An assessment of upper ocean salinity content from the Ocean Reanalyses Inter-comparison Project (ORA-IP)

Abstract

Many institutions worldwide have developed ocean reanalyses systems (ORAs) utilizing a variety of ocean models and assimilation techniques. However, the quality of salinity reanalyses arising from the various ORAs has not yet been comprehensively assessed. In this study, we assess the upper ocean salinity content (depth-averaged over 0–700 m) from 14 ORAs and 3 objective ocean analysis systems (OOAs) as part of the Ocean Reanalyses Intercomparison Project. Our results show that the best agreement between estimates of salinity from different ORAs is obtained in the tropical Pacific, likely due to relatively abundant atmospheric and oceanic observations in this region. The largest disagreement in salinity reanalyses is in the Southern Ocean along the Antarctic circumpolar current as a consequence of the sparseness of both atmospheric and oceanic observations in this region. The West Pacific warm pool is the largest region where the signal to noise ratio of reanalysed salinity anomalies is >1. Therefore, the current salinity reanalyses in the tropical Pacific Ocean may be more reliable than those in the Southern Ocean and regions along the western boundary currents. Moreover, we found that the assimilation of salinity in ocean regions with relatively strong ocean fronts is still a common problem as seen in most ORAs. The impact of the Argo data on the salinity reanalyses is visible, especially within the upper 500 m, where the interannual variability is large. The increasing trend in global-averaged salinity anomalies can only be found within the top 0–300 m layer, but with quite large diversity among different ORAs. Beneath the 300 m depth, the global-averaged salinity anomalies from most ORAs switch their trends from a slightly growing trend before 2002 to a decreasing trend after 2002. The rapid switch in the trend is most likely an artefact of the dramatic change in the observing system due to the implementation of Argo.

Appendix

Multi-system ensemble mean

In this study, the $X_{n}^{A}$ represents the anomaly (seasonal cycle removed) of corresponding total variable $X_{n}^{{}}$ for individual n ORA. Thus, the multi-system ensemble mean (i.e., EMORA) of $X_{n}^{{}}$ or $X_{n}^{A}$ from the 14 ORAs can be given by:

$$\overline{{X_{EMORA} }} = \frac{1}{nsys}\sum\limits_{n = 1}^{nsys} {X_{n} } \quad {\text{or}}\quad \overline{{X_{EMORA}^{A} }} = \frac{1}{nsys}\sum\limits_{n = 1}^{nsys} {X_{n}^{A} }$$

(1)

The nsys represents the total number of all ORAs for calculating EMORA (nsys = 14). The corresponding $\overline{{X_{EMOO} }}$ or $\overline{{X_{EMOO}^{A} }}$ can be similarly calculated by the Eq. (1) except for the $X_{n}^{{}}$ or $X_{n}^{A}$ of individual n OOA and nsys = 3.

Ensemble spread (SPD)

The ensemble spread of different variables X from 14 ORAs about their corresponding EMORA shown in Figs. 1c, 6b and 8c is given by:

$$SPD_{EMORA}^{X} (i,j) = \sqrt {\frac{1}{nsys}\sum\limits_{n = 1}^{nsys} {\left( {X_{n} \left( {i,j} \right) - \overline{{X_{EMORA} }} \left( {i,j} \right)} \right)^{2} } }$$

(2)

Here, the X represents the annual mean (AM) of S700 in Fig. 1c (i.e., $SPD_{EMORA}^{AM}$), the correlation of S700 anomalies in Fig. 6b and the correlation of T700–S700 anomalies in Fig. 8c (i.e., $SPD_{EMORA}^{COR}$), respectively. The i/j represents the longitude/latitude, respectively.

Similarly, the $SPD_{EMORA}^{A} (i,j)$, that is shown in Fig. 5a, can be calculated as:

$$SPD_{EMORA}^{A} (i,j) = \sqrt {\frac{1}{mons}\sum\limits_{t = 1}^{mons} {\frac{1}{nsys}} \sum\limits_{n = 1}^{nsys} {\left( {X_{n}^{A} \left( {i,j,t} \right) - \overline{{X_{EMORA}^{A} }} \left( {i,j,t} \right)} \right)^{2} } }$$

(3)

Here, the $X_{n}^{A} \left( {i,j,t} \right)$ denotes the S700 anomalies for individual n ORA. The mons is the total number of months for the variable X (i.e., mons = 216 for the period 1993–2010).

Uncertainty range (UCR)

The uncertainty range (i.e., the shaded band shown in Fig. 2) of the meridionally-averaged AMS700 (i.e., X) from 14 ORAs about their corresponding EMORA (i.e., $\overline{{X_{EMORA} }}$) is defined as:

$$UCR_{EMORA}^{AM} (i) = \overline{{X_{EMORA} }} (i) \pm SPD_{EMORA}^{AM} (i)$$

(4)

Here, the $SPD_{EMORA}^{AM} (i)$ can be calculated by the Eq. (2) but without the dimension j. The UCR shown in Figs. 4, 7 and 9 can be similarly calculated by the Eq. (4) except that the variable X should be replaced by standard deviation for Fig. 4, the correlation coefficients for Figs. 7 and 9, respectively. In addition, the UCR shown in Fig. 3, where the X represents the seasonal cycle of S700, can be also calculated by the Eq. (4) except for replacing the dimension i by the dimension t.

The $UCR_{EMORA}^{A} (z,t)$ shown in Fig. 11 is given by:

$$UCR_{EMORA}^{A} (z,t) = \overline{{X_{EMORA}^{A} }} (z,t) \pm SPD_{EMORA}^{A} (z,t)$$

(5)

Here, the $\overline{{X_{EMORA}^{A} }} \left( {z,t} \right)$ denotes the global averaged salinity anomaly in different ocean layers z for EMORA. And, the $SPD_{EMORA}^{A} (z,t)$ is calculated as:

$$SPD_{EMORA}^{A} (z,t) = \sqrt {\frac{1}{nsys}\sum\limits_{n = 1}^{nsys} {\left( {X_{n}^{A} \left( {z,t} \right) - \overline{{X_{EMORA}^{A} }} \left( {z,t} \right)} \right)^{2} } }$$

(6)

Here, the $X_{n}^{A} (z,t)$ denotes the global averaged salinity anomaly in different ocean layers z for the individual n ORA.

Standard deviation (STD)

The STD of the meridionally-averaged S700 anomalies (i.e., $X_{n}^{A} (i,t)$) for individual n ORA (i.e., $STD_{n}^{A} (i)$) and the corresponding EMORA (i.e., $STD_{EMORA}^{A} (i)$), which is shown in Fig. 4, is respectively given by:

$$STD_{n}^{A} (i) = \sqrt {\frac{1}{mons}\sum\limits_{t = 1}^{mons} {\left( {X_{n}^{A} \left( {i,t} \right)} \right)^{2} } }$$

(7)

and

$$STD_{EMORA}^{A} (i) = \sqrt {\frac{1}{mons}\sum\limits_{t = 1}^{mons} {\left( {\overline{{X_{EMORA}^{A} }} \left( {i,t} \right)} \right)^{2} } }$$

(8)

The corresponding $STD_{EMOO}^{A} (i)$ in Fig. 4 can be similarly calculated by the Eq. (8) except for replacing the $\overline{{X_{EMORA}^{A} }} \left( {i,t} \right)$ by the $\overline{{X_{EMOO}^{A} }} \left( {i,t} \right)$. Additionally, the STD of S700 anomaly for EMORA (i.e., $STD_{EMORA}^{A} (i,j)$), which is shown in Fig. 5b, can be also calculated by Eq. (8) except for adding the dimension j.

Centred pattern correlation (CPCOR)

The centred pattern correlation (i.e., CPCOR(z t)) of salinity anomalies (seasonal cycle removed) between EMORA (i.e., $\overline{{X_{EMORA}^{A} }} (i,j,z,t)$) and EMOO (i.e., $\overline{{X_{EMOO}^{A} }} (i,j,z,t)$) as a function of depth (0–1500 m) and time (1993–2010), which is shown in Fig. 10, is defined as:

$$CPCOR(z,t) = {{\left[ {\frac{1}{m \times n}\sum\limits_{j = 1}^{n} {\sum\limits_{i = 1}^{m} {\left( {\left( {\overline{{X_{EMORA}^{A} }} (i,j,z,t) - M_{EMORA} } \right)\,\left( {\overline{{X_{EMOO}^{A} }} (i,j,z,t) - M_{EMOO} } \right)} \right)} } } \right]} \mathord{\left/ {\vphantom {{\left[ {\frac{1}{m \times n}\sum\limits_{j = 1}^{n} {\sum\limits_{i = 1}^{m} {\left( {\left( {\overline{{X_{EMORA}^{A} }} (i,j,z,t) - M_{EMORA} } \right)\,\left( {\overline{{X_{EMOO}^{A} }} (i,j,z,t) - M_{EMOO} } \right)} \right)} } } \right]} {\left( {S_{EMORA} S_{EMOO} } \right)}}} \right. \kern-0pt} {\left( {S_{EMORA} S_{EMOO} } \right)}}$$

(9)

Here, the m/n denotes total longitude/latitude grids of the calculated ocean band. The $M_{EMORA} /M_{EMOO}$ denotes the total mean of the $\overline{{X_{EMORA}^{A} }} (i,j,z,t)/\overline{{X_{EMOO}^{A} }} (i,j,z,t)$ over the calculated ocean band, respectively. Thus, the $M_{EMORA}$ can be given by:

$$M_{EMORA} = \frac{1}{m \times n}\sum\limits_{j = 1}^{n} {\sum\limits_{i = 1}^{m} {\overline{{X_{EMORA}^{A} }} (i,j,z,t)} }$$

(10)

The $M_{EMOO}$ can be similarly calculated by the Eq. (10) except for replacing the $\overline{{X_{EMORA}^{A} }}$ by the $\overline{{X_{EMOO}^{A} }}$. The S _EMORA /S _EMOO in Eq. (10) denotes the spatial standard deviations of the $\overline{{X_{EMORA}^{A} }} /\overline{{X_{EMOO}^{A} }}$, respectively. The S _EMORA can be obtained by:

$$S_{EMORA} (z,t) = \sqrt {\frac{1}{m \times n}\sum\limits_{j = 1}^{n} {\sum\limits_{i = 1}^{m} {\left( {\overline{{X_{EMORA}^{A} }} (i,j,z,t) - M_{EMORA} } \right)^{2} } } }$$

(11)

The corresponding S _EMOO can be also obtained by the Eq. (11) except for replacing the $\overline{{X_{EMORA}^{A} }}$ by the $\overline{{X_{EMOO}^{A} }}$.