Targeted observation for the climatology temperature in the Kuroshio region based on the CNOP approach

To reduce the cost of ocean observations and improve prediction accuracy of the Kuroshio region temperature, this study investigates the related targeted observation by using the conditional nonlinear optimal perturbation (CNOP) approach. Results show that the scheme of vertical-integrated energy is more suitable for the identification of sensitive area in the related targeted observation. By conducting a set of observation system simulation experiments (OSSEs), we discovered that the sensitive areas identified by the CNOP exert substantial influence on temperature predictions within the target area. The dynamic diagnosis further indicated that the pressure gradient and Coriolis force in the momentum equations greatly contribute the development of the prediction biases. These findings implied that the implement of CNOP-based targeted observation represents a cost-effective strategy for enhancing temperature predictions in the Kuroshio region.


Introduction
As the western boundary current of the wind-driven subtropical gyre in the North Pacific, the Kuroshio exerts a distinctive influence on a wide range of human activities.Therefore, accurate prediction in this area holds paramount importance.
Currently, ocean observation is indispensable for accurate prediction.Previous studies have noted that oceanic numerical prediction is sensitive to the initial conditions (ICs) and reliable ICs provided by assimilation of ocean observation is an effective way to improve oceanic numerical prediction [1], [2], [3].Nevertheless, owing to the substantial expenses associated with ocean observation, it is necessary to design the observation strategy and implement key observation to optimize observation resources [4].Targeted observation is such a strategy by implementing additional observation in specific region (called sensitive area) for better ICs estimation.To date, targeted observation has been found extensive application in the examination of high-impact atmospheric and oceanic event predictions [5], [6], [7], [8].
A vital issue in targeted observation is identifying the sensitive area, which guided the optimal location for observing.Currently, several approaches have been adopted for identifying the sensitive area.Among them, the approach proposed by Mu et al. (2003) [9] and named conditional nonlinear optimal perturbation (CNOP) has shown potential on identifying the sensitive area in the oceanic targeted observation.Previous studies have shown that the observation guided by the CNOP-based sensitive area effectively enhances temperature predictions in the waters surrounding China [10], [11], [12].
The structure of this paper is as follows: Section 2 outlined the Regional Ocean Modeling System (ROMS) and the CNOP approach.Section 3 described the identification of sensitive area.Section 4 presented the process of OSSEs and dynamic diagnosis.Section 5 presented the results of this study.

Model Simulation
The ROMS, which offers a range of parameterization schemes for horizontal diffusion and vertical mixing [13], is adopted in this study to simulate the dynamic and thermal environment of the East China Sea.
The model domain (Figure 1) spans from 23.7°N to 41.3°N meridionally and 117°E to 133°E zonally with a resolution of 1/12° (5km×5km).It has 506×302 horizontal grid points and 32 vertical levels, which are refined in the upper ocean with   = 6 and   = 0.The initial and boundary conditions are interpolated from the HYCOM.The forcing conditions, including heat flux and shortwave radiation flux, are derived from the ECMWF.The bathymetric data utilized in this study are derived from the ETOPO2.In addition, the K-profile vertical parameterization [14], the Flather and Radiation + Nudging boundary conditions are adopted in this study.

CNOP and its calculation
The governing equations of the nonlinear model can be written in a general form: where  represents the vector of model state variables including sea surface level, velocities, ocean temperature and salinity,  0 represents the  at initial time, and F represents the partial differential operator.The solution of the nonlinear model is denoted as: where  is the nonlinear propagator of discrete F;  t is the state vectors at the prediction time t.According to Mu et al. (2003) [9], the initial perturbation δx * is called CNOP, if and only if: where J(δx) is the objective function used to estimate the nonlinear evolution of δx at the prediction time t.β is the constraint of initial perturbation δx.
In practical applications, it is essential to define the objective function and initial constraint to suit the particular problem under consideration.To assess the influence of initial errors in temperature prediction, the quadratic sum of temperature prediction errors within the target area is denoted as the objective function: where the target area is set to (27.0°N-29.0°N,125°E-127°E) in this study, and the initial constraint is expressed as follows: where T 0 ′ (U 0 ′ , V 0 ′ , S 0 ′ , η 0 ′ ) is the perturbation of the temperature (zonal velocities, meridional velocities, salinity and sea surface level), respectively.We use its standard deviation to make it nondimensional.
In addition, the adjoint-free algorithm proposed by Wang et al. ( 2009) [15] is used in this study to calculate the CNOP.

Identification of sensitive area
We firstly compared the sensitive area identified by CNOP and determined by three different schemes (shown in Figure 2), namely the scheme of vertical-integrated energy, single-point energy and horizontal-projection.The above three scheme is detailed in Zhou and Zhang (2014) [16].To compare the quality of the above three sensitive areas, the evolution of the CNOP total energy in the target area measured by the decreasing percentage of [G i,j (X cnop ) − G i,j (X cnop /2)] G i,j (X cnop ) ⁄ is examined (shown in Figure 3), where the CNOP energy is approximately defined by: where U a (V a , T a , η a ) is the standard deviation of U (V, T and η), which is derived from the statistics of the historical prediction perturbation samples and set to 0.52 (0.36,1.2,0.16).Figure 3 shows a significant difference among the three schemes.The scheme based on vertical-integrated energy consistently exhibits the highest percentage decrease of CNOP total energy as compared to the other two schemes.Therefore, the scheme of vertical-integrated energy is used to the identification of sensitive area in this study.

OSSEs
To assess the effect of sensitive area determined by the scheme of vertical-integrated energy, the following OSSEs is designed.We use the HYCOM as the non-perturbated initial condition (denoted as ICT), and use a perturbated ensemble as the perturbated initial condition (denoted as ICP) so as to form a control experiment.As shown in Table 1, five comparative experiments with different observing strategies are formulated and denoted as CE1, CE2, CE3, CE4, and CE5, respectively.CE1 is identical to the control experiment with the sole distinction being the substitution of ICP in the CNOP-based sensitive area with ICT.We limit the size of CNOP-based sensitive area by selecting the first 1% of all oceanic grids in a sequence ranked from the descending order of the CNOP norm.That is to say only 1% of oceanic grids have been 'observed'.While CE2, CE3, CE4, and CE5 are the same as CE1, except that their pseudo-observations are distributed in the target area, evenly distributed in the whole model grid, in the south of target area and the west of target area (shown in Figure 4).The target-area averaged root mean square errors (RMSEs) of temperature predictions is applied to evaluate the results of OSSEs.  Figure 5 shows the evolution of RMSEs averaged in the target area.The observations implemented in the CNOP-based sensitive area (green line) result in the larger reduction of the RMSEs compared to that induced by observations implemented in the target area (blue line).In addition, there are only marginal reductions of the RMSEs at the end of the prediction time when the observations are distributed evenly distributed in the whole model grid (red line), in the south of target area (yellow line) and in the west of target area (purple line).These findings implied that the implement of CNOP-based targeted observation is effective in enhancing temperature predictions in the Kuroshio region.
where x, y, and z are the Cartesian coordinates;  and  are zonal and meridional components of velocity; (x, y, z, t) is the dynamic pressure;   is the vertical eddy viscosity coefficient;  is the molecular viscosity coefficient; (x, y) is the Coriolis parameter;  represents the exogenic forcing;  represents the horizontal diffusion, respectively.Term I to Term IV in the equations ( 7) and ( 8) are referred to as Pressure gradient, friction stress, Coriolis force, nonlinear advection and diffusion, respectively.As depicted in Figures 6a and 6b, the biases of pressure gradient (Term I) and Coriolis force (Term III) are of comparable magnitude but of opposite signs and obviously much larger than that of Term II and Term IV.This implies that the prediction biases in the target area are mainly induced by the pressure gradient and Coriolis force.In other words, the friction stress and the nonlinear advection and diffusion make trivial contribution to the development of the prediction biases.

Summary
With the CNOP approach and the ROMS model, the targeted observation for the climatology temperature in the Kuroshio region was investigated in this study.We employed different determined schemes to identify the CNOP-based sensitive area and found that the scheme of vertical-integral energy is effective.Subsequently, we designed a set of OSSEs to evaluate the effect of the CNOP-based sensitive area determined by the scheme of vertical-integral energy.The results implied that the implement of CNOP-based targeted observation is effective in enhancing temperature predictions in the Kuroshio region.In addition, the dynamic diagnosis further indicated that the Pressure gradient and Coriolis force in the momentum equations make great contribution to the development of the prediction biases, while the friction stress and the nonlinear advection and diffusion have tiny impact.
This study revealed that the targeted observation guided by the CNOP approach could be useful to design an observation network in the Kuroshio region.However, only one target area case in this paper was evaluated by OSSEs owing to the limitations of computational resource.More cases will be explored in our future work.In addition, more details on field-deployed observation design, including the variables and depth range to be observed, will also be investigated in the continued work.

Figure 1 .
Figure 1.The bathymetry (units: m) of the model domain.

Figure 2 .
Figure 2. CNOP-based sensitive area determined by (a) the scheme of vertical-integrated energy; (b) the scheme of single point energy and (c) the scheme of horizontal projection.

Figure 3 .
Figure 3.The decrease percentage of CNOP total energy induced by different schemes.

Figure 5 .
Figure 5.The evolution of RMSEs averaged in the target area.

Figure 6 .
Figure 6.The evolutions of biases induced by each term.(a) represents the zonal momentum equations.(b) represents the meridional momentum equations.

Table 1 .
Design of the OSSEs To analyse the mechanisms of initial errors in the CNOP-based sensitive area on affecting the prediction in the target area in terms of nonlinear ocean dynamics, we employed the following vertically integrated momentum equations: