Multivariate Empirical Orthogonal Function analysis of the upper thermocline structure of the Mediterranean Sea from observations and model simulations

Abstract

Abstract. Multivariate vertical Empirical Orthogonal Functions (EOF) are calculated for the entire Mediterranean Sea both from observations and model simulations, in order to find the optimal number of vertical modes to represent the upper thermocline vertical structure. For the first time, we show that the large-scale Mediterranean thermohaline vertical structure can be represented by a limited number of vertical multivariate EOFs, and that the "optimal set" can be selected on the basis of general principles. In particular, the EOFs are calculated for the combined temperature and salinity statistics, dividing the Mediterranean Sea into 9 regions and grouping the data seasonally. The criterion used to establish whether a reduced set of EOFs is optimal is based on the analysis of the root mean square residual error between the original data and the profiles reconstructed by the reduced set of EOFs. It was found that the number of EOFs needed to capture the variability contained in the original data changes with geographical region and seasons. In particular, winter data require a smaller number of modes (4-8, depending on the region) than the other seasons (8-9 in summer). Moreover, western Mediterranean regions require more modes than the eastern Mediterranean ones, but this result may depend on the data scarcity in the latter regions.The EOFs computed from the in situ data set are compared to those calculated using data obtained from a model simulation. The main results of this exercise are that the two groups of modes are not strictly comparable but their ability to reproduce observations is the same. Thus, they may be thought of as equivalent sets of basis functions, upon which to project the thermohaline variability of the basin.

Mass loss and imbalance of glaciers along the Andes Cordillera to the sub-Antarctic islands

“…Figure In order to obtain a comprehensive spatiotemporal perspective on glacier Ba, we performed an EOF analysis. The EOF analysis is widely used in atmospheric sciences and oceanography (e.g., Preisendorfer 1998;Sparnocchia et al 2003). EOF analyses take the time by spatial location Ba data matrix and ordinates these data using singular value decomposition to return major axes of variation in Ba.…”

Assimilation scheme of the Mediterranean Forecasting System: operational implementation

“…This allows us to get the benefit of XBT assimilation throughout the first 500 m of the water column where most of the XBT are collected. Such a large number of vertical modes, as demonstrated by Sparnocchia et al (2003), also captures the mixed layer information.…”

“…It is interesting to note that the first (dominant) EOFs in the Algerian and Tyrrhenian Sea have a structure below 120 m similar to that of the EOF used in SLA assimilation but this is not the case for the Ionian Sea. In fact, as explained by Sparnocchia et al (2003), the EOFs are very different in the western and eastern Mediterranean basins, accounting for the different water mass variability in the two sub-basins.…”

“…Our particular state vector contains the model predictive variables such as temperature, salinity and barotropic stream function. The existence of dominant EOFs' for the Mediterranean temperature-salinity relationship is discussed and demonstrated in Sparnocchia et al (2003). Here, as in many other operational schemes, we use EOFs deduced from data rather than from an analysis of the forecast error covariance matrix.…”

“…The EOFs were computed from an historical data set of the Mediterranean (Sparnocchia et al, 2003) in 9 different regions, chosen on the basis of the data coverage and known regional dynamical regimes. The EOFs retained only the variance around the seasonal signal and thus they vary every three months (winter consists of January, February and March, spring of April, May and June, summer of July, August, September and autumn of October, November and December).…”