A Subtidal Model of Temperature for a Well-Mixed Narrow Estuary: the Guadalquivir River Estuary (SW Spain) Enrique M. Padilla 1,2 & Manuel Díez-Minguito 1 & Miguel Ortega-Sánchez 1 & Miguel A. Losada 1 Received: 16 May 2014 /Revised: 2 August 2015 /Accepted: 6 August 2015 # Coastal and Estuarine Research Federation 2015 Abstract This paper analyzes thermal energy transport in the narrow and tidally energetic Guadalquivir River Estuary (SW Spain). Measurements from a comprehensive monitoring campaign (2008–2011) reveal the forcing factors of the temper- ature field and its spatio-temporal variability. The along- channel thermal energy gradient reaches magnitudes of ∼375 J/m 4 near the mouth during the summer and winter. The water temperature is primarily controlled by shortwave radia- tion, latent heat transfer through the free surface, and tidal ad- vection, whereas it depends less on freshwater discharge and longitudinal dispersion. The tidally averaged effective longitu- dinal thermal dispersion coefficient was evaluated at several stretches for each tidal cycle. The mean values of the coefficient tend to increase landward and are on the order of ∼10 3 , larger than (but of the same order of magnitude as) the salinity coef- ficient values. Based on these analyses, a deterministic opera- tional model for thermal energy transport was developed. The model solves the tidally and cross-sectionally averaged advec- tion–dispersion equation for the thermal energy balance and obtains accurate fits of the subtidal temperature field at any location within the estuary. The modeled water temperatures agreed well with the observations at all the stations (coefficients of determination, R 2 greater than 0.98), even after the seasonal oscillation in radiation was removed (R 2 >0.77). Keywords Guadalquivir estuary . Water temperature . Heat exchange . Effective dispersion coefficient . Deterministic operational model Introduction Heat transfer processes are important in estuarine ecosystems. These processes are drivers of biological interactions, which in turn determine zooplankton and phytoplankton concentra- tions, uptake, and degassing of oxygen and carbon dioxide (Cai 2011) and the life cycles of many species of ecological and commercial interest (Hickey et al. 2010). Furthermore, thermal energy exchanges between estuaries and the atmo- sphere and between estuaries and the outer shelf play a major role in hydrodynamics, the potential energy of the water col- umn, and the transport of substances (O’Donnell 1993). Most studies of thermal energy dynamics have focused on continental shelves and estuary inlets due to their influ- ence on coastal processes, plume dynamics, and regional circulation (Chawla et al. 2008; Valle-Levinson et al. 2007; Prandle and Lane 1995;O’Donnell 1993). The few studies that have focused on the analysis, modeling, and prediction of temperature variations in inner estuaries have been inspired by their influence on biota (Wagner et al. 2011; Monismith et al. 2009; Uncles and Stephens 2001). Within this context, studies in the Guadalquivir estuary, which is located on the Iberian margin of the Gulf of Cádiz (Fig. 1), have focused on the circulation of the shelf and its influence on the pelagic ecosystem (García-Lafuente and Ruiz 2007; García-Lafuente et al. 2006; Ruiz et al. 2006). Ruiz et al. ( 2006) and Prieto et al. (2009) analyzed the variability in biological activity and its response to meteorological and oceanographic forcings. These studies were performed using surface Communicated by Robert D. Hetland * Enrique M. Padilla e.padilla14@imperial.ac.uk 1 Andalusian Institute for Earth System Research, University of Granada, 18071 Granada, Spain 2 Department of Civil and Environmental Engineering, Imperial College of Science, Technology and Medicine, London SW7 2AZ, UK Estuaries and Coasts DOI 10.1007/s12237-015-0024-6