Forecasting front displacements with a satellite based ocean forecasting (SOFT) system
Introduction
Predicting future states of the ocean has a valuable operational interest on human related activities. Examples of these activities include warning announcements (of coastal floods, ice and storm damage, harmful algal blooms and contaminants, etc.), optimizing routes for ships, prediction of seasonal or annual primary productivity and ocean currents, obtaining offshore design criteria, determining ocean climate variability etc. The information required from the ocean environment varies greatly with the operational activity.
Traditionally, systems forecasting certain aspects of the ocean variability are comprised of explanatory models supported with field observations. Explanatory models are based on mathematical descriptions and physical understanding of that part of the ocean variability we are interested to predict. In this way, wave prediction systems usually involve energy balance models for wind–sea. Moreover, predicting ocean circulation requires the whole ocean hydrodynamical–thermodynamical model, incorporating the law of conservation of momentum, mass and energy. Initial conditions and atmospheric forcing needed to integrate forward in time the models are obtained from observations and weather forecasts, respectively. Further observations are assimilated into models as the forecasts advance in time. Assimilation of measurements into models has significant impact on the accuracy of the forecasts (Anderson et al., 1996, Swanson and Ward, 1999). Unfortunately, ocean observations are sparse, difficult and expensive to acquire.
Satellite remote sensing is the only observing technique able to systematically and continuously monitor some aspects of the dynamic variability of spatially extended ocean areas. Spatio–temporal time series of sea surface temperature (SST), sea level anomaly (SLA) and ocean colour are now available from satellites. This data is usually employed to remotely diagnose present ocean states or to study past ocean variability. Besides, empirical predictive models can be built on the basis of satellite data. These empirical models are the so-called satellite based ocean forecasting (SOFT) systems (Alvarez et al., 2003).
The working procedure of a SOFT system, sketched in Fig. 1, is divided in three major tasks (a more detailed explanation can be found in Alvarez et al., 2004): First, the space–time variability of the satellite-observed data is decomposed into its spatial and time components. The Empirical Orthogonal Function (EOF) technique (Preisendorfer, 1988) is employed to accomplish this task. In this way, the space-and time-distributed satellite data is decomposed into modes ranked by their temporal or spatial variance. Among both possibilities, EOF covariance analysis has shown to be slightly superior to EOF gradient decomposition in terms of predictability (Alvarez, 2003).
Spatial patterns and corresponding amplitude functions obtained from EOF decomposition show some degree of noisy nature. Thus, the second task of the SOFT system is to reduce the degree of noise in the reconstructed spatial pattern, neglecting those EOFs of small variance. Besides, Singular Spectral Analysis (SSA) or data adaptive approach (Broomhead and Lowe, 1987, Elsner and Tsonis, 1996) is employed to remove noise in the time dependent amplitude functions of the considered spatial patterns. In real-time forecasting situations, SSA filtering must be prevented due to the appearance of spurious filtering border effects that reduce prediction capabilities (Alvarez et al., 2004).
The third task involved in a SOFT system is to obtain a predictive model for each filtered amplitude function. Various prediction techniques can be employed to accomplish this task (Casdagli et al., 1992). Due to its robustness and performance, genetic programming (Szpiro, 1997, Alvarez et al., 2001) has been frequently employed in previously developed SOFT systems. Finally, prediction of a satellite-observed field is achieved by adding the most relevant modes previously multiplied by their corresponding forecast amplitudes.
SOFT systems have been successfully implemented at different time scales and ocean regions. Specifically, accurate forecasts of monthly averaged SST patterns were obtained in the Alboran, Ligurian and Adriatic seas by SOFT systems (Alvarez et al., 2000, Alvarez, 2003, Alvarez et al., 2003). A SOFT system predicting the SST field at weekly time scales in real-time has been recently implemented in the Ligurian Sea (Alvarez et al., 2004).
Previous SOFT systems were focussed to predict quasi-static and spatially constrained features at sub-basin scale. In these cases, the purpose of EOF analysis was to identify patterns that characterize variations in the current state of the scalar field without taking into account the time evolution of the analyzed field. Thus, EOF decomposition is not the most adequate for encoding satellite data when propagating features are present. Instead its extrapolation to the complex plane, the so called Complex Empirical Orthogonal Functions (CEOFs) (Horel, 1984), account for such time evolution quantifying the time series in terms of complex numbers by adding to its Hilbert transform. This procedure gives information about the rate of change of the field as an artificial imaginary part. The result is that the information contained in the Hilbert scalar field is greater than that in the original field. Specifically, information about the spatial distribution of variability, the phase fluctuation among various spatial locations and the amplitude and phase of the temporal variability of each mode are obtained from the CEOF analysis. Propagating phenomena are represented by CEOF modes with regions of roughly constant spatial amplitudes and spatial and temporal phases varying with distance and time, respectively. The variation of the spatial and temporal phase with position and time provides a measure of the “local” wavenumber and “instantaneous” frequency, respectively. Phase speed can be inferred from the ratio of these magnitudes. Conversely, standing oscillations are found in areas with maximum spatial amplitudes and roughly constant spatial and temporal phases. CEOF analysis is useful when the signal shows a stationary or weakly stationary behavior. Otherwise, this technique can introduce extra modes to explain nonstationarity.
In this study the performance of two SOFT systems forecasting the motions of a thermal front in real-time and at weekly time scales, is investigated. The SOFT systems were based on EOF and CEOF decompositions respectively, to determine the impact of the encoding methodology when forecasting a moving structure. The area of study is the Northern Balearic Sea, (Western Mediterranean Sea) (Fig. 2), where a propagating thermal front is present during late summer and fall. The article is organized as follows: Section 2 briefly sketches the oceanography of the Northern Balearic Sea. A description of the satellite data used in this study is provided in Section 3. Details on the implementation of the SOFT systems are described in Section 4. Section 5 shows the results obtained from the application of the SOFT systems. Finally, discussion and conclusions are presented in Section 6.
Section snippets
Oceanographic conditions in the Northern Balearic Sea
The Northern Balearic Sea is geographically located in the north-western Mediterranean, near the upper boundary of the Balearic subbasin (Fig. 2). This region is dominated by the presence of a slope current, the Northern-Current, cyclonically flowing along the continental slope towards the Channel of Ibiza (Millot, 1987). The flow presents marked seasonal variability being narrower in winter and wider and with reduced mesoscale variability on summer (Millot, 1999). In the south of the Balearic
Data
Unlike other oceanographic variables, SST has been systematically recorded from satellite since the last two decades. Thus, relatively long spatio–temporal time series of SST data are now available. This makes SST the most adequate magnitude to investigate empirical predictive models built on the basis of satellite data. A time series of 459 weekly averaged SST images of the Northern Balearic Sea, from March 1st 1993 to December 10th 2001, has been obtained from the German Aerospace Research
Implementation of the soft system
The period of time ranging from March 1st 1993 to January 10th 2000 was employed to build two SOFT systems: a SOFT system employing the EOF-based encoding and a second one based on CEOF data decomposition. Thus, EOFs, CEOFs and corresponding amplitude functions were first computed for this period. Determination of predictive laws for the amplitude functions of the most relevant EOFs and CEOFs was then attempted. The genetic program called DARWIN (Alvarez et al., 2001) was directly applied to
EOF based SOFT system
The first four EOFs from the decomposition of the SST time variability were selected for physical interpretation based on their percentage of the total temporal variance. Fig. 3 displays the mean SST field averaged from March 1st 1993 to January 10th 2000 and subtracted from the images during the EOF computation. The mean SST field reveals a southward temperature gradient generated by the thermal differences between the Northern Balearic Sea and Southern Gulf of Lion. The spatial patterns
Discussion and conclusion
This work has explored the forecasting skill of an EOF and CEOF based SOFT systems, predicting in real time the SST signature of a moving structure at weekly time scales. The selected moving structure was a strong frontal system located at the Northern Balearic Sea. The front results from the differential heating occurring in late summer and fall between the Balearic and Ligurian Seas. After its formation, the front propagates southwards following the advection of cold waters into the Balearic
Acknowledgements
This work has been supported by the SOFT-EVK3-CT-2000-0028 European Project and the Spanish Project REN 2001-3982-E.
References (19)
- et al.
Darwin-an evolutionary program for nonlinear modelling of chaotic time series
Comput. Phys. Commun.
(2001) Circulation in the Western Mediterranean Sea
J. Mar. Syst.
(1999)Performance of satellite based ocean forecasting (SOFT) systems: a study in the Adriatic Sea
J. Atmos. Ocean. Technol.
(2003)- et al.
Forecasting the SST space–time variability of the Alboran Sea with genetic algorithms
Geophys. Res. Lett.
(2000) - et al.
Satellite based forecasting of sea surface temperature in the Tuscan Archipelago
Int. J. Remote Sens.
(2003) - et al.
Real-time forecasting at weekly time scales of the SST and SLA of the Ligurian Sea with a satellite based ocean forecasting (SOFT) system
J. Geophys. Res.
(2004) - et al.
Data assimilation in ocean models
Rep. Prog. Phys.
(1996) - et al.
Long-lead seasonal forecasts, where do we stand?
Bull. Am. Meteorol. Soc.
(1999) - et al.
Extracting qualitative dynamics from experimental data
Physica, D
(1987)