Intercomparison of Near-Surface Temperature and ... - AMS Journals

VOLUME 18

JOURNAL OF CLIMATE

15 DECEMBER 2005

Intercomparison of Near-Surface Temperature and Precipitation Extremes in AMIP-2 Simulations, Reanalyses, and Observations VIATCHESLAV V. KHARIN

AND

FRANCIS W. ZWIERS

Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, Victoria, British Columbia, Canada

XUEBIN ZHANG Climate Monitoring and Data Interpretation Division, Meteorological Service of Canada, Downsview, Ontario, Canada (Manuscript received 2 October 2004, in final form 15 April 2005) ABSTRACT The extremes of near-surface temperature and 24-h and 5-day mean precipitation rates are examined in simulations performed with atmospheric general circulation models (AGCMs) participating in the second phase of the Atmospheric Model Intercomparison Project (AMIP-2). The extremes are evaluated in terms of 20-yr return values of annual extremes. The model results are validated against the European Centre for Medium-Range Weather Forecasts and National Centers for Environmental Prediction reanalyses and station data. Precipitation extremes are also validated against the pentad dataset of the Global Precipitation Climatology Project, which is a blend of rain gauge observations, satellite data, and model output. On the whole, the AGCMs appear to simulate temperature extremes reasonably well. Model disagreements are larger for cold extremes than for warm extremes, particularly in wet and cloudy regions, and over sea ice and snow-covered areas. Many models exhibit an exaggerated clustering behavior for temperatures near the freezing point of water. Precipitation extremes are less reliably reproduced by the models and reanalyses. The largest disagreements are found in the Tropics where the parameterizations of deep convection affect the simulated daily precipitation extremes.

1. Introduction The Atmospheric Model Intercomparison Project (AMIP) is a major international effort for the comprehensive evaluation and validation of current atmospheric models under realistic conditions in a systematic and consistent manner. AMIP defines a standard experimental protocol for global atmospheric general circulation model (AGCM) simulations and provides a community-based infrastructure in support of climate model diagnosis, validation, intercomparison, documentation, and model output access. Virtually the entire international climate modeling community has participated in this project since its inception in 1990. The first phase of the project (AMIP-1: Gates 1992) resulted in numerous publications in recent years and was followed by the second phase (AMIP-2) in 1996

Corresponding author address: Dr. Viatcheslav V. Kharin, Canadian Centre for Climate Modelling and Analysis, University of Victoria, Box 1800 STN CSC, Victoria, BC V8W 2Y2, Canada. E-mail: [email protected]

(Gleckler 1996). The first AMIP-2 results were presented at the AMIP workshop in Toulouse, France, in November 2002. This paper reports results from an AMIP-2 diagnostic subproject that examines the ability of the current generation of AGCMs to simulate extremes of the near-surface climate. Climatic extremes are an important aspect of climate variability with significant societal impacts. By definition, extremes occur at the outer limits of spatial and temporal climate variability and, therefore, simulating extremes represents a considerable challenge for global climate models. Many of the processes crucial for the development of extreme events are unresolved and, thus, are parameterized in global models. It is therefore of great interest to document extremes as simulated by modern AGCMs and to validate them against the available observational evidence. In this study we consider extremes of near-surface temperature and 24-h and 5-day mean precipitation rates. The extremes are evaluated in terms of estimated 20-yr return values of the annual extremes of the con-

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sidered quantities. These are thresholds that are exceeded by the annual extremes once every 20 years, on average. This approach has been applied in several recent papers (Zwiers and Kharin 1998; Kharin and Zwiers 2000, 2005; Wehner 2004). The model results are verified against a number of available reanalyses and observed datasets. One of the goals of the AMIP-2 diagnostic subproject on climate extremes is to identify key model characteristics and features that are important for simulating climate extremes. However, the dependence of the simulated climate variability on model characteristics such as spatial horizontal and vertical resolution, type of physical parameterizations, etc., can often be established only in very general terms, if at all. Therefore our primary goal here is only to document the performance of the participating AMIP-2 models in simulating climate extremes. Nonetheless, our findings do provide indicators of the role of some parameterized processes in the simulation of extremes. The outline of this paper is as follows. First we describe the available model and validation datasets and summarize the key features of the participating AMIP-2 models in section 2. The extreme value methodology and model intercomparison approach are introduced in section 3. The simulated near-surface warm and cold temperature extremes are described in section 4. The precipitation extremes are discussed in section 5. The findings of the study are summarized in section 6.

2. Datasets a. The AMIP-2 simulations The AMIP-2 simulations span a 17-yr period extending from January 1979 to December 1995. The AMIP-2 experimental protocol specifies that all simulations use the same observed sea surface temperatures (SSTs) and sea ice concentrations as the lower boundary conditions (Fiorino 1996). The complete AMIP-2 guidelines are summarized in the AMIP Newsletter, No. 8 (Gleckler 1996). Not all modeling groups that participated in AMIP-2 (about 25 in total) were able to submit high-frequency model output. Table 1 lists the AMIP-2 models that are analyzed in this study and summarizes their spatial discretization and resolution. Six-hourly accumulated precipitation amounts were available from 16 AMIP-2 simulations performed by 14 institutions. Daily nearsurface air temperature extremes were available from 12 models. Ten modeling groups provided both 6-hourly precipitation amounts and daily temperature extremes. A prominent omission in Table 1 is the atmospheric model of the Hadley Centre for Climate

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Prediction and Research of the U.K. Meteorological Office (UKMO HadAM3) for which only monthly output was available. However, high-frequency precipitation output was available for the UGAMP-98a model, a higher-vertical-resolution version of the AMIP-2 UKMO HadAM3 model. Both models utilize identical physical parameterizations and dynamical formulations and have the same horizontal resolution. The UGAMP-98a model has higher vertical resolution in the stratosphere and upper troposphere with a total of 58 levels in the vertical as compared to 19 levels in the UKMO HadAM3 model. Annual temperature and precipitation extremes in the coupled UKMO HadCM3 model that uses HadAM3 as the atmospheric component are examined in Hegerl et al. (2004). A detailed intercomparison of all model features was not possible at the time of this writing because the complete AMIP-2 model documentation was not available for all participating models at that time. Model characteristics such as spatial discretization, horizontal and vertical resolution, and the representation of parameterized processes vary considerably from one model to another. The majority of participating AMIP-2 models use a spectral representation of the basic prognostic quantities with either a triangular or rhomboidal truncation. The remaining models use various types of finite difference discretization. The horizontal grid resolution ranges from 72 ⫻ 45 to 192 ⫻ 96 with a median grid size of 128 ⫻ 64. The vertical resolution ranges from 9 to 60 levels. There are several “twin model” simulations that were performed by different groups, but using atmospheric models closely related to each other. For example, the NCAR-98a and SUNYA-99a models (Table 1) are both based on the NCAR Community Climate Model (CCM3). Two contributions from Japan [the Japan Meteorological Agency 1998a (JMA-98a) and the Meteorological Research Institute 1998a (MRI-98a)] are also similar with the latter being a lower resolution descendant of the former. Two modeling centers, the European Centre for Medium-Range Weather Forecasts (ECMWF) and National Centers for Environmental Prediction (NCEP), submitted pairs of simulations that are performed with generally identical models but with different resolutions. These simulations may provide some insights into the effects of resolution on the extreme-value statistics considered in this study. The original 6-hourly precipitation output from all models was binned to obtained daily values. Some model groups performed simulations beyond year 1995. In the present study, we use only the first 17 years from 1979 to 1995. One month of 6-hourly precipitation output from the ECMWF-98b model in year 1980 appears

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TABLE 1. AMIP-2 simulations analyzed in the present study and the availability of high-frequency model output of precipitation (P) and daily extremes of near-surface temperature (T ). Model CCCMA-99a

Designation CCC GCM3 (T47 L32) 1999

Grid size 96 ⫻ 48

Institution

Canadian Centre for Climate Modelling and Analysis, Victoria, BC, Canada CCSR-98a CCSR/NIES AGCM (T42 L20) 1998 128 ⫻ 64 Center for Climate System Research, Tokyo, Japan CNRM-00a CNRM ARPEGE Cy18 (T63 L45) 2000 128 ⫻ 64 Center National de Recherche Meteorologique, Toulouse, France COLA-00a COLA V2.2 (R40 L18) 2000 128 ⫻ 102 Center for Ocean–Land–Atmosphere Studies, Calverton, Maryland DNM-98a DNM A5421 (4 ⫻ 5 L21) 1998 72 ⫻ 45 Department of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia ECMWF-98a ECMWF CY18R6 (T63 L50) 1998 180 ⫻ 91 European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom ECMWF-98b ECMWF CY18R6 (T159 L60, “reduced” 180 ⫻ 91 European Centre for Medium-Range Weather Gaussian grid) 1998 Forecasts, Reading, United Kingdom GISS-98a GISS B295DM12 (4 ⫻ 5 L9) 1998 72 ⫻ 46 Goddard Institute for Space Studies, New York JMA-98a JMA GSM9603 (T63 L30) 1998 192 ⫻ 96 Japan Meteorological Agency, Tokyo, Japan (similar to MRI-98a) MPI-98a MPI ECHAM4 (T42 L19) 1996 128 ⫻ 64 Max-Planck-Institut für Meteorologie, Hamburg, Germany MRI-98a MRI MRI/JMA98 (T42 L30) 1998 128 ⫻ 64 Meteorological Research Institute, Ibaraki-ken, Japan (similar to JMA-98a) NCAR-98a NCAR CCM3.5 (T42 L18) 128 ⫻ 64 National Center for Atmospheric Research, Boulder, Colorado (similar to SUNYA-99a) NCEP-99a NCEP REANAL2 (T42 L18) 1998 128 ⫻ 64 National Centers for Environmental Prediction, Washington, D.C. NCEP-99b NCEP REANAL2 (T62 L28) 1999 192 ⫻ 94 National Centers for Environmental Prediction, Washington, D.C. SUNYA-99a SUNYA/NCAR CCM3 (T42 L18) 1999 128 ⫻ 64 State University of New York at Albany, Albany, New York (similar to NCAR-98a) UGAMP-98a UGAMP HADAM3 (3.75 ⫻ 2.5 L58) 1998 96 ⫻ 73 U.K. Universities Global Atmospheric Modelling Programme (similar to UKMO HADAM3 3.75 ⫻ 2.5 L19) UIUC-98a UIUC ST-GCM (4 ⫻ 5 L24) 1998 72 ⫻ 46 University of Illinois at Urbana–Champaign, Urbana, Illinois YONU-98a YONU ST15 (4 ⫻ 5 L15) 1998 72 ⫻ 46 Yonsei University, Seoul, South Korea

to be corrupted, so we withheld this year from the analysis. To obtain a 17-yr record for this simulation we included the available 1996 output instead.

b. Validation datasets Validation of annual extremes of daily statistics on a global scale is a difficult task because reliable gridded data comparable to model output are not readily available. Essentially, two types of information were available to us for the validation of temperature and precipitation extremes, namely reanalyses and station records. The obvious advantage of reanalyses is that their output is gridded and global and therefore comparable to the model output, allowing model validation in areas where no direct observations are available. However, our confidence in the reanalyzed precipitation is generally much weaker than that in surface temperature because precipitation observations are generally not assimilated into the current global reanalyses.

P

T

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

On the other hand, station data have limited spatial coverage and, by their nature as point measurements, are not directly comparable to the gridded model output. Reanalyses attempt to produce long-term consistent meteorological gridded output using a fixed version of the data assimilation system. Four reanalyses were available for the current study (Table 2). The older NCEP–NCAR reanalysis (Kalnay et al. 1996), referred to hereafter as the NCEP1 reanalysis, was used to estimate temperature and precipitation extremes in some previous studies. In particular, Kharin and Zwiers (2000) indicated that the amplitude of the extreme precipitation in the Tropics may be underestimated in the NCEP1 reanalysis (see also NCEP–NCAR 1997a). Also, daily maximum temperatures are unrealistically high in some regions over land owing to problems in the boundary layer formulation (NCEP–NCAR 1997b). The newer NCEP–Department Of Energy (DOE) AMIP-II reanalysis (Kanamitsu et al. 2002), referred to

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TABLE 2. Validation datasets of daily extremes of near-surface temperature (T ) and precipitation (P). Label

Designation

Grid size

T

P

NCEP1 NCEP2 ERA-15 ERA-40 GDCN GTS CMAP

1979–95 NCEP–NCAR reanalysis, T62L28 1979–95 NCEP–DOE AMIP-II reanalysis 2, T62L28 1979–93 ECMWF reanalysis, T106L60 1979–95 ECMWF reanalysis, T159L60 Global Daily Climatology Network station dataset Global Telecommunication System station dataset Pentad CPC Merged Analysis of Precipitation

192 ⫻ 94 192 ⫻ 94 144 ⫻ 73 144 ⫻ 73 28 782 5720 144 ⫻ 72

⫻ ⫻

⫻ ⫻ ⫻ ⫻ ⫻ ⫻ ⫻

hereafter as the NCEP2 reanalysis, is a rerun of NCEP1 with updated physics and correction of known errors. Among other things, changes in NCEP2 include a smoother orography than in NCEP1, a nonlocal boundary layer parameterization, and changes to the deep convective parameterization. Both NCEP1 and NCEP2 reanalyses have T62 spectral resolution in the horizontal and 28 levels in the vertical. The model output is available on a 192 ⫻ 94 Gaussian grid in both cases. We have also used two versions of the ECMWF reanalyses; the older ECMWF Re-Analysis (ERA-15) (Gibson et al. 1997) and the more recent ERA-40 (Simmons and Gibson 2000). ERA-15 covers the period January 1979–February 1994, while ERA-40 covers the time period from mid-1957 to 2001. The vertical resolution of the assimilating model in ERA-40 was increased from 31 to 60 levels and the top level was raised from 10 to 0.1 hPa. The model physics and the surface parameterization were also updated. The spectral horizontal resolutions of ERA-15 and ERA-40 are T106 and T159, respectively. The data from both ECMWF reanalyses were available on a regular 2.5° ⫻ 2.5° latitude–longitude grid. We use only years 1979–95 from all four reanalyses to be consistent with the 17-yr AMIP-2 period. Although the older NCEP1 and ERA-15 reanalyses are essentially superseded by the newer NCEP2 and ERA-40 reanalyses, we consider all four to examine the sensitivity of the extreme value statistics to the changes in physical parameterizations, enhanced spatial resolution, and spinup procedures. With regard to the latter, ERA-15 precipitation rates are derived from 6-h accumulations at the end of 18-h or 24-h forecast periods, that is, at least 12 h from the moment of forecast initialization. Precipitation rates in all other reanalyses are based on 0–6-h forecasts. A note of caution also bears on the interpretation of daily extremes of near-surface temperature in the reanalyses. Although this quantity is generally much better constrained by the observations than the precipitation forecasts, it is still subject to limitations of the land surface schemes in the corresponding assimilation models.

⫻

Station data, being point measurements, are not necessarily representative of areas that correspond to model grid boxes, particularly on short time scales. Station measurements are affected by various local microclimatological and topographic effects. In addition, they are prone to measurement errors and inhomogeneities due to changes in observation procedures, instrumentation, exposure, and location. Moreover, station data are only available for limited areas. Despite these limitations, we use daily precipitation station records to obtain a general idea of the magnitude and spatial distribution of the observed precipitation extremes. In the present study we combine two station datasets. The majority of station records come from the Global Daily Climatology Network (GDCN) archive of the National Climatic Data Center (NCDC) of the U.S. National Oceanic and Atmospheric Administration (available online at http://www.ncdc.noaa.gov/gdcn.html). All of the GDCN data have been subjected to an extensive set of quality control procedures. To improve spatial coverage, the GDCN data were complemented with an additional set of records from the global telecommunication system (GTS) that were kindly provided by P. Xie (2002, personal communication). The GTS data have undergone only some basic quality control, and there are many missing values. A small number of conflicts with duplicate stations in the combined GDCN– GTS dataset were resolved in favor of the GDCN records. Since station observations in some parts of the world were available only for years prior to 1979, we decided to extend the observational period to include all years from 1950 onward for better spatial coverage. The total number of stations used exceeds 33 000. The station density varies greatly from one region to another (Fig. 1). There has also been an effort to produce global gridded precipitation products by merging various sources such as rain gauge observations, satellite estimates, and, optionally, reanalyses in the regions where neither rain gauge nor satellite measurements are available. These products are currently not available on a daily basis and are the subject of ongoing research. One such product

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to create the monthly CMAP products (Xie and Arkin 1997). The CMAP pentads are used to evaluate the ability of the models and reanalyses to reproduce extremes of 5-day precipitation amounts.

3. Methodology a. Return values The extreme value analysis approach follows that presented in Zwiers and Kharin (1998) and Kharin and Zwiers (2000). The basic idea is to estimate return values of annual extremes at every grid location for nearsurface temperature and precipitation rates. Return values are the thresholds that are exceeded with probability 1/T, where T is the return period in years. These thresholds are estimated from a generalized extreme value (GEV) distribution fitted to a sample of annual extremes at every grid point. The GEV distribution encompasses all three possible asymptotic extreme value distributions predicted by large sample theory (see, e.g., Leadbetter et al. 1983) and has the form

FIG. 1. Number of station records available in each grid box of the 128 ⫻ 64 Gaussian grid (approximately 2.8° ⫻ 2.8°).

used in the present study is the pentad Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) that is a blend of gauge observations, satellite observations, and precipitation fields from the NCEP– NCAR reanalysis. This product, which is available on a 2.5° ⫻ 2.5° latitude–longitude grid (Xie et al. 2003), was produced with a modified version of the algorithm used

F 共x兲 ⫽

冦

冋 冉 冋冉

exp ⫺ exp ⫺ exp ⫺ 1 ⫺ ␬

冊册 冊册

x⫺␰ ␣

x⫺␰ ␣

The GEV distribution has three adjustable parameters: the location parameter ␰ that represents the central position of the GEV distribution, the scale parameter ␣ that is associated with the interannual variability of annual extremes, and the shape parameter ␬ that controls the shape of the distribution tails. The case ␬ ⫽ 0 is known as the Gumbel distribution. The Weibull distribution (␬ ⬎ 0) is bounded from above. The Fréchet distribution (␬ ⬍ 0) is heavy tailed, that is, the upper tail of its probability density function converges to zero at a slower rate than that of the other two types of extreme value distributions. The convention for the sign of the shape parameter used in Eq. (1) is common in the hydrology literature. The current practice in the statistical literature is to represent the shape parameter as ␥ ⫽ ⫺␬. It is worthwhile to keep in mind that the GEV distribution theory is valid asymptotically, that is, when extremes are drawn from increasingly larger populations. The Gumbel distribution is the limiting distribution of extremes drawn from many standard parent distributions, including normal and exponential (Leadbet-

,

1Ⲑ␬

␬ ⫽ 0, ␬ ⫽ 0,

1⫺␬

x⫺␰ ⬎ 0. ␣

共1兲

ter et al. 1983). The main reason for using a threeparameter GEV distribution for annual temperature and precipitation extremes is to account for lack of convergence to their respective limiting distributions. The convergence rate to the asymptotic limit depends on the underlying parent distribution. Convergence occurs quickly for extremes drawn from near-exponential distributions but very slowly for those drawn from nearnormal distributions (e.g., Kharin and Zwiers 2000). The parent distribution of temperature extremes is likely to be nearly normal, whereas the upper tail of the precipitation distribution is likely to be similar to that of the exponential distribution. Also, air temperature typically has a longer decorrelation time than daily precipitation rates, which decreases the effective sample size. Therefore, we anticipate that the distribution of annual precipitation extremes is closer to an asymptotic Gumbel distribution than that of annual temperature extremes. In this study, the three parameters are estimated by the method of L moments (Hosking 1990, 1992) with the modification of Dupuis and Tsao (1998) to ensure

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the feasibility of the obtained estimates. The maximum likelihood method, which is also often used to estimate distribution function parameters (e.g., Kharin and Zwiers 2005), is a less advisable choice in the present setting because the available samples are very short (typically 17 annual extremes). The maximum likelihood method is known to occasionally result in unreliable estimates of the GEV distribution parameters in such situations (e.g., Martins and Stedinger 2000). For each dataset we calculate 20-yr return values of annual extremes of daily maximum air (2 m) temperature (Tmax), daily minimum air temperature (Tmin), and 24-h precipitation (P) at each grid location. We also calculate 20-yr return values of nonoverlapping 5-day mean precipitation rates (P5) in order to compare model and reanalyzed results with those for the CMAP pentads. The uncertainties of the local return value estimates derived from samples of 17 annual extremes are fairly large. However, in this study model performance is evaluated on a global, or continental-wide spatial scales. Hence, for intercomparison purposes, we use statistics obtained by averaging over very large regions, such as the whole globe, land, ocean, or zonal averages, for which the sampling variability is greatly reduced. The sampling variability in the estimated return values is manifested by a great deal of spatial noise, especially for precipitation annual extremes. Thus, to present maps of 20-yr return values of annual precipitation extremes we apply a spatial smoothing technique following that of Zwiers and Kharin (1998) by first averaging the L moments over nine (3 ⫻ 3) adjacent grid boxes and then estimating the GEV distribution parameters from the smoothed L moments. This smoothing procedure implicitly makes the assumption that annual extremes at a given grid box have statistical characteristics similar to those of the extremes at its nearest neighbors. This smoothing procedure has little effect on the large-scale structure of the estimated return values and practically no effect on their global averages. Generally, it is advisable to examine the goodness of fit of the assumed statistical distribution. However, the relatively short records available for this study limit the power of such tests. Our experience indicates that annual extremes of daily precipitation are generally “well behaved” and that they generally follow a Gumbel distribution (␬ ⫽ 0) over most of the globe, except in extremely dry regions where the shape parameter tends to be negative (heavy-tailed distributions). We also found that the distributions of annual temperature extremes tend to be short tailed (␬ ⬎ 0), as would be expected for extremes drawn from finite samples of normally distributed observations.

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Kharin and Zwiers (2000) found that the GEV distribution may be inappropriate for annual temperature extremes in areas where annual extremes are close to the freezing point because simulated annual temperature extremes in that study clustered around the freezing point in these areas. A similar behavior is also found in many models considered in this study. The robust method of L moments does not result in vastly unrealistic estimates of return values for moderate return periods, even under these circumstances. Since we are primarily interested in model performance on very large spatial scales and the affected regions are rather limited in space, this clustering behavior has virtually no effect on the considered extreme value statistics.

b. BLT diagram The primary focus in this study is on the ability of models to reproduce the amplitude and spatial structure of the extreme value patterns with respect to a reference (observed) pattern. To summarize numerous model results in a condensed form we adopt the Boer and Lambert (2001) version of the Taylor diagram (Gates et al. 1999), hereafter referred to as the BLT diagram. To this end, the climate statistics derived from different datasets are interpolated onto a common 128 ⫻ 64 Gaussian grid. The BLT diagram characterizes the similarity between two spatial patterns by simultaneously displaying the spatially averaged square difference between the anomaly patterns, the ratio of spatial variances, and the anomaly pattern correlation on a single graph. The three parameters are related to each other as outlined below. Let Xmod be a model field and Xref be the corresponding observed, or reanalyzed, reference. The spatial mean square difference 具d2典 (angular brackets denote spatial averaging) can be decomposed into two terms

具d2典 ⬅ 具共Xmod ⫺ Xref兲2典 ⫽ d20 ⫹ 具d⬘2典,

共2兲

where d20 is the square difference between the spatial means 具Xmod典 and 具Xref典, and 具d⬘2典 is the spatial mean square difference between the anomaly patterns X⬘mod ⫽ Xmod ⫺ 具Xmod典 and X⬘ref ⫽ Xref ⫺ 具Xref典. We will refer to the term 具d⬘2典 as the centered spatial mean square difference. It can be further decomposed as 2 ⫺ 2␳␴mod␴ref, 具d⬘2典 ⫽ ␴2mod ⫹ ␴ref

共3兲

2 where ␴2mod ⫽ 具X⬘mod 典 is the spatial variance of the 2 2 典 is the spatial variance of the model field, ␴ref⫽具X⬘ref reference field, and ␳ ⫽ 具X⬘modX⬘ref典/(␴mod␴ref) is the

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angle between the vectors indicates the pattern correlation between the spatial anomalies. The length of the model vector is a measure of spatial inhomogeneities in the model pattern as compared to that in the reference pattern. To complete the decomposition (2) we complement the BLT diagram with a bar plot of the spatial means that provides information about the mean bias d0.

4. Temperature extremes FIG. 2. The geometrical interpretation of the mean square difference decomposition (4). The reference spatial anomaly pattern Xref is represented by the filled circle at the end of the unit length vector along the abscissa (oriented from right to left). The model spatial anomaly pattern Xmod is represented by the open triangle at the end of the vector of the length ␴mod/␴ref plotted at the angle ␾ ⫽ arccos(␳) from the reference vector, where ␴2mod and ␴2ref are the spatial variances of the model and reference anomaly patterns, respectively, and ␳ is the corresponding anomaly pattern correlation. The distance d⬘/␴ref is the normalized rms error between the model and reference anomaly patterns.

centered pattern correlation between the two fields. After normalizing all terms in (3) by ␴2ref we have

具d⬘2典 2 ␴ref

⫽1⫹

2 ␴mod 2 ␴ref

⫺ 2␳

␴mod . ␴ref

共4兲

The BLT diagram provides a geometrical interpretation of the decomposition (4) as illustrated in Fig. 2. The reference pattern is represented by the filled circle at the end of the unit length vector from the origin along the abscissa. The model field is represented by an open triangle at the end of the vector of length ␴mod/␴ref oriented at the angle ␾ ⫽ arccos(␳) from the reference vector. The distance between the model and reference points represents the normalized rms error d⬘/␴ref. The

This section examines extreme value statistics of daily maximum and minimum near-surface temperature as estimated from the reanalyses and the AMIP-2 model output. Owing to space limitations, it is impractical to show global maps of extremes for each individual model. Instead we summarize the AMIP-2 results by presenting the ensemble mean of extreme value statistics calculated for all participating models, referred to as the “mean model,” and the corresponding intermodel standard deviation (spread) of simulated extremes at every grid point. The mean model can be thought of as a model consensus in simulating climatic extremes, while the intermodel standard deviation indicates the degree of disagreement between the models. Spatially averaged results are also summarized in BLT diagrams and in Table 3.

a. Daily maximum temperature extremes We begin with the analysis of daily maximum temperature extremes. The top row in Fig. 3 displays the global maps of 20-yr return values of annual daily maximum temperature extremes (Tmax,20) estimated from the 1979–95 NCEP2 (upper left panel) and ERA-40 (upper right panel) reanalyses. The NCEP1 warm extremes (not shown) are unrealistically high in some regions over continents due to a problem in the boundary

TABLE 3. Annual means of daily maximum and minimum temperature (Tmax and Tmin) and 20-yr return values (Tmax,20 and Tmin,20) estimated from the reanalyses averaged over land and oceans. The superscript “6-h” is used to indicate that daily temperature extremes are derived from 6-h sampled data. The last four rows provide the corresponding spatial averages for the AMIP-2 ensemble mean (mean model), the intermodel standard deviation, and the intermodel range (min and max). Tmax, °C

Tmax,20,°C

Tmin, °C

Tmin,20,°C

Dataset

Land

Ocean

Land

Ocean

Land

Ocean

Land

Ocean

NECP1-rean NCEP2-rean NCEP2-rean6-h ERA40-rean6-h Mean model Std dev Min Max

13.8 13.2 12.4 13.3 14.2 3.0 11.1 17.4

17.3 17.7 17.5 17.5 17.3 0.7 16.5 17.8

36.9 32.6 32.0 31.2 33.7 5.0 29.5 38.6

23.1 23.2 23.0 23.9 23.4 2.5 21.6 29.8

2.9 4.2 5.0 6.0 5.3 5.0 2.8 8.1

15.5 16.0 16.3 15.8 15.9 0.9 15.1 16.8

⫺21.9 ⫺23.2 ⫺22.6 ⫺15.2 ⫺17.1 6.4 ⫺22.7 ⫺8.9

5.9 6.3 6.7 7.3 7.1 3.8 0.9 9.7

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FIG. 3. Twenty-year return values of Tmax annual warm extremes estimated from (top left) the 1979–95 NCEP2 reanalysis and (top right) the 1979–95 ERA-40 reanalysis. Note that the ERA-40 daily maximum temperatures are estimated from 6-hourly sampled data. (bottom left) The AMIP-2 Tmax,20 ensemble mean. (bottom right) The AMIP-2 ensemble std dev. Units are in °C.

layer formulation resulting in temperature extremes in some locations that were well above 60°C when surface winds were weak (NCEP–NCAR 1997b). This problem was corrected in NCEP2 where annual warm extremes generally remain below 55°C. As a reference point, the hottest temperature ever recorded on the earth is 56.7°C (134°F) reported on 10 July 1913 in Death Valley, California. Unfortunately, daily temperature extremes were not available for the ERA-40 reanalysis. Instead, the ERA40 daily extremes are approximated by the maximum and minimum of the four temperature values sampled every 6 h. As a result, such temperature extremes are likely to be less intense than the true reanalyzed daily extremes. This is likely one of the reasons why the 20-yr return values of the annual temperature highs are lower over land in ERA-40, by about 1.4°C on average, than in NCEP2 (Table 3). The discrepancies between the two reanalyses are smaller over oceans. This is partly due to a weaker diurnal cycle over oceans so that the coarser temporal resolution of the ERA-40 temperature data has a smaller effect on the estimated daily extremes. Despite the coarser temporal sampling of the

ERA-40 surface temperature data, its annual warm temperature extremes exceed those in the NCEP2 reanalysis over North Africa, over the northwest part of North America, and in subpolar regions. Overall, the spatial patterns and the amplitude of warm extremes in the NCEP2 and ERA-40 reanalyses are very similar. Their pattern similarity, as measured by the global anomaly pattern correlation, is generally greater than the pattern correlation between either of the reanalyses and any one of the AMIP-2 models in this study. The lower left panel in Fig. 3 displays the ensemble average of Tmax,20 estimates for 12 AMIP-2 models (the mean model Tmax,20 estimate). On average, the models tend to produce warmer extremes than those in NCEP2 and ERA-40. The positive bias is mainly attributable to two models, namely COLA-00a and YONU-98a. The COLA-00a model simulates the warmest extremes over land, which are, on average, 6°C warmer than in the NCEP2 reanalysis. Annual extremes exceed 60°C in some parts of the southern United States, North Africa, the Arabian Peninsula, and Australia. Another warm outlier is the YONU-98a model, most notably over oceans. Somewhat lower daily maximum temperature

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FIG. 4. Extended BLT diagrams (see text) for the spatial patterns of the Tmax annual climatologies (open triangles) and 20-yr return values of Tmax annual warm extremes (filled circles) over (left) landmasses and (right) oceans. The reference NCEP2 reanalysis is indicated by the filled circle on the x axis. The concentric circles centered at the reference point indicate the mean square difference d2 between the model and reference anomaly patterns normalized by the spatial variance ␴2ref of the reference pattern. The concentric dashed line circles indicate the ratio of the model pattern spatial variance to that of the reference pattern. The gray straight lines indicate the anomaly pattern correlation (%). The bar plots display the corresponding mean biases with respect to the NCEP2 reanalysis in units of °C.

extremes over land are simulated by the DNM-98a), NCAR-98a, and UIUC-98a models. The intermodel standard deviation of Tmax,20 is shown in the lower right panel of Fig. 3. Not surprisingly, the spread is small over oceans where it is only half that over land. Obviously, the prescribed common lower boundary conditions over oceans moderate the differences between the models. The intermodel standard deviation in simulated warm extremes is in the 4°–6°C range over most landmasses with somewhat larger disagreement over the continental North America and Eurasia. Some of the largest disagreements may in part be attributed to the differences in the treatment of surface topography in the high terrain regions such as the Himalayas and Antarctica. The BLT diagrams in Fig. 4 summarize the performance of the models in simulating the annual mean of Tmax and the 20-yr return values of Tmax annual extremes over land and oceans as verified against the NCEP2 reanalysis. Filled circles indicate Tmax,20 and open triangles indicate the Tmax annual means. The NCEP2 reference dataset is indicated by the filled circle on the x axis. Recall that the closer a symbol is to the

reference point, the greater the similarity between the corresponding spatial anomaly patterns. The spatially averaged biases over land and oceans with respect to the NCEP2 reanalysis are displayed in the bar plots below the corresponding BLT diagrams. The open bars are for the Tmax annual climatologies, and the filled bars are for Tmax,20. Five out 12 models underestimated warm extremes while the rest overestimate them, as compared to the NCEP2 reanalysis. The models that overestimate the annual mean of Tmax over land also tend to overestimate warm extremes, and vice versa. The most notable exception is the DNM-98a model, which has a warm bias in the annual mean of daily maximum temperature relative to NCEP2, but a cold bias in the corresponding warm extremes. The mean bias is quite small over oceans due to the identical underlying SSTs that constrain the near-surface temperature variability over oceans. An obvious outlier in this respect is the YONU98a model. Not surprisingly, there is better agreement between the models for the annual mean of Tmax than for its annual extremes, as is evident both from the bar plots

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FIG. 5. As in Fig. 3 but for 20-yr return values of Tmin annual cold extremes.

of the spatially averaged biases and from the corresponding BLT diagrams for the anomaly patterns. Pattern correlations for the annual means are generally at least as good as the best correlations for the warm extremes. The magnitude of the spatial correlations remains fairly high (⬎0.9) even in the worst cases. This is partly because the spatial patterns over land and over sea are dominated by the large global-scale north–south temperature gradients. The BLT diagrams confirm again that the ERA-40 reanalysis underestimates slightly the amplitude of warm extremes and their spatial contrasts over land as compared to that in NCEP2, which is at least partly due to the coarser temporal sampling of the ERA-40 temperatures. Also, as mentioned above, the older NCEP1 reanalysis substantially overestimates warm extremes over land. The corresponding mean square distance from the reference NCEP2 anomaly pattern is larger than for most of the models. The COLA-98a model overestimates significantly the amplitude of warm extremes in the subtropical regions over land, which results in greater meridional temperature gradients and substantially larger spatial variance than in other models. The poorest spatial correlations are simulated by the YONU-98a model, both over land and oceans.

It is interesting to note that the best match to the NCEP-2 reanalysis (and ERA-40; not shown) is found for the mean model. This tendency is typical for all quantities and statistics considered in this study and has also been noticed in previous model intercomparison studies (e.g., Lambert and Boer 2001).

b. Daily minimum temperature extremes Figure 5 displays results for reanalyzed and modelsimulated cold extremes. The upper two panels show 20-yr return values of annual daily minimum temperature extremes (Tmin,20) in the NCEP2 and ERA-40 reanalyses. The lower two panels display the corresponding AMIP-2 ensemble mean and the intermodel standard deviation. Disagreements between the models and between the reanalyses are larger for cold extremes than for warm extremes. The NCEP2 cold extremes are, on average, 8°C colder over land than in ERA-40 (Table 3), while the corresponding differences in the annual mean of Tmin are more moderate (1.8°C colder in NCEP2 than in ERA-40 over land). Cold extremes in the older NCEP1 reanalysis (not shown) are similar to those in NCEP2 and are also generally much colder than in ERA-40 over land. Annual temperature lows in the NCEP reanalyses occasionally sink below ⫺90°C in

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FIG. 6. As in Fig. 4 but for the spatial patterns of the Tmin annual climatologies (open triangles) and 20-yr return values of Tmin annual cold extremes (filled circles) over (left) landmasses and (right) oceans.

some parts of Antarctica. For reference, the coldest confirmed temperature record on the earth is reported to be ⫺89.2°C from the Vostok Station, Antarctica. The discrepancies between the NCEP and ERA-40 reanalyses can only in part be attributed to the 6-hourly temperature sampling in ERA-40. To evaluate the sampling effect, we also calculated 20-yr return values of annual temperature extremes derived from the NCEP2 6-hourly sampled temperature data that were available to us. The 6-hourly sampling moderates 20-yr return values of annual temperature extremes by 0.6°–0.8°C over land and by 0.2°–0.4°C over oceans, on average. If the moderating effect due to coarser temporal sampling is of similar magnitude in the ERA-40 reanalysis, it would not be sufficient to explain the large discrepancy between the two reanalyses over land. The NCEP2 reanalysis has colder 20-yr return values Tmin,20 than most of the AMIP-2 models considered in this study, particularly over land. The AMIP-2 ensemble mean for Tmin,20 is 5°C warmer over land, on average. The intermodel standard deviation is quite a bit larger for cold extremes than that for warm extremes. The largest disagreement is found over Antarctica where cold extremes range from about ⫺35°C in the MRI-98a model to ⫺80°C and well below in the NCEP-99a model. The differences in cold extremes can be partly attributed to the differences in the annual

climatologies of Tmin over the high Antarctic terrain that are due to different treatments of surface topography. Model disagreements in simulating annual cold extremes are also relatively large in polar and subpolar regions over sea-ice-covered oceans where the intermodel discrepancies are comparable to that over snowcovered extratropical landmasses. The disagreement between the models is generally smaller over drier areas, such as the areas of the descending branches of the Hadley circulation, but it is greater in wetter regions along the equator. Temperatures usually drop at night primarily due to radiative cooling, accompanied by some conduction and convection. Maximum radiative cooling occurs under cloudless conditions. Therefore, the models agree relatively well in dry, cloud-free areas where radiative cooling dominates while daily minimum temperatures are more sensitive to model differences in moist, cloudy regions. BLT diagrams of the annual climatologies of Tmin and 20-yr return values of annual extremes of Tmin over land and oceans are displayed in Fig. 6. These diagrams reiterate some of the results discussed above. In particular, the spatially averaged quantities displayed in the bar plots indicate a positive bias, both for the annual climatologies and for annual extremes of Tmin for most models with respect to the NCEP2 reanalysis, especially over land. The amplitude of spatial contrasts of

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FIG. 7. Zonally averaged 20-yr return values of annual Tmax and Tmin extremes simulated by the 11 AMIP-2 models and in the three reanalyses over land. Units are in °C.

cold extremes is underestimated in almost all models. MRI-98a, and its close relative JMA-98a, simulate the warmest cold extremes and the smallest north–south cold temperature contrast. CCCMA-98a, DNM-98a, and NCEP-99a simulate more severe cold extremes than other models. In contrast with results for the warm extremes, discrepancies between models in simulating cold extremes over oceans are comparable to those over land. These differences result primarily from greater uncertainty over the sea-ice-covered oceans. Again, the mean model provides one of the better matches to the observed pattern of extremes as estimated from either NCEP2 or ERA-40. Given a warm bias for most models with respect to the NCEP2 reanalysis, the mean model is not the best match in terms of the total mean square difference. However the overall geographical distribution of cold extremes, as measured by the anomaly pattern correlation, is one of the best for the mean model. Curiously, the mean model is closer to the ERA-40 reanalysis than to the NCEP2 reanalysis, presumably because of much more severe cold extremes in NCEP2. The performance of the individual models and reanalyses in simulating 20-yr return values of warm and cold annual extremes over land is again summarized in terms of their zonal averages over land in Fig. 7. This figure illustrates many of the points discussed above. For example, the intermodel discrepancies are generally larger for cold extremes than for warm extremes. The mean model warm extremes are close to the ex-

tremes both in ERA-40 and NCEP2, while the cold extremes in the NCEP reanalyses and NCEP models are colder than in most of the models.

c. Temperatures near the freezing point In addition to the analysis of warm and cold extremes presented in the previous two subsections, we would also like to draw attention to a particular clustering behavior of surface temperature near the freezing point that is present to some degree in many of the AMIP-2 models as well as in the reanalyses and observations. This behavior is illustrated in Fig. 8, which shows the time series of daily Tmax in year 1979 at the grid points closest to the location of the Canadian station at 58.1°N, 68.4°W (Kuujjuaq Airport) in the NCEP2 and ERA-40 reanalyses and in two AMIP-2 models, NCEP99a and ECMWF-98a. The observed daily temperature extremes at this station are indicated by the circles in the left hand panel. The NCEP2 and ERA-40 reanalyzed temperatures follow each other fairly closely most of the time. The temporal correlation between daily anomalies from the annual cycle, defined here as the first two annual harmonics, is about 0.9. The reanalyzed time series are also well correlated with the observed station temperature record. For example, the correlation between the observed and ERA-40 anomalies from the annual cycle is also about 0.9. A closer inspection of the NCEP2 and NCEP-99a time series, however, reveals that near-surface tem-

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FIG. 8. Time series of Tmax in year 1979 as represented in (left) the NCEP2 and ERA-40 reanalyses and (right) the NCEP-99a and ECMWF-98a models at the grid point closest to the location of the Canadian station located at 58.1°N, 68.4°W (Kuujjuaq Airport). The NCEP2 reanalysis and NCEP-99a model time series are in black. The ERA-40 reanalysis and ECMWF-09a model time series are in gray. The station values are indicated by circles. Units are in °C.

perature remains nearly constant near the freezing point for several weeks in spring and early summer. This effect is particularly pronounced in the NCEP-99a model, and more so for Tmax than for Tmin. Many, but not all, AMIP-2 models share a similar behavior. Figure 9 displays histograms of relative frequencies of daily temperature extremes observed in 5°C bins that are centered at 0°C, ⫾5°C, . . . , for all land grid points northward of 45°N in the two reanalyses (upper two panels) and in the AMIP-2 models (lower panels). Instead of displaying individual histograms for all 12 models, we summarize the results with box plots that indicate the averaged value and the intermodel variations in the height of each 5°C bin. The circles in the two upper panels of Fig. 9 indicate relative frequencies of 1979–95 temperature highs and lows calculated for 67 selected Canadian stations in the 1979–95 period that are spread more or less evenly over Canada (Zhang et al. 2000). Although, the frequency distribution histograms computed for the Canadian stations are not directly comparable to those obtained for all landmasses north of 45°N, they do provide some indications about the form of the distribution of daily temperature extremes in the extratropics over land. The Tmax time series in the NCEP2 reanalysis and the NCEP-99a model exhibit a very pronounced “sticking” effect near the freezing point of water. The overly frequent occurrence of near-freezing-point temperatures happens mostly at the expense of temperatures above 0°C, as can also be seen in the time series in Fig. 8. This behavior is less noticeable in the ERA-40 reanalysis and in the Canadian station data. On the other hand, the clustering effect is somewhat more developed in

ERA-40 than in NCEP2 for Tmin, and much more pronounced in the station data. In this respect, the ERA-40 reanalysis mimics the behavior of observed temperatures more closely than the NCEP2 reanalysis. The box plot summaries of the relative frequency histograms for the AMIP-2 models indicate that the greatest disagreements between the models appear to be for temperatures near the freezing point. It is difficult to unambiguously identify specific reasons for the differences between the models in simulating the temperature distribution near the freezing point without knowing all the details of the land surface schemes and exchanges between atmosphere and land. However, there are some indications that the clustering behavior is exaggerated in models with simpler “bucket type” land surface schemes. Similar behavior was reported by Kharin and Zwiers (2000, 2005) in a coupled climate model where the atmospheric component is a predecessor of the CCCMA-99a model. This older model utilizes a bucket-type single-layer soil moisture model with a spatially varying field capacity. It was found that the ground temperature in this model does not fall below (nor rise above) 0°C until all of the latent heat of fusion contained by the moisture in the bucket has been released to (or taken from) the atmosphere. The CCCMA-99a model is used in AMIP-2 has a much more sophisticated three-layer land surface model (Verseghy 1991; Verseghy et al. 1993) and exhibits a much less pronounced clustering behavior. Presumably, this consideration may be also apply to at least some of the other models that participated in AMIP-2. However, this effect is not limited to simple one-layer surface land schemes. For example, the NCEP models, in

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FIG. 9. (top) Spatially averaged relative frequency histograms of (left) Tmax and (right) Tmin for the period 1979–95 for all land grid points north of 45°N in the NCEP2 reanalysis (dark gray) and ERA-40 reanalysis (light gray). The circles indicate the relative frequencies of daily temperature extremes calculated for 67 selected Canadian stations for the same period. The 5°C bins are centered at 0°C, ⫾5°C, etc. (bottom) The box plot summary of the corresponding histograms obtained for each of 12 AMIP-2 models. The box plots indicate the median, mean, 25th and 75th percentiles, and the maximum and minimum relative frequencies for each 5°C bin.

which the clustering effect is very pronounced for Tmax, use a three-layer soil model. The clustering effect may, under some circumstances, affect the estimated annual temperature extremes. The direct consequence is that the annual extremes may be undersimulated in the regions where climatological summer or winter temperatures are near the freezing point. This behavior may also represent a methodological difficulty if one tries to estimate return values of annual extremes from a fitted GEV distribution. Kharin and Zwiers (2000, 2005) demonstrated that a single GEV distribution may not provide a good approximation for the distribution of annual extremes in such situations. Some other distributional form, or a mixture of distributions, may be required to estimate return values more reliably. However, the small sample size prevents us from applying a more sophisticated analysis in this study forcing us to rely on the robustness

of the L-moment method for the estimation of return values for moderate return periods under these circumstances.

5. Precipitation extremes a. Overall characteristics Before we proceed with the analysis of precipitation extremes, we first examine the frequency distributions of 24-h mean precipitation rates simulated by the AMIP-2 models and reanalyses. Figure 10 displays empirical distribution functions of daily precipitation amounts in the Tropics (30°S–30°N) and northern extratropics (30°–90°N). The empirical distribution function is defined as the proportion of precipitation rates smaller than, or equal to, a specified value. The lower and upper distribution tails are plotted on separate scales to emphasize differences in the frequency distri-

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FIG. 10. The empirical distribution functions Femp(x) of 24-h mean precipitation rates x (mm day⫺1) defined as the proportion (%) of observed values smaller than x at all grid points in the (top) Tropics (30°S–30°N) and (bottom) northern extratropics (30°–90°N). (left) The lower distribution tails for precipitation rates ⬍5 mm day⫺1 displayed on a linear–linear scale. The annual mean precipitation rates in the respective regions are indicated by circles on the curves. (right) The upper tails (⬎5 mm day⫺1) displayed on a log–log scale. The spatially averaged 20-yr return values of annual 24-h precipitation extremes are indicated by triangles. The symbols for the reanalyses are highlighted by asterisks.

butions of weak to moderate and extremely large precipitation events. The lower tails for precipitation rates up to 5 mm day⫺1 are presented on a linear–linear scale in the left-hand panels of Fig. 10. The upper tails are displayed on a log–log scale in the right-hand panels. The annual mean precipitation rate in the Tropics and northern extratropics are indicated by circles on the corresponding curves of the distribution lower tails. The spatially averaged 20-yr return values of annual precipitation extremes are indicated by triangles on the corresponding curves of the upper tails. The symbols for the reanalyses are highlighted by the asterisks. In the Tropics, there are great differences in the frequency distributions of precipitation rates simulated by the models and in the reanalyses at both ends of the distribution. In particular, the frequency of dry to moderately wet days (⬍1 mm day⫺1) varies substantially from one dataset to another (upper left panel of Fig. 10). For example, almost two-thirds of all days are effectively dry in the Tropics in the NCEP-99a,b models and in the NCEP2 reanalysis. On the other hand, the

GISS-98a model simulates rainfall, on average, roughly 9 out of 10 days. The ERA-40 and NCEP1 reanalyses produce roughly the same frequency of dry days of about 35%, but the proportion of weak to moderate precipitation events (ⱗ1 mm day⫺1) is greater in ERA40 than in NCEP1. The older ERA-15 reanalysis produces zero rainfall days less frequently than ERA-40 but the precipitation distributions in the two ECMWF reanalyses become comparable for rates larger than 1 mm day⫺1. Dramatic differences are also found in the frequencies of extremely large precipitation events in the Tropics. The spatially averaged 20-yr return values of annual 24-h precipitation extremes range from about 20 mm in the DNM model to more than a 110 mm in the NCEP99b model (see also Table 4). The older NCEP1 reanalysis falls in the group of models (such as GISS-98a, NCAR-98a, and SUNYA-99a) with moderate 20-yr return values of about 35 mm. The other three reanalyses (NCEP2, ERA-15, and ERA-40) fall into a larger group of models with relatively large tropical precipi-

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TABLE 4. The global, tropical (30°S–30°N), and Northern Hemisphere (30°–90°N) averages of the annual mean precipitation rate (P), 20-yr return values of annual extremes of 24-h (P20) and of 5-day (P5,20) mean precipitation rates in the four reanalyses and CMAP data. Units are in mm day⫺1. The last four rows provide the corresponding spatial averages for the AMIP-2 ensemble mean (mean model), the intermodel std dev, and the intermodel range (min and max). P (mm day⫺1)

P20 (mm day⫺1)

P5,20 (mm day⫺1)

Dataset

Global

Tropics

NH

Global

Tropics

NH

Global

Tropics

NH

ERA15-rean ERA40-rean NCEP1-rean NCEP2-rean CMAP Mean model Std dev Min Max

3.0 2.9 2.7 3.0 2.6 3.1 0.7 2.7 3.5

4.0 3.9 3.4 3.9 3.3 3.8 1.0 3.3 4.4

2.0 1.9 2.0 2.1 1.8 2.3 0.4 1.9 2.6

70.8 75.4 39.2 82.1 — 54.2 21.5 22.1 92.9

98.8 111.1 37.7 117.0 — 67.6 33.3 17.9 130.9

44.6 41.2 41.7 49.7 — 42.5 10.0 27.5 58.0

27.0 28.4 16.9 30.9 23.6 23.1 7.3 12.2 34.4

39.5 43.5 19.8 45.1 33.0 31.6 11.5 14.2 49.8

15.9 14.2 15.0 18.0 14.4 15.9 3.3 11.2 20.7

tation extremes of about 100 mm. The DNM-98a model simulates very weak daily precipitation extremes in the Tropics and falls somewhat outside of the main bulk of models. This model has lower horizontal resolution than most others, which may explain some of this low bias. However, the GISS-98a model, which has similar resolution, simulates extremes in the Tropics that are almost twice as large. There is better agreement between the distributions of daily mean precipitation rates in the extratropics (shown in the lower panels of Fig. 10 for the Northern Hemisphere). The spatially averaged 20-yr return values range from 27 mm day⫺1 in the DNM-98a model to 58 mm day⫺1 in the NCEP-99b model. Only the DNM model simulates smaller precipitation extremes in the Tropics than in the extratropics, again indicating its somewhat unique character. The four reanalyses fall within the bulk of the models, producing on average 40–50 mm day⫺1 20-yr return values. There are still notable differences between the models in simulating dry and moderately wet days in the extratropics, although the disagreements are generally smaller than those in the Tropics. The majority of models tend to simulate fewer dry days and more total precipitation in the extratropics than the reanalyses. As suggested above, spatial resolution may be a factor in explaining the differences in the amplitude of the precipitation extremes. The common convention is to interpret gridded model output as being representative of spatially averaged values over grid box domains. The extremes are therefore expected to be generally more intense in higher-resolution models, if they are estimated at the native model grid resolution, as was done in this study. The two pairs of models, ECMWF-98a,b and NCEP-99a,b, that were run at different resolutions confirm this tendency. For example, the increase of the grid size from 128 ⫻ 64 in the NCEP-99a model to 192

⫻ 94 in the NCEP-99b model, which corresponds to a reduction of the grid box area by a factor of about 2, results in an increase in P20 of about 35% in the Tropics and 18% in the Northern Hemisphere extratropics. A similar tendency is found for the ECMWF-98a and ECMWF-98b models. Note, however, that, although the output from both ECMWF models was available on the same grid, the latter model has substantially higher internal spatial resolution than the former (Table 1). The details of the ECMWF coarse-graining procedure were not available, which precludes us from making a definite conclusion about the role of the resolution in the simulation of extremes in these two models. The overall dependence on model resolution is relatively weak for the participating models. Figure 11 displays the spatially averaged 20-yr return values in the Tropics (left-hand panel) and in the Northern Hemisphere extratropics (right-hand panel) plotted as a function of the horizontal resolution, defined here as the total number of grid points in the grid on which the precipitation datasets were made available. Although the overall trend is indeed toward larger extremes at higher resolutions, this trend explains only a small fraction of the differences between simulated extremes. Other factors, such as the parameterization of deep convective precipitation, must play a crucial role in generating extreme precipitation on short time scales, particularly in the Tropics. Interestingly, the slope coefficient of the least squares fit indicated by the straight lines in Fig. 11 is found to be significantly different from zero at less than the 1% significance level in the Northern Hemisphere extratropics but only at about the 10% significance level in the Tropics. That is, the dependence on the resolution appears to be more robust in the extratropics than in the tropical regions. The dominant form of precipitation in the extratropics is stratiform associated

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FIG. 11. Spatially averaged 20-yr return values of annual extremes of 24-h mean precipitation rates in the Tropics (30°S–30°N) and Northern Hemisphere extratropics (30°–90°N) simulated in the AMIP-2 models and several reanalyses plotted as a function of the horizontal grid resolution. Horizontal resolution is indicated by the number of grid cells in each model’s grid. The reanalyses are highlighted by the gray circles. The linear least squares fits for the 16 AMIP-2 models are indicated by the dashed lines.

with extensive large-scale horizontal air mass development, while deep convective precipitation is more common in the Tropics. The spatial scales explicitly resolved by the considered models are so much larger than the spatial scales of the processes in the tropical atmosphere governing extreme precipitation that the effect of doubling the resolution is still negligible. The model parameterizations are of dominant importance at all AMIP-2 resolutions. The knowledge of the specific scheme type used for the parameterization of unresolved convective processes in the Tropics may not be sufficient to predict model skill in simulating extreme precipitation in the Tropics. An intimate knowledge of the scheme specifics and of internal tuning parameters may also be required. For example, Scinocca and McFarlane (2004) found the variability of tropical precipitation on intraseasonal time scales in the CCCma model to be very sensitive to details of the parameterization of deep cumulus convection and to the tuning of the convection scheme.

b. Geographical distribution of 20-yr return values of annual precipitation extremes In this section we examine the geographical distribution of precipitation extremes in more detail. The validation and intercomparison of precipitation extremes is a challenge since reliable estimates of observed precipitation extremes comparable to gridded model output are not readily available. Precipitation extremes obtained from individual station records are essentially point estimates and are not directly comparable to the gridded model output that presumably represents precipitation variability on much coarser spatial scales. The reanalyses provide data that are comparable to model output. However, the observed precipitation

records are not utilized in the reanalysis data assimilation cycle. Thus reanalyzed precipitation is very much a product of the “physics package” in the reanalysis model. As such, it suffers from essentially the same drawbacks as model-simulated precipitation. In addition, reanalysis precipitation may also be affected by incomplete “spinup” of the convective processes in the reanalysis model. An alternative is to use gridded data such as the CMAP pentad product that is based on real observational records, at least over land. But CMAP estimates are available only as 5-day averages, which precludes using them to verify daily extreme value statistics. Despite the many limitations, we will use all of these observational data products in our evaluation of the AMIP-2 simulated extremes. The station return values are evaluated on the 128 ⫻ 64 Gaussian grid. The gridded values are obtained by first estimating return values for each station individually and then averaging the return value estimates for all stations within a grid box. This procedure is useful for preserving 20-yr return value estimates from station data, but it does not ameliorate the problem of comparing estimates of local precipitation rate extremes with estimates of grid box area-mean precipitation rate extremes. The proper coarse graining of station data is not a trivial task (e.g., Hulme and New 1997) and is beyond of the scope of the present paper. There are notable differences between precipitation extremes simulated in the reanalyses, both in terms of the overall amplitude and the spatial pattern, particularly in the Tropics. Figure 12 displays global patterns of 20-yr return values of annual 24-h precipitation extremes estimated from the ERA-15, ERA-40, and NCEP2 reanalyses and from the available station records. The older NCEP1 reanalysis (not shown) ap-

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FIG. 12. Spatially smoothed 20-yr return values of annual 24-h precipitation extremes in the (top left) ERA-15 reanalysis, (top right) ERA-40 reanalysis, (bottom left) NCEP2 reanalysis, and (bottom right) as estimated from the station data. Units are in mm day⫺1.

pears to underestimate precipitation extremes in the Tropics, perhaps due to spinup problems in the convection scheme. A common feature of all the maps in Fig. 12 is that the tropical extremes are substantially larger than extremes in the extratropics. The ERA-40 reanalysis simulates the most intense precipitation extremes with values well in excess of 200 mm day⫺1 along the equator. Corresponding values in ERA-15 are about 150 mm day⫺1. The NCEP2 extremes have a somewhat broader tropical maximum meridionally with the largest extremes over the tropical Indian Ocean. Not surprisingly, the precipitation extremes estimated from individual station records are generally more intense than the reanalyzed extremes. On average, the amplitude of the 20-yr return values estimated from the station records is about twice as large as the corresponding amplitude of the reanalyzed extremes. Figure 13 displays 20-yr return values of the annual extremes of nonoverlapping 5-day mean precipitation rates estimated from the ERA-15 reanalysis (left-hand panel) and the pentad CMAP dataset (right-hand panel). The global spatial structure of the 5-day precipitation extremes is similar to that for 24-h precipita-

tion extremes, but the overall amplitude is reduced by a factor of 2.5–3. The CMAP extremes are somewhat weaker in the Tropics than the ERA-15 extremes, but the overall pattern is similar in these two datasets, apart from the higher extremes over Antarctica in the CMAP dataset. The 5-day precipitation extremes in the ERA40 and NCEP2 reanalyses (not shown) are comparable to the CMAP extremes in the extratropics, but the newer reanalyses simulate much more intense extremes in the Tropics, particularly over the tropical Indian Ocean in NCEP2 and along the equator in ERA-40. The ERA-15 reanalysis “outperforms” slightly the other reanalyses when verified against the CMAP dataset. The global patterns of both the annual mean precipitation rate and 20-yr return values of the annual extremes of 5-day mean precipitation rates estimated from the ERA-15 reanalyses bear the closest resemblance to those estimated from the CMAP dataset, as measured by the anomaly pattern correlation and the total rms difference. ERA-40 and NCEP2 both produce more severe extremes in the Tropics, while the NCEP1 reanalysis has much weaker tropical extremes. However, at this point it is difficult to judge with certainty which of the reanalyses delivers the best estimates of

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FIG. 13. Spatially smoothed 20-yr return values of annual 5-day mean precipitation rate extremes (mm day⫺1) as estimated from the (left) ERA-15 reanalysis and (right) CMAP pentads. Units are in mm day⫺1.

the annual extremes of 24-h or 5-day mean precipitation rates. The pentad CMAP dataset remains the subject of active research. For example, Xie et al. (2003) noticed that the precipitation magnitude in the CMAP data is not consistent with that in the monthly CMAP or the Global Precipitation Climatology Project (GPCP) datasets and therefore adjusted the pentad CMAP analyses against the monthly GPCP-merged analyses. All reanalyses perform comparably well over moderate latitude landmasses where the CMAP data are presumably more reliable. The disagreements are much larger over tropical oceans where only a few direct precipitation measurements exist. Figure 14 displays the 16 AMIP-2 model ensemble average and intermodel standard deviation of 20-yr return values of annual 24-h precipitation extremes. The intermodel standard deviation is normalized by the amplitude of the extremes. The mean model (left-hand panel in Fig. 14) has weaker tropical extremes than most reanalyses, except for NCEP1. The intermodel uncertainties as measured by the normalized standard

deviation are of the order of 10%–20% of the mean extreme value amplitude in extratropics over oceans, with somewhat larger disagreements over extratropical landmasses. We found that inconsistencies between the models in simulating extreme precipitation in the Arctic are comparable to those for the annual-mean precipitation rates documented by Kattsov et al. (2000). The largest disagreements, in excess of 50%, are generally confined to the tropical regions. Notice that the intermodel discrepancies are also relatively large in subtropical dry regions, particularly over North Africa. Figure 15 shows zonally averaged 20-yr return values of annual extremes of 24-h (top panel) and nonoverlapping 5-day precipitation rates (bottom panel) simulated by the AMIP-2 models and in the reanalyses. The model results are indicated by the colored solid lines. The reanalyses are indicated by dashed lines in various gray shades. The black dotted line represents the mean model. The CMAP return value estimates are indicated by the black dashed line in the lower panel of Fig. 15. The AMIP-2 models disagree dramatically on the

FIG. 14. (left) The AMIP-2 ensemble average of spatially smoothed 20-yr return values of annual 24-h precipitation extremes. Units are in mm day⫺1. (right) The corresponding coefficient of variation (dimensionless) defined as the intermodel sttandard deviation of 20-yr return values divided by their ensemble mean.

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FIG. 15. Zonally averaged 20-yr return values of annual (top) 24-h and (bottom) 5-day mean precipitation rate extremes simulated by the 16 AMIP-2 models, in the reanalyses and as estimated from the CMAP dataset. Units are in mm day⫺1.

amplitude and geographical distribution of their extreme precipitation rates in the Tropics. The models can be loosely categorized into two groups: those that simulate relatively weak extremes in the Tropics and those that simulate rather strong tropical extremes. Typical examples of models in the first group are the DNM-98a, GISS-98a, and the related NCAR-98a and SUNYA-99a models; the older NCEP1 reanalysis also falls into this category. The CCCMA-99a, CNRM-00a, and both NCEP-99a,b models are examples of models with relatively large precipitation extremes in the Tropics; the ERA-15, ERA-40, and NCEP2 reanalyses fall into the latter category as well. Both ECMWF-98a,b

models lie somewhere in between these two categories. Several models, such as JMA-98a, its relative MRI-98a, and UGAMP-98a, which is related to the UKMO HadAM3 model, exhibit a pronounced minimum in the amplitude of extreme precipitation along the equator. Coincidently, the zonal-averaged mean model extremes of 5-day precipitation rates almost coincide with the CMAP estimates, except over Antarctica. The BLT diagrams in Fig. 16 summarize the differences between the spatial patterns of the annual mean and extreme precipitation as simulated by the AMIP-2 models and the reanalyses. The left-hand panel displays the results for the global patterns of the annual mean

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FIG. 16. (left) An extended BLT diagram (see text) summarizing characteristics of the global patterns of the annual mean precipitation (open triangles) and 20-yr return values of the annual extremes of 24-h precipitation rates (filled circles) as referenced against the ERA-15 reanalysis. (right) The same as above but for the mean precipitation rate and 20-yr return values of the annual extremes of nonoverlapping 5-day precipitation rates as referenced against the CMAP pentad dataset.

precipitation and 20-yr return values of the annual extremes of 24-h precipitation rates as referenced against the the ERA-15 reanalysis. The right-hand panel displays the results obtained for nonoverlapping 5-day precipitation rates as referenced to the CMAP pentad product. There is no apparent systematic bias in simulating the global annual mean, as compared to the ERA-15 annual climatology (see bar plots in Fig. 16). The AMIP-2 ensemble average, or the mean model, closely matches the global mean precipitation rate of this reanalysis. When compared to the CMAP dataset, the AMIP-2 models and reanalyses generally produce more precipitation. The model inconsistencies are much greater for the spatial distributions of precipitation extremes, indicated by the wide spread of the corresponding symbols in the BLT diagrams. The majority of the models underestimate the amplitude of 20-yr return values of annual precipitation extremes and the amplitude of the their spatial variations, occasionally quite substantially, when compared to the ERA-15 reanalysis. Since the NCEP2 and ERA-40 reanalyses have stronger tropical precipitation extremes than ERA-15, the negative bias becomes even more evident when the AMIP-2 models are referenced against these newer reanalyses (not

shown). However, the spatial pattern of extreme precipitation rates in the mean model matches the observations best, when verified against the CMAP data.

6. Summary This study documents the ability of the modern AGCMs participating in AMIP-2 to simulate the climatic extremes of near-surface temperature and 24-h and 5-day precipitation rates. The temperature extremes are evaluated for 12 AGCMs. The precipitation extremes are examined for 16 AMIP-2 simulations. The model results are validated against four reanalyses, the blended CMAP pentad products of Xie et al. (2003), and station data. A general conclusion of the study is that there are various degrees of consistency in the way current atmospheric models simulate the annual extremes of temperature and precipitation. Model disagreements appear to be the smallest for warm extremes followed by somewhat larger discrepancies for cold extremes, particularly over sea ice and snow-covered areas. Precipitation extremes are less reliably reproduced in the current generation of AGCMs, although there is better agreement in the extratropics than in the Tropics. It is

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evident from the quite substantial differences in the tropical precipitation extremes estimated from the available reanalyses and other observational datasets that our knowledge about their true amplitude remains rather limited. Another common theme throughout this and other model intercomparison studies (e.g., Lambert and Boer 2001) is that, while individual models may disagree with the available observations quite dramatically, the ensemble average of the climate statistics from many models typically provides one of the best matches to the observations. Since no single model can be selected as the clear favorite for all quantities that have been evaluated, the present study supports the importance of the multimodel ensemble approach to simulating the present-day climate and, perhaps, possible future climate changes. More specifically, the main results can be summarized as follows. • On the whole, the models do a more credible job of

simulating the 20-yr return values of annual extremes of daily maximum and minimum temperature. Temperature extremes in the AMIP-2 simulations are heavily constrained over ice free oceans by the prescribed SSTs. This has the effect of moderating the discrepancies between the models. However, cold extremes are less reliably simulated in wet and cloudy regions in the Tropics where simulated daily lows are more sensitive to model differences. Warm extremes are less reliably reproduced in the interior of the continents where the moderating effect of the prescribed SSTs is reduced and where there is greater sensitivity to the treatment of the land surface. Cold extremes are more reliably simulated in dry subtropical regions but less so over sea ice and snow-covered areas. • Many models exhibit an exaggerated clustering behavior for temperatures near the freezing point of water. We speculated that this effect might be related to the use of simple “bucket type” land surface schemes. However, this effect is not limited to onelayer land surface schemes. For example, the NCEP models, in which this effect is particularly pronounced, employ a multilayer soil model. • There is less consistency in the ability of the AMIP-2 models to simulate extremes of 24-h and 5-day precipitation rates. Major disagreements are found in the Tropics where the parameterization of deep convection plays a crucial role in generating daily precipitation extremes. It is difficult to be more specific than this because tropical precipitation variability, and by its extension its extremes, can be very sensitive to the tuning of the deep convection parameterization, as

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demonstrated by Scinocca and McFarlane (2004). There is a weak tendency for extremes to be more intense in higher-resolution models, but this dependence is not very robust in the Tropics. Unfortunately, we have not been able to associate the model formulations and key characteristics with their performance in simulating climate extremes. Modern climate models are very complex and employ a variety of parameterization packages to represent the effect of unresolved physical processes. The models are often “tuned” to match the observed mean climate. The climatic extremes are rarely used for model validation. We can only hope that the results that we have presented will stimulate the discussion of the model’s ability to simulate climate extremes in the respective modeling groups. Acknowledgments. We thank Aaron J. Berndsen and Matthieu Loussier for helping us with transferring and preparing the datasets and performing preliminary extreme value analysis. We are also thankful to AMIP-2 participants for providing the high frequency model output. AMIP is supported by the Program for Climate Model Diagnosis and Intercomparison at the Lawrence Livermore National Laboratory. The authors greatly acknowledge the technical assistance and support of Peter Gleckler. We thank John Fyfe, Vivek Arora, and three anonymous reviewers for their constructive and helpful comments on earlier versions of the manuscript. REFERENCES Boer, G. J., and S. J. Lambert, 2001: Second order space-time climate difference statistics. Climate Dyn., 17, 213–218. Dupuis, D. J., and M. Tsao, 1998: A hybrid estimator for the Generalized Pareto and Extreme-Value Distributions. Commun. Stat. Theory Methods, 27, 925–941. Fiorino, M., cited 1996: AMIP II sea surface temperature and sea ice concentration observations. [Available online at http:// www-pcmdi.llnl.gov/projects/amip/AMIP2EXPDSN/ BCS_OBS/amip2_bcs.htm.] Gates, W. L., 1992: AMIP: The Atmospheric Model Intercomparison Project. Bull. Amer. Meteor. Soc., 73, 1962–1970. ——, and Coauthors, 1999: An overview of the results of the Atmospheric Model Intercomparison Project (AMIP I). Bull. Amer. Meteor. Soc., 80, 29–55. Gibson, J. K., P. Kalberg, S. Uppala, A. Hernandes, A. Nomura, and E. Serrano, 1997: ERA description. ECMWF Reanalysis Rep. Series 1, ECMWF, Reading, United Kingdom, 72 pp. Gleckler, P., cited 1996: Atmospheric Model Intercomparison Project Newsletter. No. 8, PCMDI/LLNL. [Available online at http://www-pcmdi.llnl.gov/projects/amip/NEWS/.] Hegerl, G. C., F. W. Zwiers, P. A. Stott, and V. V. Kharin, 2004: Detectability of anthropogenic changes in annual temperature and precipitation extremes. J. Climate, 17, 3683–3700. Hosking, J. R. M., 1990: L-moments: Analysis and estimation of

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