An Objective Algorithm for Reconstructing the Three-Dimensional Ocean Temperature Field Based on Argo Profiles and SST Data

Home , Argo (oceanography), Sea surface temperature

Ocean Dynamics DOI 10.1007/s10236-017-1104-x

An objective algorithm for reconstructing the three-dimensional ocean temperature field based on Argo profiles and SST data

1,2 1 2 2 1 Chaojie Zhou & Xiaohua Ding & Jie Zhang & Jungang Yang & Qiang Ma

Received: 12 June 2017 /Accepted: 19 September 2017 # Springer-Verlag GmbH Germany 2017

Abstract While global oceanic surface information with large- resolution (0.25° ×0.25°), resulting in the capture of smaller- scale, real-time, high-resolution data is collected by satellite scale characteristics. Finally, both the accuracy and the superi- remote sensing instrumentation, three-dimensional (3D) obser- ority of the algorithm are validated. vations are usually obtained from in situ measurements, but with minimal coverage and spatial resolution. To meet the Keywords Three-dimensional temperature reconstruction . needs of 3D ocean investigations, we have developed a new Argo temperature profile . Sea surface temperature . Fitting algorithm to reconstruct the 3D ocean temperature field based method . Vertical temperature gradient on the Array for Real-time Geostrophic Oceanography (Argo) profiles and sea surface temperature (SST) data. The Argo temperature profiles are first optimally fitted to generate a series of 1 Introduction temperature functions of depth, with the vertical temperature structure represented continuously. By calculating the deriva- Various remote sensing instruments, such as an altimeter, tives of the fitted functions, the calculation of the vertical tem- scatterometer and radiometer, are designed to collect informa- perature gradient of the Argo profiles at an arbitrary depth is tion of the ocean surface, including the sea surface tempera- accomplished. A gridded 3D temperature gradient field is then ture (SST) and height (SSH). Accordingly, a considerable found by applying inverse distance weighting interpolation in amount of observations of high resolution with a global cov- the horizontal direction. Combined with the processed SST, the erage have been gathered. Unfortunately, the derived informa- 3D temperature field reconstruction is realized below the sur- tion generally only focuses on the sea surface without direct face using the gridded temperature gradient. Finally, to confirm investigation of the vertical structure of the deeper ocean. the effectiveness of the algorithm, an experiment in the Pacific Since 1998, over 1.5 million profiles have been collected Ocean south of Japan is conducted, for which a 3D temperature within the Array for Real-time Geostrophic Oceanography field is generated. Compared with other similar gridded prod- (Argo) project, which has built a real-time global ocean ob- ucts, the reconstructed 3D temperature field derived by the servation system for sampling the upper 2000 m of the ocean, proposed algorithm achieves satisfactory accuracy, with corre- thereby making available temperature and salinity (T-S) ob- lation coefficients of 0.99 obtained, including a higher spatial servations with a global coverage (Riser et al. 2016). While the data coverage and volume exceed all previous traditional Responsible Editor: Guoping Gao observations, the resolution and distribution of the profiles are insufficient in space and time. Therefore, to meet the needs of * Chaojie Zhou 3D ocean investigations, the high-resolution reconstruction of [email protected] the 3D temperature and salinity fields based on the available data is becoming a significant research issue. 1 Department of Mathematics, Harbin Institute of Technology at Since the 1980s, several methods have been proposed to Weihai, Weihai 264209, China reconstruct the 3D temperature and salinity field from sea 2 The First Institute of Oceanography, State Oceanic Administration, surface information (Guinehut et al. 2004;Carnesetal. No. 6 Xianxialing Road, Qingdao 266061, China 1994;NardelliandSantoleri2004), including physical Ocean Dynamics methods, data assimilation technology within an ocean model, Below, the data is introduced in Section 2, Section 3 refers and statistical methods. By taking characteristics of the water to the details of the algorithm process, while Section 4 de- movement and energy exchange into consideration, Hurlburt scribes the implementation and validation of the application (1986) built a numerical ocean model to dynamically transfer experiment, including the determination of the initial condi- simulated altimeter data into subsurface information. The tions, vertical gradient, and the comparison with other existing model reconstructs the deep pressure field even for situations Argo products. Some final remarks are then provided. with energetic shallow and deep circulations, baroclinic instability and a vigorous vertical exchange of energy. However, the investigation was a pure simulation and the 2Data dynamic transfer of information was not feasible for the ocean or for all regions of parameter space relevant to the 2.1 Argo profiles ocean. Chu et al. (1997a, b) developed a thermal parametric model to analyze observed regional sea temperature profiles Argo temperature profiles are obtained from the Argo Real- based on a layered structure of the temperature fields. Though Time Data Center of China (http://www.argo.org.cn/). After some characteristics of each profile were obtained, including quality control, 83 reasonable profiles are retained, with the the mixed layer depth (MLD), thermocline depth and details of every profile employed in the experiment presented thermocline temperature gradient, reconstruction of the 3D in Table 1, including the profile number, measurement time, temperature field proved difficult due to the original prupose and position. The experimental domain and original Argo of the designed model. Yan et al. (2004) proposed a data profiles are shown in Fig. 1.Inthedevelopedalgorithm, assimilation scheme based on 3D variational analysis every profile is optimally fitted to obtain the continuous (3DVAR) to estimate T-S profiles from surface dynamic vertical variation of the temperature gradient, from which we height information. Both vertical correlations for temperature obtain a gridded 3D gradient field by application of the and salinity background errors, as well as the nonlinear T-S inverse distance weighted (IDW) method horizontally. relation, were taken into consideration. While the results of the designed experiment showed potential usefulness in altimetry 2.2 Sea surface temperature data assimilation, the conducted experiment does not represent the complicated nature of the ocean state satisfactorily. To The National Oceanic and Atmospheric Administration meet the U.S. Navy’s requirement for rapid estimates of pres- (NOAA) Advanced Very High Resolution Radiometer ent and near-term ocean conditions, Fox et al. (2002)com- (AVHRR) 1/4° daily Optimum Interpolation Sea Surface bined in situ measurements, remotely sensed temperatures and Temperature (or daily OISST) is an analysis constructed by heights to form a single integrated analysis of temperature and combining observations from different platforms (satellites, salinity on a regular grid. The regression coefficients relating ships, buoys) on a regular global grid (Reynolds et al. 2007). the subsurface temperature to the SSH and SST were calculat- Here, the AVHRR SST data is applied to initialize the recon- ed based on a large number of in situ T-S profiles. struction algorithm at the surface. Combined with the vertical Benefiting from the Argo project, many near real-time temperature gradient obtained by the fitted Argo temperature monthly global gridded ocean T-S productions have been de- profiles, the surface temperature information may be readily veloped (e.g., Jamestec-Argo (Hosoda et al. 2008), transferred downward to the subsurface. Roemmich-Argo (Roemmich and Gilson 2009), EN4-Argo (Good et al. 2013), and BOA-Argo (Li et al. 2017)) by merg- 2.3 Validation data ing Argo T-S observations into a climatological initial condition directly based on optimum interpolation or more sophis- According to the analysis of Li et al. (2017), we select two of ticated variational analysis methods (Troupin et al. 2010). the existing Argo-derived gridded products, the version 4 of However, the smaller-scale signals from the original observa- the Met Office Hadley Centre BEN^ series of data sets (EN4) tional data have been smoothed and concealed, and the hori- and Barnes objective analysis (BOA)-Argo datasets, to vali- zontal resolution of the most recent productions is 1° ×1°, date the reconstructed temperature, because of their good per- which is insufficient for mesoscale research. formance. The EN4 dataset is generated by the optimal inter- A new algorithm is proposed here to construct a monthly polation method, where the climatological World Ocean Atlas oceanic 3D temperature field with a horizontal resolution of (WOA98) is considered as the background. Moreover, tem- 0.25° ×0.25°, which is realized by the combination of Argo perature and salinity information from all types of ocean pro- temperature profiles and SST data. To validate the effective- filing instruments are merged. Unlike the EN4 dataset, the ness of the algorithm, an experiment is performed for the background condition of the BOA-Argo dataset is generated Pacific Ocean south of Japan (25° N–32° N, 136° E–143° from original Argo observations by the Cressman scheme, so E) with a gridded temperature product for January 2009. that signals from the original data are retained, with the noise Ocean Dynamics

Table 1 The Argo profiles (number, date, longitude, and latitude) used in the reconstruction algorithm

Number Date Lon (°E) Lat (°N) Number Date Lon (°E) Lat (°N)

2900157_332 2009-01-02 141.491 26.962 2900683_074 2009-01-26 137.435 27.090 2900157_333 2009-01-07 141.583 26.953 2900686_070 2009-01-16 137.494 25.191 2900157_334 2009-01-12 141.599 27.032 2900686_071 2009-01-27 137.109 25.327 2900157_335 2009-01-17 141.773 27.091 2900688_059 2009-01-04 142.803 30.138 2900157_336 2009-01-22 141.975 27.342 2900688_060 2009-01-14 142.300 30.176 2900157_337 2009-01-27 142.018 27.301 2900688_061 2009-01-24 141.889 29.975 2900489_261 2009-01-01 141.741 27.709 2900715_090 2009-01-06 136.392 26.340 2900489_262 2009-01-06 141.747 27.983 2900715_091 2009-01-11 136.216 26.655 2900489_263 2009-01-11 141.658 28.464 2900715_092 2009-01-16 136.172 26.889 2900489_264 2009-01-16 141.558 28.782 2900719_016 2009-01-03 138.391 31.683 2900489_265 2009-01-21 141.603 28.946 2900719_017 2009-01-09 138.595 31.267 2900489_266 2009-01-26 141.676 29.090 2900719_018 2009-01-13 138.648 30.945 2900489_267 2009-01-31 141.800 29.152 2900719_019 2009-01-18 138.731 30.842 2900501_263 2009-01-03 139.388 31.022 2900719_020 2009-01-23 138.676 30.775 2900501_264 2009-01-08 139.548 30.928 2900719_021 2009-01-29 138.659 30.772 2900501_265 2009-01-13 139.387 30.639 2900725_034 2009-01-02 137.518 27.052 2900501_266 2009-01-18 139.203 30.600 2900725_035 2009-01-12 137.513 26.936 2900501_267 2009-01-23 139.291 30.464 2900725_036 2009-01-22 137.772 26.702 2900501_268 2009-01-28 139.046 30.357 2900752_014 2009-01-08 142.083 25.770 2900510_107 2009-01-11 139.005 26.868 2900752_015 2009-01-18 141.606 25.944 2900510_108 2009-01-22 139.648 26.563 2900752_016 2009-01-28 141.301 26.053 2900512_201 2009-01-04 138.196 28.256 2900815_131 2009-01-01 137.770 29.708 2900512_202 2009-01-08 138.080 28.049 2900815_133 2009-01-06 138.203 29.405 2900512_203 2009-01-12 138.097 27.828 2900815_135 2009-01-10 138.316 29.210 2900512_204 2009-01-16 138.236 27.691 2900815_137 2009-01-13 138.265 28.687 2900512_205 2009-01-20 138.321 27.599 2900815_139 2009-01-17 138.378 28.176 2900512_206 2009-01-24 138.454 27.552 2900815_141 2009-01-22 138.665 27.914 2900512_207 2009-01-28 138.665 27.457 2900815_145 2009-01-30 139.623 27.708 2900582_121 2009-01-02 136.467 27.920 2900819_131 2009-01-01 136.097 30.193 2900582_122 2009-01-07 136.415 28.234 2900936_007 2009-01-05 142.330 31.635 2900582_123 2009-01-12 136.202 28.610 5900997_109 2009-01-08 137.056 25.329 2900582_124 2009-01-17 136.150 28.905 5900997_110 2009-01-18 136.840 25.488 2900582_125 2009-01-22 136.232 29.067 5900997_111 2009-01-28 136.389 25.670 2900582_126 2009-01-27 136.431 29.109 5901533_067 2009-01-06 139.964 25.820 2900665_139 2009-01-01 137.857 31.306 5901533_068 2009-01-16 139.821 25.631 2900665_140 2009-01-06 137.862 31.092 5902094_013 2009-01-09 140.074 27.765 2900665_141 2009-01-11 137.972 31.033 5902094_014 2009-01-19 140.142 27.842 2900665_142 2009-01-16 137.872 30.828 5902094_015 2009-01-29 140.108 28.114 2900665_143 2009-01-21 137.690 30.578 5902096_012 2009-01-03 140.854 28.313 2900665_144 2009-01-26 137.504 30.306 5902096_013 2009-01-14 140.694 28.545 2900665_145 2009-01-31 137.269 30.079 5902096_014 2009-01-24 140.355 28.785 2900683_072 2009-01-06 137.250 27.380 from other analyzed fields eliminated. Therefore, the BOA- 3 Algorithm description Argo dataset captures some mesoscale features better than other gridded Argo datasets. Hence, because of the relatively The vertical structure of the 3D temperature field of the ocean superior quality of these two datasets, both are applied to varies considerably depending on the location. The simple validate the efficiency of the proposed algorithm. model of Chu et al. (2000) is not accurate enough to represent Ocean Dynamics

Argo temperature profile is optimally fitted, the corresponding vertical temperature gradient is calculated. In the following, some details of the fitting process, including the calculation of the vertical temperature gradient, are

illustrated. Let hb represent the MLD determined from the Argo measurements, so that the measurements of a profile are separated into two groups. For measurements within the

mixed layer whose measurement depth satisfies h ≤ hb,a piecewise linear fitting method is applied. Supposing (hi, T(xA, yA, hi)) and (hi +1, T(xA, yA, hi +1)) represent two arbitrary adjacent measurements in the mixed layer, the derived

temperature function T(xA, yA, h) between the two points can be represented as

TxA; y ; h TxA; y ; hi ðÞ¼A ðÞA

Gi xA; yA ⋅ h−hi ; hi ≤h≤hi 1 ≤hb ; 1 Fig. 1 Experimental domain (black box) and Argo profiles (red dots) þ ðÞðÞðÞþ ð Þ during January 2009 where Gi(xA, yA)istheverticaltemperaturegradientfrom the vertical characteristics of the ocean temperature, in which (hi, T(xA, yA, hi)) to (hi +1, T(xA, yA, hi +1)), which is calcu- the constant, linear and exponential function of depth are lated by employed to describe the 3D temperature in the mixed layer, 0 T xA; y ; h and the thermocline and abyssal layers, respectively. ðÞA Considering the authenticity of Argo in situ observations TxA; yA; hi 1 −TxA; yA; hi (Riser et al. 2016), the actual vertical temperature variation Gi xA; yA ðÞþ ðÞ: 2 ¼ ðÞ¼ hi 1−hi ð Þ may be represented. However, the sampling points of a single þ temperature profile are discrete in the vertical direction. To For the measurements beyond the MLD hb,themulti- acquire the 3D temperature structure continuously, we apply Gaussian fitting procedure is used to fit the temperature varia- N a fitting method to every single Argo temperature profile to 2 tion, which generally has the form ∑ ai exp − x−bi =ci , obtain a series of temperature functions T(xA, yA, h), where i 1 ðð ðÞÞ Þ ¼ xA, yA are the longitude and latitude of the Argo profile, re- where ai, bi,andci are the parameters to be determined by the spectively, and h is the depth of the measurements. The verti- least-squares method (Lawson and Hanson 1974), and N rep- cal gradient of temperature at an arbitrary depth is calculated resents the Gaussian order. The appropriate choice for the algo- ′ by the function T (xA, yA, h). Then, by applying the IDW meth- rithm is discussed in Section 4.2.Thefittedtemperaturebelow od horizontally, the 3D vertical temperature gradient field is the MLD is written as calculated. As remote sensing instrumentation provides global TxA; y ; h temperature information at the surface, the 3D temperature ðÞA field is reconstructed by the incorporation of SST and vertical N 2 ai exp h bi =ci ; h > h ; 3 temperature gradients. ∑ xA;y − − xA;y xA;y b ¼ i 1 A A A ðÞð Þ To begin the reconstruction, the fitted temperature func- ¼ ′ tion T(xA, yA, h)anditsderivativeT (xA, yA, h)shouldfirst where it is worth mentioning that these parameters of the dif- be determined. Since the temperature variation in the ferent profiles are not the same. Because the function T(xA, yA, mixed layer is smaller, and the density of Argo measure- h)iscontinuouslydifferentiablewhenh > hb,itsderivativeis ments is more centralized than the layers below, a single calculated by fitting procedure for the whole profile is difficult to realize. 2 0 i i As shown in Fig. 2,themeasurementsofthetemperature T xA; yA; h −2 ∑ a =c ðÞ¼xA;yA xA;yA profile are divided into two parts based on the MLD, in- i cluding that above and below the MLD. Considering the 2 h−bi exp − h−bi =ci : irregular fluctuations within the mixed layer, a piecewise Â xA;yA xA;yA xA;yA linear fitting strategy is adopted. The higher measurement 4 density allows a linear estimation between two adjacent ð Þ measurements, so that any error introduced is limited. By applying the piecewise fitting method to every single Below the MLD, we apply a multi-Gaussian fitting method profile, we obtain a series of temperature variation functions to approximate the temperature variation. After the whole of depth denoted as {T(x1, y1, h), T(x2, y2, h), ⋯, T(xNA, yNA, Ocean Dynamics

Fig. 2 Strategy to divide the Argo profiles based on the MLD. The red dot represents the estimation of the MLD, with fourth-order Gaussian fitting used for profile fitting below the MLD

h)}, where NA is the total number of the original Argo profiles. Additionally, the reconstruction is initialized at depth hmin Once the fitting process for all Argo profiles is completed, the rather than h = 0. The flowchart of the whole algorithm is vertical temperature gradient at an arbitrary depth is calculated presented in Fig. 3. at the horizontal position of the Argo profile. Using the IDW method in the horizontal direction, a 3D temperature gradient ′ field T (xg, yg, h)isconstructed,where(xg, yg) is a horizontally 4 Algorithm implementation and validation meshed grid. Hence, there exists a relation between the temperature field and its gradient An experiment in the Pacific Ocean south of Japan is conducted to validate the algorithm. First, the initial conditions of the dT xg; yg; h reconstruction are modified by the regression analysis, which 0 T xg; y ; h ; 5 dh ¼ g ð Þ aims to build a linear relationship between the shallowest measurements of the Argo profiles and the SST data obtained with the initial condition T0 (h = 0) at (xg, yg)enablingcon- by remote sensing. The piecewise fitting process of each Argo struction of the 3D temperature field using a numerical proce- profile is then conducted accompanied by the calculation of dure to solve Eq. 5. the vertical temperature gradient. To obtain the 3D tempera- Fortunately, as many global SST products with high spatial ture gradient field, the IDW method is employed horizontally. resolution have been developed, they may be applied to esti- Finally, the 3D temperature field is constructed and validated. mate the surface temperature (h =0)forEq.5. However, the remote sensing SST does not represent the true in situ obser- 4.1 Determination of the initial conditions vation, so that differences with the measured in situ temperature reach ±1 °C (Reynolds et al. 2007). To avoid this, a linear Normally, the Argo floats measure the temperature of the up- regression between the remote sensing SST and the Argo per ocean from ~ 4–6 m below the surface, while that provided measurements is developed. Let h represent the minimum min by the remote sensing products give the SST, resulting in an measurement depth of the Argo profile, where the developed information gap between the surface and the shallowest Argo formula is a linear relationship between the SST and T(x , y , A A measurements. Moreover, the remotely sensed SST is not ac- h ), which can be represented as min curate enough, and a non-negligible bias would be introduced if we were to initialize the algorithm with this SST directly. To TxA; yA; hmin k SST l: 6 ðÞ¼Â þ ð Þ eliminate these errors, we apply the algorithm initialization at Once the regression coefficients k, l are obtained from the shallowest measurement depth of the Argo profiles, rather statistics of the SST and the Argo observations, the relation- than the ocean surface, for which a regression analysis is ship Eq. 6 is applied to modify the initial condition at (xg, yg) employed to translate the remotely sensed SST to this mea- for the reconstruction of the 3D temperature field. surement depth. Ocean Dynamics

Fig. 3 Flowchart of the 3D Start temperature field reconstruction algorithm Initial Argo profile measurement

Y Piecewise linear Mixed layer SST Regression function fitting N Gaussian function fitting

Gradient of the profile IDW 3D gradient field

Initial Numerical method condition

End

Unfortunately, the shallowest measurement depths of dif- than the Argo measurements. Since the relationship be- ferent Argo profiles are not consistent. At first, the average tween the temperature at the surface and depth hmin has minimum depth hmin of the Argo profiles used in the recon- been constructed, the initial condition T(xg, yg, hmin)ofthe struction is evaluated. As the measurements of Argo for ~ 4– reconstruction at the grid (xg, yg)iscalculatedbytakingthe 6 m may be absent, a filter (hmin < 6) is used to select the gridded AVHRR SST as x in Eq. 7.Here,theresolutionof normal ones in the 83 source profiles, of which 76 profiles the 3D mesh grid is 0.25° ×0.25° in the horizontal direc- are finally obtained and denoted 1–76. As shown in Fig. 4a, tion, which is derived from the projection of the AVHRR the averaged depth of the shallowest measurement is dataset. To confirm the effect of the regression equation, hmin 4:47 m, where here we assume hmin 4:5 m for the corresponding root-mean-square error (RMSE) of the approximation.¼ According to Levitus (1982), the¼ temperature original AVHRR SST and the modified one with the in the mixed layer varies little, allowing the transfer of the shallowest Argo measurements are calculated, with results shallowest measurements of the identified profiles to the uni- showing the RMSE reduced by 0.2 °C after the regression form depth of 4.5 m, with the 3D reconstruction initialized at procedure. hmin. To obtain the initial conditions of the 3D temperature reconstruction, the regression method builds a relationship 4.2 Determination of the vertical temperature gradient between the AVHRR monthly averaged SST and Argo measurements at h in the experimental domain during January min Based on the regression analysis, the modified SST data are 2009. Figure 4b presents the scatter diagram of the two mea- taken as the initial conditions of the reconstruction algorithm. surements and the linear regression between the Argo temper- In the following, we focus on the generation of the 3D vertical ature at 4.5 m depth (y) and the SST (x)as temperature gradient field used in the algorithm, whose details have been illustrated in Section 3. For each original Argo y 0:545x 9:81: 7 ¼ þ ð Þ profile, the piecewise fitting method is employed and a series of temperature functions {T(x1, y1, h), T(x2, y2, h), …, While Eq. 7 may suggest a poor linear relationship between T(xNA, yNA, h)} are obtained. As the temperature presents dif- the AVHRR observed SST and the Argo measurements, it is ferent characteristics in the vertical layers (González-Pola nonetheless reasonable because the ocean skin temperature is et al. 2007), the classical 0.5 °C threshold value from influenced by the prevailing winds, solar radiation, and many Monterey and Levitus (1997) is chosen as the criterion to other factors, so that the ocean surface is cooled or heated determine the MLD hb of each Argo profile roughly as fol- accordingly, resulting in more complicated characteristics lows. Let {Ti} be the vertical temperature measurements of a Ocean Dynamics

Fig. 4 Distribution of the minimum measure depth of the identified Argo profile (a); the linear relationship between the shallowest measurements of the Argo profiles and the remotely sensed SST based on a regression analysis (b)

single Argo profile, where T0 represents the shallowest mea- 5, 6). The RMSE of the fitting results is presented in Fig. 7a, surements. For the measurements (hi, Ti)satisfying showing the improved accuracy of the fitting method with increasing fitting order. However, the benefit of a higher order T i−T 0 > 0:5 jj is not necessarily optimal as the fitted temperature may result and in the Bover fit^ phenomenon, in which the fitted temperature is extremely high at some depths. By taking both the RMSE 2 2 and the smoothness of the fitting function into consideration, a T i 1−T 0 > 0:5 a b ; jjþ þ fourth-order Gaussian fitting function is chosen. To validate pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the shallowest depth hi is considered as the MLD hb.This the determination, all the Argo measurements below the strategy for the determination of the MLD of two Argo pro- mixed layer used in the experiment are collected and fitted files (2900157_333, 2900719_019) is presented in Fig. 5, where the MLD derived from the 0.5 °C threshold strategy 0 are 99.3 and 199.5 m, respectively, and both agree well with 2900157_333 the manual identification. 2900719_019 200 Based on the MLD of an Argo profile, the measurements hb=99.3m are divided into two parts: within and below the mixed layer. h =199.5m Within the mixed layer, the linear fitting procedure is 400 b employed between the adjacent measure points, from which a piecewise linear function of depth is obtained. As shown in 600 Fig. 6, any depth difference between two measurements is generally limited to 5 and 10 m, while the corresponding Depth(m) 800 temperature difference is minor. From the proportional distribution presented in Fig. 6b, we find 66% of the ad- 1000 jacent measurements have a temperature difference of ~0–0.01 °C, with almost 90% < 0.1 °C. Therefore, the fitting procedure of the piecewise linear function within 1200 the mixed layer is reliable, and the error introduced by the fitting process is acceptable. 1400 0 5 10 15 20 25 In Section 3, the choice of the multi-Gaussian fitting meth- Temp(oC) od below the MLD has been illustrated without a specified Fig. 5 The MLD determined by the threshold of 0.5 °C (Monterey fitting order N. In the following, the optimal N is determined and Levitus 1997)fortwoArgoprofiles:2900157_333(red), by a fitting test including five Gaussian fitting orders (2, 3, 4, 2900719_019 (blue) Ocean Dynamics

Fig. 6 Difference of temperature and depth between two adjacent Argo measurements in the mixed layer in terms of a a scatter diagram and b the proportional distribution of the temperature difference by the fourth-order Gaussian function. As shown in Fig. 7b, 4.3 Three-dimensional temperature field reconstruction the variation of vertical temperature with the depth is well and validation described. As mentioned above, the piecewise fitting strategy is applied From the piecewise fitting procedure, both the vertical tem- to each Argo profile to obtain a series of vertical temperature perature and the gradient function are available at the posi- functions {T(x1, y1, h), T(x2, y2, h), ⋯, T(xNA, yNA, h)}, as well tion of the Argo profiles. In the following, the 3D temper- as the vertical gradient function. The fitting results of two ature is reconstructed from the initial conditions and the ′ profiles (5902096_013, 2900688_061) shown in Fig. 8 dem- vertical temperature gradient. Let T (xA, yA, h)denotethe onstrate well-fitted measurements with RMSE of 0.17 and vertical temperature gradient of an Argo profile at an arbi-

0.09 °C, respectively. As it is the vertical temperature gradient trary depth and (xg, yg, h)the3Dmeshedgrid,whichisbuilt that is calculated in the 3D reconstruction algorithm, the error by the projection of the AVHRR grid downward from the ′ in the final temperature field introduced by the fitting process surface, then T (xg, yg, h)isderivedfromtheinterpolation ′ is limited, which is represented by the ratio of the fitting of T (xA, yA, h)horizontallybasedontheIDWmethod.The RMSE to the depth. Moreover, because the temperature tends spatial decorrelation scale is set as 200 km to guarantee the to be well-behaved below 1000 m, the estimation beyond the data source for each grid. Since the initial conditions and measurements of Argo are conducted by the temperature the 3D temperature gradient field are obtained, the recon- fitting function T(h). struction of the 3D temperature field is conducted by

Fig. 7 Impact of Gaussian function order on the fitting accuracy (a) and the effect of fourth-order choice applied to the entire Argo measurements below the mixed layer (b) Ocean Dynamics

Fig. 8 Complete T − h fitting function of the two Argo profiles 5902096_013 (a) and 2900688_061 (b)

solving Eq. 5.LetTn(xg, xg)representtheoceantempera- and EN4 datasets is 0.63 °C, which is just a little smaller than ture at layer n,thenthereconstructionschemeis that of the FRT (0.67 °C), the accuracy of the reconstruction is verified indirectly. T n xg; y ; hn T n 1 xg; y Δh The horizontal resolution of the reconstruction of g ¼ − g þ 0.25° ×0.25° deems it more valuable than the existing prod- 0 T xg; y ; hn 1 ; 8 ucts. As a result, more mesoscale information is represented in Â g − ð Þ the reconstruction. Since the resolution of the BOA-Argo, where Δh = hn − hn − 1 and T0(xg, yg)=T(xg, yg, hmin). EN4, and FRT results are different vertically, the temperatures To verify the efficiency of the developed algorithm, the are both interpolated to the 100 and 500 m layers. For com- vertical layer from the BOA-Argo dataset for depths of 10– parison, the reconstruction captures the main spatial structures 1200 m is employed, including the minimum averaged depth of the ocean temperature well, with more mesoscale charac- of 4.5 m. By the combination of the derived initial conditions teristics represented by the higher temporal resolution. As and the temperature gradient, the 3D temperature field is shown in Fig. 10,thehorizontaltemperatureoftheEN4 reconstructed using Eq. 8,andisdenotedhereafterasthe dataset is the least resolved. Because the WOA98 climatolog- FRT result (reconstructed temperature based on fitting ical background data is applied directly in the data generation method). According to Li et al. (2017), the performance based on the optimal interpolation method, the original infor- of the BOA-Argo dataset demonstrates both an accuracy mation of the Argo measurements is eliminated. Unlike the and retainment of mesoscale features. The EN4 monthly EN4 dataset, the monthly initial conditions of the BOA-Argo objective analysis is also reliable as many types of ocean dataset are generated from the original Argo profiles after profiling instruments have been used. Therefore, both the quality control, so that the mesoscale signals are retained BOA-Argo and EN4 gridded products are employed to and, therefore, some broader structure is represented. For our validate the derived FRT results. temperature reconstruction, only the original Argo tempera- Figure 9 shows the absolute bias (Abs), standard deviation ture profiles are employed and applied directly in our algo- (Std), correlation coefficient (Cor), and RMSE between the rithm without any interaction with the other analyzed fields, FRT results and the BOA-Argo (a) and EN4 (b) datasets, with more details of the surface temperature also introduced demonstrating that the FRT results are highly consistent with by the high-resolution AVHRR SST data. Therefore, the me- the two existing datasets, with correlation coefficients of 0.99 soscale structure captured by our reconstruction is largely im- for both datasets. Though the relative RMSE (0.67 °C, proved based on the proposed algorithm. 0.76 °C) of the two comparisons are presented, the quality of the FRT results could not be confirmed definitively. Therefore, to validate the FRT precisely, the BOA-Argo dataset is taken as the reference value to evaluate the EN4 5 Conclusion dataset. If the FRT’s RMSE is comparable with that of the EN4 dataset, we suggest that the accuracy of the 3D recon- An efficient algorithm is proposed to reconstruct the 3D ocean struction is validated. As the RMSE between the BOA-Argo temperature field based on the Argo profiles and the AVHRR Ocean Dynamics

Fig. 9 Scatter diagram between the FRT results and BOA-Argo (a) and EN4 (b)products

SST data. Considering the discrete measurements of an Argo existing Argo products, the Argo measurements are merged profile, a piecewise fitting strategy is adopted to obtain the into the background directly, and the original information is continuous vertical temperature variation, which is obtained eliminated; when modifying the initial conditions by the at the Argo measurement position, and interpolated with the merged Argo temperature in the BOA-Argo product, the cor- IDW method to the grid. Initialized by the modified SST, the responding capacity is improved. However, the ocean temper- algorithm could be realized downward from the surface. ature is a complicated variable, so that the temperature esti- To verify the efficiency of the proposed algorithm, an ex- mation by interpolation where data is lacking is not accurate periment in the southern ocean of Japan is conducted for enough. Since the gradient of temperature is more stagnant which the 3D temperature field is reconstructed. Compared than the temperature itself, the estimation by gradient interpo- with the BOA-Argo and EN4 products, the reconstructed 3D lation seems to be a better choice in the developed algorithm. temperature field achieves a satisfactory accuracy, but with a As the temperature field becomes less variable in the higher resolution, so that more mesoscale information is cap- deeper ocean, the continuous T − h function may provide an tured in the reconstructed temperature field. For most of the estimation of the temperature beyond the profile. While the

Fig. 10 Spatial pattern of temperature at 100 m (top) and 500 m (bottom) depths derived from the BOA-Argo (left), EN4 (middle), and FRT (right) datasets Ocean Dynamics validation of the 3D temperature reconstruction algorithm has Good SA, Martin MJ, Rayner NA (2013) EN4: quality controlled ocean been conducted over a relatively small region, in the future, a temperature and salinity profiles and monthly objective analyses with uncertainty estimates. J Geophys Res Oceans 118(12):6704–6716 larger region or global application will be performed to further Guinehut S, Le Traon PY, Larnicol G et al (2004) Combining Argo and validate the algorithm. remote-sensing data to estimate the ocean three-dimensional temperature fields—a first approach based on simulated observations. J Acknowledgments We would like to give thanks to the China Argo Mar Syst 46(1):85–98 Real-Time Data Center for providing the Argo profile data product (http:// Hosoda S, Ohira T, Nakamura T (2008) A monthly mean dataset of global www.argo.org.cn/). The study is supported by the National Key Research oceanic temperature and salinity derived from Argo float observa- and Development Program of China under contract nos. tions. Jamstec Rep Res Dev 8:47–59 2016YFA0600102 & 2016YFC1401800; the National Natural Science Hurlburt HE (1986) Dynamic transfer of simulated altimeter data into Foundation of China under contract no.41576176; the Key Project of subsurface information by a numerical ocean model. J Geophys Science and Technology of Weihai under contract no. 2014DXG J14 Res Oceans 91(C2):2372–2400 and the Disciplinary Construction Guide Foundation of Harbin Institute Lawson C L, Hanson R J (1974) Solving least squares problems. of Technology at Weihai under contract no. WH20140206. Prentice-Hall Levitus S (1982) Climatological atlas of the World Ocean. NOAA Prof Paper No 13. 64(49):173 pp Li H, Xu F, Zhou W et al (2017) Development of a global gridded Argo References data set with Barnes successive corrections. J Geophys Res Oceans 122(2):866–889 Monterey G, Levitus S (1997) Seasonal variability of mixed layer depth Carnes MR, Teague WJ, Mitchell JL (1994) Inference of subsurface for the world ocean. U S Gov Printing Office, Washington D C, p 96 thermohaline structure from fields measurable by satellite. J Atmos Nardelli BB, Santoleri R (2004) Reconstructing synthetic profiles from Ocean Technol 11(2):551–566 surface data. J Atmos Ocean Technol 21(4):693–703 Chu PC, Fralick CR, Haeger SD et al (1997a) A parametric model for the Reynolds RW, Smith TM, Liu C et al (2007) Daily high-resolution- Yellow Sea thermal variability. J Geophys Res Oceans 102(C5): blended analyses for sea surface temperature. J Clim 20(22): 10499–10507 5473–5496 Chu PC, Tseng HC, Chang CP et al (1997b) South China Sea warm Riser SC, Freeland HJ, Roemmich D et al (2016) Fifteen years of pool detected in spring from the Navy’smasteroceanographic ocean observations with the global Argo array. Nat Clim Chang observational data set (MOODS). J Geophys Res Oceans 6(2):145–153 102(C7):15761–15771 Roemmich D, Gilson J (2009) The 2004–2008 mean and annual cycle of Chu PC, Fan C, Liu WT (2000) Determination of vertical thermal struc- temperature, salinity, and steric height in the global ocean from the ture from sea surface temperature. J Atmos Ocean Technol 17(7): Argo Program. Prog Oceanogr 82(2):81–100 971–979 Troupin C, Machín F, Ouberdous M et al (2010) High-resolution clima- Fox DN, Teague WJ, Barron CN et al (2002) The modular ocean tology of the northeast Atlantic using Data-Interpolating Variational data assimilation system (MODAS). J Atmos Oceanic Technol Analysis (Diva). J Geophys Res Oceans 115(C8):20 15(1):22–28 Yan C, Zhu J, Li R et al (2004) Roles of vertical correlations of back- González-Pola C, Fernández-Díaz JM, Lavín A (2007) Vertical structure ground error and TS relations in estimation of temperature and sa- of the upper ocean from profiles fitted to physically consistent func- linity profiles from sea surface dynamic height. J Geophys Res tional forms. Deep-Sea Res I Oceanogr Res Pap 54(11):1985–2004 Atmos 109(8):383–402