, MAM, JJA, and SON) reveals the seasonal path through the SOM in the three-model ensemble in Figure 4. The seasons take a counterclockwise route through the SOM. Nodes with highest frequencies in winter are located in the bottom rows of the SOM (IL, NA, and some ST nodes). By springtime, the highest frequencies occur in nodes along the left portion of the SOM (W, ST, and NA nodes). In summer, synoptic patterns in W, LC, and BB nodes across the top of the SOM take place most often, which all have cyclones west of Greenland in common, indicating the North Atlantic storm track s weakening and northward shift in summertime. Autumn patterns share both summer and winter patterns with W and IL nodes occurring most frequently. The fall pattern shifts back to the winter pattern of mostly bottom row nodes, making the seasonal path through the SOM approximately counterclockwise (bottom, left, top, right, bottom of SOM) Precipitation [20] The mean annual precipitation (1961 to 1999) for ERA-40 is displayed in Figure 5a. (All precipitation values discussed are displayed in liquid water equivalent, although 8of20

9 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 4. Three-model ensemble seasonal node frequencies (%) for months (a) DJF, (b) MAM, (c) JJA, and (d) SON. Node frequencies that are significantly different than the three-model ensemble frequency for all seasons (Figure 3f), at a 95% confidence level, are shown in bold, where significantly larger values are only bold but significantly lower values are bold and italic. The darkest shades in all plots indicate the largest values and the contour interval is 0.5. most precipitation on Greenland falls as snow.) This study uses ERA-40 precipitation as the best representation of reality and the advantages and shortcomings of ERA-40 Greenland precipitation is discussed in section 2.1, as well as by Schuenemann et al. [2009]. Large amounts of precipitation dominate the southern portion of the domain where the North Atlantic storm track lies. Precipitation over Greenland is often a result of the interactions between the topography of the ice sheet and onshore flow from passing cyclones [Schuenemann et al., 2009]. A precipitation maximum of 150 cm yr 1 is located on the southeast coast of Greenland where onshore flow from cyclonic winds of passing low-pressure systems causes orographic lift at the margins of the ice sheet where elevation ranges from sea level to over 2000 m just 100 km from the coast. Orographic lift then leads to heavy precipitation events along the southeast coast. Onshore flow over the more gradual slope of the southwest coast (Figure 1) causes fair amounts of precipitation to fall there. The northern half of Greenland, farther away from the North Atlantic storm track, receives less than 40 cm yr 1 precipitation. The central interior of the ice sheet has a minimum precipitation of less than 10 cm yr 1. [21] Mean annual precipitation from the three-model ensemble (Figure 5b) is quite similar to that of ERA-40, with the difference (five-model ensemble minus ERA-40) shown in Figure 5c. The three-model ensemble shows the southeast coast maximum as occurring near the southern tip of Greenland (Figure 5b) while the ERA-40 precipitation extends farther north along the southeast coast (Figure 5a), making the upper southeast coast 15 cm yr 1 too dry in the three-model ensemble representation of precipitation (Figure 5c). However, in the center of the maximum, the three-model ensemble is more than 10 cm yr 1 wetter than 9of20

10 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 5. Annual mean precipitation (cm yr 1 ) for years 1961 to 1999 for (a) ERA-40, (b) three-model ensemble, (c) three-model ensemble difference from ERA-40, (d) CCCMA-CGCM3.1(T63), (e) MIROC3.2(hires), and (f) MPI-ECHAM5. Contour interval is 10 cm yr 1 for all plots. ERA-40. The southwest coast in the three-model ensemble is drier than ERA-40 by more than 10 cm yr 1. The northern half of the ice sheet has similar values for both ERA-40 and the three-model ensemble. [22] The mean annual precipitation from the three models that make up the three-model ensemble reveal that a wet bias from the ECHAM (Figure 5f), a dry bias of the CCCMA (Figure 5d), and the well performing MIROC (Figure 5e) combine to form the three-model ensemble with only subtle differences from ERA-40 (Figure 5c). All of the models have a precipitation maximum on the southeast coast of Greenland, except CCCMA, which has large values on the southeast coast and a precipitation maximum off of the coast. This model underrepresents precipitation along the southeast coast by 60 cm yr 1. On the other hand, ECHAM has a maximum of precipitation on the southeast tip of Greenland of over 210 cm yr 1, approximately 60 cm yr 1 too wet (Figure 5f). The ECHAM is the only model that represents the southwest to northeast extent of the maxima in ERA-40 precipitation along Greenland s southeast coast (Figure 5a). [23] The minimum precipitation (>10 cm yr 1 ) in northern central Greenland is well represented in the models, but it is displaced northward in CCCMA (Figure 5d). This model also fails to show the higher amounts of precipitation that fall in western Greenland near Baffin Bay and is 20 cm yr 1 too dry compared to ERA-40 in this region (Figure 5d). ECHAM has a precipitation maxima in western Greenland approximately 10 cm yr 1 wetter than ERA-40 (Figure 5f). MIROC in Figure 5e shows many of the same features as ERA-40 and of the three models, performs best in reproducing the mean annual precipitation shown in ERA-40. Recall that this model also performed best when correlated to the frequency of synoptic patterns (Table 2). [24] Annual precipitation is the result of the cumulative addition of precipitation from synoptic time scale (several days) events. To understand how the mean annual precipitation comes about, daily precipitation data is used in the 10 of 20

11 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 6. Node averaged three-model ensemble precipitation anomaly (cm d 1 ) (shading) and node anomaly SLP (hpa) from the master SOM (solid contour lines for positive SLP anomalies and dashed contour lines for negative SLP anomalies with 2-hPa contour intervals). Blue shading indicates positive precipitation anomalies, and orange shading indicates negative precipitation anomalies. Node group abbreviations are as in Figure 2. SOM analysis. The average daily precipitation can be calculated for each SLP pattern represented in the SOM. Calculation of the daily precipitation for each model, and the difference from ERA-40, along with the information on the SLP pattern frequency in the models and ERA-40 allows for a detailed analysis and attribution of the differences in precipitation between the models and ERA-40. [25] The three-model ensemble node averaged precipitation anomaly was calculated by subtracting the three-model ensemble mean precipitation (similar to Figure 5b, but with units of cm d 1 ) from the node averaged precipitation for each grid point. This was done for each of the 35 nodes on the SOM and the resulting node averaged three-model ensemble precipitation anomalies (cm d 1 ) are shown by the color shading in Figure 6 (positive anomalies in blue, negative anomalies in orange) overlaid with the SLP anomaly contours from Figure 2 to show the location of cyclones and anticyclones. Therefore, the precipitation plotted in any node represents the average expected precipitation anomaly over the domain, should that node occur on any given day. [26] Figure 6 indicates a strong correspondence between node SLP patterns and precipitation. NA cyclones, along with ST and IL cyclones show above average precipitation at the center of low pressure due to upward vertical motions from surface convergence, as well as along a comma shaped cold front extending southward from the center of circulation. Precipitation is enhanced beyond the expected cyclone precipitation when cyclones interact with Greenland and cause onshore flow and orographic lift. Negative precipitation anomalies occur when cyclones cause offshore flow on Greenland and orographic decent, and also under areas of 11 of 20

12 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 high pressure, where in both cases, subsidence causes dry conditions. [27] The nodes in each of the six node groups discussed in section 3.1 share common precipitation patterns. W nodes show little precipitation over Greenland due to weak cyclones or cyclones too far from Greenland to create strong onshore flow. These nodes, however, commonly take place in summertime when atmospheric moisture is at a maximum; therefore, precipitation over Greenland does result from the weak flows in some of the nodes (Figure 6). LC nodes have cyclones over the Labrador Sea wrapping cyclonic winds onshore at the southernmost portion of Greenland and causing the largest amounts of precipitation to fall over southern Greenland. BB nodes contain cyclones west of Greenland causing onshore flow over primarily the southwest coast of Greenland. The close proximity of BB cyclones to the ice sheet also allows the surface convergence associated with the center of low pressure to cause precipitation to fall farther north along the western portion of Greenland. The circulation around the low-pressure center in ST nodes results in onshore flow wrapping air onto the ice sheet and causing high precipitation amounts over the southeast coast of Greenland and below average precipitation over the southwest coast of Greenland where the cyclone causes offshore flow and descending air. IL nodes contain cyclones east of Greenland causing onshore flow farther north than ST cyclones. The IL nodes show precipitation on the central and upper east coast of Greenland where the cyclonic winds come ashore and below average precipitation over the southern tip of Greenland where IL cyclones cause offshore flow, descending air, and the associated dry conditions. NA cyclones are located too far from Greenland to significantly affect precipitation there. [28] These precipitation patterns are similar to those discussed for ERA-40 by Schuenemann et al. [2009]. There are, however, slight differences between the node averaged precipitation in ERA-40 and the three-model ensemble. Figure 7 shows a selection of three nodes from the master SOM: (6,0) is a BB node, (2,2) is an ST node, and (2,4) is an NA node. The simulated ERA-40 mean daily precipitation for each node is plotted in the ERA-40 precipitation column. The next columns show ERA-40 precipitation subtracted from the three-model ensemble precipitation, and each of the models that make up the three-model ensemble, CCCMA, MIROC, and ECHAM. Each of the top models and the ensemble perform differently in different synoptic situations. [29] Node (6,0), in Figure 7 is a BB node. The synoptic pattern in this node consists of a cyclone over Baffin Bay west of Greenland, creating onshore flow over southern Greenland. This onshore flow produces on average in ERA- 40, a maximum precipitation over southern Greenland of between 0.2 and 1.0 cm d 1. The difference between the three-model ensemble node average precipitation and that of ERA-40 never reaches magnitudes greater than 0.2 cm d 1 in any area on the domain. The three-model ensemble underestimates precipitation over the southern tip of Greenland, but overestimates precipitation just north of the tip (Figure 7). Breaking this difference down into the models that make up the ensemble, the CCCMA is up to 0.6 cm d 1 too dry on the southern tip and the MIROC is up to 0.3 cm d 1 too dry. Both models, however, overestimate precipitation north of the southern tip (<0.2 cm d 1 in CCCMA < 0.1 cm d 1 in MIROC). The ECHAM model, on the other hand, overestimates precipitation over much of southern Greenland by up to 0.5 cm d 1, which is not enough to balance the deficit in the other two models. A feature common to all three models and the ensemble is a dry central east coast between 65 N and 70 N. Recall from Figures 5b, 5d, 5e, and 5f that on a mean annual basis, the models and the ensemble fail to capture the entirety of the north-south extent of the precipitation maxima on the southeast coast in ERA-40 (Figure 5a). Node (6,0) is an example of a node where the three-model ensemble reproduces ERA-40 precipitation reasonably well, but this is more a result of averaging than of three perfectly performing models. [30] In Figure 7 is the ST node, (2,2). The node contains a cyclone southeast of the tip of Greenland wrapping air onshore to the southeast coast of Greenland. Orographic lift causes up to 1.0 cm d 1 of precipitation to fall off the southeast coast of Greenland in ERA-40. The mild difference between the three-model ensemble and ERA-40 precipitation again only reaches 0.2 cm d 1. The three-model ensemble underestimates precipitation over the southern portion of Greenland by less than 0.1 cm d 1. This is due to a combination CCCMA underestimating precipitation by 0.5 cm d 1 and the ECHAM overestimating precipitation by nearly 0.4 cm d 1 on the southeast coast, while the MIROC underestimates precipitation by 0.1 cm d 1 over Greenland and up to 0.3 cm d 1 off the upper southeast coast. These sometimes drastic differences between the models and ERA-40 balance each other to produce minimal differences in the three-model ensemble. [31] Figure 7 shows an NA node (node (2,4)) whose synoptic pattern has a cyclone too far from Greenland to significantly affect precipitation, but this node shows the underestimation of precipitation along the position where a cold front would lie in the ensemble and models. (This feature also exists in node (2,2) in Figure 7.) The common position of a cold front with respect to a cyclone is a comma shape extending southward from the center of circulation in the cyclone. ERA-40 produces up to 0.6 cm d 1 along the cold front in node (2,4). In the ensemble this is underestimated by up to 0.2 cm d 1. This underestimation of precipitation along the cold front is evident by a swath of orange shades, surrounded by blue shades, extending from the low-pressure center to the bottom of the domain in each of the models and the ensemble. This dry cold front could be a result of faulty front positioning or intensity in the three models. [32] Figure 7 has shown that even though the magnitude of precipitation differences between ERA-40 and the threemodel ensemble are small, these differences are amplified in the individual models. The CCCMA is consistently too dry and the ECHAM consistently too wet. The MIROC shows more subtle differences from ERA-40. When choosing a single model to reproduce the ERA-40 precipitation over the domain, the MIROC is the best choice. The best overall option, however, is the three-model ensemble Precipitation Over Greenland [33] To add to the knowledge base of the state of the mass balance of the GrIS, precipitation over only Greenland 12 of 20

13 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 7. For the three selected nodes are given: the ERA-40 precipitation, the difference between the three-model ensemble and ERA-40 precipitation, CCCMA-CGCM3.1(T63) and ERA-40 difference, MIROC3.2(hires) and ERA-40 difference, and MPI-ECHAM5 and ERA-40 difference (cm d 1 ). For the ERA-40 column, refer to the color bar at the bottom of the column (note that these are not precipitation anomalies). Precipitation differences (see color bar at bottom of difference columns) are shown by the colored shading, where blue colors in the difference plots indicate where the model predicts too much precipitation and orange shades show where the model underestimates precipitation compared to ERA- 40. Contour lines in all plots indicate node anomaly SLP (hpa) from the master SOM (Figure 2). Note that this is not a SOM, but nodes taken from the SOM for comparison among the models. becomes the focus of the remainder of this paper, with an analysis of the ability of the three-model ensemble to reproduce ERA-40 precipitation over the ice sheet. Assessment of the skill of the three-model ensemble in predicting Greenland precipitation from 1961 to 1999 will provide confidence for using the three-model ensemble precipitation predictions for the 21st century in part 2 of this paper, which will ultimately assist in making future GrIS mass balance predictions. [34] Node averaged daily net Greenland precipitation was calculated by averaging, for each node, the precipitation over all of Greenland each time that node occurred in the input data, and is plotted in Figure 8a for ERA-40 and Figure 8b for the three-model ensemble. The general pattern in the SOM of high and low averaged daily Greenland precipitation nodes is similar among ERA-40 and the threemodel ensemble. The synoptic patterns represented by BB and LC nodes in the upper right portion of the SOM produce the greatest daily net Greenland precipitation amounts with values in these nodes exceeding cm d 1 due to the large area of positive precipitation anomalies over Greenland in these LC and BB nodes (Figure 6). [35] The node averaged daily net Greenland precipitation difference between ERA-40 and the three-model ensemble, plotted in Figure 8c, indicates that the three-model ensemble usually overestimates these highest values in the BB and LC nodes (represented by solid contours). Recall the discussion of one of these nodes, (6,0), in Figure 7, where the overestimated daily precipitation was broken down into the 13 of 20

14 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 8. Greenland precipitation by node, where each number represents the node in the same position in the master SOM (Figure 2). Positive values have solid contours, while negative values in difference plots are contoured with dashed lines. The darkest shades in all plots indicate the largest values, and in the difference plots, largest absolute values. (a) Node averaged daily net Greenland precipitation from ERA- 40 (cm d 1 ), (b) same as Figure 8a but for the three-model ensemble, (c) difference between three-model ensemble and ERA-40 (cm d 1 ), (d) ERA-40 mean annual node contribution to Greenland precipitation (cm yr 1 ), (e) same as Figure 8d but for the three-model ensemble, and (f) difference between threemodel ensemble and ERA-40 (cm yr 1 ). Figures 8a and 8b are comparable with a contour interval of 0.019, and Figures 8d and 8e are comparable with a contour interval of of 20

15 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Table 3. Attribution of Greenland Precipitation Difference Between ERA-40 and the Model Ensembles as Well as Individual Models a Model Precipitation Net Difference Intrapattern Variability Component Pattern Frequency Component Combined Term ERA model ensemble CCCMA-CGCM3.1(T63) MIROC3.2(hires) MPI-ECHAM model ensemble GFDL-CM NCAR-CCSM a Precipitation difference is in cm yr 1. The annual mean precipitation over Greenland for each model is listed in the precipitation column. The net difference (model minus ERA-40 precipitation) between the model and ERA-40 is listed in the net difference column. The attribution of this difference is divided into and listed in the intrapattern variability component, pattern frequency component, and combined term columns. contributions from each of the three models making up the ensemble. The lowest node averaged daily net precipitation values occur in NA and some W nodes, as would be expected due to the weak onshore flow in both of these node groups. The three-model ensemble underestimates ERA-40 daily net Greenland precipitation (represented by dashed contours) for most of the W nodes as well as half of the ST nodes (Figure 8c), of which node (2,2) was analyzed in greater detail in Figure 7. The node average daily net precipitation differences between ERA-40 and the threemodel ensemble are all low magnitude and make up only a small percentage, up to 20%, of the daily precipitation for each node. [36] The node averaged daily net Greenland precipitation only tells how much precipitation on average should be expected, should a given synoptic pattern take place one day; however, not all nodes take place equally as often (Figure 3). Therefore, it is necessary to take the node frequency of occurrence into consideration when calculating the contribution of each synoptic pattern to the total Greenland precipitation. The mean annual node contribution to Greenland precipitation was calculated by multiplying the node averaged daily net Greenland precipitation (p n ) (cm d 1 ), displayed in Figure 8a (Figure 8b), by the frequency of occurrence (f n ) (%), shown in Figure 3a (Figure 3f), and 365 d yr 1. The results of this calculation for ERA-40 (threemodel ensemble) are displayed in Figure 8d (Figure 8e) in cm yr 1. Summing over all nodes (n) gives the annual precipitation over Greenland (P annual )givenby P annual ¼ 365 day yr X 35 n¼1 f n p n : Nodes with the highest mean annual contribution to Greenland precipitation are BB nodes in the upper right portion of the SOM for both ERA-40 and the three-model ensemble (Figures 8d and 8e). Synoptic patterns represented by BB nodes (6,0) and (6,1) both contribute more than 2 cm yr 1 of precipitation to Greenland by wrapping air onto the southern region of Greenland combined with the high precipitation in western Greenland (Figure 6). ERA-40 has higher magnitudes of annual contribution for these nodes. [37] The difference between three-model ensemble and ERA-40 node contribution to annual precipitation is shown ð3þ in Figure 8f where solid contours show annual node contributions that are greater in the three-model ensemble and dashed contours show nodes whose values are greater in ERA-40. The annual contribution to Greenland precipitation by BB node (6,1) in the three-model ensemble is 0.63 cm yr 1 less than in ERA-40 (Figure 8f). While the node averaged daily precipitation value for that node is the same in ERA-40 and the three-model ensemble (Figures 8a and 8b) the smaller annual contribution is due to the lower frequency of occurrence of this node by 1.05% in the threemodel ensemble than in ERA-40 (Figure 3g), W nodes, similarly to BB nodes, contribute less to annual precipitation in the ensemble than in ERA-40. On the contrary, LC and NA nodes have higher annual node contributions in the three-model ensemble than in ERA-40 (Figure 8f). The difference in annual contribution between the three-model ensemble and ERA-40 (Figure 8f) takes on an almost identical shape as the difference in frequency (Figure 3f), rather than the node average precipitation differences (Figure 8c), but the production of precipitation by the synoptic pattern in each node, as well as the frequency of occurrence of the nodes, are both responsible for differences in annual contribution to precipitation by node Attribution of Precipitation Differences [38] The mean annual net precipitation over Greenland for the reanalysis, three- and five-model ensembles, as well as the individual models that make up the ensembles was calculated by performing the summation over all nodes in equation (3) and is shown in the precipitation column of Table 3. The difference between each of the models and ERA-40 (model minus ERA-40) is shown in the net difference column of Table 3. The three-model ensemble produces 35.8 cm yr 1 precipitation over Greenland, the same as ERA-40. This number, when broken down into the contribution from the three individual models, is a balance between the CCCMA that is 8.2 cm yr 1 too dry and both the MIROC and the ECHAM models, which is 1.1 cm yr 1 and 7.1 cm yr 1 too wet (Table 3). Even though this average shows that the three-model ensemble gets the correct precipitation overall, Figure 8f showed that the ensemble did not get the same magnitude of Greenland precipitation as ERA-40 in the same way from the same nodes, which is further emphasized by the different mean annual precipitation values of the models making up the ensemble. 15 of 20

16 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 [39] The source of differences between the modeled and ERA-40 Greenland annual precipitation can be determined by rewriting equation (3) as P annual ¼ 365 day yr X 35 n¼1 ðf n þ Df n Þðp n þ Dp n Þ: ð4þ The annual modeled precipitation equals the summation over all nodes of the ERA-40 values plus a difference (delta) term. The frequency is now represented by the ERA-40 frequency plus the difference in frequency between the model and ERA-40 (f + Df), where the ERA-40 values were shown in Figure 3a and difference values for the three-model ensemble in Figure 3g. The precipitation is then represented by the ERA-40 precipitation plus the difference in precipitation between the model and ERA- 40 (p + Dp), where the ERA-40 values were shown in Figure 8a and difference values in Figure 8c. Expanding the expression in equation (4) gives P annual ¼ 365 day yr X 35 n¼1 f n p n þ f n Dp n þ Df n p n þ Df n Dp n ; which indicates that the total annual Greenland precipitation in a model data set can be represented as the ERA-40 precipitation (first term), plus three terms that represent the net difference in annual precipitation between the model and ERA-40. The first difference term (f n Dp n ) is referred to as the intrapattern variability component, the second difference term (Df n p n ) is the pattern frequency component, and the third difference term (Df n Dp n ) is referred to as the combined term. These three terms, when summed, are the net difference between the model precipitation and ERA-40 precipitation, which is shown on a node-by-node basis for the three-model ensemble in Figure 8f. [40] The intrapattern, or within-node, variability term represents the contribution to the model precipitation difference from ERA-40, assuming that that the model frequency of occurrence of synoptic patterns in the atmosphere are correct (matching that of ERA-40 in Figure 3a) in the model, but the node average precipitation does not match that of ERA-40 (Figure 8c). Therefore this term represents Greenland precipitation differences between ERA-40 and the model resulting from differences in the amount of precipitation produced when the correct frequency of synoptic patterns takes place. The difference between the modeled and ERA-40 node average precipitation could stem from a number of differences between the simulations. Models may have different amounts of precipitable water in the atmosphere or different precipitation physics, leading to the precipitation differences indicated by this term. It should be noted that because this term only accounts for differences in node average precipitation, the differences are mainly due to noncirculation differences between the model and reanalysis, although small circulation differences between the model and ERA-40 within a single node may also make a small contribution to this term (i.e., differences in circulation that are smaller than differences in circulation between adjoint nodes). [41] The pattern frequency component term represents differences in precipitation between the model and ERA- 40 that are driven by the different frequency of occurrence ð5þ of nodes in the model and ERA-40 (Figure 3g for the threemodel ensemble). This is what would take place if the model reproduced the ERA-40 node average daily precipitation (Figure 8a) when a given synoptic pattern took place, but the frequency of occurrence of this pattern in the model does not match the ERA-40 frequency. Therefore this term represents precipitation differences resulting from differences in the frequency of occurrence of synoptic patterns in the model. One caveat of attributing the difference to synoptic pattern frequency (circulation) differences is that the difference between the three-model ensemble node frequency (Figure 3g) and the ERA-40 frequency (Figure 3a) must sum to zero. In other words, because the node frequencies are percentages, the node frequency values in Figure 3g sum to 100%, as do those in Figure 3a. When taking the difference of these node frequencies, the sum of the node s differences in Figure 3g must equal 0%. Therefore, when calculating the summation in equation (5), the pattern frequency component can only be nonzero if nodes that are increasing in frequency have different node averaged daily net precipitation values than those that are decreasing in frequency. Therefore, throughout the following discussions, the intrapattern variability component dominates in magnitude. [42] The combined term is a term representing errors in the modeled precipitation (Figure 8c) that are due to errors in the modeled frequency of occurrence of weather patterns (nodes) (Figure 3g). These values make up only a small fraction of the net difference in precipitation (Table 3) and will not be discussed explicitly. [43] This partitioning of the annual precipitation differences between ERA-40 and the models were performed for the three-model ensemble, five-model ensemble, and each of the models making up the ensembles. The mean annual precipitation over Greenland, net difference between the model and ERA-40 (model minus ERA-40), and results for the intrapattern variability component, pattern frequency component, and combined terms are listed in Table 3. Positive values in the right columns of Table 3 indicate where the models have a wet bias and negative values indicate a dry bias in the models. [44] The calculation from equation (5) can be done for the entire EASE grid over the domain as well, where node averaged net daily precipitation is the average at each grid point in the EASE grid for the three-model ensemble and the three models that make up the ensemble. In Figure 9, blue shades show areas where the three models overestimate precipitation and orange shades show where the models underestimate precipitation compared to ERA-40. Note that the color scales differ for each column, as shown in the color bar at the bottom of Figure 9. [45] Table 3 indicates that the net difference between the annual Greenland precipitation from the three-model ensemble and ERA-40 is approximately zero, but this is actually a balance of 0.4 cm yr 1 positive intrapattern variability component and 0.4 cm yr 1 negative pattern frequency component in the three-model ensemble (Table 3). The positive intrapattern frequency component indicates that when a given synoptic pattern takes place, on average, it drops more precipitation over Greenland in the three-model ensemble than in the ERA-40 reanalysis, primarily over northeastern Greenland, by up to 20 cm yr 1 (Figure 9). 16 of 20

17 SCHUENEMANN AND CASSANO: GREENLAND PRECIPITATION, 1 Figure 9. The net difference in annual mean precipitation (model minus ERA-40) for the three-model ensemble and the three separate models that make up the ensemble and the contribution to this difference from the intrapattern variability component, pattern frequency component, and combined terms discussed in the text. The negative pattern frequency component ranges from 4.5 cm yr 1 drier over western Greenland to up to 9 cm yr 1 wetter over the southeast coast, but over a smaller area than the drier west (Figure 9). The wetter eastern Greenland is from a higher frequency of ST and LC nodes in the models compared to ERA-40, both of which are representative of synoptic patterns that produce large amounts of precipitation over the southeast coast. The drier west is from a lower frequency of BB and W nodes in the three-model ensemble that favor western Greenland precipitation. Essentially, nodes that drop less precipitation over Greenland take place more often in the three-model ensemble than the higher precipitation nodes. These differences in the three-model ensemble can then be broken down further into the individual models that make up the ensemble. The frequency and node average daily net Greenland precipitation used for 17 of 20