## 1. Introduction

Recently, advances have been made in both dynamical and statistical prediction (Goddard et al. 2001). The commonly used statistical tools are canonical correlation analysis (CCA; Barnett and Preisendorfer 1987) and singular value decomposition (SVD; Bretherton et al. 1992). The statistical approach is empirical. The forecasts are made based on the covariability between predictors and predictand during the training period. The CCA method assumes that the relationships between predictors and the predictand are linear. The forecast will be skillful if the relationships determined during the training period remain true during the forecast period.

One of the important predictors for the surface temperature (*T*_{surf}) over the United States is the sea surface temperature (SST) field, which represents boundary forcing (Barnston and Smith 1996). In addition to SSTs, atmospheric fields can also be used as predictors. Multiple predictors can enter the CCA together to perform forecasts. However, the forecast skill depends on the weighting function, which has to be given a priori. Barnston (1994) used both SSTs and 700-hPa heights as predictors to predict *T*_{surf} over the United States. He discovered that the forecasts have the highest skill when the weighting between SSTs and 700-hPa heights is two to one. In general, it is difficult to find the optimum weighting function among predictors before entering the CCA.

The dynamical forecasts based on global general circulation models (GCMs) do not depend on the past history or weighting function. Because of model errors, statistical forecasts based on the CCA and dynamical model forecasts have comparable skill at the present time. Therefore, model errors need to be removed before the model forecasts can be utilized. In addition to removing the mean model bias, the error correction methods based on CCA or SVD can also be used to improve model forecasts (Feddersen et al. 1999; Smith and Livezey 1999; Ward and Navarra 1997). Model outputs are adjusted based on the common modes between the model forecasts and the observed fields. The CCA method corrects not only the mean field, but also the leading modes of variability. Since the model errors are regime dependent (Mo and Wang 1995; O'Lenic and Livezey 1989), the CCA correction method improves forecast skill.

The nomenclature ensemble has been used to represent a set of forecasts made from different models or forecasts made from the same model but different initial conditions. Lau et al. (2002) developed the ensemble canonical correlation (ECC) prediction method and used the term ensemble to represent forecasts from the CCA based on SSTs from different ocean basins. In this paper, the term ensemble is expanded to cover a set of CCA forecasts based on observations as well as model forecasts. Lau et al. (2002) used the ECC to specify summer precipitation over the United States. The global ocean is separated into different basins. The SSTs from each ocean basin enter the CCA separately to specify summer precipitation. These predicted fields form an ensemble. The ensemble mean is the weighted average of its members. The weighting is determined according to the previous forecast performance. To separate the global ocean into different basins, the weaker and more regional forcing can be recognized.

Later, Mo and Thiaw (2002) adopted the ECC prediction concept to predict summer seasonal mean rainfall over the Sahel. Instead of using SSTs from different ocean basins as predictors, they used different variables, such as SSTs, and 200-hPa streamfunction anomalies over the Tropics. In addition to the CCA forecasts, their ensemble also included model forecasts. Because forecasts from different variables recognize different forcing, they are skillful over different regions of the Sahel. The ensemble mean forecasts have high skill. This method is easy to use. The ensemble can contain as many members as needed. Since each variable enters the CCA prediction separately, the training period for each variable can also vary. This gives the forecast system needed flexibility.

The weighting function among variables can be determined after the CCA. There are many ways to construct the ensemble mean forecasts. The simplest way is to take an equally weighted average of its members (Mo and Thiaw 2002). The superensemble method proposed by Krishnamurti et al. (2000a,b) can also be a candidate. Kharin and Zwiers (2002) called the superensemble forecast the regression-improved forecast to emphasize the regression scheme used. If the forecasts are given in categories, then a Bayesian method developed by Rajagopalan et al. (2002) can also be applied.

For any statistical prediction, the selection of predictors is important. As stated by Goddard et al. (2001), the main sources of predictability on the seasonal and interannual timescales come from the long-term trends in SSTs and El Niño–Southern Oscillation (ENSO). The low-frequency components of the SST forcing contribute to the forecast skill because of its large global impact (Ropelewski and Halpert 1987, 1989; Halpert and Ropelewski 1992; Mason and Goddard 2001; Gershunov and Barnett 1998). In addition to SSTs, the surface temperature field in summer is influenced by soil moisture (Huang et al. 1996; Koster et al. 2000). Atmospheric variables like sea level pressure (SLP; Barnett and Preisendorfer 1987) or 700-hPa heights have also been used as predictors (Barnston 1994). The atmospheric variables are influenced by soil moisture, snow cover, and sea ice in addition to SSTs. Therefore, they may capture variability not associated with the leading SST modes.

The purpose of this paper is to apply the ECC method to forecast *T*_{surf} over the United States for summer (July–August–September, JAS) and winter (January–February–March, JFM). These two seasons were selected because the National Centers for Environmental Prediction/Climate Prediction Center (NCEP/CPC) operational seasonal forecasts had the highest skill in JFM and the lowest skill in JAS. Instead of using SSTs from different ocean basins as suggested by Lau et al. (2002), different variables are used as predictors. The data and procedures are outlined in section 2. Section 3 presents the ensemble forecasts for summer *T*_{surf}. The model forecasts used in the operational environment are forecasts made with predicted SSTs from a coupled model with a lead time of 1 month. Such forecasts for the current model are available only from September 2000 to the present. Therefore, model simulations from the Atmospheric Model Intercomparison Project (AMIP) were used to represent the model outputs. The current NCEP seasonal forecast model was used to perform the AMIP experiments. They were performed with the observed SSTs. These runs can be considered as the *T*_{surf} “forecasts” with perfect SSTs. The actual forecast skill with predicted SSTs will be lower because the errors of SSTs are not included in the AMIP simulations. Since the goal of this paper is to compare the ECC ensemble forecasts with its members, the model simulations serve this purpose. The ECC prediction is applied to the winter *T*_{surf} (JFM) forecasts in section 4. Conclusions are given in section 5.

## 2. Data and procedures

### a. Data

#### 1) Observations

The seasonal mean sea level pressure (SLP) anomalies were obtained from the NCEP–National Center for Atmospheric Research (NCEP–NCAR) reanalysis for the period from 1 January 1950 to 31 December 2000 (Kalnay et al. 1996). The data were reduced to a 10° × 10° latitude–longitude grid because only the large-scale anomalies are recognized by the CCA.

SSTs were reconstructed using empirical orthogonal functions (EOFs; Smith et al. 1996, 1998). The reconstruction was based on the historical data obtained from the U.K. Met Office. This dataset has a resolution of 2°, and covers the recent period from 1950–80. After 1981, SSTs were derived from the in situ and satellite data using the optimum interpolation method of Reynolds and Smith (1994). Climatological seasonal means were removed from each dataset to obtain SST anomalies (SSTAs) before merging. Following Barnston and Smith (1996), SSTAs were reduced to a resolution of 6° before entering CCA to reduce the matrix size. The SSTA data cover the period from 1950–2000.

The seasonal mean soil moisture dataset of Huang et al. (1996) was updated to 2000 using their procedure. This dataset covers 344 climate divisions over the United States from 1950–2000. The locations of divisions are marked in Fig. 1a. The seasonal mean *T*_{surf} data cover 102 climate divisions from 1950–2000. This is the same dataset used for the operational seasonal forecasts at the NCEP/CPC. The locations of divisions are plotted in Fig. 1b. All anomalies are defined as departures from seasonal means determined for the base period 1950–2000.

#### 2) Model simulations

The model AMIP simulations were performed using the (NCEP) seasonal forecast model (Kanamitsu et al. 2002) for the period 1950–98. The simulations were forced by the observed SSTs and the initial conditions were taken from the reanalysis. The soil conditions including soil moisture and soil temperature were predicted by the model. Details of the model are described in Kanamitsu et al. (2002). There are 12 members in its ensemble. The leading modes of *T*_{surf} simulated by members in the ensemble are similar (Ward and Navarra 1997). Therefore, the ensemble seasonal means for JFM and JAS were used for the ECC prediction.

### b. Procedure

#### 1) CCA for a single predictor

The CCA procedure for a single predictor is outlined in Barnston (1994) and Barnston and Smith (1996). The predictand is the *T*_{surf} over the United States. The predictors are the global SST; SLP over the Northern Hemisphere from 20°–90°N; *T*_{surf}, and soil moisture over the United States. In order to compare with the operational seasonal forecasts issued by the NCEP/CPC, the lead time is 1 month (Barnston 1994). For example, forecasting *T*_{surf} for JAS based on SST, 1 month lead forecast is performed using SST (March–May; MAM). The reason is that the seasonal forecast for JAS is issued in mid-June. Therefore, the season closest to JAS with data available is MAM.

The forecast skill for each year can be expressed in terms of the anomaly correlation defined as the spacial pattern correlation between the observed and predicted anomalies over the United States for that year. The mean anomaly correlation averaged over all years gives a general indication of the overall skill of the forecasts.

The standard deviations for the predictor and the predictand are averaged over the domain of the datasets. The standardized predictor and predictand separately enter the EOF analysis. The truncated EOF time series then enter the CCA program. The truncation for each variable is determined based on specification using the cross-validation procedure (Barnston and Smith 1996). It will be explained later. For summer, the JAS SSTs are used to specify the JAS *T*_{surf}. The mean anomaly correlations (ACs) between predicted and observed *T*_{surf} are determined for different modes of truncation. The mean AC increases as the member of modes increases until it reaches a maximum. After that, the AC decreases. The number of modes that gives the highest AC in the specification experiment is used for prediction. The same process is also used to determine the truncation for soil moisture and SLP. The truncation depends on the variable. It varies from 11 modes for SST to 16 modes for soil moisture.

The CCA modes are determined based on the covariability between the predictor and the predictand from data in the training period. The predictor data for the target year *T* are projected onto the predictor CCA loading patterns, and the predictand values are generated and verified against the observed *T*_{surf} for the target year *T.*

Cross validation is used in all skill evaluations (Barnston 1994; Barnston and Smith 1996). Let *N* be the data record length. All data for the target year *T* are withheld. The length of the training period is *N* − 1. All calculations are repeated for each target year including the means, standard deviations, EOFs, and CCA modes. The predicted field for the target year *T* should be verified against the observed field for the same target year *T.* The process then is repeated *N* times for *N* different target years. Because of the strong trends in SSTs, the cross validation by taking 1 year out may still inflate skill. The purpose of this paper is to compare the ECC ensemble mean forecasts with the individual members in the ensemble. Therefore, the inflation of skill does not impact conclusions significantly. The CCA procedure produces loading patterns for predictor and predictand as well as the amplitude time series. For diagnostic purposes, the loading patterns and the amplitude time series are determined from the CCA using all data available.

#### 2) Equally weighted ensemble mean (EE)

The ensemble members include the CCA-predicted *T*_{surf} fields based on observations and model forecasts from different models or from the same model but different initial conditions. The model outputs are treated the same way as observations. The predictor entering the CCA is the model-forecasted *T*_{surf}. The predictand is the corresponding observed *T*_{surf}. The CCA gives the model-corrected *T*_{surf} (Livezey and Smith 1999).

Let *N* be the length of the record and *M* be the number of predictors from observations and from the GCM outputs. For the data period (1950–2000), *N* = 51. If one uses three predictors from observations (SST, SLP, soil moisture) and the AMIP run, then *M* = 4.

*T.*For each single predictor m, the CCA is performed using data for the remaining

*N*− 1 yr using the procedure described in the previous section. There are

*M*predicted

*T*

_{surf}fields

*R*(

*m,*

*x,*

*T*) for the withheld year

*T,*climate division

*x*and predictor m. Here,

*x*= 1, 102 and

*m*= 1,

*M.*The simple ensemble mean

*E*(

*x,*

*T*) for the target year

*T*can be written as

*E*(

*x,*

*T*) is the ensemble mean for the climate division

*x*and the target year

*T.*

*E*(

*x,*

*T*) should be verified against the observed field

*P*(

*x,*

*T*) for the withheld year

*T.*In this case, all members in the ensemble are weighted equally.

#### 3) Superensemble mean (SE) or the regression-improved forecast

*R*(

*m,*

*x,*

*T*) for the withheld year

*T*:

*R*(

*m,*

*x,*

*T*) is the

*T*

_{surf}predicted from the observed predictor or model forecast. The linear regression method is used to determine the coefficients

*b*(

*m,*

*x*) for each target year

*T.*To perform regression, one needs to have

*N*− 1 pairs of predicted and observed

*T*

_{surf}. They are obtained the following way:

*N*− 1 data records, data from another year

*y*are withheld. Now, there are two withheld years:

*T*and

*y.*The CCA is then performed using the remaining

*N*− 2 yr for each predictor m separately. The standard deviations, means, EOFs, and CCA modes are calculated each time for different

*T*and

*y.*Let

*r*(

*m,*

*x,*

*y*) be the predicted field for predictor

*m,*at climate division

*x*for the withheld year

*y*. The ensemble mean

*e*(

*x,*

*y*) can be written the same way as Eq. (2):

*e*(

*x,*

*y*) should be verified against the observed field

*P*(

*x,*

*y*) for each year

*y.*This procedure is then repeated

*N*− 1 times for different year

*y.*During this whole process, data from

*T*are not used. There are

*N*− 1 pairs of

*e*(

*x,*

*y*) and the corresponding observed

*P*(

*x,*

*y*).

*b*(

*m,*

*x*) are determined by minimizing the variance

*V*(

*x*) between the ensemble mean

*e*(

*x,*

*y*) and the corresponding observed field

*P*(

*x,*

*y*) for the training period

*N*− 1:

*b*(

*m,*

*x*) are substituted into Eq. (2) to get

*E*(

*x,*

*T*).

In this process, data from the withheld year *T* are not used to obtain the coefficients *b*(*m,* *x*) or *R*(*x,* *m,* *T*). This process is then repeated for each year *T* = 1, *N* for cross validation. *E*(*x,* *T*) is verified against *P*(*x,* *T*) for the withheld year *T.* For 51-yr data and 3 predictors, there are 7650 separate CCA calculations performed.

#### 4) Verification

In addition to the mean AC described above, the geographic distribution of the skill is also presented (Barnston and Smith 1996) for verification. The temporal correlation between the predicted and observed pairs of *T*_{surf} at each climate division for 51 yr (1950–2000) gives the cross-validated skill for that division. All climate divisions together give the geographic distribution of skill. Assume the *T*_{surf} obeys a normal distribution, then the correlation values greater than 0.28 are statistically significant at the 5% level for *N* = 50.

*T*

_{surf}is given in three categories: below normal, normal, and above normal. The Heidke score is defined as

*S*

*E*

*N*

*E*

*N*is the total number of locations verified so here

*N*= 102. The value

*E*is the number of categorically correct matches by chance. For three equally likely categories,

*E*=

*N*/3. The comparison between the Heidke score and other measures of skill were reviewed by Barnston (1992).

The field significance test (Livezey and Chen 1983) is performed by randomly shuffling the forecasts and the corresponding observational fields 1000 times. One counts the number of times that the mean of the correlation in the domain exceeds that of the random statistics. Unless otherwise stated, maps presented below pass the field significance test a the 5% level.

## 3. Summer surface temperature

The predictand field is the summer mean (JAS) *T*_{surf} over United States (25°–49°N, 70°–125°W). The standard deviation for the period 1950–2000 (Fig. 1c) shows large values located over the central United States with a maximum over Oklahoma and Kansas. Over the western United States and Florida, the standard deviations are small. The leading mode of variability can be described by the first rotated EOF. EOF was performed for seasonal mean (JAS) *T*_{surf} for the period 1950–2000. Eight EOFs were used for the Varimax rotation. Rotated empirical orthogonal function 1 (REOF 1; Fig. 1d), which explains 27% of the total variance has weak negative loadings over the West Coast and positive loadings over the central United States. The maximum is located over Oklahoma and Kansas. This is the same location of the standard deviation maximum (Fig. 1c).

### a. Forecasts based on predictors from observations

Figure 2 shows the geographical distribution of the cross-validated skill measured by the correlation between *T*_{surf} forecasts and verifying observations at each climate division. The mean anomaly correlation averaged over 51 yr (1950–2000) is also given. Forecasts based on SST for MAM, February–March–April (FMA), and JFM were made. Overall, the forecasts based on SST (JFM; mean AC = 0.23) (Fig. 2a) have the highest skill. This is consistent with Barnston (1994) and Barnston and Smith (1996) that forecast skill does not decrease with the forecast lead time for summer *T*_{surf}. For most years, the anomaly correlations for forecasts based on SST (JFM), and SST (MAM) differ less than 0.1. There are 13 [5] cases that forecasts based on SST (JFM) [SST (MAM)] are more skillful. The forecasts based on SST (FMA) are similar to those based on SST (MAM) with the mean AC = 0.21 (not shown). Overall, the mean skill is comparable with the skill given by Barnston (1994) for a shorter period (1955–91). Both SST forecasts (Figs. 2a,b) show skill over the Pacific Northwest, the southern states, the Great Lakes, and Florida. There is no skill over the central United States.

Following Barnett and Preisendorfer (1987), SLP field was used to represent the atmospheric conditions. Forecasts based on SLP (MAM) are skillful over the central United States and the western Plains, where forecasts based on SSTs have low skill.

Huang et al. (1996) found that soil moisture is a good predictor for *T*_{surf} over the central United States in summer. This is confirmed by the CCA prediction based on soil moisture for MAM (Fig. 2d). The forecasts based on soil moisture (MAM) have slightly higher skill, with the mean AC = 0.25, than forecasts based on SSTs. The forecasts based on soil moisture have useful skill over the central and eastern United States and the West Coast. Overall, the forecasts based on SLP (MAM), soil moisture, and SST (JFM) have comparable skill with the mean anomaly correlations between 0.2 and 0.25. They also show skill in different regions of the United States. Therefore, they are good candidates to form an ensemble.

### b. Sources of forecast skill

The sources of skill are indicated by the CCA modes. Here they are presented for each predictor.

#### 1) SSTs

The first two CCA modes for SST (JFM) are given in Fig. 3. The *T*_{surf} pattern is expressed in correlations between *T*_{surf} (JAS) and the amplitude time series. The purpose is to show the relative influence of different SST modes on *T*_{surf}.

The first CCA mode explains 41% of the total covariance (Figs. 4a–c). As noted by Goddard et al. (2001) and Barnston and Smith (1996), most forecast skill comes from the tropical SST forcing. The first CCA mode represents the ENSO and the long-term trends (Figs. 3a–c). The SST loading pattern shows broad positive loadings over the tropical Pacific and along the west coast of North America and cold SSTs in the North Pacific. It resembles the interdecadal mode of Zhang et al. (1997) with the ENSO signals mixed in. The amplitude series (Fig. 3c) shows both the long-term trends and ENSO. The *T*_{surf} pattern shows positive values over the West Coast, the Southwest, Texas, and areas east of 93°W. The CCA may not be able to separate the trends and ENSO because of the orthogonality requirement. Livezey and Smith (1999) suggested using the rotation of CCA modes to separate the interdecadal and interannual timescales. Because the purpose of this paper is to demonstrate the ECC method, CCA modes are not rotated.

The second CCA mode (Figs. 3d–f) shows the influence of SSTAs in the North Atlantic. It explains about 24% of the covariance. The SST loading pattern shows a three-cell pattern in the North Atlantic. In the Pacific, there are weak negative loadings in the North Pacific and positive loadings near the west coast of North America. The *T*_{surf} pattern shows negative loadings extending from Texas and New Mexico northward to Colorado and positive loadings over the West Coast. The first two CCA modes together explain about 65% of the covariability. Basically, the CCA captures the leading SST REOF modes that have influence on *T*_{surf} (JAS).

One interesting point is that forecasts based on SST (JFM) have equal or better skill in comparison with forecasts based on SST (MAM), even though the MAM season is closer to the target season JAS. This may be explained by the first CCA mode for MAM, which explains about 39% of the covariability (Fig. 4). There are many similarities among the first CCA modes for SST (MAM) and SST (JFM) (Figs. 3a–c, and Fig. 4). Both SST loading patterns show positive loadings in the central Pacific and negative loadings in the North Pacific. Both amplitude time series contain the long-term trends and ENSO. However, the *T*_{surf} loadings for two seasons are different. The SST (MAM) has weaker influence on *T*_{surf} in comparison with SST (JFM) (Figs. 3a and 4a). The differences are located over the area east of 90°W. This is the area that forecasts based on SST (JFM) are more skillful (Figs. 2a,b). This is the major reason that forecasts based on SST (MAM) have equal or lower skill than forecasts based on SST (JFM).

The forecasts based on SSTs have low skill over the central United States (Figs. 2a,b) because the leading SST modes do not have strong influence on *T*_{surf} there (Fig. 3). The predicted *T*_{surf} based on SSTs also has small projection onto REOF 1 for *T*_{surf} (JAS) (Fig. 1d).

#### 2) Soil moisture

The *T*_{surf} over the central United States is influenced by soil moisture (MAM) as indicated by the geographic distribution map of skill (Fig. 2d). The first CCA mode explains about 18% of the covariance (Fig. 5). The *T*_{surf} pattern is the negative phase of REOF 1 (*T*_{surf}). It is associated with wet soil extending from Texas northeastward and dryness over the Southeast and California. As indicated by Huang et al. (1996) that cool (warm) temperature in summer is associated with wet (dry) soil in spring. The amplitude time series for the soil moisture (Fig. 5c) shows a slight positive trend.

#### 3) SLP

The first CCA mode for SLP (MAM) (Figs. 6a–c) explains 21% of the covariance. The SLP loading pattern shows positive loadings extending from the North Pacific to Alaska and negative loadings over the eastern Pacific near the Baja coast. The corresponding *T*_{surf} mode shows negative loadings over Texas and positive loadings centered over Montana. The correlation pattern between the CCA time series and SST (MAM) is not statistically significant. Therefore, this SLP pattern is not associated with SSTs.

The influence of SSTs dominates the second CCA mode (Figs. 6d–f), which explains about 17% of the covariance. The *T*_{surf} pattern has negative loadings over the central United States with a minimum over northern Utah. The SLP pattern has negative loadings extending from the central and eastern United States to the Atlantic and positive loadings extending from the North Pacific to the west coast of North America. The SLP pattern is related to the tropical SSTs as indicated by the correlation pattern between SST (MAM) and the amplitude time series for SLP. The correlation pattern shows cold SSTs over the central Pacific, the tropical North Atlantic, and the Indian Ocean. Some of the SLP anomalies are the responses to SSTs, but the SLP modes can also be influenced by forcing in the midlatitudes or locally. This may be the reason that to add SLP as a predictor improves the ensemble forecasts.

Different predictors capture the low-frequency *T*_{surf} variability in different parts of the United States. The long-term trends in SST and ENSO influence *T*_{surf} over the Southwest, the West Coast, and the eastern United States and Florida, while soil moisture and SLP have large impact on *T*_{surf} over the central United States and the western plains. This is the key reason that the ensemble mean improves the forecast skill.

### c. Ensemble forecasts based on observations

Because the CCA forecasts based on SST (JFM), SLP (MAM), and soil moisture (MAM) are skillful in different regions of the United States, they were chosen to form an ensemble. The simplest ensemble forecast is the equally weighted mean of its members. It is referred to as EE (list of members). One can also test the superensemble forecast (Krishnamurti et al. 2000a,b), or the regression-improved forecast (Kharin and Zwiers 2002). It is referred to as SE (list of members). The geographic distributions of the cross-validated skill for the SE and the EE forecasts are given in Figs. 7a and Fig. 7b, respectively. Both EE and SE forecasts have higher skill than their members (Fig. 2).

The SE gives the best performance. The mean AC is 0.40. Correlations of 0.5 and above are located over the Southwest, the Pacific Northwest, California, Florida, and the central United States. The EE (SST, SLP, soil moisture) and SE forecasts are skillful in same areas, but correlations for EE forecasts are overall lower over the Southwest, Florida, and southern United States. Anomaly correlation for each year was calculated for EE and SE (Fig. 7c). In most cases, the differences in ACs are less than 0.1. There are 14 cases that show the SE forecasts are more skillful than the EE forecasts. For those cases, the ACs for the SE forecasts do not drop as low as for the EE. However, there are also 9 yr that the EE forecasts have higher skill. The SE forecasts are better than SST (MAM) as a single predictor about 86% of cases. For both SE and EE forecasts, the skill over the South and the West Coast is contributed by the SST field and the skill over the central United States is contributed by both SLP and soil moisture. The EE is the mean of the forecasts based on its members, therefore, it is a compromise. If the EE is constructed, members should be chosen carefully. Each member should contribute to the forecast skill in different regions of the United States. The superensemble does not have such concern. The linear regression is able to find the best combination among its members based on their performance during the training period.

Kharin and Zwiers (2002) tested many statistical methods to combine model simulations from the AMIP runs. They found that the superensemble mean (Krishnamurti et al. 2000a,b) gives poor performance in comparison to the simple ensemble mean (EE). Here the SE has overall higher skill than the EE. The reasons are given next.

The coefficient *b*(*x,* *m*) for variable *m* at the climate division *x* is determined by linear regression [Eq. (2)] for each target year independently. In this case, *b*(*x,* *m*) does not vary randomly from one target year to another. The consistency is the major reason that the SE forecasts are skillful. This can be demonstrated by displaying the regression coefficients *b*(*x,* *m*) [Eq. (2)] averaged over 51 yr (Fig. 8). If the regression coefficient *b*(*x,* *m*) for any given *x* and *m* varies randomly from one target year to another, then the mean *b*(*x,* *m*) average over all years should have no signal. Figure 8 shows that the mean coefficients have clear patterns. The large values of *b*(*x,* SST) are located over the southern states and the west coast of the United States, where the forecasts based on SSTs are skillful (Fig. 2a). Similarly, the coefficients for the SLP *b*(*x,* SLP) and the soil moisture *b*(*x,* soil moisture) have large values in the western plains and the central United States, where forecasts for these predictors are skillful.

The performance of each predictor is determined by physical processes. For example, SSTs have impact on *T*_{surf} over the Southwest, Florida, the West Coast, and the southern United States. In these areas, forecasts based on SSTs are skillful and the SE weights these forecasts over these areas heavily. On contrary, soil moisture and SLP have large influence on *T*_{surf} over the central United States. The SE gives more weight to forecasts based on SLP and soil moisture over the central United States. This consistency also means that the relationships determined from the training period are likely to be true for the target year. Therefore, the SE has high skill.

In an operational situation, both SE and EE should be made available to forecasters because they are far more skillful than forecasts based on any individual variable. Any forecast should be examined together with the geographic distribution of skill based on the past history to give forecasters the indication of reliability of the forecast.

### d. Model simulations

The JAS ensemble means from the NCEP AMIP simulations were used to represent model outputs. They were evaluated against the observed JAS mean *T*_{surf} for the period (1950–97). In this case, the total year is *N* = 48. Cross validation was used in all skill evaluations. For a given target year *T,* all data for that year *T* are withheld. Both the *T*_{surf} model anomalies and the corresponding observed *T*_{surf} anomalies are calculated based on data from the remaining 47 yr. The model errors can be corrected by performing the CCA. In this case, the model-forecasted *T*_{surf} is the predictor and the observed *T*_{surf} is the predictand. The CCA modes are then determined according to the covariability between the model forecasts and observations (Livezey and Smith 1999).

The first CCA model explains 45% of the covariance (Fig. 9). The model displaces the maximum of the first REOF for *T*_{surf} (Fig. 1d) eastward and shows negative values over the Southwest. The errors are not dominated by one or two events as indicated by the amplitude time series. After the CCA correction, the model simulations with the mean AC = 0.26 (Fig. 10a) are as skillful as the CCA forecasts based on SSTs (Fig. 2). It shows skill over Florida and the area extending from the Southwest northward to Colorado. Before the CCA correction, skill is low. The uncorrected simulations have skill only over the southeastern United States. The CCA correction is able to “correct” the model-simulated REOF 1 for *T*_{surf} (Fig. 1d). Therefore, the skill is higher.

The model simulations can be added to the previous ensemble, which consists of SST (JFM), SLP (MAM), and soil moisture (MAM). Adding the model simulations to the ensemble only improves the forecast skill slightly. There is almost no difference in the mean AC for the SE with (AC = 0.42; Fig. 10b) and without the model simulations (AC = 0.40; not shown). The EE with the model simulations has higher mean AC = 0.37 (Fig. 10d) than the EE without the model simulations (AC = 0.34; not shown). However, the improvements are regionally dependent. For example, to add the CCA-corrected model simulations to the EE, forecast skill over the Southwest and Florida improves, but forecast skill over the west region decreases. There is no advantage to add the model simulations to the SE. The model simulations and the CCA forecasts based on SSTs are skillful over the same regions. Therefore, forecast skill does not improve by adding the model simulations.

### e. Comparison with the operational NCEP forecasts

The forecast skill scores of the NCEP/CPC operational seasonal mean forecasts are available from 1995 to 2001. The JAS *T*_{surf} forecast is issued in mid-June prior to the season. The detailed procedure and evaluation methods were reviewed by Barnston et al. (1999). The forecasts are given in three categories (above, near, and below normal). They are evaluated using the Heidke scores.

The model forecasts are available from 2000 on. They are not long enough to perform the CCA correction and are not used in this experiment. For the target year *T,* forecasts were made based on SST (JFM), SLP (MAM) and soil moisture (MAM) separately as a single predictor using data from January 1950 to May of the target year *T* as the training period. These forecasts formed an ensemble and the SE mean was constructed. No data after June of the target year were used. For example, data from 1950 to MAM 1995 were used to perform the 1995 JAS forecast. The skill was assessed based on all climate divisions. They were compared with the Heidke scores of the operational forecasts with all locations counted including the “climatology” forecasts (Barnston et al. 1999). Results are given in Table 1.

The scores for SE are higher than the operational forecasts for all years except the strong warm ENSO year 1997. For 1997, the scores for the SE and the operational forecasts are comparable. The NCEP/CPC forecasts in general have low forecast skill in summer and the ECC ensemble forecasts improve the forecast skill.

## 4. Winter surface temperature

Figure 11 shows the geographical distribution of the cross-validated skill measured by the correlations between *T*_{surf} (JFM) forecasts and verifying observations at climate divisions. For the *T*_{surf} (JFM) forecasts, the forecast skill decreases as the lead time increases. The mean anomaly correlation for SST (JAS) is only 0.13 and the skillful forecasts are limited to the northern states (not shown). The forecasts based on SST [September–October–November (SON)] have the mean AC = 0.32. The correlations higher than 0.5 are located over the eastern and central part of the United States and the West Coast. Results are consistent with those reported by Barnston and Smith (1996).

The forecasts based on SLP (SON) have the mean AC = 0.15. The forecasts based on the persistence of the *T*_{surf} (SON) have AC = 0.1 (Fig. 11c). If data for December are available, then the forecasts based on the October–November–December (OND) mean have the mean AC = 0.15 and skill increases over the northern states (Fig. 11d). The NCEP model simulation is able to capture ENSO responses in general. After the CCA correction, the forecast skill with the mean AC = 0.30 is comparable with forecast skill based on SST (SON). The CCA correction improves the forecast skill.

The sources of skill come from SSTs in the Pacific. Consistent with Barnston and Smith (1996), the leading CCA modes for SST (SON) represent the long-term trends and ENSO (Fig. 12). The first three CCA modes explain 22%, 20%, and 17% of the covariance respectively. (Fig. 12). The degeneracy among the first three CCA modes makes the separation of signal difficult. The first CCA mode represents the long-term trends. The SST loading pattern resembles the ENSO-like decadal mode (Zhang et al. 1997). Positive SST loadings are located over three oceans with a maximum over the central Pacific and negative loadings are found over the North Pacific. The corresponding *T*_{surf} pattern shows warming over the west coast of the United States and the northern states. Cooling is found over the Southeast. The second mode shows positive SSTs in the central Pacific and *T*_{surf} pattern shows cooling over the southeastern United States and Minnesota. The third mode represents warming over the central Pacific and the west coast of North America. The corresponding *T*_{surf} shows cooling over the Southwest and warming over the Northeast.

The leading CCA mode for SLP is influenced by SSTs (Fig. 13). The correlation pattern between the amplitude time series and SST (SON) shows warm SSTs in the central Pacific and negative SSTs over the western Pacific. The *T*_{surf} and the SLP loading patterns resemble the composites during the warm ENSO years (Barnston 1994; Barston et al. 1999). The SLP pattern shows large zonal components with positive loadings over high latitudes and negative loadings to the south (Barnston 1994). The *T*_{surf} loadings show warming located over the northern states and cooling over the Southeast.

Both the simple ensemble mean EE and super ensemble mean SE forecasts were constructed. The members are the CCA forecasts based on SST, SLP, and *T*_{surf} for SON. The skill of the simple EE ensemble forecast depends on its members. The EE (SST, SLP) forecasts have higher skill over the northern states, but lower skill over the southern states in comparison with the forecasts based on SST (SON). Overall, the EE (SST, SLP) forecasts have a slightly higher mean AC = 0.34 (Fig. 14a). The EE (SST, SLP, *T*_{surf}) forecasts have lowest skill with mean AC dropping to 0.26 (Fig. 14b). The EE (SST, SLP, model) forecasts have the highest mean AC = 0.37 (Fig. 14c). The improvements are located over the Southeast where the model forecasts are skillful. This indicates that members should be chosen carefully in constructing the EE ensemble forecasts.

The skill of the SE ensemble forecast is not sensitive to its members. The SE (SST, SLP, *T*_{surf}), SE (SST, SLP), and SE (SST, SLP, model) forecasts are similar with the mean AC = 0.39–0.40. For example, to add forecasts based on *T*_{surf} (SON) to the ensemble does not degrade the SE. The forecasts based on *T*_{surf} are consistently poor. The regression assigns lower weights to *T*_{surf} (SON), therefore, the SE forecasts are not affected by adding *T*_{surf} (SON). The SE mean forecasts (Fig. 14d) are more skillful than forecasts based on any individual member (Fig. 11). The geographic distribution of skill for the SE forecasts (Fig. 14d) shows that correlations greater than 0.5 are located over the southern and the southeastern United States, the Pacific Northwest, and the area over the Great Lakes. Similar to the summer *T*_{surf} forecasts, the SE forecasts have high skill because the forecasts for each variable behave consistently.

The NCEP operational forecasts had the highest skill in JFM (Barnston et al. 1999). In comparison with summer, the scores for winter forecasts are much higher (Table 1). During this period, there were two strong warm ENSO events in 1995 and 1998, and one strong cold ENSO event in 1999. The NCEP forecasts were always more skillful during the ENSO winters. The Heidke scores for ENSO seasons vary between 17 and 20. The CCA forecasts were made each year based on variables for SON, and the SE (SST, SLP, *T*_{surf}) ensemble mean was constructed. Again, no data after SON year *T* − 1 were used to predict *T*_{surf} (JFM) for year *T.* Except 2000, the SE gives better or comparable skill than the operational forecast. For winter, the NCEP seasonal forecast model is able to capture the ENSO signals well. That contributes to the successful forecasts.

## 5. Conclusions

The concept of the ECC prediction method developed by Lau et al. (2002) has been applied to predict summer JAS and winter JFM surface temperature *T*_{surf} over the United States. The predictors are the global SST and SLP over the Northern Hemisphere, soil moisture and *T*_{surf} persistence over the United States from one to two seasons lead, as well as model AMIP simulations from the NCEP seasonal forecast model. Each variable enters the CCA prediction separately as a single predictor. The predicted fields form an ensemble. The ensemble means are the weighted average of its members. Both the simple ensemble mean and the superensemble mean are tested. The simple ensemble forecast is the equally weighted average of its members. For the superensemble forecast, the weighting function among the members is determined by linear regression (Krishnamurti 2000a,b). Because the linear regression is used, Kharin and Zwiers (2002) called it the regression-improved forecast.

The *T*_{surf} winter forecasts have overall higher skill than the summer forecasts. The major sources of skill in winter comes from the decadal SST trends in the central Pacific and ENSO. The *T*_{surf} field for summer JAS is influenced by both SST and soil moisture. For JAS, the CCA forecasts based on SSTs recognize the long-term warming trends and ENSO in the tropical Pacific. In addition to the tropical SSTs, SSTs over the North Pacific and the North Atlantic also contribute to the forecast skill because they appear as the second and high CCA modes. One can also test the importance of the extratropical SSTs by performing the CCA forecast based on SST (JFM) in the tropical Pacific (30°S–30°N, 120°E–90°W) alone. The forecasts based on SSTs in the tropical Pacific alone have the mean AC = 0.18. They are less skillful in comparison to forecasts based on the global SSTs. This suggests that SSTs in the North Pacific and the North Atlantic also contribute to the *T*_{surf} forecast skill in summer.

For the *T*_{surf} JAS forecasts, soil moisture has large influence on *T*_{surf} over the central United States. *T*_{surf} is also influenced by SLP. The SLP anomalies are associated with SSTs, but they are also influenced by other boundary forcing such as soil moisture, sea ice, snow, and many other factors. The SLP as a predictor may capture forcing that is not represented in the leading modes of SSTs.

Different variables recognize different forcing and give skillful forecasts over different regions of the United States. This is the major reason that the ensemble forecasts have high skill. Both the ensemble EE and SE forecasts are more skillful than forecasts based on a single predictor. The improvements are more impressive for summer (JAS) than in winter (JFM). The skill of the EE forecast depends on its members. The EE members should be chosen in such a way that each members shows forecast skill in different regions of the domain. If the superensemble is constructed, the linear regression will select the best combination of members at each climate division.

The SE forecasts are skillful because forecasts from different variables behave consistently. For example, the summer forecasts for *T*_{surf} based on SSTs are skillful over the southern states and over the west coast of the United States. The linear regression scheme will weight forecasts based on SSTs heavily over these areas. On contrary, the forecasts based on soil moisture are more skillful in the central United States, so the regression scheme assigns more weights to forecasts based on soil moisture. The weights do not vary much from one target year to another. This is the major reason that the SE forecasts are skillful.

This does not mean that the SE forecasts are always better than the EE forecasts over the United States everywhere. Therefore, in the operational forecast situation, both EE and SE forecasts or forecasts based on other regression methods (Kharin and Zwiers 2002) should be presented to forecasters together with the geographic distribution of skill determined, based on forecasts from the previous years. The consistency and differences among the ensembles can be used to determine the reliability of the forecasts.

One of the advantages of the ECC method is the flexibility. One can add model outputs to the ensemble. The ensemble simulations of the AMIP runs are used to represent model forecasts. The simulations were performed with observed SSTs. They can be viewed as forecasts made with “perfect SSTs.” In a real forecast situation, the SSTs are predicted from a coupled model or from persistence. Therefore, the skill is much lower. Overall, the CCA correction increases the forecast skill because that the CCA corrects errors in the leading modes of variability.

For cases tested here, to add ensemble model outputs to a SE or EE ensemble only increases the forecast skill slightly. The areas in which the model simulations are skillful are also the regions that the forecasts based on observations are skillful. Therefore, there is little new information. However, this is highly dependent on the region and the model. Mo and Thiaw (2002) applied the same method to prediction of rainfall over the Sahel. In that case, the model simulations and the forecasts based on SSTs are skillful over different parts of the Sahel. Therefore, to add model simulations to an ensemble improves the forecast. The method is flexible and easy to use. It has potential to improve seasonal forecasts.

## Acknowledgments

The author would like to thank Dr. Tom Smith for providing her the CCA program, Dr. William Lau for giving her an advanced copy of the ECC paper. Thanks to Drs. Tom Smith, Steven Tracton, Francis Zwiers, and reviewers. Their suggestions improved the paper.

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Geographical distribution of the cross-validated CCA skill expressed as the correlation between the observed and predicted *T*_{surf} fields at each climate division in forecasting U.S. JAS *T*_{surf} based on seasonal mean (a) SST (JFM), (b) SST (MAM), (c) SLP (MAM), and (d) soil moisture (MAM) as a single predictor for the period (1950–2000). The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less than 0.2 are omitted. The mean anomaly correlation averaged over 1950–2000 is also given.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated CCA skill expressed as the correlation between the observed and predicted *T*_{surf} fields at each climate division in forecasting U.S. JAS *T*_{surf} based on seasonal mean (a) SST (JFM), (b) SST (MAM), (c) SLP (MAM), and (d) soil moisture (MAM) as a single predictor for the period (1950–2000). The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less than 0.2 are omitted. The mean anomaly correlation averaged over 1950–2000 is also given.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated CCA skill expressed as the correlation between the observed and predicted *T*_{surf} fields at each climate division in forecasting U.S. JAS *T*_{surf} based on seasonal mean (a) SST (JFM), (b) SST (MAM), (c) SLP (MAM), and (d) soil moisture (MAM) as a single predictor for the period (1950–2000). The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less than 0.2 are omitted. The mean anomaly correlation averaged over 1950–2000 is also given.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on SST (JFM) as a single predictor. (a) The *T*_{surf} pattern expressed in correlations between *T*_{surf} for JAS and the CCA time series. The contour interval is 0.1. Areas where positive (negative) correlations are statistically significant at the 5% level are shaded dark (light). Values less than 0.28 are omitted. (b) The predictor SST loading pattern. The contour interval is 0.2 nondimensional units. Positive values are shaded. (c) The CCA amplitude time series for the predictor SST (JFM). (d)–(f) Same as in (a)–(c) but for the second CCA mode.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on SST (JFM) as a single predictor. (a) The *T*_{surf} pattern expressed in correlations between *T*_{surf} for JAS and the CCA time series. The contour interval is 0.1. Areas where positive (negative) correlations are statistically significant at the 5% level are shaded dark (light). Values less than 0.28 are omitted. (b) The predictor SST loading pattern. The contour interval is 0.2 nondimensional units. Positive values are shaded. (c) The CCA amplitude time series for the predictor SST (JFM). (d)–(f) Same as in (a)–(c) but for the second CCA mode.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on SST (JFM) as a single predictor. (a) The *T*_{surf} pattern expressed in correlations between *T*_{surf} for JAS and the CCA time series. The contour interval is 0.1. Areas where positive (negative) correlations are statistically significant at the 5% level are shaded dark (light). Values less than 0.28 are omitted. (b) The predictor SST loading pattern. The contour interval is 0.2 nondimensional units. Positive values are shaded. (c) The CCA amplitude time series for the predictor SST (JFM). (d)–(f) Same as in (a)–(c) but for the second CCA mode.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

(a)–(c) Same as in Fig. 3(a)–(c) but for the first CCA mode for *T*_{surf} (JAS) based on SST (MAM).

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

(a)–(c) Same as in Fig. 3(a)–(c) but for the first CCA mode for *T*_{surf} (JAS) based on SST (MAM).

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

(a)–(c) Same as in Fig. 3(a)–(c) but for the first CCA mode for *T*_{surf} (JAS) based on SST (MAM).

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on soil moisture (MAM) as a single predictor. (a) The *T*_{surf} loading pattern. The contour interval is 0.1 nondimensional units. Zero contours are omitted and positive values are shaded. (b) Same as in (a), but for the soil moisture loading pattern, and (c) the CCA amplitude time series for soil moisture

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on soil moisture (MAM) as a single predictor. (a) The *T*_{surf} loading pattern. The contour interval is 0.1 nondimensional units. Zero contours are omitted and positive values are shaded. (b) Same as in (a), but for the soil moisture loading pattern, and (c) the CCA amplitude time series for soil moisture

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on soil moisture (MAM) as a single predictor. (a) The *T*_{surf} loading pattern. The contour interval is 0.1 nondimensional units. Zero contours are omitted and positive values are shaded. (b) Same as in (a), but for the soil moisture loading pattern, and (c) the CCA amplitude time series for soil moisture

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for JAS *T*_{surf} based on SLP (MAM) as a single predictor. (a) The same as in Fig. 3a. (b) The loading pattern for the SLP. The contour interval is 0.1 nondimensional units. Positive values are shaded. (c) The correlation between the CCA amplitude time series for the SLP and SST (MAM). The contour interval is 0.1. Negative values are shaded. Values less than 0.2 are omitted. (d)–(f) Same as in (a)–(c) but for the second CCA mode

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for JAS *T*_{surf} based on SLP (MAM) as a single predictor. (a) The same as in Fig. 3a. (b) The loading pattern for the SLP. The contour interval is 0.1 nondimensional units. Positive values are shaded. (c) The correlation between the CCA amplitude time series for the SLP and SST (MAM). The contour interval is 0.1. Negative values are shaded. Values less than 0.2 are omitted. (d)–(f) Same as in (a)–(c) but for the second CCA mode

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for JAS *T*_{surf} based on SLP (MAM) as a single predictor. (a) The same as in Fig. 3a. (b) The loading pattern for the SLP. The contour interval is 0.1 nondimensional units. Positive values are shaded. (c) The correlation between the CCA amplitude time series for the SLP and SST (MAM). The contour interval is 0.1. Negative values are shaded. Values less than 0.2 are omitted. (d)–(f) Same as in (a)–(c) but for the second CCA mode

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated skill presented as the correlation between the observed and the predicted fields at each climate division in forecasting JAS *T*_{surf} based on (a) the superensemble forecasts SE [SST(JFM), SLP (MAM), soil moisture (MAM)] for the period 1950–2000. The contour interval is 0.1 Areas where the correlation is significant at the 5% level are shaded. Values less than 0.2 are omitted. (b) Same as in (a) but for the EE [SST (JFM), SLP (MAM), Soil moisture (MAM)] forecasts. (c) Anomaly correlation between the observed *T*_{surf} and the SE (open circles) and the EE (dark circles) forecasts for each year from 1950–2000. (d) Same as in (c) but for the SE forecasts (open circles) and forecasts based on SST (MAM) (dark circles)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated skill presented as the correlation between the observed and the predicted fields at each climate division in forecasting JAS *T*_{surf} based on (a) the superensemble forecasts SE [SST(JFM), SLP (MAM), soil moisture (MAM)] for the period 1950–2000. The contour interval is 0.1 Areas where the correlation is significant at the 5% level are shaded. Values less than 0.2 are omitted. (b) Same as in (a) but for the EE [SST (JFM), SLP (MAM), Soil moisture (MAM)] forecasts. (c) Anomaly correlation between the observed *T*_{surf} and the SE (open circles) and the EE (dark circles) forecasts for each year from 1950–2000. (d) Same as in (c) but for the SE forecasts (open circles) and forecasts based on SST (MAM) (dark circles)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated skill presented as the correlation between the observed and the predicted fields at each climate division in forecasting JAS *T*_{surf} based on (a) the superensemble forecasts SE [SST(JFM), SLP (MAM), soil moisture (MAM)] for the period 1950–2000. The contour interval is 0.1 Areas where the correlation is significant at the 5% level are shaded. Values less than 0.2 are omitted. (b) Same as in (a) but for the EE [SST (JFM), SLP (MAM), Soil moisture (MAM)] forecasts. (c) Anomaly correlation between the observed *T*_{surf} and the SE (open circles) and the EE (dark circles) forecasts for each year from 1950–2000. (d) Same as in (c) but for the SE forecasts (open circles) and forecasts based on SST (MAM) (dark circles)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

The regression coefficient *b*(*x,* *m*) used to construct the SE [SST (JFM), SLP (MAM), soil moisture (MAM)] ensemble mean averaged for the period 1950–2000 for (a) SST (JFM). The contour interval is 0.2 nondimensional units. Positive values greater than 0.8 are shaded. (b) Same as in (a) but for SLP(MAM); and (c) same as in (a), but for soil moisture (MAM)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

The regression coefficient *b*(*x,* *m*) used to construct the SE [SST (JFM), SLP (MAM), soil moisture (MAM)] ensemble mean averaged for the period 1950–2000 for (a) SST (JFM). The contour interval is 0.2 nondimensional units. Positive values greater than 0.8 are shaded. (b) Same as in (a) but for SLP(MAM); and (c) same as in (a), but for soil moisture (MAM)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

The regression coefficient *b*(*x,* *m*) used to construct the SE [SST (JFM), SLP (MAM), soil moisture (MAM)] ensemble mean averaged for the period 1950–2000 for (a) SST (JFM). The contour interval is 0.2 nondimensional units. Positive values greater than 0.8 are shaded. (b) Same as in (a) but for SLP(MAM); and (c) same as in (a), but for soil moisture (MAM)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on the ensemble simulations from the NCEP AMIP runs as a predictor. (a) The observed *T*_{surf} loading pattern. The contour interval is 0.1 nondimensional units. Zero contours are omitted and positive values are shaded. (b) Same as in (a) but the loading pattern for the model outputs. (c) The CCA amplitude time series for the model outputs.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on the ensemble simulations from the NCEP AMIP runs as a predictor. (a) The observed *T*_{surf} loading pattern. The contour interval is 0.1 nondimensional units. Zero contours are omitted and positive values are shaded. (b) Same as in (a) but the loading pattern for the model outputs. (c) The CCA amplitude time series for the model outputs.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

First CCA mode for *T*_{surf} (JAS) based on the ensemble simulations from the NCEP AMIP runs as a predictor. (a) The observed *T*_{surf} loading pattern. The contour interval is 0.1 nondimensional units. Zero contours are omitted and positive values are shaded. (b) Same as in (a) but the loading pattern for the model outputs. (c) The CCA amplitude time series for the model outputs.

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the skill presented as the correlation between the observed *T*_{surf} and the ensemble model simulations from the AMIP run after the (a) CCA correction at each climate division. The contour interval is 0.1. Areas where the correlation is significant at the 5% level are shaded. Values less than 0.28 are omitted. (b) Same as in (a) but for the cross-validated skill for the superensemble forecasts SE [SST (JFM), SLP (MAM), soil moisture (MAM), model simulation]. (c) Same as in (a) but without the CCA correction. (d) Same as in (b), but for the EE [SST (JFM), SLP (MAM), soil moisture (MAM), model simulation]

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the skill presented as the correlation between the observed *T*_{surf} and the ensemble model simulations from the AMIP run after the (a) CCA correction at each climate division. The contour interval is 0.1. Areas where the correlation is significant at the 5% level are shaded. Values less than 0.28 are omitted. (b) Same as in (a) but for the cross-validated skill for the superensemble forecasts SE [SST (JFM), SLP (MAM), soil moisture (MAM), model simulation]. (c) Same as in (a) but without the CCA correction. (d) Same as in (b), but for the EE [SST (JFM), SLP (MAM), soil moisture (MAM), model simulation]

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the skill presented as the correlation between the observed *T*_{surf} and the ensemble model simulations from the AMIP run after the (a) CCA correction at each climate division. The contour interval is 0.1. Areas where the correlation is significant at the 5% level are shaded. Values less than 0.28 are omitted. (b) Same as in (a) but for the cross-validated skill for the superensemble forecasts SE [SST (JFM), SLP (MAM), soil moisture (MAM), model simulation]. (c) Same as in (a) but without the CCA correction. (d) Same as in (b), but for the EE [SST (JFM), SLP (MAM), soil moisture (MAM), model simulation]

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated CCA skill expressed in correlation between the observed and predicted *T*_{surf} fields at each climate division in forecasting U.S. JFM *T*_{surf} based on seasonal mean (a) SST (SON), (b) SLP (SON), (c) *T*_{surf} (SON), and (d) *T*_{surf} (OND) as a single predictor for the period 1951–2000. The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less than 0.2 are omitted. The mean anomaly correlation averaged over the period 1950–2000 is also given. (e) Same as in (a) but for the NCEP model simulations after the CCA correction. (f) Same as in (e) but without the CCA correction

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated CCA skill expressed in correlation between the observed and predicted *T*_{surf} fields at each climate division in forecasting U.S. JFM *T*_{surf} based on seasonal mean (a) SST (SON), (b) SLP (SON), (c) *T*_{surf} (SON), and (d) *T*_{surf} (OND) as a single predictor for the period 1951–2000. The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less than 0.2 are omitted. The mean anomaly correlation averaged over the period 1950–2000 is also given. (e) Same as in (a) but for the NCEP model simulations after the CCA correction. (f) Same as in (e) but without the CCA correction

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated CCA skill expressed in correlation between the observed and predicted *T*_{surf} fields at each climate division in forecasting U.S. JFM *T*_{surf} based on seasonal mean (a) SST (SON), (b) SLP (SON), (c) *T*_{surf} (SON), and (d) *T*_{surf} (OND) as a single predictor for the period 1951–2000. The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less than 0.2 are omitted. The mean anomaly correlation averaged over the period 1950–2000 is also given. (e) Same as in (a) but for the NCEP model simulations after the CCA correction. (f) Same as in (e) but without the CCA correction

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

(a) The SST loading for the first CCA mode for *T*_{surf} (JFM) based on the predictor SST (SON). The contour interval is 0.2 nondimensional units. Zero contours are omitted. Positive values are shaded. (b) Same as in (a) but for the second CCA mode. (c) Same as in (a) but for the third CCA mode. (d) Same as in (a), but for the *T*_{surf} loading pattern for the first CCA mode expressed in correlations between *T*_{surf} for JAS and the CCA time series. The contour interval is 0.1. Areas where positive (negative) correlations are statistically significant at the 5% level are shaded dark (light). (e) Same as in (d) but for the second CCA mode. (f) Same as in (d) but for the third CCA mode

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

(a) The SST loading for the first CCA mode for *T*_{surf} (JFM) based on the predictor SST (SON). The contour interval is 0.2 nondimensional units. Zero contours are omitted. Positive values are shaded. (b) Same as in (a) but for the second CCA mode. (c) Same as in (a) but for the third CCA mode. (d) Same as in (a), but for the *T*_{surf} loading pattern for the first CCA mode expressed in correlations between *T*_{surf} for JAS and the CCA time series. The contour interval is 0.1. Areas where positive (negative) correlations are statistically significant at the 5% level are shaded dark (light). (e) Same as in (d) but for the second CCA mode. (f) Same as in (d) but for the third CCA mode

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

(a) The SST loading for the first CCA mode for *T*_{surf} (JFM) based on the predictor SST (SON). The contour interval is 0.2 nondimensional units. Zero contours are omitted. Positive values are shaded. (b) Same as in (a) but for the second CCA mode. (c) Same as in (a) but for the third CCA mode. (d) Same as in (a), but for the *T*_{surf} loading pattern for the first CCA mode expressed in correlations between *T*_{surf} for JAS and the CCA time series. The contour interval is 0.1. Areas where positive (negative) correlations are statistically significant at the 5% level are shaded dark (light). (e) Same as in (d) but for the second CCA mode. (f) Same as in (d) but for the third CCA mode

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Same as Figs. 6a–c but for the first CCA mode for *T*_{surf} (JFM) based on the predictor SLP (SON)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Same as Figs. 6a–c but for the first CCA mode for *T*_{surf} (JFM) based on the predictor SLP (SON)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Same as Figs. 6a–c but for the first CCA mode for *T*_{surf} (JFM) based on the predictor SLP (SON)

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated skill expressed in correlation between the observed and predicted fields at each climate division in forecasting *T*_{surf} over the United States for JFM based on (a) EE [SST (SON), SLP (SON)], (b) EE [SST (SON), SLP (SON), *T*_{surf} (SON)], (c) EE [SST (SON), SLP (SON), model simulation] and (d) SE [SST (SON), SLP (SON), *T*_{surf}] for the period 1951–97. The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less 0.2 are omitted

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated skill expressed in correlation between the observed and predicted fields at each climate division in forecasting *T*_{surf} over the United States for JFM based on (a) EE [SST (SON), SLP (SON)], (b) EE [SST (SON), SLP (SON), *T*_{surf} (SON)], (c) EE [SST (SON), SLP (SON), model simulation] and (d) SE [SST (SON), SLP (SON), *T*_{surf}] for the period 1951–97. The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less 0.2 are omitted

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Geographical distribution of the cross-validated skill expressed in correlation between the observed and predicted fields at each climate division in forecasting *T*_{surf} over the United States for JFM based on (a) EE [SST (SON), SLP (SON)], (b) EE [SST (SON), SLP (SON), *T*_{surf} (SON)], (c) EE [SST (SON), SLP (SON), model simulation] and (d) SE [SST (SON), SLP (SON), *T*_{surf}] for the period 1951–97. The contour interval is 0.1. Areas where the correlation is statistically significant at the 5% level are shaded. Values less 0.2 are omitted

Citation: Journal of Climate 16, 11; 10.1175/1520-0442(2003)016<1665:ECCPOS>2.0.CO;2

Heidke skill scores for the operational forecasts, and the superensemble forecasts for *T*_{surf} (JAS) and *T*_{surf} (JFM) for the period 1995–2000

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*Corresponding author address:* Kingtse C. Mo, NCEP/NWS/NOAA, Climate Prediction Center, Rm. 605, WWB, 5200 Auth. Rd., Camp Springs, MD 20746. Kingtse.Mo@noaa.gov