Study on linear and nonlinear bottom friction parameterizations for regional tidal models using data assimilation

Data assimilation technique (adjoint method) is applied to study the similarities and the differences between the Ekman (linear) and the Quadratic (nonlinear) bottom friction parameterizations for a two-dimensional tidal model. Two methods are used to treat the bottom friction coefficient (BFC). The first method assumes that the BFC is a constant in the entire computation domain, while the second applies the spatially varying BFCs. The adjoint expressions for the linear and the nonlinear parameterizations and the optimization formulae for the two BFC methods are derived based on the typical Largrangian multiplier method. By assimilating the model-generated ‘observations’, identical twin experiments are performed to test and validate the inversion ability of the presented methodology. Four experiments, which employ the linear parameterization, the nonlinear parameterizations, the constant BFC and the spatially varying BFC, are carried out to simulate the M₂ tide in the Bohai Sea and the Yellow Sea by assimilating the TOPEX/Poseidon altimetry and tidal gauge data. After the assimilation, the misfit between model-produced and observed data is significantly decreased in the four experiments. The simulation results indicate that the nonlinear Quadratic parameterization is more accurate than the linear Ekman parameterization if the traditional constant BFC is used. However, when the spatially varying BFCs are used, the differences between the Ekman and the Quadratic approaches diminished, the reason of which is analyzed from the viewpoint of dissipation rate caused by bottom friction. Generally speaking, linear bottom friction parameterizations are often used in global tidal models. This study indicates that they are also applicable in regional ocean tidal models with the combination of spatially varying parameters and the adjoint method.     

Data assimilation with the EnKF in a 1-D numerical model of a North Sea station

A series of numerical experiments for data assimilation with the Ensemble Kalman Filter (EnKF) in a shallow water model are reported. Temperature profiles measured at a North Sea location, 55°30ˊ North and 0°55ˊ East (referred to as the CS station of the NERC North Sea project), are assimilated in 1-D simulations. Comparison of simulations without assimilation to model results obtained when assimilating data with the EnKF allows us to assess the filter performance in reproducing features of the observations not accounted for by the model. The quality of the model error sampling is tested as well as the validity of the Gaussian hypothesis underlying the analysis scheme of the EnKF. The influence of the model error parameters and the frequency of the data assimilation are investigated and discussed. From these experiments, a set of optimal parameters for the model error sampling are deduced and used to test the behavior of the EnKF when propagating surface information into the water column.     

Simulation of the 1953 storm surge in the North Sea

The 1953 North Sea floods, the Big Flood, was one of the worst natural disasters in Europe in modern times and is probably one of the most studied severe coastal floods. Several factors led to the devastating storm surge along the southern North Sea coast in combination of strong and sustained northerly winds, invert barometric effect, high spring tide, and an accumulation of the large surge in the Strait of Dover. However, the storm waves and their roles during the 1953 North Sea storm surge are not well investigated. Therefore, the effect of wave setup due to breaking waves in the storm surge processes is investigated through numerical experiments. A coupled process-based tide-wave-surge model was used to investigate and simulate the storm surge in the North Sea during January 31–February 1, 1953 and validated by comparing with historical water level records at tide gauges and wave observations at light vessels in the North Sea. Meteorological forcing inputs for the period, January 27–February 3, 1953 are reproduced from ERA-20C reanalysis data with a constant correction factor for winds. From the simulation results, it is found that, in addition to the high water due to wind setup, wave setup due to breaking waves nearshore play a role of approximately 10% of the storm surge peaks with approximately 0.2 m. The resulting modeling system can be used extensively for the preparedness of the storm surge and wave of extreme condition, and usual barotropic forecast.     

Numeric modelling and risk assessment of pollutions in the Chinese Bohai Sea

To simulate the dynamic process of total nitrogen (TN) in seas, numerical modelling combined with the adjoint method is implemented in this study. Because nonpoint source terms (ST) and initial values (IV) of TN are essential but difficult to determine, the adjoint method was applied to a numerical model, and the ST and IV terms of TN were inverted via routine monitoring data in the Bohai Sea. In twin experiments, the adjoint method was capable of inverting the prescribed spatio-temporally distributed ST and the spatial distributed IV. In practical experiments, the results demonstrated that the simulation precision with ST inversion was higher than that with IV inversion and was accurate with joint initial values and source term (IST) inversion. This result indicates that nonpoint source TN is essential for the simulation of TN concentration. Furthermore, the simulated results indicate that the pollution in three bays of the Bohai Sea is rather severe. The model in this study is not specific to the Bohai Sea and can be generalized to other areas, such as the Beibu Gulf. These findings may assist in the development of cost-effective controls for accidental or planned industrial pollutant releases into coastal waters.     

Analysis on observing optimization for the wind-driven circulation by an adjoint approach

The adjoint approach is a variational method which is often applied to data assimilation widely in meteorology and oceanography. It is used for analyses on observing optimization for the wind-driven Sverdrup circulation. The adjoint system developed by Thacker and Long (1992), which is based on the GFDL Byran-Cox model, includes three components, i. e. the forward model, the adjoint model and the optimal algorithm. The GFDL Byran-Cox model was integrated for a long time driven by a batch of ideal wind stresses whose meridional component is set to null and zonal component is a sine function of latitudes in a rectangle box with six vertical levels and 2 by 2 degree horizontal resolution. The results are regarded as a "real" representative of the wind-driven Sverdrup circulation, from which the four dimensional fields are allowed to be sampled in several ways, such as sampling at the different levels or along the different vertical sections. To set the different samples, the fields of temperature, salinity and velocities function as the observational limit in the adjoint system respectively where the same initial condition is chosen for 4D VAR data assimilation. By examining the distance functions which measure the misfit between the circulation field from the control experiment of the adjoint system with a complete observation and those from data assimilation of adjoint approach in these sensitivity experiments respectively, observing optimizations for the wind-driven Sverdrup circulation will be suggested under a fixed observational cost.     

Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics

Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.     

Assimilation of near-surface temperature using extended Kalman filter

In order to improve the soil temperature profile predictions in land-surface models, an assimilation scheme using the extended Kalman filter is developed. This formulation is based on the discretized diffusion equation of heat transfer through the soil column. The scheme is designed to incorporate the knowledge of the uncertainties in both the model and the measurement. Model uncertainty is estimated by quantifying the model drift from observations when the model is initialized using the observed values. Furthermore, the initial error covariance has a significant influence on the performance of the assimilation scheme. It is shown that an inaccurate initial value for the error covariance can actually diminish the predictive capabilities of the model. When an appropriate initial error covariance is specified, using the top layer soil temperature observations in the assimilation scheme allows for improved predictive capabilities in lower layers. Observations at 30 min intervals have a significant effect on the model predictions in the lower layers. Assimilation of observations at 24 h intervals also has an effect on the lower layer predictive capability of the model, albeit more slowly than the 30 min assimilation scenario.     

Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation

Data assimilation is mainly concerned with the proper management of uncertainties. The main objective of the present work is to implement and analyze a data assimilation technique capable of assimilating bathymetric data into a coupled flow, wave, and morphodynamic model. For the case presented here, wave significant height, wave direction of incidence, and wave peak period are being optimized based on bathymetric data taken from a twin experiment. An adjoint-free variational scheme is used. In this approach, a linear reduced order model (ROM) is constructed as an approximation of the full model. The ROM is an autoregressive model of order 1 (AR1) that preserves the parametrization. Since the ROM is linear, the construction of its adjoint is straightforward, making the implementation of 4D variational data assimilation effortless. The scheme is able to update the morphodynamic model satisfactorily despite the fact that the model shows nonlinear behavior even for very small perturbations of all three parameters. The size and direction of the perturbations necessary for constructing the ROM have a significant impact on the performance of the technique.     

Assimilation of sea surface temperature into CECOM by flux correction

Sea surface temperature (SST) from a near real-time data set produced from satellites data has been assimilated into a coupled ice–ocean forecasting model (Canadian East Coast Ocean Model) using an efficient data assimilation method. The method is based on an optimal interpolation scheme by which SST is melded into the model through the adjustment of surface heat flux. The magnitude and space–time variation of the adjustment depend on the depth of heat diffusion into the water column in response to changes in surface flux, the correlation time scale of the data, and model and data errors. The diffusion depth is scaled by the eddy diffusivity for temperature. The ratio of the model and data errors is treated as an adjustable parameter. To evaluate the quality of the assimilation, the results from the model with and without assimilation are compared to independent ship data from the Atlantic Zone Monitoring Program and the World Ocean Circulation Experiment. It is shown that the assimilation has a significant impact on the modeled SST, reducing the root mean square difference (RMSD) between the model SST and the ship SST by 0.63°C or 37%. The RMSD of the assimilated SST is smaller than that of the satellite SST by 0.23°C. This suggests that model simulations or predictions with data assimilation can provide the best estimate of the true SST. A sensitivity study is performed to examine the change of the model RMSD with the adjustable parameter in the assimilation equation. The results show that there is an optimal value of the parameter and the model SST is not very sensitive to the parameter.     

Optimal boundary conditions for ORCA-2 model

A 4D-Var data assimilation technique is applied to ORCA-2 configuration of the NEMO in order to identify the optimal parametrization of boundary conditions on the lateral boundaries as well as on the bottom and on the surface of the ocean. The influence of boundary conditions on the solution is analyzed both within and beyond the assimilation window. It is shown that the optimal bottom and surface boundary conditions allow us to better represent the jet streams, such as Gulf Stream and Kuroshio. Analyzing the reasons of the jets reinforcement, we notice that data assimilation has a major impact on parametrization of the bottom boundary conditions for u and v. Automatic generation of the tangent and adjoint codes is also discussed. Tapenade software is shown to be able to produce the adjoint code that can be used after a memory usage optimization.     

State analysis using the Local Ensemble Transform Kalman Filter (LETKF) and the three-layer circulation structure of the Luzon Strait and the South China Sea

A new circulation model of the western North Pacific Ocean based on the parallelized version of the Princeton Ocean Model and incorporating the Local Ensemble Transform Kalman Filter (LETKF) data assimilation scheme has been developed. The new model assimilates satellite data and is tested for the period January 1 to April 3, 2012 initialized from a 24-year simulation to estimate the ocean state focusing in the South China Sea (SCS). Model results are compared against estimates based on the optimum interpolation (OI) assimilation scheme and are validated against independent Argo float and transport data to assess model skills. LETKF provides improved estimates of the western North Pacific Ocean state including transports through various straits in the SCS. In the Luzon Strait, the model confirms, for the first time, the three-layer transport structure previously deduced in the literature from sparse observations: westward in the upper and lower layers and eastward in the middle layer. This structure is shown to be robust, and the related dynamics are analyzed using the results of a long-term (18 years) unassimilated North Pacific Ocean model. Potential vorticity and mass conservations suggest a basin-wide cyclonic circulation in the upper layer of the SCS (z?>??570 m), an anticyclonic circulation in the middle layer (?570 m?≥?z?>??2,000 m), and, in the abyssal basin (<?2,000 m), the circulation is cyclonic in the north and anticyclonic in the south. The cyclone–anticyclone abyssal circulation is confirmed and explained using a deep-layer reduced-gravity model as being caused by overflow over the deep sill of the Luzon Strait, coupled with intense, localized upwelling west of the strait.     

Identification of extreme storm surges with high-impact potential along the German North Sea coastline

Planning and design of coastal protection rely on information about the probabilities of very severe storm tides and the possible changes that may occur in the course of climate change. So far, this information is mostly provided in the form of high percentiles obtained from frequency distributions or return values. More detailed information and assessments of events that may cause extreme damages or have extreme consequences at the coast are so far still unavailable. We describe and compare two different approaches that may be used to identify highly unlikely but still physically possible and plausible events from model simulations. Firstly, in the case when consistent wind and tide-surge data are available, different metrics such as the height of the storm surge can be derived directly from the simulated water levels. Secondly, in cases where only atmospheric data are available, the so called effective wind may be used. The latter is the projection of the horizontal wind vector on that direction which is most effective in producing surges at the coast. Comparison of events identified by both methods show that they can identify extreme events but that knowledge of the effective wind alone does not provide sufficient information to identify the highest storm surges. Tracks of the low-pressure systems over the North Sea need to be investigated to find those cases, where the duration of the high wind is too short to induce extreme storm tides. On the other hand, factors such as external surges or variability in mean sea level may enhance surge heights and are not accounted for in estimates based on effective winds only. Results from the analysis of an extended data set suggest that unprecedented storm surges at the German North Sea coast are possible even without taking effects from rising mean sea level into account. The work presented is part of the ongoing project “Extreme North Sea Storm Surges and Their Consequences” (EXTREMENESS) and represents the first step towards an impact assessment for very severe storm surges which will serve as a basis for development of adaptation options and evaluation criteria.     

An explicit four-dimensional variational data assimilation method

A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost func-tion with respect to the control variables, is no longer needed. The new technique significantly simpli-fies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.     

Investigating the effects of a summer storm on the North Sea stratification using a regional coupled ocean-atmosphere model

The influence of a summer storm event in 2007 on the North Sea and its effects on the ocean stratification are investigated using a regional coupled ocean (Regional Ocean Modeling System, ROMS)-atmosphere (Weather Research & Forecasting model, WRF) modeling system. An analysis of potential energy anomaly (PEA, Φ) and its temporal development reveals that the loss of stratification due to the storm event is dominated by vertical mixing in almost the entire North Sea. For specific regions, however, a considerable contribution of depth-mean straining is observed. Vertical mixing is highly correlated with wind induced surface stresses. However, peak mixing values are observed in combination with incoming flood currents. Depending on the phase between winds and tides, the loss of stratification differs strongly over the North Sea. To study the effects of interactive ocean-atmosphere exchange, a fully coupled simulation is compared with two uncoupled ones for the same vertical mixing parameters to identify the impact of spatial resolution as well as of SST feedback. While the resulting new mixed layer depth after the storm event in the uncoupled simulation with lower spatial and temporal resolution of the surface forcing data can still be located in the euphotic zone, the coupled simulation is capable to mix the entire water column and the vertical mixing in the uncoupled simulation with higher resolution of the surface forcing data is strongly amplified. These differences might have notable implications for ecosystem modeling since it could determine the development of new phytoplankton blooms after the storm and for sediment modeling in terms of sediment mobilization. An investigation of restratification after the extreme event illustrates the persistent effect of this summer storm.     

A 4D variational assimilation scheme with partition method for nearshore wave models

This paper summarizes the development steps of a 4D variational assimilation scheme for nearshore wave models. A partition method is applied for adjusting both wave boundary conditions and wind fields. Nonstationary conditions are assimilated by providing defined correlations of model inputs in time. The scheme is implemented into the SWAN model. Twin experiments covering both stationary and nonstationary wave conditions are carried out to assess the adequacy of the proposed scheme. Stationary experiments are carried out considering separately windsea, swells, and mixed sea. Cost functions decline to less than 5% and RMS spectrum errors are reduced to less than 10%. The nonstationary experiment covers 1 day simulation under mixed wave conditions with assimilation windows of 3 h. RMS spectrum errors are reduced to less than 10% after 30 iterations in most assimilation windows. The results show that for spacially uniform model inputs, model accuracy is improved notably by the assimilation scheme throughout the computational domain. It is found that under wave conditions in which observed spectra can be well classified, the assimilation scheme is able to improve model results significantly.     

Development of a new operational system for monitoring and forecasting coastal and open-ocean states around Japan

We developed a new system to monitor and forecast coastal and open-ocean states around Japan for operational use by the Japan Meteorological Agency. The system consists of an eddy-resolving analysis model based on four-dimensional variational assimilation and a high (2-km) resolution forecast model covering Japanese coastal areas that incorporates an initialization scheme with temporal and spatial filtering. Assimilation and forecast experiments were performed for 2008 to 2017, and the results were validated against various observation datasets. The assimilation results captured well the observed variability in sea surface temperature, coastal sea level, volume transport, and sea ice. Furthermore, the volume budget for the Japan Sea was significantly improved by the use of the 2-km resolution forecast model compared with the 10-km resolution analysis model. The forecast results indicate that this system has a predictive limit longer than 1 month in many areas, including in the Kuroshio current area south of Japan and the southern Japan Sea. In the forecast results of case studies, the 2017 Kuroshio large meander was well predicted, and warm water intrusions accompanying Kuroshio path variations south of Japan were also successfully reproduced. Sea ice forecasts for the Sea of Okhotsk largely captured the evolution of sea ice in late winter, but sea ice in early winter included relatively large errors. This system has high potential to meet operational requirements for monitoring and forecasting ocean phenomena at both meso- and coastal scales.

     

Correcting surface winds by assimilating high-frequency radar surface currents in the German Bight

Surface winds are crucial for accurately modeling the surface circulation in the coastal ocean. In the present work, high-frequency radar surface currents are assimilated using an ensemble scheme which aims to obtain improved surface winds taking into account European Centre for Medium-Range Weather Forecasts winds as a first guess and surface current measurements. The objective of this study is to show that wind forcing can be improved using an approach similar to parameter estimation in ensemble data assimilation. Like variational assimilation schemes, the method provides an improved wind field based on surface current measurements. However, the technique does not require an adjoint, and it is thus easier to implement. In addition, it does not rely on a linearization of the model dynamics. The method is validated directly by comparing the analyzed wind speed to independent in situ measurements and indirectly by assessing the impact of the corrected winds on model sea surface temperature (SST) relative to satellite SST.     

Exploring the effect of data assimilation by WRF‐3DVar for numerical rainfall prediction with different types of storm events

The mesoscale Numerical Weather Prediction (NWP) model is gaining popularity among the hydrometeorological community in providing high‐resolution rainfall forecasts at the catchment scale. Although the performance of the model has been verified in capturing the physical processes of severe storm events, the modelling accuracy is negatively affected by significant errors in the initial conditions used to drive the model. Several meteorological investigations have shown that the assimilation of real‐time observations, especially the radar data can help improve the accuracy of the rainfall predictions given by mesoscale NWP models. The aim of this study is to investigate the effect of data assimilation for hydrological applications at the catchment scale. Radar reflectivity together with surface and upper‐air meteorological observations is assimilated into the Weather Research and Forecasting (WRF) model using the three‐dimensional variational data‐assimilation technique. Improvement of the rainfall accumulation and its temporal variation after data assimilation is examined for four storm events in the Brue catchment (135.2 km²) located in southwest England. The storm events are selected with different rainfall distributions in space and time. It is found that the rainfall improvement is most obvious for the events with one‐dimensional evenness in either space or time. The effect of data assimilation is even more significant in the innermost domain which has the finest spatial resolution. However, for the events with two‐dimensional unevenness of rainfall, i.e. the rainfall is concentrated in a small area and in a short time period, the effect of data assimilation is not ideal. WRF fails in capturing the whole process of the highly convective storm with densely concentrated rainfall in a small area and a short time period. A shortened assimilation time interval together with more efficient utilisation of the weather radar data might help improve the effectiveness of data assimilation in such cases. Copyright © 2012 John Wiley & Sons, Ltd.     

Simultaneous estimation of soil moisture and hydraulic parameters using residual resampling particle filter

Land data assimilation (DA) has gradually developed into an important earth science research method because of its ability to combine model simulations and observations. Integrating new observations into a land surface model by the DA method can correct the predicted trajectory of the model and thus, improve the accuracy of state variables. It can also reduce uncertainties in the model by estimating some model parameters simultaneously. Among the various DA methods, the particle filter is free from the constraints of linear models and Gaussian error distributions, and can be applicable to any nonlinear and non-Gaussian state-space model; therefore, its importance in land data assimilation research has increased. In this study, a DA scheme was developed based on the residual resampling particle filter. Microwave brightness temperatures were assimilated into the macro-scale semi-distributed variance infiltration capacity model to estimate the surface soil moisture and three hydraulic parameters simultaneously. Finally, to verify the scheme, a series of comparative experiments was performed with experimental data obtained during the Soil Moisture Experiment of 2004 in Arizona. The results show that the scheme can improve the accuracy of soil moisture estimations significantly. In addition, the three hydraulic parameters were also well estimated, demonstrating the effectiveness of the DA scheme.     

Geoid and Sea Surface Topography Derived from ERS-1 Altimeter Data by the Adjoint Method

A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model.