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  • View in gallery

    SOM-node frequency maps (middle row) and associated errors (bottom row) expressed as a percentage of NCEP frequencies (top left) of the COLA, HADAM3, and CSIRO9 AGCMs for daily mean 500-hPa heights from Jan 1986 to Dec 1998. Also shown are two-dimensional histograms of within-node spatial variance (top middle) and north-to-south 500-hPa contour gradient (top right)

  • View in gallery

    SOM-node frequency errors (%) averaged over all nodes for the COLA, HADAM3, and CSIRO9 GCMs daily mean (left) 500-hPa heights and (right) sea level pressure for the period (top) Jan 1986–Dec 1998, (middle) DJF days only, and (bottom) DJF days during ENSO years

  • View in gallery

    Quasi-SOI series calculated using model grid boxes closest to Tahiti and Darwin. (left column) AGCM output using observed SSTs (gray shading indicates ensemble spread) and the solid black line the quasi SOI using NCEP reanalysis data. (right column) Output from the climatological SST simulation

  • View in gallery

    Percentage improvement of 500-hPa height temporal variability when using observed SSTs relative to climatological SSTs in AGCM simulations

  • View in gallery

    Frequency of occurrence of 1-mm daily rainfall bins over central interior of South Africa and nearest AGCM grid-box values for COLA, HADAM3, and CSIRO9

  • View in gallery

    Time series of DJF total rainfall observed over central interior of South Africa and nearest grid-box values from COLA, HADAM3, and CSIRO9 AGCMs. Dashed line indicates climatological SST AGCM simulation

  • View in gallery

    (top row) Barotropic and baroclinic kinetic energy for daily winds from NCEP reanalysis and COLA, HADAM3, and CSIRO9 AGCM biases expressed as a percentage of the NCEP values for DJF days from 1986 to 1998. Areas of positive bias are shaded.

  • View in gallery

    SOM-node frequency maps for (top left) NCEP reanalysis data and the (top right) HADAM3 AGCM errors expressed as a percentage of the NCEP frequencies for daily mean sea level pressure for DJF days during Jan 1986–Dec 1998. The actual SOM nodes in the two positions marked A and B on the frequency map are shown at the bottom, with the position of the tropical-temperate trough and truncated trough, respectively, marked by the heavy dashed line

  • View in gallery

    Fig. A1. A 4 × 3 node self-organized map of monthly mean sea level pressure (hPa) from Jan 1979 to Dec 1999

  • View in gallery

    Fig. A2. Frequency of mapping of monthly mean sea level pressure fields to SOM nodes during the four seasons

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An Assessment of Intraseasonal Variability from 13-Yr GCM Simulations

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  • 1 Climate Systems Analysis Group, Department of Environmental and Geographical Science, University of Cape Town, Rondebosch, South Africa
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Abstract

An assessment of 13-yr simulations of three atmospheric general circulation models (AGCMs) forced by observed sea surface temperatures (SSTs) is presented. The National Centers for Environmental Prediction (NCEP) reanalysis data are used as a baseline for the comparisons. Daily circulation characteristics and interannual variability are investigated in order to improve understanding of the causes of systematic model errors. The focus is to determine the utility of these models in the field of seasonal forecasting.

Daily circulation statistics are well represented by the Hadley Centre Atmospheric Climate Model (HADAM3) but the specific versions of the Center for Ocean–Land–Atmosphere Studies (COLA) and Commonwealth Scientific and Industrial Research Organization (CSIRO9) models examined here produce flow patterns biased toward atmospheric archetype modes characteristic of low spatial variability. All three models show relatively large errors in kinetic energy fields of the vertical mean and shear flow, both in latitudinal placement of the midlatitude jet and geographical location of energy maxima. Evidence suggests that model resolution and model physics affect the accuracy of these simulations.

AGCM interannual variability as forced by sea surface temperatures is realistic in terms of a quasi-SOI (Southern Oscillation index) series and reproduces the El Niño–Southern Oscillation (ENSO) signal above noise levels that are determined from simulations using climatological SSTs. However, rainfall fields over southern Africa show little skill in interannual variability and daily rainfall characteristics indicate that some models are producing too many rain days by up to a factor of 2. Notwithstanding these difficulties, AGCMs, if used carefully, do provide sufficient skillful information for guidance in seasonal forecasting.

Corresponding author address: Dr. Warren Tennant, Climate Systems Analysis Group, Dept. of Environmental and Geographical Science, University of Cape Town, Private Bag, Rondebosch 7701, South Africa. Email: tennant@weathersa.co.za

Abstract

An assessment of 13-yr simulations of three atmospheric general circulation models (AGCMs) forced by observed sea surface temperatures (SSTs) is presented. The National Centers for Environmental Prediction (NCEP) reanalysis data are used as a baseline for the comparisons. Daily circulation characteristics and interannual variability are investigated in order to improve understanding of the causes of systematic model errors. The focus is to determine the utility of these models in the field of seasonal forecasting.

Daily circulation statistics are well represented by the Hadley Centre Atmospheric Climate Model (HADAM3) but the specific versions of the Center for Ocean–Land–Atmosphere Studies (COLA) and Commonwealth Scientific and Industrial Research Organization (CSIRO9) models examined here produce flow patterns biased toward atmospheric archetype modes characteristic of low spatial variability. All three models show relatively large errors in kinetic energy fields of the vertical mean and shear flow, both in latitudinal placement of the midlatitude jet and geographical location of energy maxima. Evidence suggests that model resolution and model physics affect the accuracy of these simulations.

AGCM interannual variability as forced by sea surface temperatures is realistic in terms of a quasi-SOI (Southern Oscillation index) series and reproduces the El Niño–Southern Oscillation (ENSO) signal above noise levels that are determined from simulations using climatological SSTs. However, rainfall fields over southern Africa show little skill in interannual variability and daily rainfall characteristics indicate that some models are producing too many rain days by up to a factor of 2. Notwithstanding these difficulties, AGCMs, if used carefully, do provide sufficient skillful information for guidance in seasonal forecasting.

Corresponding author address: Dr. Warren Tennant, Climate Systems Analysis Group, Dept. of Environmental and Geographical Science, University of Cape Town, Private Bag, Rondebosch 7701, South Africa. Email: tennant@weathersa.co.za

1. Introduction

A considerable amount of work in recent years has focused on assessing variability in atmospheric general circulation models (AGCMs) at seasonal to interannual time frames. Coordinated efforts to provide AGCM output such that model intercomparison can be done have been particularly useful in this endeavor. The Atmospheric Model Intercomparison Project (AMIP), initiated in 1989 (Gates 1992), is ongoing and is expected to provide increasingly more comprehensive data. Modern communication technology now enables convenient access to the data on the World Wide Web (Phillips 1996). Related projects, such as the Seasonal Model Intercomparison Project (SMIP; Sperber et al. 2001), have been initiated to address more specifically the aspects of seasonal prediction.

Techniques using ensembles of individual model and multimodel simulations have proved useful in model evaluation, by determining the uncertainty among different models in simulating certain aspects of the general circulation (e.g., Gates et al. 1999). This highlights those areas where AGCMs are not consistent with each other and the simulation of the atmosphere in these areas could be less reliable. Typically the problems occur in the Tropics and are thought to be caused by differing parameterizations of deep convection, clouds, and radiative interactions. Internal model variability, also termed model noise (Barnett et al. 1997), may be identified from the deviations of ensemble members from their mean (Harzallah and Sadourny 1995). Generally, the intermodel differences remain higher than model internal variability (Boyle 1998), suggesting that uncertainty in model parameterizations still exceeds the uncertainty of the model system. This implies that combining multiple model simulations may have an advantage over single model forecasts. This is already evident in medium-range forecasts up to 2 weeks ahead (Evans et al. 2000).

It has been known for some time that ensemble averaging is advantageous over individual forecasts (Murphy 1988). Intuitively it is apparent that creating an ensemble mean by weighting the individual models according to their skill would increase the skill of the mean. Kharin and Zwiers (2002) compare various ways of combining forecasts from different models. They found that generally the standard ensemble mean performs best in the Tropics where predictability is higher. In the midlatitudes none of the methods really demonstrate much skill. However, the superensemble technique has demonstrated improved skill in deterministic seasonal forecasts of monthly mean fields (Krishnamurti et al. 2000) and in probability forecasts (Stefanova and Krishnamurti 2002).

However, Barnett et al. (1997) studied the potential predictability of the Pacific–North American (PNA) pattern using AMIP run ensembles and found that the AGCMs only capture the leading empirical orthogonal function (EOF) mode. Sperber et al. (2001) also found that models mostly fail to project the subseasonal EOF modes onto the interannual variability leading to errors in the large-scale circulation. If AGCMs struggle with the predictability of robust patterns such as the PNA and higher-order modes of variability, this suggests the need to reassess what AGCM output should be used to produce seasonal forecasts.

Two areas in the field of model assessment are addressed in this study. The first is that the scientific focus of AGCM diagnosis, despite a comprehensive list in the AMIP program (Phillips 1996), has concentrated largely on time-averaged climate simulation, the seasonal cycle, and interannual variability (e.g., Harzallah and Sadourny 1995; Zwiers and Kharin 1998; Boyle 1998; Gates et al. 1999; Hunt 2000). In contrast, this paper examines statistics of AGCMs' daily circulation in order to investigate the simulation of higher-order modes of variability.

The second focus is to consider the value of AGCM output based on the daily characteristics. Despite improvements to AGCMs over the last decade, there are still fairly large systematic errors, largely owing to parameterization schemes (Gates et al. 1999). The situation is improving (Sperber et al. 1999) but until systematic biases of AGCMs are substantially reduced, seasonal forecasting procedures will still need to use AGCM output selectively.

Thus, the objectives of this paper are to assess which components of AGCM simulations are realistic and could be used in extended-range prediction, and to provide feedback to model developers on some aspects of model performance that have not received much attention. The approach concentrates on daily AGCM output and employs, inter alia, the self-organizing map technique for analysis and visualization of model data. The intention is not to compare the models (or the originating centers where they were developed) with each other, as the results are shown for specific model versions, some of which are dated. Rather, these results should serve as a pool of ideas that can be used in future model development.

2. Data and methodology

a. Model output

Daily output from three AGCM hindcasts is available for a 13-yr period from 1986 to 1998. The runs were performed as part of a larger project investigating seasonal forecasting and variability over southern Africa. One purpose of the hindcast simulations is to assess each model's ability to capture the general circulation from the daily to interannual scale when forced with observed global sea surface temperatures (SSTs). Very often AGCMs simulate the time-averaged circulation adequately but fail to reproduce synoptic-scale systems at the correct frequency and intensity. This can be particularly evident in long simulations after the effect of initial conditions has elapsed. For this reason the 13-yr simulations provide an ideal opportunity for AGCM evaluation in terms of the previous considerations.

The first AGCM evaluated here is the T30 resolution spectral model, developed at the Center for Ocean–Land–Atmosphere Studies (COLA). The model has been used operationally since 1995 at the South African Weather Service to produce monthly and seasonal forecast guidance. The model is described by Kirtman et al. (1997) and its application at the South African Weather Service by Tennant (1999). The model has 18 unevenly spaced sigma layers in the vertical. Prognostic variables include surface pressure, divergence, vorticity, virtual temperature, and specific humidity on all 18 levels. The physics include a Simple Biosphere model (SiB) (Sellers et al. 1986).

The second model is the Hadley Centre Atmospheric Climate Model (HADAM3). This hydrostatic gridpoint model has a resolution of 3.75° longitude by 2.5° latitude. The vertical scheme uses hybrid eta coordinates on 19 levels and the prognostic variables include zonal and meridional wind components, geopotential height, specific humidity, and liquid-water potential temperature. A comprehensive description of this model, an evaluation in terms of mean climate and the impacts of the physical parameterizations can be found in Pope et al. (2000). A local version of the model is installed at the Climate Systems Analysis Group (CSAG), University of Cape Town for research purposes.

The third model evaluated is the nine-level AGCM developed for climate research at the Division of Atmospheric Research of the Australian Commonwealth Scientific and Industrial Research Organization (CSIRO). The horizontal grid of the CSIRO9 (R21) AGCM comprises 64 zonal and 56 meridional (Gaussian) grid points, which yields a resolution of approximately 5.6° by 3.3°. In the AGCM dynamics the spectral atmospheric equations in flux formulation (Gordon 1981) are integrated over nine sigma model levels in the vertical. A comprehensive range of physical processes such as radiation and rainfall are also included (Rotstayn 1997). A more detailed description of the model is provided in McGregor et al. (1993) and Watterson et al. (1995). The Mark II version of this model is used for research purposes in the Laboratory for Research in Atmospheric Modelling (LRAM) at the Meteorology section of the University of Pretoria.

Observed SST data used for all model simulations were derived from the Reynolds monthly mean dataset on a 1° × 1° grid (Reynolds and Smith 1994). An ensemble of five simulations for each model was generated by initializing the models with different initial conditions. The COLA runs used real atmospheric conditions, derived from the NCEP reanalysis, one month apart from 1 July to 1 November 1985. The HADAM3 and CSIRO models used different restart dumps from 1984 that where obtained from earlier perpetual runs of these models. Data from 1985 were discarded to avoid the effects of initial conditions in the assessment. Simulations were continued until the end of 1998. An additional simulation, over the same hindcast period, using climatological SSTs was performed with each AGCM, specifically to assess the sensitivity of the AGCMs to SST forcing.

National Centers for Environmental Prediction (NCEP) reanalysis data (Kalnay et al. 1996), at 2.5° horizontal resolution, were used as a baseline for the model assessment. For this purpose four standard pressure levels in the vertical were extracted from the AGCMs, namely, 850, 700, 500, and 200 hPa. These were also used for intermodel comparative analyses. It is felt that the four standard pressure levels are sufficient for the purpose of evaluation in this instance. It should be noted that the NCEP reanalysis data, although constrained by observations, are also products of an atmospheric model. However, these data are more than sufficient and appropriate for the type of assessment done here.

Owing to the difference in the horizontal resolution of the AGCMs and the reanalysis data, an interpolation function using the model output grid-box average was used to convert all the data to a common 3.75° × 3.75° grid. This common grid size is equivalent to the coarsest AGCM resolution (except the CSIRO9 longitudinal resolution) and has the advantage of placing all the models on an equal footing in terms of spatial variability. Where direct intercomparisons are done on daily circulation data, in section 3, model biases could become problematic. This necessitated subtracting the respective long-term mean from all the datasets before these analyses.

b. Data analysis and visualization techniques

Owing to the high level of variability in daily circulation fields, a reduction in the number of degrees of freedom is helpful to perform a meaningful analysis. A useful way of doing this is to determine the core archetypical synoptic modes of a given variable using the self-organizing map (SOM) technique. Initially developed by Kohonen (Kohonen 1995) at the Helsinki University of Technology (available online at http://www.cis.hut.fi/research/som-research/), SOMs are used in a broad range of applications. This powerful technique identifies dominant modes within the span of a dataset and provides a mechanism for visualizing an array of atmospheric states. A review of SOMs and the application to synoptic climatology is described in detail by Hewitson and Crane (2002) with another application example in Tennant and Hewitson (2002). A brief description of the technique is given here, with a more comprehensive description in the appendix.

Essentially the SOM seeks to identify a number of nodes within the given data space such that the distribution of the nodes represent the observed distribution—thus providing a generalization to a few number of archetypes. One could describe the process as a nonlinear projection of the probability density function of high-dimensional input data onto a two-dimensional array of nodes (referred to as the SOM map), effectively as a mapping of high dimensionality onto a low dimensionality. The SOM technique is different from other cluster techniques in that representative points (nodes) are identified effectively and span the data space, as opposed to grouping data points. In addition, the SOM offers a powerful means of visualizing the continuum of data space, whereby the reference vectors of the two-dimensional array of nodes may be used to display a continuum of states spanning the range of data space.

Association of data points with a SOM node (in effect, clustering), is accomplished in a postprocessing phase after archetype points within the data space have been identified. Once the SOM map has been developed, each input data sample is assigned to a best-matching node in the map. This mapping of data points to the SOM nodes allows one to calculate frequencies of each archetype, and which may in turn be displayed as a two-dimensional histogram across the array of states represented by each node.

3. Daily circulation statistics

The approach in this paper is to use daily AGCM output without averaging, thus utilizing all the information in the ensemble set. In this way the ensemble members of each model essentially provide more realizations of the future atmospheric state with greater representation of the atmospheric variability, and which, collectively, are hopefully closer to the observed probability density function. This section will concentrate on 500-hPa heights and sea level pressure fields as basic indicators of synoptic-scale circulation.

a. Full period of the hindcast, 1986–98

SOMs, of 35 nodes each, were initially trained on NCEP reanalysis sea level pressure and 500-hPa height data, respectively, from January 1986 to December 1998. The data cover the area 0°–60°S and 30°W–60°E and provide 35 archetypical modes of circulations for each parameter. The number of SOM nodes was arbitrarily chosen to represent the daily circulation over a year in approximately a tenth of the original degrees of freedom. The actual array of the SOM nodes is secondary to this discussion and is not shown. However, the frequency of association of each day in the input data to a particular node may be mapped in a two-dimensional plane across the 35 nodes (five rows and seven columns) of the SOM. It is these patterns that are relevant in this study, and the frequency map for the NCEP reanalysis data 500-hPa heights is shown in Fig. 1.

Using this frequency distribution of NCEP “observed” synoptic states, a model's simulation at the daily time frame may be evaluated by how closely it matches the observed frequencies. In other words, does the model simulate the observed weather systems at the correct frequency? The frequency of association between the model data and SOM nodes is determined in the same way that the original input data, used to train the SOM, is assigned to the closest matching node in the SOM.

The differences in node frequency are divided by the original NCEP frequencies to present the figures as percentage errors. The absolute values of these are averaged over all nodes producing a summary for comparative purposes (Fig. 2).

In a worst-case scenario, if all the model fields were to link to a single node, the average node difference has an upper bound of approximately 200%. A reasonably evenly spread frequency mapping in a SOM of 35 nodes would report an error of 100% in 34 nodes and an error of 3400% in the node to which all the AGCM fields are associated. The average of all these is 194%. In reality, some nodes have higher frequencies than others so the 200% value is approximate.

Combining the daily output from all the ensemble members of a particular model (Fig. 2, Comb bar), has lower or similar errors in the SOM-node frequency distribution (as compared against NCEP) than the individual members (Fig. 2, Ens 1–5 bars). This neatly demonstrates the utility of ensemble forecasting techniques. However, there is a large difference between the models, with the HADAM3 being most realistic and the COLA least realistic. Combining the output from all (Fig. 2, All bar) the models ends up degrading the skill again and it is apparent that simply using the HADAM3 alone yields the best result.

An analysis of the frequency of data on the individual nodes (specific circulation archetypes) can be used to determine the strengths and weaknesses of each model. In this case the full ensemble of simulations for each model is used. Starting with the 500-hPa heights, is it striking that COLA's circulation is dominated by one node in particular (Fig. 1, central-right side of the SOM frequency map). This node has the lowest spatial variance of all the nodes (Fig. 1), indicating that the model has problems in simulating higher modes of atmospheric variability. CSIRO9 also has increased frequencies in this area of the SOM but the problem is not as acute as COLA. Node-frequency differences in the HADAM3 are relatively low and nodes with the greatest errors do not appear to correspond to particular aspects of node spatial variance (Fig. 1).

AGCM horizontal resolution is known to play a role in model accuracy by reducing climate drift (Palmer et al. 1990; Tibaldi et al. 1990) and capturing observed atmospheric processes better (Stratton 1999; Chandrasekar et al. 1999). The problem of variability, as found above with COLA and CSIRO9, has been shown to be reduced in an earlier version of the HADAM3 model run at higher spatial resolution (Stratton 1999). However, the CSIRO9 has the lowest resolution among the three models considered here and yet fares better than COLA in this respect. Furthermore, the difference between the HADAM3 and COLA resolutions is rather small and surely cannot account for all the improvements in the simulation of daily circulation statistics by the HADAM3. This would support the notion that improved parameterization schemes lead to more realistic model simulations (Ulbrich and Ponater 1992; Sperber et al. 1999), as the COLA model version used here is the oldest.

Another area where there is a relatively large difference between the observed and simulated frequency of a SOM node is found on the central-left side of the SOM (Fig. 1). In this case all three models have relatively large differences compared to the NCEP reanalysis. Nodes in this region of the SOM relate to a large meridional gradient in geopotential heights shown by darker shading on the central-left side of the panel (Fig. 1). The HADAM3 generates up to 44% too many days with strong meridional gradients whereas COLA simulates too few days with the strongest gradients by about 59%.

Sea level pressure fields show similar results to those of 500-hPa heights. All three models oversimulate a low-variance node, characteristic of winter. This mode represents the passage of a weak low pressure system south of the country. COLA also oversimulates weak ridging anticyclones, characteristic of summer, found on the central-left part of the SOM. The difference between the models is not as marked as with the 500-hPa heights (Fig. 2) but the HADAM3 still performs best.

In order to assess these findings in the global context, two additional SOMs of 35 nodes were done for daily 500-hPa heights for the Southern and Northern Hemispheres, respectively, over the full period from January 1986 to December 1998. The average node-frequency errors are given in Table 1 for comparative purposes. The data were presented to the SOM on a polar-stereographic projection to account for convergence of the meridians near the poles. Overall the HADAM3 produces the most realistic archetype frequencies, particularly for 500-hPa heights. The largest differences between the models occur for the southern Africa domain with the smallest differences over the Southern Hemisphere domain. This shows that regionally there are still quite large differences between models.

For the Southern Hemisphere, the COLA model is again biased toward nodes of low spatial variability. CSIRO9 is biased toward a zonal pattern while HADAM3 represents the observed frequency reasonably well. All three models simulate the winter three-wave and summer four-wave patterns close to the observed frequency. Northern Hemisphere wave patterns are much stronger than in the Southern Hemisphere and necessitate a more complex assessment of model performance. However, it is clear that all three models do show similar tendencies to favor certain oscillation patterns over others, indicating possible problems in simulating blocking events correctly. The mechanisms of these would need to be explored further before any reasons for such biases could be given. Specifically, the COLA model struggles to simulate the full magnitude of the extreme circulations, as seen in the Southern Hemisphere, while HADAM3 and CSIRO9 models simulate some nodes at 2 and 3 times the observed frequency, respectively. Generally, the models do a reasonable job at simulating synoptic archetypes but there are indeed fairly large high-frequency circulation errors that need to be addressed.

b. DJF seasons within the overall period

The same analysis over southern Africa is now performed for the summer December–January–February (DJF) months, the main rainfall season in southern Africa. Corresponding SOMs of the observed DJF circulation frequencies were re-created, as the previous SOMs would be constructed according to the seasonal cycle, and the DJF circulations would be confined to only a smaller subset of nodes in the SOM. In effect this allows the variability of DJF synoptic modes to be represented in finer detail, as the full 35 nodes are now used to identify DJF archetypes of summer circulation.

Average SOM-node frequency differences between GCMs and the NCEP reanalysis for the DJF period are consistent with those from the full year, but the difference in errors between COLA and the other two models is even larger, particularly at 500 hPa (Fig. 2). Overall, the error percentages in node-frequency are greater during DJF, indicating that the model simulation of this period is poorer in relation to the full year.

Inspection of the individual nodes shows that again the COLA model shows preferential synoptic modes related to an area in the SOM with nodes of low spatial variance, but also simulates too many days with a strong north to south gradient in the 500-hPa heights. For sea level pressure fields it has the largest errors in the nodes corresponding to a strong north–south pressure gradient. These findings are determined analogously to those in the preceding section. Combining results from these two sections indicate that this version of the COLA model suffers significant inadequacies in simulating the full extent of the seasonal cycle from winter to summer.

c. DJF seasons with strong anomalous SST forcing

Predictability of the atmosphere at the seasonal range is known to be higher during years with stronger tropical SST anomalies (Graham et al. 2000). Simulations with climatological SSTs can also aid in determining any improvement in model performance related to SST forcing (Owen and Palmer 1987; Zwiers et al. 2000).

Cold and warm episodes in the tropical Pacific SSTs are provided by the Climate Prediction Center (CPC; available online at http://www.cpc.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.html). During the 1986–99 period the DJF seasons that have been designated moderately to strongly warm by CPC are 1986/87, 1991/92, 1994/95, and 1997/98 and those designated cool are 1988/89 and 1998/99. To evaluate the GCM response to cool and warm SST forcing, the statistics of the daily circulation are now assessed again, but only for the DJF periods of these years.

These results are comparable to the full set of DJF seasons (Fig. 2). However, in terms of daily sea level pressure and 500-hPa height statistics, the climatological SST run of COLA and CSIRO fares best during periods of strong SST forcing. This suggests that these models are not setting up the correct teleconnections in response to strong SST forcing, because using realistic SSTs actually worsen the model simulation. This is consistent with Sperber et al. (2001) who found that the GCMs are failing in simulating the higher-order modes of variability, even during seasons of strong boundary forcing. However, it should be noted that the training of the SOMs described earlier is controlled largely by midlatitude circulation patterns, where daily variability is an order greater than in the Tropics, and it is known that seasonal predictability is lower in the midlatitudes.

Notwithstanding the difficulties in simulating the circulation of the midlatitudes, the analysis of daily AGCM output brings us closer to the reasons for systematic model errors. This information can then hopefully be used to decrease these biases. In terms of seasonal forecasting, aspects related to interannual variability become as important as systematic errors. These are investigated in the next section.

4. Interannual variability

Signal-to-noise ratios in AGCM output may be enhanced using ensemble techniques. A climatological SST simulation is particularly useful when doing this as it demonstrates what the model would produce in the absence of any anomalous boundary forcing. Simulations using real SST data can then be considered to have a signal when the variation they produce exceeds the noise produced by the climatological run. Owen and Palmer (1987) recognized that SST anomalies force realistic atmospheric responses in AGCMs irrespective of the model skill, necessitating the use of climatological SST runs and the ensemble spread of observed SST simulations to determine the skill of the model interannual variability.

As a broad measure of model response to SST boundary forcing, a time series of a quasi Southern Oscillation index (SOI) are shown for each model, including the reanalysis data (Fig. 3). These are calculated using the model grid points closest to Darwin and Tahiti and standardized over the period 1986–98. The spread of the ensemble is plotted as an envelope to determine if the model response to SST forcing is consistent. All the AGCMs capture the two cold episodes of 1988/89 and 1998/99. Similarly the warm episode of 1991/92 was captured well. However, CSIRO9 underestimates the warm episode of 1997/98 and COLA overestimates it somewhat. It is clear that all ensemble members respond in the same way to the SST forcing, a good indicator of interannual signal.

The climatological SST run yields some interesting results. While COLA and HADAM3 constrain the atmospheric sea level pressure response (shown by the quasi SOI in Fig. 3) to within one standard deviation (except HADAM3 early in 1988), CSIRO9 generates responses to the same magnitude as the observed SST runs. This finding coupled with the daily circulation statistics of CSIRO9 being better under climatological SST forcing suggest that CSIRO9 has a high level of internal variability, which may be to its advantage in terms of daily circulation but possibly jeopardizes its value as a seasonal forecasting tool.

Temporal variance of 500-hPa heights at the daily, monthly, and interannual scale can show how these models do react to SST forcing (Table 2). Observed SSTs force an increase in globally averaged temporal variance at these scales for all three models and is especially noticeable in the January monthly mean interannual variance. Again the COLA model consistently underestimates temporal variability, as with spatial variability, while HADAM3 tends to overestimate temporal variability of 500-hPa heights. CSIRO9 lies between the other two models in terms of temporal variability. These patterns, calculated as a global average, are similar in the southern Africa region.

Looking at the geographical distribution of 500-hPa temporal variance it is evident that observed SSTs introduce an improved 500-hPa height temporal variance during DJF over most of the globe (Fig. 4). There is only a slight degradation in some areas. The largest improvement is in the Tropics over land areas, indicating the models' direct response to tropical SST anomalies. However, the translation of this signal to the midlatitudes is not as well captured. This is indicated by the lower values over those regions.

5. AGCM rainfall fields

Rainfall is probably one of the most widely used variables in AGCM output, particularly in seasonal forecasting, and warrants a separate analysis. The problem is that rainfall fields are a product of various responses and feedbacks within an AGCM that are highly sensitive to the parameterization scheme used. Although they may look reasonable on a global scale, local rainfall fields may differ drastically from observed records.

First, it is instructive to investigate the temporal spread of model-simulated rainfall. Daily rainfall amounts for a summer-rainfall homogeneous region in the central interior of South Africa (region 3 in Tennant and Hewitson 2002) from 1986–98 were compared to AGCM grid-box amounts closest to 28°S and 26°E. The observed regional data were derived from 106 stations using a cross-correlation matrix as a weighting factor. Rainfall bins of 1 mm, from 0 to 20 mm day−1, were defined and the frequency of days related to each bin calculated (Fig. 5). It is clear that COLA and CSIRO9 simply produce rain too often in the range of 2–20 mm day−1. They also do not simulate enough dry days. The HADAM3 model, on the other hand, does a far better job and even tends to err on the dry side, especially in the 1–2 mm day−1 range.

These findings are consistent with globally averaged values (Table 3). COLA and CSIRO9 have a wet bias relative to CPC Merged Analysis of Precipitation (CMAP) data (Xie and Arkin 1997) while HADAM3 is reasonably accurate with only a small dry bias.

However, on an interannual scale none of the models show significant skill for the DJF season (Fig. 6). In this case the observed rainfall is taken from the central and northern interior of South Africa (regions 2 and 3 in Tennant and Hewitson 2002) and the AGCM output from a grid-box average over the area 22°–30°S and 24°–32°E. Here the positive bias in the COLA and CSIRO9 model rainfall is evident in the DJF totals being nearly twice that observed. There is little coherency between the ensemble members and the climatological SST run is indistinguishable from the observed SST runs. However, isolated cases of skill are apparent. For example, the CSIRO9 model shows a clear dry signal for the 1991/92 season and COLA a wet signal for the 1995/96 season. Overall the patterns are not particularly useful, with correlations for the ensemble mean of each model ranging from −40% for the HADAM3 to +45% for COLA. These are below a reasonable significance level for this relatively short 12-season period.

These results highlight the critical shortcomings of GCMs in seasonal forecasting, and even in climate change simulations, when used to inform hydrological impact studies. At present the only apparent approach to such end user needs appears to be some form of downscaling, either empirical or through nested models.

6. Atmospheric energetics

Atmospheric energetics is a useful tool to diagnose the fundamental processes simulated by an AGCM, where incoming solar energy is converted to kinetic energy of the general circulation. This is particularly suitable when trying to understand the model's response to parameterized processes (Ulbrich and Ponater 1992). Pope and Stratton (2002) used energetics to assist in determining those resolutions where the HADAM3 dynamical core began converging and was no longer sensitive to the effects of a coarse horizontal resolution.

Vertical integrals of kinetic energy separated into vertical-mean (barotropic) and shear (baroclinic) components (Wiin-Nielsen 1962; Eastin and Vincent 1998) were calculated using the four available pressure levels, namely, 850, 700, 500, and 200 hPa. The vertical-mean component is simply the mean wind integrated from 850 to 200 hPa and the shear component the vertically integrated deviation from the mean (shear) at each level. The terms barotropic and baroclinic will be used for identification of these components in this paper. These fields are useful in studying the subtropical jet stream and how shear–kinetic energy maintains the mean jet. Tennant and Hewitson (2002) showed how these two components of the wind fields can be linked to rainfall variability over South Africa. Consequently, biases in these fields may reveal some causes for model forecast errors over southern Africa.

The average bias of the ensemble of AGCM kinetic energy fields for DJF are shown as a percentage of the NCEP reanalysis climatological value (Fig. 7). All three models suffer from a northward displacement of the mean (barotropic) jet, which is indicated by a positive bias around 40°S and a negative bias around 60°S. There is also a longitudinal dependency in the barotropic bias with maximums in the southern Indian Ocean, Tasman Sea, and South Pacific Ocean. The bias between 40° and 60°E corresponds roughly to the climatological energy maximum shown by NCEP. Again the HADAM3 has the smallest bias and the COLA the largest bias. Over the Tropics models differ in their bias, with COLA and CSIRO9 simulating too little barotropic energy while HADAM3 overestimates it to an excess of 60%.

The baroclinic component shows more mixed patterns (Fig. 7), but there is still a positive bias in all three models in the Southern Hemisphere westerlies. Overall the HADAM3 has a fairly ubiquitous positive bias. It is worth noting that the NCEP data show maxima in the baroclinic energy anchored to the Southern Hemisphere continents. It is in these areas where the models show the greatest underestimation of baroclinic energy.

The energy biases are significant because they are occasionally of the same order of magnitude as the fields themselves. There are also some clear geographic links, common to all three models. These biases point to some basic problems in AGCM modeling, possibly evident in the physics, which contaminate the dynamical fields. These issues are probed in context with the other analyses in the discussion section.

7. Discussion

Systematic errors over the southern Africa region documented for earlier AMIP model assessments (Joubert 1997), such as poor rainfall and the placement of the midlatitude westerlies (Gates et al. 1999), remain in evidence with the particular version of the three GCMs evaluated here. Certain aspects of interannual variability are captured adequately by the AGCMs but many features in the subtropics and midlatitudes are not being captured correctly, which leads to the systematic errors found in the mean state. It is therefore becoming more crucial that the reason for these systematic errors is explored.

All three models show maxima in the frequency of synoptic archetypes associated with tropical-temperate troughs and truncated troughs, relative to other archetypes as defined by the SOM of DJF mean sea level pressure. The HADAM3 produces both these archetypes at a frequency roughly double to that observed (Fig. 8). These trough systems, that are often identified as cloud bands (Tyson and Preston-Whyte 2000, 212–217), have been found to be major individual contributors to the annual rainfall in the central parts of South Africa (Harrison 1984). These cloud bands, found in preferred locations around the Southern Hemisphere (Todd and Washington 1999; Cook 2000), correspond to the maxima in observed (NCEP reanalysis) baroclinic energy (Fig. 7) and are generally associated with transient midlatitude troughs. Incorrect simulation of these important features of the general circulation must have an impact on the model energetics and so contribute to the systematic errors documented in this paper.

Although the biases in AGCM kinetic energy over continental southern Africa are relatively low, the large biases southeast of the region do indicate errors in the simulations of tropical–extratropical interaction. Despite the northward displacement of the westerlies by the models during DJF, temporal variance of 500-hPa heights is still being underestimated over continental southern Africa (see bracketed values in Table 2). It is unclear what ratio of the temporal variance bias may be attributed to low model resolution and how much to errors in modeled land surface processes. The NCEP reanalysis data, although also a relatively coarse resolution model, is constrained to observations over southern Africa and may generate more 500-hPa height variability than the free-running AGCMs.

Notwithstanding, the fact that there is a negative bias in AGCM temporal 500-hPa height variability suggests that midlatitude wave activity is not solely responsible for generating too much rainfall, at least in the COLA and CSIRO9 models, and subsequent positive biases in downstream kinetic energy in all three models. This suggests that model physical parameterizations, particularly land surface processes that can be influenced by topography (e.g., Pope and Stratton 2002), soil moisture (e.g., Douville et al. 2001), and vegetation (e.g., Zheng and Eltahir 1998) could play an important role in the energy biases in these models. Similar sensitivities have been found elsewhere, for example, Arora and Boer (2002). Errors in land surface processes would have a ripple effect on other model physics, like convection and cloud processes, which in turn could set up a feedback mechanism that is responsible for the observed model errors (Cess et al. 1990; Zhang et al. 1994). Obviously this would need to be quantified through a study of different land surface schemes in these models, but there is enough evidence to justify further investigation into this area. The argument, however, remains consistent with the notion of improved physics being a major contributor in reducing AGCM biases (Sperber et al. 1999).

Intermodel comparison, made possible by the availability of data from three separate AGCMs, can be quite revealing in terms of understanding model behavior under SST forcing. It has been shown that of the three models evaluated, HADAM3 clearly produces the best climate simulation in terms of daily circulation statistics. However, the HADAM3 interannual DJF seasonal rainfall signal is the least skillful, with a negative correlation to observations. The other two AGCMs have positive correlations and reproduce the broad signal in rainfall, albeit with a low significance. This raises two possible scenarios.

First, are the COLA and CSIRO9 models getting rudimentary aspects of the interannual rainfall signal right for the wrong reasons? In this case there is no forecast skill in these models in the southern Africa region and none of the three models' rainfall fields should be used for seasonal forecast guidance at all.

Second, and more likely, is that the COLA and CSIRO9 models produce rainfall fields in more direct response to global SST forcing by setting up the leading EOF modes realistically. The improvement in 500-hPa height temporal variance during DJF when using observed SSTs is highest in the COLA simulations, indicating the ability of this model to react to SST forcing. The circulation in COLA and CSIRO9 is more constrained than HADAM3, which has a higher degree of internal variability or more freedom to develop its own circulation. These differences could well explain the varying rainfall signals between the models.

Another reason for these differences could be ascribed to the fact that although SST–rainfall associations have been established for southern Africa (Mason 1995), the explained rainfall variance is relatively low. Consequently, using only SSTs as external forcing in AGCM simulations could be limited in terms of producing realistic rainfall responses.

Essentially, each AGCM should be rigorously evaluated before being used in long-term forecasting. In the case of southern Africa it would be advisable to use the HADAM3 circulation, as it performed best in terms of daily circulation statistics, while COLA and CSIRO9 rainfall fields could be included in guidance for rainfall forecasts. This needs to be done with a clear understanding of the caveats involved. Basically, as AGCMs become more complex their simulation of the general circulation appears to improve. However, these additions add more variability such that certain fields, particularly parameterized quantities like rainfall, can degrade somewhat.

Fairly robust associations between South African summer rainfall and kinetic energy fields of the vertical-mean wind have been demonstrated in Tennant and Hewitson (2002). All three models in this assessment have shown realistic representations of these fields and, more importantly, a clear distinction between wet and dry seasons in terms of daily circulation statistics. Therefore, optimal use of ACGMs in seasonal forecasting appears to be selecting large-scale circulation parameters, such as barotropic and baroclinic energy, as primary guidance. These fields may be downscaled to regional rainfall where stable associations have been determined. Rainfall and other output, where reliability and accuracy may be in question, should be included only as secondary forecast guidance.

The importance of high-frequency model error in seasonal forecasting is becoming more crucial as the demand for higher spatial- and temporal-resolution forecasts increases. Downscaling in the seasonal context, as in this discussion, relies on models simulating daily circulation statistics accurately, but also, as shown by Sperber et al. (2001), these high-order errors translate directly to errors in the large-scale circulation.

8. Conclusions

Evaluation of AGCMs and intermodel comparison are useful in determining the progress in model simulations of the atmosphere and to better understand the causes of model error. The approach adopted in this paper to study daily circulation patterns provides much more insight into model variability, particularly of higher order, and model circulation regime statistics. The comparisons shown here are done for specific model versions and do not necessarily reflect the best modeling capability of the originating centers.

Some AGCMs have constrained atmospheric circulation regimes and underestimate variability on many scales. These models are also not reproducing the observed circulation archetypes at the correct frequency. However, AGCMs in general do simulate many of the gross features of interannual variability forced by SSTs. Observed SSTs also contribute to better AGCM simulations in nearly all aspects considered in this paper, relative to simulations using climatological SSTs.

Intermodel differences are large, as seen in other studies, indicating that a high level of uncertainty remains in atmospheric modeling. However, some models, such as the HADAM3 analyzed in this study, are beginning to show reduced errors and promising improvements in daily circulation statistics. A large part of these advances is related to improvements in model physics, while increased resolution has also been shown to play an important role.

In terms of using AGCMs in seasonal forecasting, it was found that modeled rainfall fields are still poor despite recent improvements to models and the reduction of systematic biases. It remains more viable to use large-scale circulation that can be downscaled to regional rainfall. AGCMs are shown to be setting up altered frequencies of large-scale daily circulation statistics realistically in response to SST forcing. Where these can be related to regional rainfall in a reliable fashion, improved forecast skill should realized.

Acknowledgments

The author wishes to thank Mark Tadross and Hannes Rautenbach who have managed the HADAM3 and CSIRO9 simulations and who have partaken in discussions on the analyses presented in this paper. Additionally, funding from the Water Research Commission project K5/1154/0/1, and the Department of Arts, Culture, Science and Technology Innovation Fund are acknowledged. These organizations are thanked for their support in enabling much of the modeling activities.

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APPENDIX

Self-Organizing Maps (SOM)

As the SOM technique application to atmospheric sciences is relatively new, a more detailed description of the technique and an example are presented in this appendix.

Initially developed by Kohonen (Kohonen 1995) at the Helsinki University of Technology (available online at http://www.cis.hut.fi/research/som-research/), SOMs are now used in a broad range of applications. SOMs are a powerful technique to identify dominant modes within the span of a dataset, and provide a mechanism for visualizing an array of atmospheric states. The use of this technique for atmospheric applications is somewhat in its infancy but in other disciplines SOMs have widespread application (e.g., automatic speech recognition, analysis of electrical signals from the brain, and analysis and visualization of large collections of statistical data). More information is available online at http://www.cis.hut.fi/research/som-bibl/.

Essentially the SOM seeks to identify a number of nodes within the given data space such that the distribution of the nodes represent the observed distribution—thus providing a generalization to few number of archetypes. One could describe the process as a nonlinear projection of the probability density function of high-dimensional input data onto a two-dimensional array of nodes. The SOM technique is different from other cluster techniques in that representative points (nodes) are identified effectively spanning the data space. Individual data elements may then be associated with a node. In addition, it offers a powerful means of visualizing the continuum of data space.

The process begins by initializing the reference vectors of the map using random numbers or in an orderly fashion along a two-dimensional subspace spanned by the two principal eigenvectors of the input data vectors. Upon investigation, it was found that both initialization methods were equally effective. The size of the map is subjective and is chosen according to the generalization that is required. Basically, number of nodes is analogous to the number of clusters in traditional methodologies. Typical sizes range from a rectangular array of 2 by 3 nodes to one of 6 by 8 nodes.

The next stage consists of a two-phase iterative training process where the weight vectors on a node are adjusted toward the training vectors, such that they effectively span the variance structure of the data space. In the first phase the reference vectors of the map units converge to the dominant variance structure of the data. This phase develops the broad mapping of the SOM. The second phase then develops the finer aspects of the SOM array.

During the update process a data element is presented and a winning node identified by the minimum error between the node vector and data vector. The winning node vector is updated maximally and other nodes within the predefined radius of update are updated by an amount proportional to the distance away from the winning node. The learning rate (a measure of how much a node vector is adjusted around each input data sample on each iteration) is taken as the software default (0.05) and the radius of update is the smaller of the SOM array dimensions. During the second phase the learning rate is smaller and the radius of update covers nodes in the immediate vicinity, starting at 3. In both phases the learning rate decreases to zero and the radius of update to unity. The result of the training stage is a two-dimensional map of nodes whose weight vectors span the continuum of data space as represented by the input data.

In the last stage the trained map is now used for visualization of the input data. The program generates a list of coordinates for the best-matching node in the map for each sample in the input data. Each node's reference vector now represents a particular archetype of the original data, and the node vectors can be plotted as an array of maps. The mapping coordinates for each data element may be used to calculate frequencies of each archetype.

The utility of SOMs is demonstrated using a step-by-step, practical example, applied to monthly averaged sea level pressure fields around southern Africa. The first step is to subjectively choose the number of nodes to represent the range of variability in monthly average sea level pressure fields. In this example, each of the four seasons may be supposed to contain three major monthly mean patterns over the course of 20 yr (duration of NCEP record used), giving a total of 12 nodes. Next, the nodes are initialized randomly and the monthly data over a 20-yr period from 1979 to 1999 applied in the training procedure. The visualization stage follows with a mapping of the input data to the SOM nodes.

The SOM, from the example above, is shown in Fig. A1. The SOM distinguishes between cyclonic (right-hand side) and anticyclonic (left-hand side) circulation over southern Africa, characteristic of summer and winter, respectively. The center of the SOM shows a set of bridging nodes between these two scenarios, typical of spring and autumn.

A further useful aspect of a SOM analysis is to inspect the frequency of each node for different subsets of the period used in training the SOM, to determine what patterns are more prevalent under those circumstances. For example, the summer months map clearly to the right-hand side of the SOM, winter to the left, spring to the center, and autumn, with a bimodal tendency, towards the bottom left and upper right (Fig. A2). This technique is used in this paper to identify the types of circulation associated with seasons of different rainfall characteristics.

Fig. 1.
Fig. 1.

SOM-node frequency maps (middle row) and associated errors (bottom row) expressed as a percentage of NCEP frequencies (top left) of the COLA, HADAM3, and CSIRO9 AGCMs for daily mean 500-hPa heights from Jan 1986 to Dec 1998. Also shown are two-dimensional histograms of within-node spatial variance (top middle) and north-to-south 500-hPa contour gradient (top right)

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Fig. 2.
Fig. 2.

SOM-node frequency errors (%) averaged over all nodes for the COLA, HADAM3, and CSIRO9 GCMs daily mean (left) 500-hPa heights and (right) sea level pressure for the period (top) Jan 1986–Dec 1998, (middle) DJF days only, and (bottom) DJF days during ENSO years

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Fig. 3.
Fig. 3.

Quasi-SOI series calculated using model grid boxes closest to Tahiti and Darwin. (left column) AGCM output using observed SSTs (gray shading indicates ensemble spread) and the solid black line the quasi SOI using NCEP reanalysis data. (right column) Output from the climatological SST simulation

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Fig. 4.
Fig. 4.

Percentage improvement of 500-hPa height temporal variability when using observed SSTs relative to climatological SSTs in AGCM simulations

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Fig. 5.
Fig. 5.

Frequency of occurrence of 1-mm daily rainfall bins over central interior of South Africa and nearest AGCM grid-box values for COLA, HADAM3, and CSIRO9

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Fig. 6.
Fig. 6.

Time series of DJF total rainfall observed over central interior of South Africa and nearest grid-box values from COLA, HADAM3, and CSIRO9 AGCMs. Dashed line indicates climatological SST AGCM simulation

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Fig. 7.
Fig. 7.

(top row) Barotropic and baroclinic kinetic energy for daily winds from NCEP reanalysis and COLA, HADAM3, and CSIRO9 AGCM biases expressed as a percentage of the NCEP values for DJF days from 1986 to 1998. Areas of positive bias are shaded.

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Fig. 8.
Fig. 8.

SOM-node frequency maps for (top left) NCEP reanalysis data and the (top right) HADAM3 AGCM errors expressed as a percentage of the NCEP frequencies for daily mean sea level pressure for DJF days during Jan 1986–Dec 1998. The actual SOM nodes in the two positions marked A and B on the frequency map are shown at the bottom, with the position of the tropical-temperate trough and truncated trough, respectively, marked by the heavy dashed line

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

i1520-0493-131-9-1975-fa01

Fig. A1. A 4 × 3 node self-organized map of monthly mean sea level pressure (hPa) from Jan 1979 to Dec 1999

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

i1520-0493-131-9-1975-fa02

Fig. A2. Frequency of mapping of monthly mean sea level pressure fields to SOM nodes during the four seasons

Citation: Monthly Weather Review 131, 9; 10.1175/1520-0493(2003)131<1975:AAOIVF>2.0.CO;2

Table 1.

SOM-node frequency errors (%) averaged across the SOM for the COLA, HADAM3, and CSIRO9 AGCMs daily mean sea level pressure (MSLP) and 500-hPa heights (Z500) from Jan 1986 to Dec 1999. The five-member ensemble combined results are given for the southern Africa region, Southern Hemisphere, and Northern Hemisphere

Table 1.
Table 2.

Global 500-hPa height temporal variance. Brackets denote values for continental southern Africa. Obs is the observed SSTs and clim is the climatalogical SST runs

Table 2.
Table 3.

Global mean precipitation (mm day−1 )

Table 3.
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