Memory of HF radar surface-current assimilation on different forecasting variables of ocean circulation models

In this study, using nudging method, the current data from a pair of HF radar along Jiangsu coast was assimilated to unstructured grid models based on FVCOM. Several experiments were conducted to examine the effect of radar data on surface velocity, elevation and sea surface salinity forecast. The results show that the gain of assimilation on surface velocity and elevation forecasts disappeared fast within a few hours, while salinity forecasts can be influenced for more than 10 days. This fast diminishing of the gain of data assimilation on current and elevation can be attributed to the fast wave propagation from elsewhere to the radar coverage area.


Introduction
Most of the coastal and estuarine areas in the world are densely populated and many human activities occur in these coastal waters.Understanding and forecasting the current in these areas is of great importance for marine transportation, tourism, search and rescue, ecological protection among others, and can be beneficial for regional social and economic development.However, due to the islands and complex topography, as well as various forcings such as tides, river input and winds, the study and prediction of ocean currents in these areas are more difficult than those in the open ocean, and it is not likely to make precise prediction without observations.Ocean current can be measured with traditional equipment like current meter, ADCP or inverted from satellite data.HF radar emerged from the middle of the 20th century.The radar transmits high frequency radio waves to the sea surface with range from 3MHz to 50MHz, and the waves can reach beyond visual range with the aid of sea water conductivity.Compared with other current mapping equipment, HF radar has the advantages of large coverage area, high space and time resolution, allweather and low maintenance cost.Its data are widely used in the study of nearshore ocean dynamics, ocean model validation, data assimilation, marine ecosystems, and other fields.
In the field of data assimilation using HF radar observations, there have been many previous work to investigate if the assimilation of ocean surface current data from HF radar into coastal ocean models can improve their forecasting results at the surface as well as for some distance under the surface.Breivik and Saetra [1] created a real time assimilation and forecasting system for coastal currents using a modified optimal interpolation method.Their system could get an analysis field and provide 6 hours of current forecast, and the forecasting results were significantly improved compared to model results without assimilation.On New Jersey's inner shelf area, Wilkin et al. [2] built a coastal ocean forecasting system from ROMS.Surface current data from HF radar were projected vertically for assimilation using a statistically based extrapolation conducted from mooring sites.They found that the k profile parameterization for vertical turbulence closure and assimilation by intermittent melding method made the forecast system with the best performance.While most researchers used u and v velocity components of the mapped vector velocities in assimilation methods, Shulman & Paduan [3] found that improved results can be obtained by directly assimilating radial current component data from individual HF radar sites, presumably because the spatial coverage is increased when radial currents are used.In the work of assimilation of HF radar current data from south Africa, Couvelard et al. [4] showed that model could reproduce surface circulation more realistically, and even though the effect of the assimilation on surface current intensity greatly reduced after a day, the correction in direction lasts after 48 hours.
The goal of this study is to examine the effect of assimilation of HF radar observed currents on forecasting model variables.In section 2, the HF radar data, the model and the assimilation method used for this study are described.Section 3 provides the outcome of the assimilation experiments.Finally, summary and conclusions are given in Section 4.

HF radar observations
The surface currents are measured by a pair of radars (OSMAR-S) located at coasts of Jiangsu (Figure 1).The radar is the compact version of the OSMAR radar developed by Wuhan University of China.The single radar measures the radials every 6 minutes, with a distance resolution of 2.5km and direction resolution of 3°.In our assimilation experiments, we use the composited vectors with a spatial resolution of 0.03°and a time resolution of 20 minutes.Although this pair of radars were validated by previous scholars [5], quality control (QC) of the data is necessary due to observational errors.The main procedure of QC is to eliminate the 'abrupt' values in space and time by standard deviation threshold method [6].A threshold on data coverage rate is also used to screen out the grid points with less data.The observations used in this study cover three months from July 1 to August 31, 2021.The vector currents at grid points with data coverage over 50% are kept.[7].The CE-FVCOM was developed originally by Ge et al. [8] and well validated by tidal gauge and ADCP measurements.The ECS-FVCOM was originally built to study the offshore detachment of the Chanjiang diluted water [9].The models are driven by astronomical tidal forcing with eight constituents (M2, S2, N2, K2, K1, P1, O1, and Q1) extracted from TPXO 9.0 Global Tidal Solution, surface wind from ECMWF reanalysis and monthly mean river discharge of Datong hydrological station.The grids of the two models are shown in figure 2. Horizontally, CE-FVCOM has a grid size of ~200 m in the river estuary, 500m~1km in the adjacent coasts, and 1km~5km in other regions; while ECS-FVCOM has a resolution of about 3km near the coasts where the radars are located.Vertically, a 10 layers terrain-following coordinate was used in both models.
The model was initialized with constant T/S field and spun up from zero velocity and undisturbed sea surface elevation.Salinity of river discharge and the ocean is set to zero and a constant value of 32, separately.To simplify the question, we neglected the calculation of temperature since it has less influence on surface currents.

Assimilation methods
In this study Nudging method was adopted to assimilate the radar currents.The advantage of this method is its simplicity and computational efficiency [10].The fundamental equations in nudging method is as follows, Where is a variable to be assimilated, 0 is the observed value, is the model-predicted value, represents the sum of all the terms in the governing equation except the local temporal change term, is a nudging factor that keeps the nudging term to be scaled by the slowest physical adjustment process, normally, is set to approximately the magnitude of the Coriolis parameter, is the total number of the observations, is quality factor of the th observation ranging from 0 to 1, and is a product of weight functions given as , , , = • • • Where , , and are horizontal, vertical, temporal and directional weight functions, respectively.Because the HF radar currents are only on the surface, we simply assimilate the observation to the surface layer and neglect the weight in the horizontal differences and consider all data are good after QC, which leads the value of , and set to 1.Only and are functional in our assimilation model.The two terms can be calculated as where is the search radius， is the distance from the radar location to the computational grid center.is the assimilation time window.=10km and =20 minutes are adopted in the following experiments.

Basic experiments
We conducted several experiments to evaluate the effect of assimilation on surface current, elevation and salinity forecast.Details of the basic experiments are given in table 1. Case 1 and 2 are the free run and the assimilation run to provide initial conditions.Case 3 and case 4 perform one day forecast from the initial fields with and without assimilation.Figure 3 shows the difference between surface current velocities of Case 3 and Case 4 on some representative forecast stages in CE-FVCOM.We could see biggest velocity difference at starting time with obvious discontinuity at the edge of the radar data coverage.The magnitude of difference decreased sharply in the first three hours without the 'feed' of radar data.Upon 6th hour, the angle difference between two runs' velocity vectors were already very small.Figure 4 shows CE-FVCOM and ECS-FVCOM results on three selected stations denoted in figure 1.The velocity difference decreased to around zero at A and C in three hours and B in about one hour, and the difference in magnitudes became larger around the peek values.After about 9 hours, the two velocity curves almost coincide to each other.Results of elevation are shown in Figure 5.The discontinuity at the edge of the radar data coverage is not as obvious as the currents because the elevation is not the variable to be assimilated in the model as the current.The gaps in elevation between two runs were most distinct in the first few hours and gradually faded away after that.The magnitude of the differences are around 1-2cm at 6th hour, compared to around 4cm in the beginning.It can be concluded that the effect on elevation forecasts lasts a bit longer than that on velocity.Cases 5~7 are designed to examine the sea surface salinity forecasts affected by assimilating radar data.As we can see in Figure 6, the change in 24-hour averaged salinity difference was much slower than that of velocity and elevation.During the first five days, the salinity difference could maintain above 1psu.The memory of the influence on salinity was long because the tidal currents did not transport matter in tidal cycles and the residual currents, either tidally induced or wind induced, were small.We could see that the salinity difference moved slowly northward and faded away due to diffusion process with surrounding less 'polluted' waters.

Contrast runs
To find the reason why the influence of assimilation on forecasts of current and elevation diminish so fast, we repeated case 3 and 4 by removing wind forcing and tidal boundary condition.We found that the influence still diminishes very fast (figures not shown).This maybe because the tidal wave or wind induced circulation built in the model domain dissipate very slow.The depth at the radar coverage area is about 15m, where the wave propagation speed is estimated as ℎ =43.6km/h.After 3 hours, wave can propagate approximately 130km, which span the coverage of the radar.As can be seen in figure 3, the biggest velocity difference is in the area where radar data exists, while the other areas seems as if not disturbed by the data assimilation.The fast wave propagation from elsewhere to the radar data area helps explain the fast diminishing of the gain of data assimilation at forecast stage.

Summary and outlook
In this study, we used FVCOM to conduct several numerical experiments to investigate the effects of radar current assimilation on model forecasts of sea surface velocity, elevation and salinity.Upon comparison between assimilation runs and free runs, we found that the assimilation change the initial conditions and its influence on surface velocity and elevation forecasts decreased sharply in about three hours.The influence of radar current data assimilation on the salinity forecasts could last up to 10 days.
Several contrast experiments were conducted by running a larger domain model whose open boundaries are far enough from the radar coverage area, and by removing the surface forcing and tidal boundary at forecast run stage to conclude that the rapid diminish of the current difference of assimilation and free run has nothing to do with the boundary or the forcings.The time scale is comparable with the fast propagation of the tidal waves from the area outside the radar coverage area.
Given that the effect of current assimilation last only a few hours, it is necessary to do forecast at a very high frequency (say, hourly).The analysis and short-range forecasts can be useful in many circumstances such as ship transport through narrow channels and during the critical process of the construction of marine structures.
Our next work is to assess the performance of the assimilation model forecasts against observations and to investigate how long can the assimilation effects last on different motions such as inertial, tidal, shelf waves and seasonal coastal currents.

Figure 1 .
Figure 1.Study area and a snapshot of the composited radar currents (blue vectors).Green circles are radar locations and red triangles are three representative points to be studied.

Figure 2 .
Figure 2. Computational grids of the CE-FVCOM (a) and ECS-FVCOM (b).The grids of the two models are shown in figure2.Horizontally, CE-FVCOM has a grid size of ~200 m in the river estuary, 500m~1km in the adjacent coasts, and 1km~5km in other regions; while ECS-FVCOM has a resolution of about 3km near the coasts where the radars are located.Vertically, a 10 layers terrain-following coordinate was used in both models.The model was initialized with constant T/S field and spun up from zero velocity and undisturbed sea surface elevation.Salinity of river discharge and the ocean is set to zero and a constant value of 32, separately.To simplify the question, we neglected the calculation of temperature since it has less influence on surface currents.

Figure 3 .
Figure 3. Difference of velocity forecasts between Case 3 and Case 4 at representative forecast stages, the color indicates the difference in current speed.Figure4shows CE-FVCOM and ECS-FVCOM results on three selected stations denoted in figure1.The velocity difference decreased to around zero at A and C in three hours and B in about one hour, and the difference in magnitudes became larger around the peek values.After about 9 hours, the two velocity curves almost coincide to each other.

Figure 4 .
Figure 4. Velocity output from different runs for three points denoted in figure 1.Results of elevation are shown in Figure5.The discontinuity at the edge of the radar data coverage is not as obvious as the currents because the elevation is not the variable to be assimilated in the model as the current.The gaps in elevation between two runs were most distinct in the first few hours and gradually faded away after that.The magnitude of the differences are around 1-2cm at 6th hour,

Figure 5
Figure 5 As figure 3 but for elevation.

Figure 6 .
Figure 6.Difference of salinity forecasts from the free run derived and the assimilated initial conditions at representative forecast stages.

Table 1 .
List of the basic model runs.