Proceedings on 15th Symposium on Integrated Observing and Assimilation Systems for the Atmosphere, Oceans and Land Surface (IOAS-AOLS), American Meteorological Society, 23-27 January 2011, Seattle 1001

Determination of Ocean Mixed Layer Depth from Profile Data

Peter C. Chu and Chenwu Fan

than in the mixed layer due to strong salinity isolates the constant- Abstract—Vertically quasi-uniform layer of temperature (T, isothermal layer) and density (ρ, mixed layer) usually exists in upper oceans. The thickness of the mixed layer density water from cool water. However, determines the heat content and mechanical inertia of the ILD may be thinner than MLD when negative salinity layer that directly interacts with the atmosphere. Existing stratification compensates for positive temperature methods for determining mixed layer depth from profile stratification (or the reverse situation) to form a data have large uncertainty. Objective and accurate compensated layer (CL) (Stommel and Fedorov, 1967; determination of the mixed layer depth is crucial in and climate change. This paper describes recently Weller and Plueddemann, 1996). The compensated layer developed optimal linear fitting, maximum angle, and thickness (CLT) is defined by CLT = HD - HT. relative gradient methods to determine mixed layer depth Occurrence of BL and CL affects the ocean heat and salt from profile data. Profiles from the Global Temperature budgets and the heat exchange with the atmosphere, and and Salinity Profile Program (GTSPP) during 1990-2010 in turn influences the climate change. are used to demonstrate the capability of these objective Objective and accurate identification of HT and methods and to build up global mixed (isothermal) layer HD is the key to successfully determining the BL or CL. depth datasets. Application of the data in climate study is However, three existing types of criteria (on the base of also discussed. difference, gradient, and curvature) to determine H and T Key Words—Mixed layer depth, isothermal depth, HD are either subjective or inaccurate. The difference difference criterion, gradient criterion, curvature criterion, criterion requires the deviation of T (or ρ) from its near optimal linear fitting method, maximum angle method, surface (i.e., reference level) value to be smaller than a relative gradient method, GTSPP, global mixed layer certain fixed value. The gradient criterion requires ∂T/ ∂z depth, global isothermal layer depth, barrier layer, (or ∂ρ/ ∂z) to be smaller than a certain fixed value. The compensated layer curvature criterion requires ∂2T/ ∂z2 (or ∂2ρ/∂z2) to be maximum at the base of mixed layer (z = -HD). 1. Introduction Obviously, the difference and gradient criteria are subjective. For example, the criterion for determining HT Transfer of mass, momentum, and energy across the for temperature varies from 0.8oC (Kara et al., 2000), bases of surface isothermal layer and constant-density 0.5oC (Wyrtki, 1964) to 0.2oC (de Boyer Montegut et al., layer (usually called mixed layer) provides the source for 2007). The reference level changes from near surface almost all oceanic motions. Underneath the mixed and (Wyrtki, 1964) to 10 m depth (de Boyer Montegut et al., isothermal layers, there exist layers with strong vertical 2007). Defant (1961) was among the first to use the gradient such as the and thermocline. The gradient method. He uses a gradient of 0.015oC/m to constant-density (or isothemal) layer depth is an determine HT for temperature of the ; important parameter which largely affects the evolution while Lukas and Lindstrom (1991) used 0.025oC/m. The of the sea surface temperature (SST), and in turn the curvature criterion is an objective method (Chu et al, climate change. 1997, 1999, 2000; Lorbacher et al., 2006); but is hard to The isothermal layer depth (ILD, HT) is not use for profile data with noise (even small), which will necessarily identical to the mixed layer depth (MLD, HD) be explained in Section 5. Thus, it is urgent to develop a due to salinity stratification. There are areas of the World simple objective method for determining mixed layer Ocean where HT is deeper than HD (Lindstrom et al., depth with capability of handling noisy data. 1987; Chu et al., 2002; de Boyer Montegut et al., 2007). In this study, we use several recently developed The layer difference between HD and HT is defined as the objective methods to establish global (HD, HT ) dataset barrier layer (BL), which has strong salinity stratification from the Global Temperature and Salinity Profile and weak (or neutral) temperature stratification (Fig. 1). Program (GTSPP) during 1990-2010. The quality indices The barrier layer thickness (BLT) is often referred to the for these methods are approximately 96% (100% for difference, BLT = HT - HD. Less turbulence in the BL perfect determination). The results demonstrate the existence and variability of (BL, CL).

1001 1002 The outline of this paper is as follows. Section 2 be available. That is, GTSPP participants will permit the describes the GTSPP data. Section 3 shows the large selection of data from their archives based on quality uncertainty of the existing methods. Section 4 presents flags as well as other criteria. These flags are always the methodology. Section 5 shows the comparison to the included with any data transfers that take place. Because existing objective method (i.e., the curvature method). the flags are always included, and because of the policy Section 6 presents the quality index for validation. regarding changes to data, as described later, a user can Section 7 shows the global (HD, HT) dataset calculated expect the participants to disseminate data at any stage of from the GTSPP profile data (1990-2010). In Section 8 processing. Furthermore, GTSPP participants have we present the conclusions. agreed to retain copies of the data as originally received and to make these available to the user if requested 2. GTSPP (GTSPP Working Group, 2010).

The following information was obtained from the website of the International Oceanographic Commission of UNESCO (IODE) http://www.iode.org/. GTSPP is a cooperative international project. It seeks to develop and maintain a global ocean Temperature-Salinity resource with data that are both up-to-date and of the highest quality possible. Making global measurements of ocean temperature and salinity (T-S) quickly and easily accessible to users is the primary goal of the GTSPP. Both real-time data transmitted over the Global Telecommunications System (GTS), and delayed-mode data received by the NODC are acquired and incorporated into a continuously managed database. . Countries contributing to the project are Australia, Fig. 1. The number of stations reported as BATHYs and Canada, France, Germany, Japan, Russia, and the United TESACs (from Sun, 2008). States. Canada's Marine Environmental Data Service (MEDS) leads the project, and has the operational responsibility to gather and process the real-time data. MEDS accumulates real-time data from several sources via the GTS. They check the data for several types of errors, and remove duplicate copies of the same observation before passing the data on to NODC. The quality control procedures used in GTSPP were developed by MEDS, who also coordinated the publication of those procedures through the Intergovernmental Oceanographic Commission (IOC). Fig. 2. World-wide distribution of floats (from the The GTSPP handles all temperature and salinity website: http://www.argo.ucsd.edu/). profile data. This includes observations collected using water samplers, continuous profiling instruments such as 3. Large Uncertainty of the Existing Methods CTDs, thermistor chain data and observations acquired using thermosalinographs. These data will reach data As pointed in the introduction section, the criteria for processing centres of the Program through the real-time the difference and gradient methods are subjective. For o channels of the IGOSS program or in delayed mode the difference method, the criterion changes from 0.2 C through the IODE system. Real-time data in GTSPP are (Thompson, 1976, Crieterion-1) for the North Pacific, o acquired from the Global Telecommunications System 0.5 C (Wyrtki, 1964; Obata et al., 1996, Crieterion-2) for o in the bathythermal (BATHY) and temperature, salinity the global oceans, 0.8 C (Kara et al., 2000, Crieterion-3) o & current (TESAC) codes forms supported by the for the global oceans, to 1.0 C (Rao et al., 1989, Crieterion-4) for the Indian Ocean. Four datasets of WMO. Delayed mode data are contributed directly by mixed layer depth were obtained from the GTSPP member states of IOC (Sun, 2008). Fig. 1 shows temperature profiles using these criteria. The probability increasing of observational stations especially the density functions (PDF) for the four datasets (Fig. 3) TESAC due to input of Argo floats (Fig. 2). show large difference. The root-mean square difference The GTSPP went through quality control procedures (RMSD) between Criterion-i and Criterion-j is calculated that make extensive use of flags to indicate data quality. by To make full use of this effort, participants of the GTSPP have agreed that data access based on quality flags will

1002 1003

N 1 2 RMSD(ij , ) =− h()ij h ( ) . Recently, Chu and Fan (2010a, b) developed several ∑()nn N n=1 objective methods for identify (HD, HT): optimal linear The relative RMSD (RRMSD) between Criterion-i and fitting, maximum angle, and relative gradient. Among Criterion-j is calculated by them, the first two methods are used for analyzing high (less than 5 m) resolution profiles and the third one is RRMSD(ij , )=+ 2 * RMSD( ij , ) /( H()ij H ( ) ) , suitable for analyzing low (greater than 5 m) resolution TT profiles.

()i ()j where HT and HT are the mean isothermal layer depth 4.1. Optimal Linear Fitting (OLF) Method using Criterion-i and Criterion-j. The RMSD has a minimum value of 43 m between Criterion-2 (0.5oC) and We use temperature profile as example for illustration. Criterion-3 (0.8oC) and a maximum value of 109 m For detailed information, please see Chu and Fan between Criterion-1 (0.2oC) and Criterion-4 (1.0oC). (2010a). Assume a temperature profile which can be Such a large uncertainty makes the difference method represented by [T(zi)]. A linear polynomial is used to fit less credible in determine the mixed layer depth from the the profile data from the first point near the surface (z1) profile data. to a depth, zk (marked by a circle in Fig. 3). The original Similarly, the gradient method also uses various and fitted data are represented by (T1, T2, …, Tk) and o ˆˆ ˆ criterion such as 0.015 C/m (Defant, 1961) and (TT12, ,..., Tk ), respectively. The root-mean square error 0.025oC/m (Lukas and Lindstrom, 1991). The RMSD E1 is calculated by between the two is around 70 m. 1 k Ek()=− ( T Tˆ )2 . (1) 1 ∑ ii k i=1

The next step is to select n data points (n << k) from the depth zk downward: Tk+1, Tk+2…, Tk+n. A small number n is used because below the mixed layer temperature has large vertical gradient and because our purpose is to identify if zk is at the mixed layer depth. The linear polynomial for data points (z1, z2, …, zk) is extrapolated ˆˆ ˆ into the depths (zk+1, zk+2, …, zk+n): TTkk+12,++ ,..., T kn. The bias of the linear fitting for the n points is calculated by 1 n Bias(kTT )=− (ˆ ) . (2) ∑ kj++ kj n j=1

If the depth zk is inside the mixed layer (Fig. 3a), the Fig. 1. PDF of the isothermal depth determined by the linear polynomial fitting is well representative for the difference method using different criterion: (a) 0.2oC, (b) o o o data points (z1, z2, …, zk+n). The absolute value of the 0.5 C, (c) 0.8 C, and (d) 1.0 C. bias,

Table-1. RMSD and RRMSD between two different criterion using the difference method. E2(k)= |Bias(k)|, (3) Between RMSD (m) RRMSD Criteria for the lowest n points are usually smaller than E1 since (1,2) 51 0.82 differences between observed and fitted data for the lowest n points may cancel each other. If the depth z is (1,3) 74 1.09 k located at the base of the mixed layer, E (k) is large and (1,4) 109 1.49 2 E (k) is small (Fig. 3b). If the depth z is located below at (2,3) 43 0.57 1 k the base of the mixed layer (Fig. 3c), both E (k) and (2,4) 88 1.08 1 E2(k) are large. Thus, the criterion for determining the (3,4) 71 0.81 mixed layer depth can be described as

4. Recently Developed Objective Ez2 ()k Determination of MLD and ILD →=−max, H Tkz , (4) Ez1 ()k

1003 1004 used as optimization to determine the mixed (or which is called the optimal linear fitting (OLF) method. isothermal) layer depth, The OLF method is based on the notion that there exists a near-surface quasi-homogeneous layer in which the θ →=−max, H z . standard deviation of the property (temperature, salinity, kDk or density) about its vertical mean is close to zero. Below In practical, the angle θ is hard to calculate. We use tan the depth of H , the property variance should increase k T θ instead, i.e., rapidly about the vertical mean. k 30

tanθkDk→=− max, H z . (7) 40

50 Linear Polynomial (1) (2) With the given fitting coefficients GGkk, , the value k 60 k+1 of tan θ can be easily calculated by k+2 Linear Polynomial k Depth(m) k+3 k+4 70

k Linear Polynomial (2) (1) k+1 k+2 GGkk− 80 k+3 k+4 k tanθk = . (8) Bias k+1 (1) (2) k+2 1 + GG k+3 kk k+4 90 Bias 24 24.5 25 25.5 26 24 24.5 25 25.5 26 24 24.5 25 25.5 26 temperature (C) temperature (C) temperature (C) Inside ML At ML Depth Below ML Small θ Largest θ Small θ Fig. 3. Illustration of the optimal linear fitting (OLF) 55 method: (a) zk is inside the mixed layer (small E1 and E2), 60 (b) zk at the mixed layer depth (small E1 and large E2), and Vector−1

(c) z below the mixed layer depth (large E and E ) (after 65 k 1 2 Vector−1 Chu and Fan, 2010a). 70 Vector−2 Vector−1 θ 4.2. Maximum Angle Method 75 Vector−2

Depth(m) θ

Vector−2 80 θ We use density profile as example for illustration. Let 85 density profiles be represented by [ρ(zk)]. The density profile is taken for illustration of the new methodology. 90

A first vector (A1, downward positive) is constructed 95 1024.5 1025 1024.5 1025 1024.5 1025 with linear polynomial fitting of the profile data from Density (kg/m3) Density (kg/m3) Density (kg/m3) zk-m to a depth, zk (marked by a circle in Fig. 4) (m < k). Fig. 4. Illustration of the method: (a) zk is inside the mixed layer (small θ), (b) z at the mixed layer depth (largest θ), A second vector (A2, pointing downward also) from one k and (c) zk below the mixed layer depth (small θ) (after Chu point below that depth (i.e., zk+1) is constructed to a deeper level with the same number of observational and Fan, 2010b). points as the first vector (i.e., from zk+1 to zk+m). The dual- linear fitting can be represented by 5. Comparison to the Existing Objective cGzzzz(1)+= (1) , , ,... z k k km−−+ km1 k Method ρ()z = { , (5) cGzzz(2)+= (2) , ,... z kk kkm++1 The existing objective method is the curvature

criterion, which requires ∂2T/ ∂z2 (or ∂2ρ/∂z2) to be (1) (2) (1) (2) where ccGkk, , k , G kare the fitting coefficients. minimum (maximum) at the base of mixed layer. We For high resolution (around 1 m), we set compare the maximum angle method to the curvature method as an example. To illustrate the superiority of the 10, for k > 10 recently developed methods, an analytical temperature m = { . (6) profile with ILD of 20 m is constructed by kk−≤1, for 10 ⎧

⎪ 21o C, -20 m <≤ z 0 m Since the vertical gradient has great change at the ⎪ Tz( )=+×+ 21oo C 0.25 C ( z 20 m), -40 m < z ≤ -20 m constant-density (isothermal) layer depth, the angle θk ⎨ ⎪ reaches its maximum value if the chosen depth (zk) is the o o ⎛⎞z + 40 m ⎪7CC+× 9 exp⎜⎟ , -100 m ≤≤ z -40 m. mixed layer depth (see Fig. 4a), and smaller if the chosen ⎩⎪ ⎝⎠50 m depth zk is inside (Fig. 4b) or outside (Fig. 4c) of the mixed layer. Thus, the maximum angle principle can be (9)

1004 1005 This profile was discretized with vertical resolution of 1 each depth. The isothermal depth is 9 m (error of 11 m) m from the surface to 10 m depth and of 5 m below 10 m using the curvature method (Fig. 6b) and 20 m (no error) depth. The discrete profile was smoothed by 5-point using the maximum angle method. Usually, the moving average in order to remove the sharp change of curvature method requires smoothing for noisy data the gradient at 20 m and 40 m depths. The smoothed (Chu, 1999; Lorbacher et al., 2006). To evaluate the profile data [T(zk)] is shown in Fig. 5a. usefulness of smoothing, a 5-point moving average was applied to the 1000 “contaminated” profile data. For the The second-order derivatives of T(z ) versus depth is k profile data (Fig. 6a) after smoothing, the second computed by nonhomogeneous mesh difference scheme, derivatives were calculated for each depth (Fig. 6c). The isothermal depth was identified as 8 m. Performance 2 for the curvature method (with and without smoothing) ∂−−TTTTT1 ⎛⎞kkkk+−11 z ≈−, (10) and the maximum angle method is determined by the 2 k ⎜⎟ ∂−−−zzzzzzzkkkkkk+−+111⎝⎠ − 1 relative root-mean square error (RRMSE),

Here, k = 1 refers to the surface, with increasing values N indicating downward extension of the measurement. 11 ()iac 2 RRMSE=− (HH ) , (12) ac ∑ TT Eq.(10) shows that we need two neighboring values, Tk-1 HNi=1 and T , to compute the second-order derivative at z . T k+1 k ac For the surface and 100 m depth, we use the next point where HT (= 20 m) is the ILD for the original value, that is, temperature profile (Fig. 7a); N (= 1000) is the number ()i of “contaminated” profiles; and HT is the calculated ∂∂22TT ∂ 2 T ∂ 2 T ==, . (11) ILD for the i-th profile. Without 5-point moving ∂∂zz22zz==−=−=−0 1 m ∂ z 2 z 100 m ∂ z 2 z 95 m average, the curvature method identified only 6 profiles (out of 1000 profiles) with ILD of 20 m, and the rest Fig. 5b shows the calculated second-order derivatives profiles with ILDs ranging relatively evenly from 1 m to from the profile data shown in Fig. 5a. Similarly, tan θk is 10 m. The RRMSE is 76%. With 5-point moving calculated using Eq.(8) for the same data profile (Fig. average, the curvature method identified 413 profiles 5c). For the profile data without noise, both curvature with ILD of 20 m, 164 profiles with ILD of 15 m, 3 method (i.e., depth with minimum ∂2T/∂z2, see Fig. 5b) profiles with ILD of 10 m, and the rest profiles with and maximum angle method [i.e., depth with max (tan θ), ILDs ranging relatively evenly from 2 m to 8 m. The see Fig. 5c)] have the capability to identify the ILD, i.e., RRMSE is 50%. However, without 5-point moving HT = 20 m. average, the maximum angle method identified 987 profiles with ILD of 20 m, and 13 profiles with ILD of Without Noise Curvature Method Maximum Angle Method 0 15 m. The RRMSE is less than 3%.

10 With Noise (σ=0.02 C) Curvature Method Smoothed Curvature Method Maximum Angle Method 20 0

30 10

40 20

50 30 Depth (m) 60 40

70 50 Depth (m) 80 60

90 70

100 80 5 10 15 20 25−0.03 −0.02 −0.01 0 0.01−0.1 0 0.1 0.2 0.3 2 θ Temperature (C) Second Derivative (C/m ) tan 90

100 5 10 15 20 −0.125 −0.05 0 0.05 −0.030.1 −0.02 −0.01 0 0.01−0.1 0 0.1 0.2 0.3 2 2 θ Fig. 5. (a) Smoothed analytic temperature profile (6) by 5- Temperature (C) Second Derivative (C/m ) Second Derivative (C/m ) tan 2 2 point moving average, calculated (b) (∂ T/∂z )k, and (c) (tan 2 2 θ)k from the profile data (Fig. 5a). At 20 m depth, (∂ T/∂z )k Fig. 6. One out of 1000 realizations: (a) temperature profile has a minimum value, and (tan θ)k has a maximum value shown in Fig. 7a contaminated by random noise with mean (after Chu and Fan 2010b). of zero and standard deviation of 0.02oC, (b) calculated 2 2 (∂ T/∂z )k from the profile data (Fig. 8a) without smoothing, 2 2 Random noises with mean of zero and standard (c) calculated (∂ T/∂z )k from the smoothed profile data deviation of 0.02oC (generated by MATLAB) are added (Fig. 6a) with 5-point moving average, and (d) calculated to the original profile data at each depth for 1000 times. (tan θ)k from the profile data (Fig. 6a) without smoothing After this process, 1000 sets of temperature profiles were (after Chu and Fan, 2010b). produced. Among them, one temperature profile data is shown in Fig.6a. For this particular profile, the second- 6. Quality Index for Validation order derivatives (∂2T/∂z2) and tan θ were calculated at

1005 1006 Lorbacher et al. (2006) proposed a quality index (QI) Fig. 7. Atlantic Ocean (January): (a) calculated isothermal for determining HD (similar for HT), layer depth (m), and (b) quality index.

Jul (212185 Profiles) with Mean Qulity Index: 0.966 rmsd()ρρ− ˆ | 80 400 kkHH(,1 D ) QI=− 1 , (13) 380 ˆ 360 rmsd()ρρkkHH− |(,1.5)× 60 1 D 340 which is one minus the ratio of the root-mean square 320 40 300 difference (rmsd) between the observed to fitted 280 260 temperature in the depth range from the surface to HD to 20 240 that in the depth of 1.5× HD. HD is well defined if QI > 220 0.8; can be determined with uncertainty for QI in the 0 200

Latitude 180 range of 0.5-0.8; and can’t be identified for QI < 0.5. For 160 the curvature criterion, QI above 0.7 for 70% of the −20 140 Mixed Layer Depth (m) profile data, including conductivity-temperature-depth 120 −40 100 and expendable bathythermograph data obtained during 80 60 World Ocean Circulation Experiment (Lorbacher et al., −60 40 2006). 20 0 −80 −60 −40 −20 0 20 80 1 7. Global (HD, HT) Dataset 0.98

60 0.96

The global (HD, HT) dataset has been established from 0.94 the GTSPP (T, S) profiles using the recently developed 40 0.92 objective methods (optimal linear fitting, maximum 0.9 mix 20 0.88 angle, and relative gradient). The quality index (QI) is of h computed for each profile using (13). To show the 0.86 mix 0 0.84 seasonal variability, the global (HD, HT) data were binned Latitude o o 0.82 by month and averaged in 2 ×2 grid cells. The overall −20 Qulity Index QI value of the quality index is around 0.95 (Figs. 7-12) 0.8 0.78 −40 much higher than the curvature method reported by 0.76

Lorbacher et al. (2006). 0.74 −60 Jan (187730 Profiles) with Mean Qulity Index: 0.949 0.72 80 400 380 0.7 360 −80 −60 −40 −20 0 20 Longitude 60 340 320 Fig. 8. Atlantic Ocean (July): (a) calculated isothermal 40 300 280 layer depth (m), and (b) quality index. 260 20 240 220

0 200

Latitude 180 160

−20 140 Mixed Layer Depth (m) 120

−40 100 80 60 −60 40 20 0 −80 −60 −40 −20 0 20 80 1 0.98

60 0.96

0.94

40 0.92

0.9 mix 20 0.88 of h

0.86 mix 0 0.84 Latitude

0.82 −20 0.8 Qulity Index QI

0.78 −40 0.76

0.74 −60 0.72

0.7 −80 −60 −40 −20 0 20 Longitude

1006 1007

Jan (215506 Profiles) with Mean Qulity Index: 0.978 400 are listed as follows: (a) Procedure is totally objective 60 380 360 without any initial guess (no iteration); and (b) No any 340 40 320 differentiations (first or second) are calculated for the 300 280 profile data. The calculated (HD, HT) are ready to use for 20 260 240 various studies such as the global distribution of barrier

0 220 200 and compensated layers, heat content in the surface

Latitude 180 −20 160 isothermal layer ( heat source for exchange with the

140 Mixed Layer Depth (m) 120 atmosphere), and impact on climate change. −40 100 80 60 −60 40 20 Acknowledgments 0 120 140 160 180 200 220 240 260 280 1 60 0.98 The Office of Naval Research, the Naval 0.96 Oceanographic Office, and the Naval Postgraduate 40 0.94

0.92 School supported this study. We thank DR. Charles Sun

20 0.9

mix at NOAA/NODC for providing GTSPP profile data. 0.88 of h

0 0.86 mix

0.84 Latitude −20 0.82

0.8 Qulity Index QI −40 0.78 0.76

−60 0.74 0.72 0.7 120 140 160 180 200 220 240 260 280 Longitude Jan (HR: 5559 Profiles) with Mean Qulity Index: 0.95 Fig. 9. Pacific Ocean (January): (a) calculated isothermal 400 380 layer depth (m), and (b) quality index. 20 360 340 Jul (253202 Profiles) with Mean Qulity Index: 0.977 10 320 400 300 60 380 0 280 360 260 340 −10 240 40 320 220 −20 300 200

Latitude 180 280 20 −30 160 260

140 Mixed Layer Depth (m) −40 240 120 0 220 100 −50 200 80

Latitude 180 60 −60 40 −20 160 20 140 Mixed Layer Depth (m) −70 0 120 20 40 60 80 100 120 140 1 −40 100 0.98 80 20 60 0.96 −60 40 10 0.94

20 0.92 0 0 0.9 120 140 160 180 200 220 240 260 280 mix 1 −10 0.88 of h

60 0.86 mix 0.98 −20 0.84

0.96 Latitude −30 0.82 40 0.94

0.8 Qulity Index QI −40 0.92 0.78 20 0.9 −50 0.76 mix 0.88 0.74

of h −60

0 0.86 mix 0.72 −70 0.84 0.7 Latitude 20 40 60 80 100 120 140 Longitude −20 0.82

0.8 Qulity Index QI Fig. 11. Indian Ocean (January): (a) calculated isothermal −40 0.78 layer depth (m), and (b) quality index. 0.76 −60 0.74

0.72

0.7 120 140 160 180 200 220 240 260 280 Longitude Fig. 10. Pacific Ocean (July): (a) calculated isothermal layer depth (m), and (b) quality index.

8. Conclusions

In this paper, we established global mixed (isothermal) layer data set using recently developed objective methods with high quality indices (optimal linear fitting, maximum angle). Several advantages of this approach

1007 1008

Jul (HR: 6520 Profiles) with Mean Qulity Index: 0.962 400 GTSPP Workin Group, 2010: GTSPP Real-Time Quality 380 20 360 Control Manual. IOC Manual and Guides 22, pp. 148. 340 10 320 Kara, A. B., P.A. Rochford, and H. E. Hurlburt, 2000: 300 0 280 260 Mixed layer depth variability and barrier layer formation −10 240 220 over the north Pacific Ocean. J. Geophys. Res., 105, −20 200

Latitude 180 16783-16801. −30 160

140 Mixed Layer Depth (m) Lindstrom, E., R. Lukas, R. Fine, E. Firing, S. Godfrey, −40 120 100 −50 G. Meyeyers, and M. Tsuchiya, 1987: The western 80 60 −60 Equatorial Pacific ocean circulation study. Nature, 330, 40 20 −70 0 533-537. 20 40 60 80 100 120 140 1 Lorbacher, K., Dommenget, D., Niiler, P.P., Kohl, A. 0.98 20 0.96 2006. Ocean mixed layer depth: A subsurface proxy of 10 0.94 ocean-atmosphere variability. J. Geophys. Res., 11, 0.92 0 0.9 mix C07010, doi:10.1029/2003JC002157. −10 0.88 of h

0.86 mix Lukas and Lindstrom, 1991: The mixed layer of the −20 0.84 Latitude western equatorial Pacific Ocean. J. Geophys. Res., 96, −30 0.82

0.8 Qulity Index QI −40 3343-3357. 0.78 −50 0.76 Sun, L.C., 2008: GTSPP Bi-Annual Report for 2007 – −60 0.74 2008. pp.14. The document can be downloaded from: 0.72 −70 0.7 http://www.nodc.noaa.gov/GTSPP/document/reports/GT 20 40 60 80 100 120 140 Longitude SPPReport2007-2008V2.pdf. Fig. 12. Indian Ocean (July): (a) calculated isothermal Wyrtki, K., 1964. The thermal structure of the eastern layer depth (m), and (b) quality index. Pacific Ocean. Dstch. Hydrogr. Zeit., Suppl. Ser. A, 8, 6- 84.

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