海洋模式中Boussinesq近似误差讨论

根据全球增暖的特点，设计了一个理想的数值试验方案，用Boussinesq POP海洋模式和改进的非Boussinesq POP海洋模式定量讨论了Bousiinesq近似在海洋模式计算中的误差。结果发现，在只有热力驱动的热力环流背景下，由热膨胀引起的海平面上升在水平方向上是基本均匀的，在所给的初始边界条件下，这种由Boussinesq近似引起的最大海平面误差可以达到59％，在Boussinesq POP模式中，热源中心处的海面高度要远小于由非Boussinesq模式计算的海面高度，而其周围有虚假的海面高度下降；在只有加热引起的热盐环流过程中，当模式作了Boussinesq假设以后，计算的经向和纬向垂直环流都会产生虚假的加强，虽然这种误差只是在1％左右；在Bousiinesq近似假定下，热量经向通量在赤道上垂直剖面的积分误差比质量经向通量在赤道上垂直剖面的积分误差大一个量级；非Boussinesq模式计算的气压梯度所做功的垂向分布在3000m以下是有波动的，而Boussinesq模式计算的气压梯度所做功的垂向分布在3000m以下基本上是均匀的，它的误差在10％以上。

On the Errors of Boussinesq Approximation in Ocean Models

In this paper, based on the global warming characteristics, an ideal numerical experiment plan is designed, and a Boussinesq POP ocean model and a modified non-Boussinesq POP ocean model are used to quantitatively discuss the errors of Boussinesq approximation in ocean models. It is shown from the computation results that under the thermodynamic circulation condition by heating, the horizontal sea level rise distribution is basically uniform, and under the given initial and boundary conditions, the sea level error due to Boussinesq approximation can be as high as 59%, the sea surface height at the heat source center in Boussinesq model is much smaller than that in non-Boussinesq model, and there is false sea surface height fall around the heat source; under the thermohaline circulation condition by heating, the computed latitudinally and longitudinally vertical circulations are falsely strengthened due to Boussinesq approximation although this error is only about 1%; on the assumption of Boussinesq approximation, the error of vertically-integrated longitudinal heat flux at the equator is one-order greater than that of mass flux, the vertical distributions of air pressure gradient work calculated by non-Boussinesq model are fluctuating in water depths of greater than 3 000 m, but those calculated by Boussinesq model are basically uniform in water depths of greater than 3 000 m, and the error of Boussinesq approximation is more than 10%.