Development of a High Performance Ocean Model using Julia Language

줄리아 언어를 이용한 고성능 해양모델의 개발

Abstract

In order to develop a high performance ocean model, we used Julia, a Just-In-Time compile language, and to obtain the solution of the momentum equation, we made the code to solve the Poisson equation by the Successive Over-Relaxation method. And then we made two models to test Julia calculation codes. First, a simple channel form is modeled to test constant source/sink conditions. Second, the simplified Yellow Sea was modeled to test tidal forcing, Coriolis forces, and the effect of vertical eddy diffusivity coefficients. The model has been tested with a total of eight cases in the two scenarios. As a result of the test, the depth-averaged current speed of the three cases in Scenario 1 converged perfectly to the theoretical value, and that showed well a vertical flow velocity gradient due to the bottom friction. Also, the result of Scenario 2 represented well the amphidromic points of Yellow Sea and the tidal characteristics of mid-western and southwestern coast of Korea. Therefore, it is considered that the ocean model using Julia language has developed successfully, this suggests that the ocean model has come to the stage of successful transition from a classical compile language to a Just-In-Time compile language.

고성능 해양모델을 개발하기 위하여 적시 컴파일(Just-In-Time) 언어인 줄리아 언어를 사용하였고, 운동량 방정식의 해를 구하기 위해 연속완화법으로 푸아송 방정식을 푸는 코드를 작성하였다. 다음으로, 줄리아 계산 코드를 시험하기 위하여 두 가지의 모델을 구축하였다. 첫 번째로, 일정한 유량의 생성/소멸(source/sink) 조건을 시험하기 위해 단순한 수로 형태를 모델링하였고, 두 번째로, 조석 외력(tidal forcing) 및 전향력(Coriolis force), 난류확산계수로 인한 효과 등을 시험하기 위해 황해(Yellow Sea)를 단순화하여 모델링하였다. 모델은 두 가지 시나리오 안에서 총 8개의 실험안으로 테스트되었다. 테스트 결과, 시나리오 1에서 3가지 실험안의 수심 평균된 유속은 이론 값에 완벽하게 수렴하였고, 해저마찰로 인한 수직적 유속 구배를 잘 보여주었다. 또한 시나리오 2에서는 황해의 무조점과 우리나라 서해 중부와 남부 연안의 조석 특성을 잘 재현하였고, 전향력과 수직 난류확산계수에 따른 결과의 차이를 잘 보여주었다. 따라서, 줄리아 언어를 이용한 해양모델을 개발하는 데에 성공하였다고 판단되며, 이는 해양모델이 고전적인 컴파일 언어에서 적시 컴파일 언어로 성공적으로 넘어가는 단계에 오게 됐다는 것을 시사한다.

Fig. 1. Grid design for model scenario 1. (a) is horizontal water depth colormap, (b) is vertical water depth colormap from the south to the north in the center line.

Fig. 2. Open boundary forcing cells in scenario 1 with constant flow forcing at two points of each source (+) and sink (-).

Fig. 3. Open boundary forcing cells in scenario 2 with tidal forcing at south and east boundaries, and comparison points between observations and computations.

Fig. 4. The results of scenario 1. (a) is the surface current vector of Case 1 after 24 hours, (b) is the time series of current speed at point A of each test case.

Fig. 5. The vertical current vectors of three test cases in the center line after 24 hours, (a) is Case 1(r=0), (b) is Case 2(r=0.1), (c) is Case 3(r=0.2).

Fig. 6. The time series of current speed at point A in each test case, (a) is the current speed at the surface layer, (b) is the current speed at the bottom layer.

Fig. 7. The tidal co-amplitude and co-phase chart for the 4 major tidal constituents of Case 1. (a) is M₂, (b) is S₂, (c) is K₁, and (d) is O₁.

Fig. 8. The tidal co-amplitude and co-phase chart for the M₂ tidal constituent of each case. (a) is Case 2(f = 1 × 10^-4, (b) is Case 3(f = 0), (c) Case 4(A_z ≦ 0.001), and (d) is Case 5(A_z ≦ 0.01).

Fig. 9. The tidal co-amplitude and co-phase chart for the K₁ tidal constituent of each case. (a) is Case 2(f = 1 × 10^-4, (b) is Case 33(f = 0), (c) Case 4(A_z 0.001), and (d) is Case 5(A_z ≦ 0.01).

Fig. 10. The comparison of amplitude and phase of M₂, K₁ constituent for each case. (a) is M₂ amplitude, (b) is K₁ amplitude, (c) is M₂ phase, and (d) is K₁ phase.

Table 1. Julia model files and contents

Table 2. The raw and adjusted harmonic constants for open boundary forcing

Table 3. The model test cases in two scenarios, the simple channel and Yellow Sea

Table 4. The root mean square error for the amplitude and the phase of the 4 major tidal constituents in each case