考虑内潮耗散的南海潮波伴随同化研究
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摘要
南海位于中国大陆南端，是沟通太平洋和印度洋的重要通道之一，地理位置非常重要。南海地形变化剧烈，岛礁众多，使得南海的潮波系统非常复杂。南海潮能耗散较强，在深水处，仅考虑底摩擦耗散不能充分体现潮能耗散的实际情况，还必须考虑表面潮向内潮转换时的能量损失，即内潮耗散。
本文建立了南海潮波模式及其伴随同化模式，在传统二维潮波方程的基础上加入了内潮耗散项，考虑了内潮耗散对南海潮波系统的影响。在前人工作基础上，改进了内潮耗散参数化方案，并给出了内潮耗散项中地形效应参数的计算公式。
评估了全球大洋潮汐模式TPXO7.2、GOT00.2、NAO.99b和DTU10在南海的准确度。依据对比分析结果，选用DTU10模式来计算本研究的开边界条件。
以63个验潮站和24个TOPEX/Poseidon卫星高度计轨道交叉点处的调和常数作为观测值，利用伴随同化方法来优化模式中的底摩擦系数和内潮耗散系数，使得模拟结果与观测值更加接近。为了寻找最优的优化方案，设计了7组数值实验。实验1~7M2分潮模拟结果与观测值的均方根偏差分别为29.78cm、24.08cm、12.64cm、12.56cm、10.19cm、10.63cm和10.15cm，可以看出实验7先优化内潮耗散系数再优化底摩擦系数的模拟结果最优。
确定了同化方案后，本文建立了1/8°和1/4°两种水平分辨率的M2分潮的单分潮数值模式，通过对比发现，水平分辨率1/4°模式的计算时长大约为1/8°模式的1/5，而误差仅略大。考虑到4个分潮耦合模拟需要积分时间更长，为了提高计算效率，采用分辨率为1/4°的模式进行最终的M2、S2、K1、O1四个分潮耦合同化模拟。对于1/4°模式而言，7个实验方案中结果最优的仍为实验5、6和7，实验7最优，其次是实验5，与1/8°模式情况相同。
采用先优化内潮耗散系数再优化底摩擦系数的方案，对南海M2、S2、K1、O1分潮进行了耦合同化模拟。M2、S2、K1和O1分潮模拟值与观测值的均方根偏差分别为12.35cm、6.47cm、9.79cm和8.21cm，模拟结果与观测符合良好。基于该模拟结果，分析了南海M2、S2、K1、O1四个分潮的潮汐潮流特征，较好地体现了南海潮波的传播规律。
基于四个分潮耦合同化模拟结果，分析了南海M2、S2、K1、O1四个分潮的潮能通量分布情况。四个分潮的潮能都由太平洋经吕宋海峡传入，然后向西南方向传播。S2分潮的潮能通量量级明显小于另外三个分潮的潮能通量。不论对于半日分潮还是对于全日分潮来说，都是在吕宋海峡处的潮能通量最大。
基于四个分潮耦合同化模拟结果，还分析了南海的潮能耗散情况。南海的潮能耗散除了底摩擦造成的底摩擦耗散外，还通过表面潮向内潮转换的方式来进行耗散，即内潮耗散。南海的底摩擦耗散主要发生在沿岸浅水区域，内潮耗散主要集中在吕宋海峡等深水区，吕宋海峡处为最大。
The South China Sea (SCS) is located in the south of China mainland. It is animportant area to connect the Pacific Ocean and Indian Ocean. The steep bottomtopography and numerical islands form a complex tidal system in the SCS. The tidalenergy dissipation in the SCS is very strong. In the deep water area, the bottomfriction dissipation can not represent the dissipation of tidal energy sufficiently. Thetidal energy dissipation also occurs through the scattering of surface tides into internaltides, which is called internal tide dissipation.
In this paper, the tidal and adjoint model are built in the SCS. A parameterizationof internal tide dissipation is added to the traditional2-D tidal equations, consideringthe internal tide dissipation on the influence of the tidal wave system in the SCS.Based on previous studies, the parameterization of internal tide dissipation isimproved, and the expression of the bottom roughness parameter is given.
In order to obtain better open boundary conditions, the global tide modelsTPXO7.2, GOT00.2, NAO.99b and DTU10are compared in the SCS. Accoding tothe results of comparison, DTU10is chosen to compute the open boundary conditionsin this study.
The harmonic constants at63tide gauge stations and24TOPEX/Poseidonsatellite altimeter crossover points are used as observations. The bottom frictioncoefficient and the internal tide dissipation coefficient are optimized by using adjontmethod to minimize the distance between the simulated results and observations. Inorder to get the best optimizing scheme, seven experiments are designed. The rootmean square deviations between the results for M2tide of seven experiments andobservations are29.78cm,24.08cm,12.64cm,12.56cm,10.19cm,10.63cm and10.15cm respectively. It can be seen that the results of Experiment7is best.
After the optimizing scheme is confirmed, numerical models for M2tide with thehorizonal resolution of1/8degree and1/4degree are built. By comparing the results,the computational time of the model with the horizontal resolution of1/4degree isone five of that of the model with the horizontal resolution of1/8degree. But the erroris slightly bigger. In order to improve the computional efficiency, the model with thehorizontal resolution of1/4degree is choosen to simulate the principal tidalcomponents M2, S2, K1and O1simultaneously.
By using the scheme of Experiment7, the adjoint numerical simulation of tidalcomponents M2, S2, K1and O1in the SCS are achieved. The root mean squaredeviations between the simulations of the four tidal components and obsernations are12.35cm,6.47cm,9.79cm and8.21cm respectively. The simulated results coincidewith the observed. The cotidal charts for M2, S2, K1and O1are given, and they reflectthe characteristics of tides in the SCS.
The tidal energy flux of the four principal tidal constituents is analysed in thispaper based on the numerical results. The tidal energy propagates to the SCS throughthe Luzon Strait from the Pacific Ocean, and then propagates southwestward. Themagnitude of tidal energy flux for S2tide is less than the other three tides. Thestrongest tidal energy is in the Luzon Stait for both semidiurnal and diurnal tidalconstituents.
According to the numerical results, the tidal energy dissipation in the SCS isstudyed. In the SCS, the tidal energy is dissipated not only by the bottom friction butalso by scattering of the surface tide into the internal tide. The bottom frictiondissipation occures in shallow water area, the internal tide dissipation mainlyconcentrates in the Luzon Strait.
本文建立了南海潮波模式及其伴随同化模式，在传统二维潮波方程的基础上加入了内潮耗散项，考虑了内潮耗散对南海潮波系统的影响。在前人工作基础上，改进了内潮耗散参数化方案，并给出了内潮耗散项中地形效应参数的计算公式。
评估了全球大洋潮汐模式TPXO7.2、GOT00.2、NAO.99b和DTU10在南海的准确度。依据对比分析结果，选用DTU10模式来计算本研究的开边界条件。
以63个验潮站和24个TOPEX/Poseidon卫星高度计轨道交叉点处的调和常数作为观测值，利用伴随同化方法来优化模式中的底摩擦系数和内潮耗散系数，使得模拟结果与观测值更加接近。为了寻找最优的优化方案，设计了7组数值实验。实验1~7M2分潮模拟结果与观测值的均方根偏差分别为29.78cm、24.08cm、12.64cm、12.56cm、10.19cm、10.63cm和10.15cm，可以看出实验7先优化内潮耗散系数再优化底摩擦系数的模拟结果最优。
确定了同化方案后，本文建立了1/8°和1/4°两种水平分辨率的M2分潮的单分潮数值模式，通过对比发现，水平分辨率1/4°模式的计算时长大约为1/8°模式的1/5，而误差仅略大。考虑到4个分潮耦合模拟需要积分时间更长，为了提高计算效率，采用分辨率为1/4°的模式进行最终的M2、S2、K1、O1四个分潮耦合同化模拟。对于1/4°模式而言，7个实验方案中结果最优的仍为实验5、6和7，实验7最优，其次是实验5，与1/8°模式情况相同。
采用先优化内潮耗散系数再优化底摩擦系数的方案，对南海M2、S2、K1、O1分潮进行了耦合同化模拟。M2、S2、K1和O1分潮模拟值与观测值的均方根偏差分别为12.35cm、6.47cm、9.79cm和8.21cm，模拟结果与观测符合良好。基于该模拟结果，分析了南海M2、S2、K1、O1四个分潮的潮汐潮流特征，较好地体现了南海潮波的传播规律。
基于四个分潮耦合同化模拟结果，分析了南海M2、S2、K1、O1四个分潮的潮能通量分布情况。四个分潮的潮能都由太平洋经吕宋海峡传入，然后向西南方向传播。S2分潮的潮能通量量级明显小于另外三个分潮的潮能通量。不论对于半日分潮还是对于全日分潮来说，都是在吕宋海峡处的潮能通量最大。
基于四个分潮耦合同化模拟结果，还分析了南海的潮能耗散情况。南海的潮能耗散除了底摩擦造成的底摩擦耗散外，还通过表面潮向内潮转换的方式来进行耗散，即内潮耗散。南海的底摩擦耗散主要发生在沿岸浅水区域，内潮耗散主要集中在吕宋海峡等深水区，吕宋海峡处为最大。
The South China Sea (SCS) is located in the south of China mainland. It is animportant area to connect the Pacific Ocean and Indian Ocean. The steep bottomtopography and numerical islands form a complex tidal system in the SCS. The tidalenergy dissipation in the SCS is very strong. In the deep water area, the bottomfriction dissipation can not represent the dissipation of tidal energy sufficiently. Thetidal energy dissipation also occurs through the scattering of surface tides into internaltides, which is called internal tide dissipation.
In this paper, the tidal and adjoint model are built in the SCS. A parameterizationof internal tide dissipation is added to the traditional2-D tidal equations, consideringthe internal tide dissipation on the influence of the tidal wave system in the SCS.Based on previous studies, the parameterization of internal tide dissipation isimproved, and the expression of the bottom roughness parameter is given.
In order to obtain better open boundary conditions, the global tide modelsTPXO7.2, GOT00.2, NAO.99b and DTU10are compared in the SCS. Accoding tothe results of comparison, DTU10is chosen to compute the open boundary conditionsin this study.
The harmonic constants at63tide gauge stations and24TOPEX/Poseidonsatellite altimeter crossover points are used as observations. The bottom frictioncoefficient and the internal tide dissipation coefficient are optimized by using adjontmethod to minimize the distance between the simulated results and observations. Inorder to get the best optimizing scheme, seven experiments are designed. The rootmean square deviations between the results for M2tide of seven experiments andobservations are29.78cm,24.08cm,12.64cm,12.56cm,10.19cm,10.63cm and10.15cm respectively. It can be seen that the results of Experiment7is best.
After the optimizing scheme is confirmed, numerical models for M2tide with thehorizonal resolution of1/8degree and1/4degree are built. By comparing the results,the computational time of the model with the horizontal resolution of1/4degree isone five of that of the model with the horizontal resolution of1/8degree. But the erroris slightly bigger. In order to improve the computional efficiency, the model with thehorizontal resolution of1/4degree is choosen to simulate the principal tidalcomponents M2, S2, K1and O1simultaneously.
By using the scheme of Experiment7, the adjoint numerical simulation of tidalcomponents M2, S2, K1and O1in the SCS are achieved. The root mean squaredeviations between the simulations of the four tidal components and obsernations are12.35cm,6.47cm,9.79cm and8.21cm respectively. The simulated results coincidewith the observed. The cotidal charts for M2, S2, K1and O1are given, and they reflectthe characteristics of tides in the SCS.
The tidal energy flux of the four principal tidal constituents is analysed in thispaper based on the numerical results. The tidal energy propagates to the SCS throughthe Luzon Strait from the Pacific Ocean, and then propagates southwestward. Themagnitude of tidal energy flux for S2tide is less than the other three tides. Thestrongest tidal energy is in the Luzon Stait for both semidiurnal and diurnal tidalconstituents.
According to the numerical results, the tidal energy dissipation in the SCS isstudyed. In the SCS, the tidal energy is dissipated not only by the bottom friction butalso by scattering of the surface tide into the internal tide. The bottom frictiondissipation occures in shallow water area, the internal tide dissipation mainlyconcentrates in the Luzon Strait.
引文
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