Modelling Thermohaline Properties in an Estuarine Upwelling Ecosystem (Rı́a de Vigo: NW Spain) Using Box-Jenkins Transfer Function Models

Abstract

Since 1987, twice weekly, hydrological variables have been monitored at a fixed station in the Rı́a de Vigo (NW Spain), aiming to examine the time scales of variability and the relationships to meteorological conditions. The present paper analyses: (1) the advantage of Box-Jenkins transfer function (TF) models (single output–multiple input), a type of linear stochastic model, to describe the dynamic behaviour of the system; and (2) the coupling between the Rı́a and meteorological events at the time scale of autonomy of this coastal inlet affected by the Iberian coastal upwelling, approximately a fortnightly period. In order to achieve these objectives, thermohaline properties have been used to characterize the estuarine ecosystem (output variables), while wind regime, runoff in the drainage basin and incoming solar radiation have been considered as the main forcing variables (input variables). The use of the amplitude time series, derived from principal component analysis (PCA) applied to the deseasonalized meteorological variables, is also explored as a different set of input variables.When compared with standard regression models, all TF models built to describe thermohaline behaviour had reduced residual variance. Similar TF models, as well as percentage of explained variance, were also obtained when meteorological variables or the amplitude time series were used as input variables. The fitted TF models provided an insight into the ‘inertial’ behaviour of the system and the time scales of coupling of the system with the forcing variables. The plausible physical mechanisms which link the response of the system with the observed meteorological variability are also discussed. As could be expected, bottom thermohaline properties show a stronger inertial behaviour than the surface ones, which is particularly marked for bottom temperature. Besides, the shelf domain, by means of upwelling-downwelling events, strongly influences surface and bottom temperature, as well as bottom salinity; by contrast, surface salinity is mainly influenced by the effect of wind along the main axis of the Rı́a and runoff. In relation to the time scales of coupling between the system and the forcing variables, thermohaline properties show a dependance with the meteorological conditions in, at least, the immediately preceding fortnight period. It was concluded that: (1) TF models that incorporate meteorological information described the dynamic behaviour of the system adequately; and (2) this type of model can be useful as a first approximation to develop more sophisticated (deterministic) models, since, with the purpose of modelling any state variable of the system, both the coupling between different domains and the time scales of the interactions must be taken into account.