Section 14.4: Climatic Applications of SSA
275
14.4.2 Empirical Long-Range Forecasts Using MSSA
Predictors
The expansion of a signal into T-PCs or ST-PCs provides a decomposition of
the flow in time patterns that are generally band-limited in frequency. The
first ST-EOFs are usually associated with large-scale slow or oscillatory motions, that are presumably more predictable than synoptic eddies (Shukla,
1984). In a certain manner, MSSA not only compresses the space-time information, but also gathers the most predictable components into a few time
series, the first ST-PCs. Hence, using these ST-PCs as empirical predictors
should provide an improved basis for long-range forecasting. In order to illustrate this point, we describe here a hindcast experiment in which we attempt
to forecast the average of the 700 hPa geopotential height (Z700) over the
forthcoming month, and over the Atlantic area. For technical details, the
reader is referred to Vautard et al. (1994).
The dataset, consisting of NMC final analysis up to december 1992, and
ECMWF data during 1993, covers the 42-year period from july 1951 to july
1993. Data are gathered in pentads (5-day averages). Here, MSSA is used
with a shorter window of 3 months, with data where the annual cycle is
removed beforehand, and only the first 6 spatial EOFs are used. Thus, L = 6
channels and m" = 18 lags are used. The results, however, are very stable to
changes in the MSSA parameters. The sampling rate ß is also 5 days.
Assurne that today is time t = 0, and we want to fore cast the forthcoming
monthly mean of Z700 over the Atlantic domain. Since it would be far
too ambitious to fore cast the exact monthly mean values, our goal is to
forecast, at each Atlantic grid point, the terci/e in which this value falls
(high, near-average, or low). Moreover, it would also be too ambitious to
give deterministic forecasts, hence only probabilities of falling within each
tercile are estimated. We proceed in three steps:
1. Analysis: An empirical model is built from a learning period that does
not contain the forecast verification period. From this period onIy, MSSA
is performed and ST-PCs are calculated. A linear regression of the STPCs is performed 6 pentads ahead. The regression coefficients are estimated from the learning period, as weIl as the climatologies.
2. Forecasting: The ST-PCs at time t = 0 are calculated and forecast at
lead time t = 30, using the regression model. The regressors are the
first 100 ST-PCs at time 0, and the fore cast values are the first 15 STPCs. We emphasize that the filtered values given in the ST-PCs are
calculated, each fore cast day, using only past data covering the latest 18
pentad period. However, the MSSA analysis, i.e. the calculation of the
ST-EOFs is performed over the whole learning period.
275
14.4.2 Empirical Long-Range Forecasts Using MSSA
Predictors
The expansion of a signal into T-PCs or ST-PCs provides a decomposition of
the flow in time patterns that are generally band-limited in frequency. The
first ST-EOFs are usually associated with large-scale slow or oscillatory motions, that are presumably more predictable than synoptic eddies (Shukla,
1984). In a certain manner, MSSA not only compresses the space-time information, but also gathers the most predictable components into a few time
series, the first ST-PCs. Hence, using these ST-PCs as empirical predictors
should provide an improved basis for long-range forecasting. In order to illustrate this point, we describe here a hindcast experiment in which we attempt
to forecast the average of the 700 hPa geopotential height (Z700) over the
forthcoming month, and over the Atlantic area. For technical details, the
reader is referred to Vautard et al. (1994).
The dataset, consisting of NMC final analysis up to december 1992, and
ECMWF data during 1993, covers the 42-year period from july 1951 to july
1993. Data are gathered in pentads (5-day averages). Here, MSSA is used
with a shorter window of 3 months, with data where the annual cycle is
removed beforehand, and only the first 6 spatial EOFs are used. Thus, L = 6
channels and m" = 18 lags are used. The results, however, are very stable to
changes in the MSSA parameters. The sampling rate ß is also 5 days.
Assurne that today is time t = 0, and we want to fore cast the forthcoming
monthly mean of Z700 over the Atlantic domain. Since it would be far
too ambitious to fore cast the exact monthly mean values, our goal is to
forecast, at each Atlantic grid point, the terci/e in which this value falls
(high, near-average, or low). Moreover, it would also be too ambitious to
give deterministic forecasts, hence only probabilities of falling within each
tercile are estimated. We proceed in three steps:
1. Analysis: An empirical model is built from a learning period that does
not contain the forecast verification period. From this period onIy, MSSA
is performed and ST-PCs are calculated. A linear regression of the STPCs is performed 6 pentads ahead. The regression coefficients are estimated from the learning period, as weIl as the climatologies.
2. Forecasting: The ST-PCs at time t = 0 are calculated and forecast at
lead time t = 30, using the regression model. The regressors are the
first 100 ST-PCs at time 0, and the fore cast values are the first 15 STPCs. We emphasize that the filtered values given in the ST-PCs are
calculated, each fore cast day, using only past data covering the latest 18
pentad period. However, the MSSA analysis, i.e. the calculation of the
ST-EOFs is performed over the whole learning period.