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1 Detecting regional deep ocean warming below 2000m based on altimetry,

2 GRACE, Argo, and CTD data

3 Yuanyuan YANG1,2, Min ZHONG1,2,3, Wei FENG*1,3 Dapeng MU4

4 1 State Key Laboratory of Geodesy and Earth’s Dynamics, Institute of Geodesy and

5 Geophysics, Innovation Academy for Precision Measurement Science and

6 Technology, Chinese Academy of Sciences, Wuhan 430077, China.

7 2 University of the Chinese Academy of Sciences, Beijing 100049, China.

8 3 School of Geospatial Engineering and Science, Sun Yat-sen University, Zhuhai

9 519082, China.

10 4Institute of Space Sciences, Shandong University, Weihai 264209, China.

11 ABSTRACT

12 The deep ocean below 2000m is a large water body with the sparsest data coverage,

13 challenging the closure of sea level budget and estimate of the Earth’s energy

14 imbalance. Whether the deep ocean below 2000m is warming globally has been debated

15 in the recent decade. However, as the regional signals are generally larger than global

16 average, it is intriguing to investigate the regional temperature changes. Here we adopt

17 an indirect method that combines altimetry, GRACE, and Argo data to examine the

18 global and regional deep ocean temperature changes below 2000m. The consistency

19 between high quality conductivity-temperature-depth (CTD) data from repeated

*Corresponding author: Wei FENGEmail: fengwei@whigg.ac.cn)

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20 hydrographic sections and our results confirms the validity of the indirect method. We

21 find that the deep oceans are warming in the Middle East Indian Ocean, subtropical

22 North and Southwest Pacific, and Northeast Atlantic, but cooling in the Northwest

23 Atlantic and Southern oceans from 2005 to 2015.

24 Key words: Deep ocean warming, GRACE, Argo, GO-SHIP, Altimetry

25 http://doi.org/10.1007/s00376-021-1049-3

26 Article Highlights:

27 An indirect method is used to estimate global and regional deep ocean temperature

28 changes below 2000m

29 Repeated hydrographic sections confirm the effectiveness of the indirect method

30 to detect potential deep ocean changes.

31 The deep ocean changes are inhomogeneous and contain robust warming and

32 cooling signals at different locations.

33

34 1. Introduction

35 Ocean absorbs more than 90% of heat excess accumulated in the climate system

36 caused by greenhouse gases since 1970s and contributes about 40% to global sea level

37 rise since 1990s (IPCC, 2013). Thus ocean heat content (OHC) change and steric sea

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38 level change are vital climate metrics. Recent estimates of OHC and associated steric

39 sea level rise based on observational records and models indicate that ocean warming

40 is significant in the past half century and the warming is accelerating in recent decades

41 (Durack et al., 2018; Cheng et al., 2019; Cheng et al., 2020). However, these estimates

42 are limited to the upper 2000m of the ocean, mainly due to the lack of sufficient

43 temperature observations in the deep ocean below 2000m. Whether the deep ocean

44 below 2000m is warming has been a great controversy (Meyssignac et al., 2019). The

45 deep ocean mentioned in this study refers to the ocean below 2000m, exceeding the

46 current maximum sampling range of the Argo floats.

47 Both the international World Ocean Circulation Experiment (WOCE)

48 Hydrographic Programme and Global Ocean Ship-based Hydrographic Investigations

49 Program (GO-SHIP) have offered the direct and high-quality measurements (including

50 temperature, salinity etc.) to monitor the deep ocean changes based on repeated

51 hydrographic sections (Desbruyeres et al., 2016; Desbruyères et al., 2016). However, it

52 is still a challenge to give a time series for the deep ocean changes, instead, only a long-

53 term trend estimate is provided (e.g., Purkey and Johnson, 2010; Desbruyères et al.,

54 2014; Talley et al., 2015). In addition to the in situ observations, there are many model

55 or reanalysis products available, but these data suffer from model bias or strength of

56 the observation constraint, therefore, how does the deep ocean change is still debatable

57 (Song and Colberg, 2011; Palmer et al., 2017; Garry et al., 2019).

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58 At the beginning of this century, the emergence of Gravity Recovery and Climate

59 Experiment (GRACE) satellites, altimetry satellites, along with in situ Argo floats has

60 provided a completely new perspective to study the deep ocean warming (Purkey et al.,

61 2014; Volkov et al., 2017). Theoretically, one can deduct the barystatic sea-level

62 change (GRACE-derived) and steric sea-level change of the upper 2000m depth (Argo-

63 derived) from the total sea-level change (altimeter-derived), and estimate the steric

64 contribution from the deep ocean, which is an affirmative indicator of ocean warming

65 (Llovel et al., 2014; Chen et al., 2018; Asbjørnsen et al., 2019; Chang et al., 2019;

66 Royston et al., 2020). Previous studies found that the global sea-level budget (SLB)

67 based on altimetry, GRACE, and Argo (0-2000m) appears to be closed within

68 uncertainty over various time scales, and the remaining part (the deep ocean under 2000

69 m) contributes almost zero with great uncertainty (Llovel et al., 2014; Dieng et al.,

70 2015; Kleinherenbrink et al., 2016; Volkov et al., 2017; WCRP, 2018; Frederikse et al.,

71 2020; Royston et al., 2020). This indicates that the deep ocean changes below 2000m

72 are currently still too small to be detectable from data uncertainty with current Earth

73 Observation System.

74 However, regional changes are always larger than global averages, where the

75 signals are cancelled out, it is desirable to estimate regional changes based on altimetry,

76 GRACE, and Argo data. In this study, we estimate the regional pattern of deep steric

77 sea-level (DSSL) change from 2005 to 2015 by using an indirect method with multiple

78 datasets of altimetry, GRACE, and Argo, i.e. “Alt.–Argo–GRACE”. And then we

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79 assume that the DSSL changes are mainly due to temperature changes rather than

80 salinity. Consequently, the pattern of global temperature in the deep ocean can be

81 obtained. This pattern has great interest to the community as it highlights the “hot spots”

82 or “cold spots”, which are important to the deep ocean heat uptake. This regional pattern

83 could also guide the deployment of Deep-Argo floats.

84 As indicated before, our study relies on a basic assumption that the DSSL change

85 is dominated by the temperature change. This assumption is valid in most of the global

86 regions except for the birthplace of deep-water mass, such as the subpolar region of

87 North Atlantic and Southern Oceans (Stammer et al., 2013). Therefore, the location

88 where the DSSL changes drastically is probably a good indicator of the deep ocean

89 temperature changes. To test this assumption, we have compared our results with direct

90 hydrographical measurements from GO-SHIP and such a comparison supported this

91 assumption.

92 In addition, recent investigations found a significant signal of long-term

93 accelerated deep-ocean warming in the subtropical South Pacific Basin based on GO-

94 SHIP and pilot Deep-Argo floats from 2005 to 2018 (Johnson and Doney, 2006; Volkov

95 et al., 2017; Johnson et al., 2019; Purkey et al., 2019), which is also confirmed by our

96 indirect method.

97 The paper is structured as follows. Section 2 introduces the data and methodology

98 used in this study. Section 3 presents the spatial-temporal variability of the deep ocean

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99 steric sea-level change and the results of verification. Section 4 shows the main

100 discussion and summary.

101 2.Data and Methodology

102 To derive the deep ocean steric sea level changes, estimate their uncertainty, and

103 verify the results, four groups of datasets are used: satellite altimetry, satellite gravity,

104 Argo, and GO-SHIP CTD data (the detailed information is provided in Table 1 in the

105 supporting information).

106 Three monthly sea surface height (SSH) grid products derived from a series of

107 satellite altimeter missions are released by the Archiving, Validation, and Interpretation

108 of Satellite Oceanographic(AVISO), the Copernicus Marine Environment Monitoring

109 Service (CMEMS) and the Commonwealth Scientific and Industrial Research

110 Organisation (CSIRO) covering the period from 1993 to present. We remove glacial

111 isostatic adjustment (GIA) effect correction on long-term ocean bottom deformation

112 (Roy and Peltier, 2015,2017) and elastic loading ocean bottom deformation (OBD)

113 correction using GRACE data (García-García et al., 2006; Vishwakarma et al., 2020)

114 before joint calculation.

115 Ten monthly temperature and salinity datasets used to calculate steric sea-level

116 change from the sea surface to a depth of 2000 m ( ) (Jayne et al., 2003) are 2000SSL

117 retrieved from the following institutions: the Second Institute of Oceanography,

118 Ministry of Natural Resources, China (BOA), the Coriolis Ocean database for

119 ReAnalysis (CORA), France, the UK Met Office (EN4), the Institute of Atmospheric

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120 Physics, Chinese Academy of Sciences, China (IAP), the International Pacific Research

121 Center (IPRC) at the University of Hawaii, USA, the Laboratory for Ocean Physics and

122 Satellite remote sensing (ISAS15), France, the Japan Agency for Marine-Earth Science

123 and Technology (JAMSTEC), the National Centers for Environmental Information

124 (NCEI), USA, and the Scripps Institution of Oceanography (SIO) at the University of

125 California San Diego, USA. These datasets are mainly derived from Argo floats that

126 have been deployed since 1999 and achieved near global coverage since 2005 (Jayne

127 et al., 2017). Some of these products also merge Argo data with other instrumental data

128 such as CTD, Mooring, XBTs, Glider etc., hereafter, referred to simply as Argo. The

129 steric sea-level change was calculated based on temperature, salinity, and density of

130 seawater using Thermodynamic Equation of Seawater-2010 (TEOS-10).

131 Four monthly GRACE fully normalized spherical harmonic coefficient products

132 from 2002-2017 are respectively provided by four data processing centers: the Center

133 for Space Research (CSR) of the University of Texas at Austin, the German Research

134 Centre for Geosciences (GFZ), the Jet Propulsion Laboratory (JPL), and the Institute

135 of Geodesy at Graz University of Technology (ITSG). To obtain the ocean mass change

136 ( )(什么叫 mass change in SSH？), we carry out a series of standard post-

137 processing, including C20 coefficients replacement by the solutions from Satellite

138 Laser Ranging (Cheng and Ries, 2017), adding back degree-1 coefficients (Swenson et

139 al., 2008; Sun et al., 2016) and GAD product, removing global mean atmospheric

140 pressure changes (Uebbing et al., 2019), GIA corrections based on the ICE6G-D model

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141 (Peltier et al., 2018), and applying a 300 km Gaussian smoothing (Johnson and

142 Chambers, 2013). Moreover, GRACE RL06 Mascon grid solutions from CSR and JPL

143 with all corrections applied are also used (named as CSR-M, and JPL-M, respectively).

144 Due to the different spatial and temporal resolution of each product, we perform

145 the necessary linear interpolation processing to standardize the data into 1°×1°grids

146 along longitudinal or latitudinal directions, which has a negligible impact on the linear

147 trend of the DSSL changes according to some tests (not shown).

148 (1)2000 massDSSL SSH SSL SSH

149 in which, SSH represents the total sea surface height changes from altimetry, SSL2000

150 represents steric sea level changes to a depth of 2000 m from Argo, and SSHmass

151 represents the ocean mass changes from GRACE.

152 The high precision full-depth temperature and salinity hydrographic measurements

153 obtained by ship-based CTDs are shared by CLIVAR and Carbon Hydrographic Data

154 Office (CCHDO). Figure 1 shows the location and sample numbers of repeated sections

155 during the whole period of the GRACE era. The repeated sections we define here is that

156 multiple CTD records (not necessarily from the single sections) fall within the same 1°

157 grid point. In Figure 1, we can find that about 80% of the repeated sections have only

158 two occupations over 15 years. We follow the interpolation method in (Purkey and

159 Johnson, 2010) to calculate the temperature and salinity change along the GO-SHIP

160 sections, and then the formula (12)-(18) in (Jayne,2003) are used to calculate the DSSL

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161 change. During the calculation, we use the World Ocean Atlas 2018 (WOA18) as a

162 climatological mean-field for both temperature and salinity.

163 We adopted a reasonable assumption that the deep steric change is dominated by

164 temperature change. So, we can calculate the responding deep ocean heat content

165 change derived from indirect deep steric change. The conversion coefficient of these

166 two physical quantities is obtained by the following steps. First, we calculated the

167 corresponding thermal expansion coefficient and density based on the WOA18

168 temperature and salt field data. Then, the conversion factor is calculated according to

169 the formula in the previous literature (Purkey and Johnson, 2010; Meyssignac et al.,

170 2019). Benoit et al. (2019) had discussed the global OHC obtained by different

171 coefficients. But, these coefficients do not make a significant difference in the spatial

172 distribution of OHC changes (Purkey and Johnson, 2010). Since the conversion

173 coefficient fluctuates around 1.0, the spatial pattern of deep steric change is similar to

174 the map heat content change (Figure 4d and 4e).

175 All of the products are combined together to provide a super ensemble. The

176 ensemble mean is our final estimate and the uncertainty is calculated by the standard

177 deviation of the ensemble members (Figure 2). This uncertainty estimation assumes

178 that the “Gaussian” distribution of the error and neglect any common systematic biases,

179 which has been widely used because there is no clear indication of large systematic

180 errors in the current datasets. For GRACE, we also considered the uncertainty

181 associated with different GRACE processing parameters (Landerer et al., 2020).

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182 Hydrological data are used for verification. Due to the sparse sampling of

183 hydrological sections, we prefer to use the trend spread of different sections in the

184 region as its uncertainty estimate of the regional trend. Ship-based repeated

185 hydrological sections are currently recognized as high-quality data that can be used to

186 validate the DSSL change and separate the contributions of temperature and salinity.

187 However, due to the sparse spatial and temporal sampling of ship-based observations,

188 they are only used to validate the sign of the derived DSSL change by “Alt.–Argo–

189 GRACE”.

190 This study focuses on the period from January 2005 to December 2015, because

191 Argo network has near-global ocean coverage since 2005, and the accuracy of GRACE

192 data is significantly reduced since June 2016 mainly because of the great change of the

193 satellite operations status (Landerer et al., 2020). Furthermore, considering the

194 difference in the spatial coverage of the datasets, as well as the inevitably affected by

195 leakage errors and seismic deformation effects, we only consider the open ocean

196 regions with 500km buffer from the coastline and mask out the regions affected by the

197 large earthquakes, i.e., 2004 Sumatra-Andaman earthquake，2010 Maule earthquake,

198 and 2011 Tohoku-Oki earthquake (Han et al., 2006; Han et al., 2010; Han et al., 2011).

199 The same 300km Gaussian smoothing has been applied to altimetry data and Argo data

200 to maintain the same resolution with GRACE data.

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201 3.Results

202 3.1 Global and regional DSSL change

203 Figure 3 shows global mean time series of , , , and SSH 2000SSL massSSH DSSL

204 based on the combination of currently available datasets with two times standard

205 deviation uncertainty range. During the period of 2005-2015, the steric sea-level change

206 accounts for ~1/3 of global sea-level rise, and most of the steric contribution comes

207 from the ocean above 2000m (Figure 3). The linear rate of the DSSL change is 0.07±

208 0.18 mm/yr from the residuals of “Alt.–Argo–GRACE” from 2005 to 2015, which is

209 less than 1/10 of the full depth of the steric sea-level change. This is consistent with

210 recent studies that closed SLB within uncertainty (Llovel et al., 2014; WCRP, 2018).

211 Figure 4 depicts the spatial patterns of long-term trends in , , SSH 2000SSL

212 , , and OHC within shallow (0-2000m) and deep layers. The regional massSSH DSSL

213 sea-level rate and its steric component show similar spatial patterns, such as the sea-

214 saw mode in the Pacific (Royston et al., 2020) (Figure 4a and 4b). In most oceans,

215 GRACE-based ocean mass increases slowly with a smaller magnitude of trend

216 compared with altimetry and Argo (Figure 4c). The regional DSSL change is not

217 uniform and shows strong local patterns that can be 1-2 orders magnitudes larger than

218 the global mean (Figure 4d). The obvious positive trends are observed in the Middle

219 East Indian Ocean (Region 1), the Tropical Northeast Pacific (Region 2), the

220 subtropical Southwest and North Pacific (Region 3), the Kuroshio extension region,

221 and the Northeast Atlantic (Region 5). The obvious negative trends appear in the

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222 Agulhas basin, the Northwest Atlantic (Region 4), South Atlantic, and the Southeast

223 Pacific.

224 Figure 4e shows the spatial pattern of OHC trends in the deep oceans from 2005 to

225 2015 (more details in Text S2), which is similar to that of DSSL changes in Figure 4d,

226 since we assume that DSSL changes are attributed to temperature changes. Thus DSSL

227 rising corresponds to deep ocean warming, and vice versa. By comparing with the OHC

228 trends in upper oceans (Figure 4f), it is likely that the heat accumulated in the upper

229 layer of the South Pacific, Indian Ocean and subtropical Atlantic Ocean penetrates into

230 the deep oceans during 2005-2015(Volkov et al., 2017). However, the opposite signs

231 of OHC trends between the upper and deep layers appear in the sub-polar North Atlantic

232 and South Atlantic, the Agulhas Basin, which may be related to the strong deep ocean

233 circulations in these regions (Song and Colberg, 2011; Purkey and Johnson, 2013; Chen

234 and Tung, 2018; Hu et al., 2020).

235 The contribution of the deep ocean to the global mean sea-level change is so small

236 that most studies attribute the residual to observational errors. Even considering the

237 basin-scale, the SLB in most ocean basins can be closed within tolerance (Royston et

238 al., 2020). Using a global average DSSL trend of 0.1mm/yr to close the regional SLB,

239 Royston et al. [2020] found a SLB gap in the Indian-South Pacific region up to 1.2

240 mm/yr, which exceeds the uncertainty caused by different data sets, processing, and

241 corrections. Our study finds that this gap is due to the significant deep warming from

242 2015 to 2016.

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243 Although the selection of data products and post-processing strategies will

244 inevitably affect the estimation of DSSL in most oceans, we still found some significant

245 decadal regional DSSL changes highlighted in Figure 4d. For example, the DSSL in

246 subtropical Southwest Pacific increased with a rate of 1.80± 0.77mm/yr, which is

247 consistent with the estimate of 2.40±1.30mm/yr from Volker et al. (2017). Our indirect

248 liner rate is much closer to the estimation of repeated ship-based observation (Table 2),

249 which is attributed to the adoption of multiple Argo datasets, as well as the updated

250 GRACE RL06 and correction strategies.

251 3.2 Impact of GRACE processing parameters on deep steric change

252 Previous studies highlighted that different post-processing strategies of GRACE

253 essentially affects the spatial distribution of ocean mass change (Blazquez et al., 2018;

254 Chen et al., 2018; Jeon et al., 2018; Mu et al., 2020; Royston et al., 2020). However,

255 the uncertainties of spatial pattern induced by different GRACE products and post-

256 processing strategies are relatively uniform and smaller than the significant trend

257 signals in DSSL (Figure 5 and Table 3). Moreover, the STD of DSSL changes is mainly

258 due to the discrepancies in Argo datasets, such as in the South Atlantic (Figure 2), which

259 indicates that the ensemble mean from multiple Argo datasets as much as possible

260 should be used when using the indirect method to study DSSL.

261 We analyzed the effect of different GRACE solutions and post-processing

262 strategies on the estimation of the deep steric change from 2005 to 2015. We prefer to

263 the GRACE post-processing parameter selection described in Section 2 of main text as

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264 a reference and analyze the associated discrepancy on deep steric change estimation by

265 replacing a specific parameter.

266 Figure 5 illustrates the sensitivity of deep steric change to the selection of GRACE

267 processing parameters. There is no obvious difference in the pattern of deep steric

268 change when we choose different types of GRACE products, i.e., spherical harmonic

269 solutions or mascon solutions (Figure 5 b and 5c). The different correction of the first-

270 order term and C20 will more or less enhance or weaken regional signals, but it will not

271 change the spatial pattern of the obvious signal (Figure 5 d and 5e). Although the choice

272 of GIA model may affect the SLB of basin-scale, it will not affect the spatial

273 distribution of significant DSSL signals, such as North Atlantic (Figure 5f). A larger

274 filter radius will slightly weaken the signal, but it will not essentially change the pattern

275 (Figure 5g). The deep steric rate pattern will show obvious north-south stripes if a

276 destriping filter has not been applied to the GRACE data (Figure 5h). The discrepancy

277 of different GRACE empirical striping methods on the spatial distribution of deep steric

278 is also negligible (Figure 5i). Note that these processing methods may have a critical

279 effect on some regions with plausible weak signals.

280 Table 3 lists the liner trends of regional deep steric change estimated by different

281 GRACE solutions and post-processing strategies. As shown in Table 3, these subjective

282 choices affect the indirectly estimated regional deep steric linear trends, which may

283 exceed the order of 1 mm/yr. It is difficult to accurately estimate the reginal deep steric

284 change. Despite the potential spread caused by GRACE treatment, the deep steric

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285 change in these regions are significant within the 95% confidence intervals. Note that

286 these comparisons are intended to show the impact of potential GRACE treatment

287 strategies, we recommend the latest GRACE processing strategies described in the

288 section 2.

289 3.3 Validation of the deep ocean steric sea level changes

290 To validate the regional DSSL changes, we selected five regions with significant

291 signals (Figure 4d) and compared the derived DSSL changes with GO-SHIP data. The

292 criteria of the regions selection are: 1) there should be at least two repeated sections in

293 the region to quantify the temporal change of the regional DSSL; 2) the signal of

294 cooling and warming in the selected areas are significant so the comparison is

295 meaningful.

296 Figure 6a shows the spatial patterns of DSSL rates from direct and indirect methods

297 in the five selected regions. The DSSL changes along each track line are far from

298 uniform, which is likely related to the rich eddies, tides, and waves (Volkov et al., 2017).

299 Note that the color scales of the two methods are different, mainly associated with the

300 smoothing effects of the indirect datasets (the typical spatial scale of the GRACE and

301 Argo-based datasets are ~3 degree but the direct measurements include variations from

302 all scales). The different smoothness of the two data challenges the strict comparison

303 of the two methods, but we can still identify the consistency of the sign of the trends.

304 As shown in Figure 6b and Table 2, the meridional or zonal average trend along the

305 track line reveals a consistent increase or decrease trends. For example, the DSSL

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306 from indirectly method increased with a rate of 1.89±0.67 mm/yr, 0.98±0.74 mm/yr,

307 1.80 ±0.77mm/yr in the Middle East Indian Ocean, subtropical North Pacific, and

308 subtropical Southwest Pacific, respectively, while the sections along these regions also

309 captured coincidence increase rates ranging from 0.21mm/yr to 1.23 mm/yr. Especially,

310 a significant DSSL rise of 2.01±0.77mm/yr in Region 5 of North Atlantic is inferred

311 from the indirect method, agreeing well with the track line A16N and the eastern part

312 of A05 (Figure 6a). The negative DSSL rate (-3.66±1.98 mm/yr) derived from “Alt.–

313 Argo–GRACE” in the Northwest Atlantic, which is also dramatically in line with the

314 decreasing DSSL from the track line A20 and A22(-2.49 mm/yr and -0.56 mm/yr).

315 The trend signs of DSSL changes obtained by these two independent methods are

316 the same in the selected five regions (Figure 6c), which demonstrate the average result

317 calculated based on the indirect method is reliable. The difference in magnitude

318 between them may be due to the uncertainties in GRACE and Argo (Figure 2 and 5),

319 the inherent observation errors associate with the gridded datasets. Moreover, with the

320 undersampling of GO-SHIP data in both spatial and temporal domains comparing to

321 the indirect method, the positive and negative DSSL signals along the track lines are

322 canceled out, which may explain the smaller amplitude of DSSL trends from CTD

323 observations.

324 Furthermore, with the hydrographic temperature and salinity data, we can further

325 test the impact of salinity change on the DSSL change and assess the potential to

326 estimate deep ocean temperature changes. Figure 7 depicts the selected regional

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327 average trend of DSSL, deep thermosteric sea-level (DTSL) caused by temperature

328 variations, and deep halosteric sea-level (DHSL) caused by salinity variations. In the

329 Middle East Indian Ocean (Region 1), subtropical Southwest Pacific (Region 3), and

330 Northwest Atlantic (Region 4), temperature dominates the DSSL change; while the

331 salinity contribution cannot be ignored in the subtropical North Pacific (Region 2),

332 Northwest Atlantic (Region 4), and Northeast Atlantic (Region 5). In all these regions,

333 the increased steric is consistent with an increase in temperature, and vice versa. The

334 consistency signs between DTSL and DSSL suggests that the DSSL rates from the

335 indirect method can be used to infer the deep temperature changes and warming/cooling

336 in these regions.

337 Although we provide a finer resolution estimate of the deep ocean temperature

338 change pattern (Figure 4 and Figure 6), our finding corresponds well with many

339 previous results, i.e., the clear deep ocean warming in the northeastern Atlantic Ocean

340 for the period of 2002-2010 using the data from six A25-Ovide cruises (Desbruyères et

341 al., 2014). Warming signals in the abyssal southeastern Indian Ocean is captured by

342 comparing repeated hydrographic sections between 1994/95 and 2007(Johnson et al.,

343 2008). In addition to the selected five regions, the indirect method also highlights the

344 DSSL decrease i.e., ocean cooling in Agulhas basin, South Atlantic, and southeast

345 Pacific (Figure 4d). These changes are very similar to the SLB discrepancy pattern

346 given by Royston et al. [2020], but they simply assume a global mean value of 0.1

347 mm/yr for DSSL changes in all oceans. Using T waves generated by

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348 underwater earthquakes, a decadal warming trend was uncovered in the East Indian

349 Ocean by Wu at el. [2020]. The new developed seismic ocean thermometry is expected

350 to expand our ability to monitor ocean temperature changes. Moreover, the ongoing

351 deployment of Deep Argo buoys may essentially solve this problem, which is also the

352 focus of future research.

353 Climate warming has extended into most regions of the deep ocean, especially the

354 Indian Ocean, subtropical Southwest Pacific and northeast Atlantic from 2005 to 2015;

355 while the deep ocean is cooling in Northwest Atlantic. However, due to the lack of in-

356 situ measurements, significant steric changes in Agulhas basin, South Atlantic, and

357 southeast Pacific from “Alt.–Argo–GRACE” cannot be validated independently.

358 4.Conclusions

359 In this study, regional DSSL changes were estimated from altimetry, GRACE, and

360 Argo observations from 2005 to 2015. Different post-processing strategies of GRACE

361 data will more or less enhance or weaken regional signals, but it will not change the

362 spatial pattern of the obvious signal significantly. Significant deep ocean warming in

363 Middle East Indian Ocean, subtropical North Pacific, subtropical Southwest Pacific,

364 and Northwest Atlantic, and deep ocean cooling in Northwest Atlantic are detected by

365 “Alt.–Argo–GRACE”. The repeated hydrographic sections also confirmed these local

366 significant DSSL changes. Our findings indicate that the indirect method can be used

367 to detect potential local deep-warming or cooling. We also find that the sign of

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368 thermosteric sea-level trend is consistent with that of steric sea-level trend in these

369 regions.

370 Although the indirect method has the potential to detect regional deep ocean

371 warming, it is difficult to accurately estimate deep ocean warming or cooling

372 quantitatively. On the one hand, the salinity effect in the deep ocean may enhance or

373 weaken the DSSL signal obtained by the indirect method. Because DHSL in some

374 regions has a comparable contribution to DTSL, but it does not change the sign of DSSL.

375 On the other hand, the uncertainty of the ensemble is the variance between data

376 products, which may not represent the true error. The datasets derived from in-situ

377 observations have a certain level of uncertainty owing to instrumental biases and

378 insufficient data coverage in some locations. These uncertainties are inherent, not

379 independent, and hard to accurately quantify. Therefore, we recommend using

380 independent methods and multiple data to estimate and confirm deep ocean warming.

381 The results of the indirect method are highly dependent on the quality of the three

382 data sources, which will be greatly improved in the foreseeable future. Deep Argo has

383 demonstrated the near real-time and high-precision measurement capability, which can

384 help us further validate the results of the indirect method. Seismic ocean thermometry

385 provides clues to detect the potential deep ocean temperature changes with high time

386 resolution(Wu et al., 2020). The significant-signal regions detected by multi-source

387 data can also be used as the basis for the Deep Argo deployment (Johnson et al., 2015).

388 More multi-source geodetic and oceanographic datasets with higher precision and

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389 spatiotemporal resolutions in the near future can further deepen our understanding of

390 changes in ocean heat content and steric sea-level in deep oceans.

391 Acknowledgments

392 This work is supported by the National Natural Science Foundation of China (Grant

393 No. 41904081). We thank the institutions (listed in Table1) for sharing their data

394 products used in this study. These data sets are available at the websites or references

395 listed in Table 1. The authors declare no financial conflicts of interests. The authors

396 comply with AGU's data policy. The data archiving is underway. The repository we

397 plan to use is Global Change Research Data Publishing and Repository (GCdataPR,

398 http://www.geodoi.ac.cn/WebEn/Default.aspx).

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603

604

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605 Table 1. Summary of satellite and in situ datasets used in this study from 2005 to 2015.

Data Type Institution/Datasets Reference or website

AVISO https://www.aviso.altimetry.fr/

CSIRO http://www.cmar.csiro.au/sealevel/sl_data_cmar.htmlAltimetry

CMEMS https://marine.copernicus.eu/

BOA (Li et al., 2017)

CORA (Cabanes et al., 2013)

EN4_g10 (Gouretski and Reseghetti, 2010; Good et al., 2013)

EN4_l09 (Levitus et al., 2009; Good et al., 2013)

IAP (Cheng et al., 2017)

IPRC http://apdrc.soest.hawaii.edu/

ISAS15 (Gaillard et al., 2016)

JAMSTEC (Hosoda et al., 2010)

NCEI (Levitus et al., 2012)

Argo

SIO (Roemmich and Gilson, 2009)

CSR RL06

JPL RL06

GFZ RL06

http://podaac.jpl.nasa.gov/grace/

ITSG-Grace2018 (Kvas et al., 2019)

JPL-M RL06 (Wiese et al., 2016)

GRACE

CSR-M RL06 (Save et al., 2016)

GO-SHIP CTD

WOCE

https://cchdo.ucsd.edu/

606

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607 Table 2. Comparison of regional DSSL trend from direct and indirect methods in

608 mm/yr.

Trends of GO-SHIP

Region index Sections time

DSSL DTSL DHSL

Trends of Alt.-Argo-

GRACE

I05 2002.04~2009.06 0.97 0.81 0.161: Middle East

Indian Ocean I09N 2007.03~2016.05 0.38 0.65 -0.26

1.89±0.67

P02 2004.07-2014.08 0.39 0.19 0.20

P14 2003.09-2015.09 0.82 0.18 0.65

2: subtropical

North Pacific

P16N 2006.03~2015.06 0.70 0.08 0.62

0.98±0.74

P06W 2003.09~2010.03 0.21 0.03 0.18

P16S 2005.02~2015.07 0.98 0.64 0.34

3: subtropical

Southwest Pacific

P15S 2009.03~2016.07 1.23 1.17 0.06

1.80±0.77

A20 2003.10-2012.06 -2.49 -2.91 0.424: Northwest

Atlantic A22 2003.12-2013.04 -0.56 -1.10 0.54

-3.66±1.98

A16N 2003.06-2013.12 0.84 0.56 0.285: Northeast

Atlantic A05 2010.01~2016.01 0.31 -0.21 0.52

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609 Table 3. Comparison of regional deep steric trend (unit: mm/yr) from different GRACE

610 processing strategies described in Figure 5.

region_index

Figure

index

1: Middle East

Indian Ocean

2: subtropical

North Pacific

3: subtropical

Southwest Pacific

4: Northwest

Atlantic

5: Northeast

Atlantic

5(a) 1.89±0.67 0.98±0.74 1.80±0.77 -3.66±1.98 2.01±0.77

5(b) 2.10±0.73 2.00±1.43 2.50±0.83 -3.96±2.02 1.80±0.85

5(c) 1.45±0.59 1.41±1.35 2.07±0.65 -3.04±1.95 2.41±0.66

5(d) 2.77±0.58 1.31±1.39 3.03±0.65 -4.60±1.99 1.15±0.71

5(e) 2.03±0.67 1.90±1.40 2.41±0.74 -3.64±1.98 2.11±0.78

5(f) 2.28±0.67 1.81±1.39 2.30±0.74 -3.39±1.98 2.42±0.77

5(g) 1.82±0.67 1.73±1.38 2.25±0.74 -3.86±2.00 1.95±0.77

5(h) 1.56±0.65 1.35±1.39 2.14±0.72 -3.44±1.96 1.90±0.77

5(i) 1.56±0.67 172±1.40 2.16±0.73 -3.20±2.00 1.89±0.76

611

612613614

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615

616 Fig. 1. Locations of repeated oceanographic sections during the GRACE era (2002.4-

617 2017.6). The blue symbols indicate that only two occupations of each section during

618 the time period, while red symbols mean more than two occupations. The percentages

619 in the legend represent the proportions of corresponding sample numbers.

620

621 Fig. 2. The standard deviation of (a) the linear trend of and the relative DSSL

622 contribution of (b) total sea-level change from altimetry, (c) steric sea-level change (0-

623 2000m) from Argo, and (d) GRACE-based ocean mass change in the indirect method

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624 over the period of 2005-2015 based on the corresponding datasets listed in Table 2. The

625 percentages of the variance explained in (b-d) are derived from the variance of each

626 component divided by the total variance.

627

6282002 2004 2006 2008 2010 2012 2014 2016 2018 2020

Time(yr)

-40

-20

0

20

40

60

80

100

GM

SL(

mm

)

SSH : 3.24 +/- 0.53 mm/yrSSL2000 : 1.08 +/- 0.25 mm/yrSSHmass: 2.11 +/- 0.31 mm/yrDSSL : 0.07 +/- 0.18 mm/yr

629 Fig. 3. Time series of global mean sea level change including (black line) SSH

630 (blue line) (dark green line), and (red line). The solid lines 2000SSL massSSH DSSL

631 represent the average of multiple datasets, and the corresponding shaded regions

632 represent the standard deviation. The linear trend uncertainties (95% confidence

633 interval) of each series from 2005 to 2015 have been shown in the legend. We offset

634 the time series for clarity.

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635

636 Fig. 4. The estimated ensemble mean linear trend of (a) total sea-level change from

637 altimetry, (b) steric sea-level change (0-2000m) from Argo, (c) GRACE-based ocean

638 mass change, (d) DSSL change from the residuals of “Alt.–Argo–GRACE” over the

639 period 2005-2015, deep OHC change (e) below 2000m and (f) above 2000m. Note that

640 (e) is derived from panel (d) under the ideal assumption that the DSSL change is totally

641 caused by the temperature change (more details in Text S2). The black boundaries in

642 panel (d) outline the regions we selected for validation, and the numbers in brackets

643 represent the corresponding index of the regions. The purple points in panel (d) denotes

644 the repeated sections covering the GRACE era. The stipple dots in (d) denote the

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645 regions with significant trends (95% confidence interval). It should be noted that

646 different color scales are used for panel (a-c) and panel (d).

647

648

649 Fig. 5. Comparison of deep steric patterns with different GRACE processing strategies.

650 (a) The ensemble mean of spherical harmonics and mascon solutions using the latest

651 RL06 recommended processing strategy, which is used as the reference to be removed

652 from the following panels (b-i). (b) Difference from (a) with only ensemble mean of

653 spherical harmonic solutions from CSR, JPL, GFZ and ITSG, (c) Difference from (a)

654 with only mascon solutions, (d) Difference from (a) with another degree 1 correction

655 (Swenson et al., 2008)，(e) Difference from (a) with another C20 correction (Cheng et

656 al., 2013), (f) Difference from (a) with another GIA model (A et al., 2013), (g)

657 Difference from (a) with the gaussian smoothing with a radius of 500km, (h) Difference

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658 from (a) with no destriping, (i) Difference from (a) with another empirical destriping

659 method (Swenson and Wahr, 2006).

660

661

662 Fig. 6. Comparison between the direct and indirect DSSL trends for the (a) spatial

663 pattern, (b) regional time series and trend lines from different methods and track lines,

664 and (c) regional average trends over 2005-2015. Note that different color bars are used

665 for GO-SHIP and “Alt.–Argo–GRACE” in (a). In (b), the gray solid lines represent the

666 average DSSL of multiple datasets from “Alt.–Argo–GRACE”, and the corresponding

667 shaded area represents the standard deviation. The red lines show the trends from “Alt.–

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668 Argo–GRACE” fitted by the least-squares. Trend lines in other colors represent the

669 corresponding estimates from track lines in the region. The error bars in (c) represent

670 the uncertainty (95% confidence interval) of the least squares fit for Alt.-Argo-GRACE

671 and the spread around the ensemble mean from different sections for GO-SHIP.

672

673

674 Fig. 7. Comparison of trends in DSSL (red), DTSL (blue) and DHSL (green) in the five

675 regions. Error bars represent the spread of regional average DSSL rate.

676 in pre

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