Constructed Analogue Prediction of the East Central Tropical Pacific SST and the Entire World Ocean for 2001
contributed by Huug van den Dool
Climate Prediction Center, NOAA, Camp Springs, Maryland
Because natural analogues are highly unlikely to occur in high degree-of-freedom processes, we may benefit from constructing an analogue having greater similarity than the best natural analogue. As described in Van den Dool (1994), the construction is a linear combination of past observed anomaly patterns in the predictor fields such that the combination is as close as desired to the initial state (or 'base'). We use as our predictor (the analogue selection criterion) the first 5 EOFs of the global SST field at four consecutive 3-month periods prior to forecast time. Data extending from 1955 to the present are used for a priori skill evaluation.
For a given base time (previous ones extending back to 1956, or the current real time forecast ending with SON2000), a linear combination is made of the global SST (truncated to 5 EOFs) observed in all years (1956-1998) excluding the base year, so as to match the SST pattern of the base time. This is done using multiple regression, with each year's SST state as a predictor to which a weight is assigned, determined by inverting the 43 X 43 (available years) covariance matrix. Here, we wish to forecast the future SST anomaly in the Niño 3.4 region (5N-5S, 120-170W) of the tropical Pacific. The CA weights are thus applied to the subsequently occurring Niño 3.4 SST in the predictand period for these years past, forming the forecast for the base year's predictand period. Note that the predictand is not involved in the construction process. The constructed analogue is the same linear combination for all leads, i.e the weights are persisted, and can be applied to predictands other than Nino3.4.
Additional detail about the constructed analogue method (Van den Dool 1994) shows that constructed analogues usually outperform natural analogues (such as they are) in specification mode (i.e. "forecasting" one meteorological variable from another, contemporaneously). This advantage may also be expected to occur in real forecasting, as long as the (linear) construction does not compromise the physics of the system too much. A constructed analogue yields a single linear operator derived from data by which the system can be propagated forward in time. This is methodologically related to POP and linear inverse modelling. The skill of the constructed analogue method in forecasting SST is discussed in Van den Dool and Barnston (1995).
The current constructed analogue forecasts for Niño 3.4 out to 1.5 years lead are shown on the left in Fig. 1, using data through SON2000. The expected cross-validated skill is also shown (dashed;right-hand scale). The SST anomaly observed during SON1999 is plotted as the earliest "forecast" value. For the early leads the observed SST for SON enters into the plotted forecast for OND and NDJ00/01 with a 2/3 and 1/3 weight, respectively, providing continuity with the known initial condition. Fig.1 right-hand-side shows forecasts from the last 5 initial conditions - the red dots are recent obs.
A closer look at the skill of the constructed analogue method was provided by Fig. 2 in the June 1996 issue of this Bulletin (p. 73). Forecasts for late fall through winter tend to be most skillful, while summer forecasts have lower skill. While skill (dashed line in Fig. 1) generally decreases with lead time, the dependence on the target season is sometimes a stronger factor, causing what seems a 'return of skill' with increasing lead.
Skill averaged over 1956-present has gone up considerably with the addition of the 97/98/99 events added to the verification sample. The skill of CA is competitive with those of other empirical as well as dynamical methods (Barnston et al. 1994). An evaluation over 1996-98 (Barnston et al 1999) shows CA, CCA and CLIPER to be the clear frontrunners among the empirical methods and continuing to be competitive with dynamical methods, such as the NCEP and COLA models. Recent verification can be seen in a new Fig 2.
The strong cold La Nina of the last two winters had decreased in magnitude in terms of degree C over the NH summer, but has slightly strengthened again. Winter 2000/2001 looks like a neutral to weak cold event. CA forecasts Nino3.4 anomalies to further decrease but stay slightly negative thru winter 2000/2001. Zero crossing to the warm side happens sometime in March or April 2001. CA calls for some warming in the East Pacific, see maps on ftp://ftp.ncep.noaa.gov/pub/cpc/wd51hd/index.html. However, as seen in Fig.2, the degree of warming varies with initial condition, so it is too early to declare winter 2001/2002 a warm event. But we do not foresee a 4th cold event winter in a row.
With ENSO in a weakened state the weights have generally lowered from before. Years with large +ve weights (>0.15) are 1989. Only one year (1966) has a high -ve weight. While the ENSO situation definitely enters into the analogue selection, non-ENSO (remember, global SST EOFs are used - the CA knows nothing specifically about NINO3.4) processes other than ENSO also determine the weights and the resulting forecast. Weights in Table 1 have a clear upward trend, suggesting interdecadal variability or climate change.
All anomalies refer to 1961-90 base period.
( All forecasts (Global!) from March 2000 onwards can also be accessed monthly at ftp://ftp.ncep.noaa.gov/pub/cpc/wd51hd/index.html then click on SST CA and the initial condition of your choice, currently Nov2000.)
References:
Barnston, A.G., H.M. van den Dool, S.E. Zebiak, T.P. Barnett, M. Ji, D.R. Rodenhuis, M.A. Cane, A. Leetmaa, N.E. Graham, C.F. Ropelewski, V.E. Kousky, E.A. O'Lenic and R.E. Livezey, 1994: Long-lead seasonal forecasts--Where do we stand? Bull. Amer. Meteor. Soc., 75, 2097-2114.
Barnston, A. G., M. H. Glantz and Yuxiang He, 1999: Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997/98 El Nino episode and the 1998 La Nina onset. Bull. Amer. Meteor. Soc., 80, 217-243.
van den Dool, H.M., 1994: Searching for analogues, how long must we wait? Tellus, 46A, 314-324.
van den Dool, H.M. and A.G. Barnston, 1995: Forecasts of global sea surface temperature out to a year using the constructed analogue method. Proceed-ings of the 19th Annual Climate Diagnostics Workshop, Nov. 14-18, 1994, College Park, Maryland, 416-419.
Table 1. Inner products (IP; scaled such that sum of absolute values is 100) and weights (Wt multiplied by 100.) of each of the years to construct
an analogue to the sequence of 4 consecutive 3-month periods defined as the base (currently the string DJF99/00, MAM00, JJA2000 and
SON2000). Years are labeled by the middle month of the last of the four consecutive predictor seasons. 1999 is not yet used as a candidate
analogue because long lead forecasts would not be possible beyond the latest observations. Data thru Nov 2000.
| Year | IP | Wt | Year | IP | Wt | Year | IP | Wt | Year | IP | Wt |
| 56 | 0 | 7 | 67 | -3 | -3 | 78 | -6 | -10 | 89 | 6 | 20 |
| 57 | -1 | -3 | 68 | -3 | -9 | 79 | -3 | -4 | 90 | 4 | 12 |
| 58 | -3 | -11 | 69 | -3 | -9 | 80 | -2 | -8 | 91 | 2 | 11 |
| 59 | -3 | -10 | 70 | -2 | -4 | 81 | -1 | -1 | 92 | 0 | -5 |
| 60 | -1 | 2 | 71 | 0 | 5 | 82 | -1 | -3 | 93 | 0 | 2 |
| 61 | 4 | 7 | 72 | -1 | -2 | 83 | 0 | 1 | 94 | 3 | 7 |
| 62 | -1 | 3 | 73 | 1 | 0 | 84 | 4 | 11 | 95 | 3 | 4 |
| 63 | -2 | -3 | 74 | 2 | 9 | 85 | 5 | 10 | 96 | 4 | 9 |
| 64 | -2 | -11 | 75 | 1 | 3 | 86 | 3 | 8 | 97 | 1 | 11 |
| 65 | -3 | -11 | 76 | 0 | 4 | 87 | 0 | -4 | 98 | 1 | 15 |
| 66 | -7 | -16 | 77 | -5 | -4 | 88 | 2 | 6 |
Fig. 1 - left. Time series of constructed analogue forecasts (solid blue line) for Niño 3.4 SST based on the sequence of four consecutive 3-month periods ending in Nov 2000. The red dashed line indicates the expected skill (correlation) based on historical performance for 1956-mid1999. The x-axis represents the target period. The left y-axis (blue solid line) shows the SST forecast; the right y-axis (thin dashed red line) shows the skill. The observation is shown instead of the constructed analogue specification for the initial state SON 2000, and this observation also contributes by decreasing amounts to the OND and NDJ plotted values (see text).
Fig.1 - right. Nino3.4 forecasts made by constructed analogue method from initial conditions over the last 5 months. The solid blue is the same as shown on the left. The red line and red dots are the obs for the last 6 months.
Fig.2 Recent verification. Shown as bars are 6 month lead forecasts (blue) and verifying observations (red) from 1998 onward. A 6 month lead means that the DJF forecast is made with data thru previous May. Skill has been satisfactory over the 2 year+ cold event.
