The observed suspended sediment concentrations (SSCs) obtained from the water sampling are usually sparsely distributed in both space and time, which are traditionally applied just to calibrate other types of observations. In this study a dynamically constrained interpolation methodology (DCIM) is developed to interpolate these sparsely observed SSCs in the Bohai Sea. In this method the suspended sediment transport model is taken as dynamical constraints to interpolate the observations. Meanwhile, the interpolated results are optimized iteratively by adjusting the key model parameters using the adjoint method. The DCIM is first verified using the synthetic observations produced by twin model runs. The modeling results reveal that this method is effective at interpolating the sparsely observed artificial SSCs, even when the observations are heavily contaminated by data noise. Then, the sparsely observed practical SSCs obtained from a large area survey in the Bohai Sea are interpolated using the DCIM. The interpolated results are verified by randomly selected independent observations. The discrepancies between the interpolated SSCs and the observations are significantly decreased. When all the observations are interpolated, the final interpolated SSCs captured a majority (96.88%) of observations with a factor of 2 and the correlation coefficient between the observed and interpolated SSCs is 0.98. Besides, the interpolated results have presented the reasonable dynamical variations of SSCs in the space and time domains. The modeling results indicate that the DCIM is an effective tool for interpolating the sparsely observed SSCs in both space and time.

Snow depth is an important geophysical variable for investigating sea ice and climate change, which can be obtained from satellite data. However, there is a large number of missing data in satellite observations of snow depth. In this study, a methodology, the periodic functions fitting with varying parameter (PFF-VP), is presented to fit the time series of snow depth on Arctic sea ice obtained from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). The time-varying parameters are obtained by the independent point (IP) scheme and cubic spline interpolation. The PPF-VP is validated by experiments in which part of the observations are artificially removed and used to compare with the fitting results. Results indicate that the PPF-VP performs better than three traditional fitting methods, with its fitting results closer to observations and with smaller errors. In the practical experiments, the optimal number of IPs can be determined by only considering the fraction of missing data, particularly the length of the longest gaps in the snow-depth time series. All the experimental results indicate that the PPF-VP is a feasible and effective method to fit the time series of snow depth and can provide continuous data of snow depth for further study.

The seasonal variability of the M2 tide exerts a major influence on the coastal ocean environment. In this study, a novel method, namely modified enhanced harmonic analysis (MEHA), is developed to synchronously extract the temporally varying amplitudes and phase lags of significant tides and the constant values of the other constituents. The seasonal variability of the M2 tide in the Bohai Bay, China, is investigated by analyzing one-year sea level observations at two stations with MEHA.In ideal twin experiments, the artificial sea level observations were analyzed. Both the estimated temporally varying amplitude and phase lag of the M2 tide and constant values of the S2, K1 and O1 tides using MEHA were much closer to the prescribed values than those obtained using the other methods, indicating the capability and efficacy of MEHA. When the real sea level observations were analyzed using MEHA, the estimated M2 tidal amplitude has significant seasonal variability, with large values in summer and small values in winter, which is robust and not affected by experimental settings. The results of numerical experiments indicate that the seasonality of vertical eddy viscosity induces seasonal variations of the M2 tide in the Bohai Bay.