Tidal Wave Optimization Of The Model Open Boundary

Numerical model is an advantaged measurement to research tide, but it will be confronted with many material problems, such as specify open boundaries,bottom friction coefficient,dissipation coefficient and so on. Data assimilation is an approach to solve these problems, using restricted numerous tide observation data to optimize estimate for tide field, the ultimate purpose is put the mode predict data close to the observation data, avoid the mode data far from the real data too much. This paper introduces an optimized assimilation approach; an optimization approach is derived for assimilating tidal height information along the open boundaries for a numerical model. The aim is trying to make the observation data close to the momentum restriction resolution, to simulate the tide of study area. The boundary values are determined from the solution of the special optimization problem: minimization of the difference between the model and reference boundary values, to enhance tide precision of simulation areas. The approach is then extended so that similar data along transects inside a model domain can also be optimally assimilated. It shows the well-known radiation-type boundary conditions introduced by Reid and Bodine; the optimized RB (ORB) solution is the special cases of the derived optimized conditions.Based on the ECOM3D model with resolution 1/12o×1/12o, this work presents a model study on an ideal square area with only an open boundary on the east side, which locates between 117 E-120 E and38 N-40 N. We try to evaluate the performance of the model by comparing the swing mean deviation, mean absolute deviation, mean relative deviation and variances with analytic solution.The analytic resolution of the tides and tidal streams, which is needed in the assimilation model, is get by an approximate method first presented in paper"Tides and tidal streams in gulfs"by Fang Guohong and Wang Shuren in 1966. We compared the key parameters, say a, b and z of the first case study preferred in this paper and found that our results match well with the original authors'. But they have nuance, the causation maybe thin differentiate between the two methods about iterative scheme and different reserve decimal digits. Besides, we choose m=20, obtain more precise numerical value, we found that each parameters of the first ten items, with m=10 and m=20, have little ameliorate. We also can obtain each parameters of large m.To test the validity of analytical resolution, we discuss the effect on the boundary value of changing m and l; the results show that, when augmenting m with m=20, the largest module of u is 6% of u1 or u2's module; with m=100, the value is 4%; and with 1000, the value is 4%, the change is small. When l<1,ξ=0, the largest module of u is 2. when l=1,the value is 0,1,when l>1,the larger l, the less the module of u. when l=10,the value is 0.001,it can be seen zero. It tests the conclusion of FANGGUOHONG (1966).In order to test the performance of the optimal methodology, we conduct model study on the ideal square area. First, we apply the above preferred optimal open boundary method to case study of 30-meter depth. After assimilating only the analytic solutions on the open boundary into the model, the results in the whole area agree quite well with the corresponding analytic solutions with mean absolute deviation is 9.9cm, mean relative deviation is 4.0 and variances is 13.3cm, which reveals a good applicability of this optimal method on the tidal model.To further investigate the performance of this optimal assimilation method on different conditions, we conduct 3 kinds of sensitive tests:The first kind of test: for testifying this method with the best-** method more close to resolution than without it, we have compared the advantage between the conditions of ORB and RB, two rub coefficients have been used in the model, k will be equal to 0 and 0.00006 separately.The conclusion shows that, with different rub coefficient, there are both advantages in phase and swing on open boundary with ORB condition, the prior grade of covariance in the two standard results is 84.3% and 83.7% respectively. This shows that the model can be better with the previous method, and get another level. It is concluded that the simulation with k=0.00006 better than k=0.The second kind of test: using the condition of ORB and add the current with in and out, we consider current of linearity and nonlinearity instances. The results show that the precision of tide simulation depress when current adds. Compare 1Sv to 5Sv, the variances deviation is 20cm, while 0.2cm of no current. Linearity and nonlinearity current have little influence for the modle, swing and phase are close. It can be said that no matter linearity or nonlinearity, he influence is small.The third kind of test: using ORB condition not only in OBCs, but also in interior, compares the different between interior assimilation and nonassimilation to analyze solution. It shows that, using different k, swing have good simulation, but phase have not. Besides, in case of interior assimilation, consider mode solution of different k, we choose 6 k which close to the analyze solution. It is show that, swing improved much, but phase have not.From the above analysis we find that tide model results with optimal open boundary assimilation method, with a significant error decreasing, agree better with the analytic solution than that without using this method; we also find that, with the same boundary condition, parameters shifting of the depth, in and out flow or the bottom friction will also induce a change on the model results. The interior assimilation's result show that, the mode adopts different k can simulate swing good.