| Submarine groundwater discharge(SGD) is an important component of global water cycle, and recently become a hot issue in the study of land-ocean interaction. Radium isotopes methods have become the most extensive and sophisticated ways in the processes of estimating SGD, water residence time and mixing rate and other aspects of the application. Previous analytical studies of offshore radium isotopes distribution are based on the steady-state model, and generally ignore the influences of water depth and velocity of ocean currents. Researchers often use steady-state advection-diffusion equation to calculate eddy diffusion coefficient, then obtain SGD. However, there is an obvious temporal variation in the actual concentration of radium isotopes in coastal mixing zone caused by flood-ebb fluctuations, spring-neap tidal cycles and seasonal changes. Furthermore, because of the slope of continental shelf and ocean currents, the impact of variable water depths and velocity of currents on radium isotopes concentration distribution cannot be ignored. Thus, previous steady-state model has its shortcomings. This study attempts to build a new advection diffusion model considering water depth change, velocity of currents and periodic temporal variation in the radium concentration. The impacts of these three factors on the determining model parameters are discussed. Observation data by other researchers published in the literature in different seasons are used to estimate eddy diffusion coefficient with the new model, and then a comparison with the results obtained by steady-state model is carried out. It is found that the new model has significant improvements in estimating eddy diffusion coefficient and SGD.Advection-diffusion equation which reflects variations of the spatial and temporal distributions of radium isotopes has four items, namely eddy diffusion item, advection item, decay item and time-varying item. The first two items show the diffusion caused by eddy and currents, decay item shows the impact due to the radioactive decay, and time-varying item represents the impact caused by the changes or periodic variations of radium concentrations over time. According to the data obtained by Moore, the radium radioactive concentrations are often highest in summer and lowest in winter, this is due to seasonal changes of SGD. Moore’s observations from 1998 to 2000 indicated that 223 Ra concentration in Winyah Bay sea area fluctuated around 3dpm/100 L, its annual variation range was about 2~3dpm/100 L, while 224 Ra and 226 Ra fluctuated around 25dpm/100 L and seasonal variation reached 15dpm/100 L, and 228 Ra fluctuated around 35dpm/100 L, its variation range was as wide as 25dpm/100 L. Calculations with these values indicated the followings. For the long half-life isotopes, namely 226 Ra and 228 Ra, their decay item is very small, so the value of time-varying item will be larger than the decay item by 2 to 4 orders of magnitude. So there will be a large error if time-varying item is ignored. For 223 Ra, the error could reach at most 30% when we calculate the parameters by ignoring time-varying item, and for 224 Ra, this error is at most 8%. So for short half-life radium isotopes, the impact of time-varying item cannot be ignored either. We use the new model considering time-varying item to estimate the eddy diffusion coefficient of Winyah Bay sea area with all four isotopes and obtain a result of 98.5km2/d. The value obtained by the steady-state model was 87.7km2/d. The value of eddy diffusivity obtained by the new model is 1.12 times as large as the value calculated by the steady-state model, implying a significant difference between the new model and the steady-state model, and highlighting the necessity of considering seasonal variation of the activities of radium isotopes in seawater. |
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