Section 8.3: Multivariate Analysis
153
dimensionality. However, the main difficulty encountered in the interpretation of GCM sensitivity studies, namely the arbitrariness of the choice of the
guess vectors, disappears, since the obvious choice of the reduced base becomes that which allows the best representation of the main features of both
the modeled and the observed fields. On the other hand, the observational
errors need to be taken into account, which can be tedious.
a) Testing Atmospheric GeMs
Of interest is an early study of H. von Storch and Roeckner (1983), who
compared four individual January simulations with the Hamburg University
GCM to observations from 15 J anuaries. The data compression was done by
means ofEmpirical Orthogonal Functions (EOFs), and the covariance matrix
estimated from the observed data. The multivariate tests were based on the
X 2 distribution, although the Hotelling's T2 would have been more accurate,
and univariate tests were used subsequently to try detecting which structures
might have caused the significant model-observations disagreement that was
found.
b) Testing Ocean Models
Frankignoul et al. (1989) have developed a multivariate model testing
procedure which compares the main space and time structures of the modelobservation differences to those of the data uncertainties. The procedure is
illustrated here by an investigation of the ability of the LODYC 5 nonlinear
2-layer model at simulating the 1982-1984 variations of the tropical Atlantic
thermocline depth around its 3-year mean (Frankignoul et al., 1994).
The tropical oceans are primarily wind-driven, and the thermocline variations could be simulated deterministically for the most part if the wind
stress were accurately known. However, wind observations are inaccurate
with frequent gaps, and the bulk formulae used to estimate the wind stress
are uncertain. To represent these uncertainties, three independent, equally
plausible monthly wind stress fields were constructed by Monte Carlo method
and used to force the ocean model (Braconnot and Frankignoul, 1993). AIthough their dispersion only represents part of the forcing uncertainties, the
corresponding thermocline depth uncertainty has a standard deviation of several meters, nearly as large as its observed interannual variability. The mean
model response xli(z, t) at location z and time t was calculated in the spacetime intercomparison domain, as weIl as its sampIe error covariance matrix
E M. The observed thermocline depth d( z, t), as determined by the depth of
the 20°C isotherm, was derived from temperature measurements by Reverdin
et al. (1991). The data coverage was very sparse (Figure 8.5), so that the
field was mapped monthly using a function fitting algorithm and a cut-off
period of 3 months. The covariance matrix ED of the analysed field was cal5Laboratoire d'Oceanographie Dynamique et de Clirnatologie.
153
dimensionality. However, the main difficulty encountered in the interpretation of GCM sensitivity studies, namely the arbitrariness of the choice of the
guess vectors, disappears, since the obvious choice of the reduced base becomes that which allows the best representation of the main features of both
the modeled and the observed fields. On the other hand, the observational
errors need to be taken into account, which can be tedious.
a) Testing Atmospheric GeMs
Of interest is an early study of H. von Storch and Roeckner (1983), who
compared four individual January simulations with the Hamburg University
GCM to observations from 15 J anuaries. The data compression was done by
means ofEmpirical Orthogonal Functions (EOFs), and the covariance matrix
estimated from the observed data. The multivariate tests were based on the
X 2 distribution, although the Hotelling's T2 would have been more accurate,
and univariate tests were used subsequently to try detecting which structures
might have caused the significant model-observations disagreement that was
found.
b) Testing Ocean Models
Frankignoul et al. (1989) have developed a multivariate model testing
procedure which compares the main space and time structures of the modelobservation differences to those of the data uncertainties. The procedure is
illustrated here by an investigation of the ability of the LODYC 5 nonlinear
2-layer model at simulating the 1982-1984 variations of the tropical Atlantic
thermocline depth around its 3-year mean (Frankignoul et al., 1994).
The tropical oceans are primarily wind-driven, and the thermocline variations could be simulated deterministically for the most part if the wind
stress were accurately known. However, wind observations are inaccurate
with frequent gaps, and the bulk formulae used to estimate the wind stress
are uncertain. To represent these uncertainties, three independent, equally
plausible monthly wind stress fields were constructed by Monte Carlo method
and used to force the ocean model (Braconnot and Frankignoul, 1993). AIthough their dispersion only represents part of the forcing uncertainties, the
corresponding thermocline depth uncertainty has a standard deviation of several meters, nearly as large as its observed interannual variability. The mean
model response xli(z, t) at location z and time t was calculated in the spacetime intercomparison domain, as weIl as its sampIe error covariance matrix
E M. The observed thermocline depth d( z, t), as determined by the depth of
the 20°C isotherm, was derived from temperature measurements by Reverdin
et al. (1991). The data coverage was very sparse (Figure 8.5), so that the
field was mapped monthly using a function fitting algorithm and a cut-off
period of 3 months. The covariance matrix ED of the analysed field was cal5Laboratoire d'Oceanographie Dynamique et de Clirnatologie.