國立臺灣大學理學院海洋研究所 碩士論文
Institute of Oceanography College of Science
National Taiwan University Master Thesis
2018 年馬登-朱利安振盪(Madden-Julian Oscillation)活躍 期下風所引發之混合層加深
Wind-Induced Mixed Layer Deepening under the Active Phase of Madden-Julian Oscillations (MJOs) in 2018
葉伏家 Fu-Chia Yeh
指導教授：許哲源 博士 Advisor: Je-Yuan Hsu, Ph.D.
中華民國 111 年 12 月 December 2022
致謝
時間很快來台大也超過兩年了，在海研所的期間，修了不少課也參與五次的 航次，讓我對海洋更了解了不少，今天能完成論文，受到許多老師、同學們的幫 助，其中最感謝的莫過於我的指導教授許哲源老師，從暑假一開始找老師就給我 許多論文上的啟發，也循序漸進的帶領我了解論文所關注的議題與方向，這讓我 學習到如何去思考物理海洋上的問題，與做一個研究的過程，研究過程中老師也 給予我很大的彈性與自由規劃我自己的研究歷程，這都是我能在物理海洋學習的 一大助力。此外也要感謝張明輝老師和鄭宇昕老師，在每周的 meeting 中總是能 給我不同專業的觀點，讓我能從更多元的角度來討論我的研究，並最後擔任我的 口試委員，也謝謝曾于恒老師在模式上給予的建議，碩一跟曾老師修的課十分受 用。最後要謝謝清森跟芳瑜，雖然研界領域差比較多，但你們總是能抽空一起練 習報告或分享研究生活大小事，能和你們一路從中山來台大當同學十分的幸運，
我也會珍惜這段和你們一起學習的時光。
摘要
在北半球冬季，馬登-朱利安振盪 (MJO) 為季節內天氣系統具有顯著的深對 流，從印度洋西部開始沿著赤道向東移動。2018 年 11 月在澳洲西北所佈放的兩個 EM-APEX floats、兩個 ALAMO floats 和一個 FIO buoy，測量 2018 年 12 月中旬 MJO 通過期間的海洋溫度、鹽度、水平流速與基本大氣參數。自 12 月 14 日以來，
浮標量測到混合層在五天內從25m 快速加深到 50m，並且該段時間內 MJO 所帶來
的西風維持9 ms-1以上，引起高達0.4 ms-1的海流，破壞上層海洋的穩定。透過計
算梯度理查森數(Ri)以發現不穩定性，由於經常觀測到小於 0.25 的 Ri，因此推測
在強風作用下，上層海洋可能會出現不穩定和強烈的紊流混合。本研究使用Thorpe
scale 方法估算紊流耗散率，結果顯示混合層的紊流耗散率約為 10-7 Wkg-1至 10-6
Wkg-1，大於典型溫躍層內的紊流耗散率。在MJO 連續幾天的風力作用下，剪切不
穩定可能會發生強烈的紊流混合，從而使混合層加深。混合層加深導致海表溫度
(SST)冷卻約 1.1°C，SST 的變化改變了潛熱加顯熱量由 100 Wm-2增至400Wm-2，
並有可能影響MJO 的發展。由於混合層加深可能有助於海表冷卻，因此 MLD 變
化在模式模擬中至關重要，研究中模式結果顯示，在MJO 下使用 COARE 3.0 算法
計算的風應力可能低估。因此通過觀測資料測量與估算正確風應力，可以在模式中
更好地模擬MJO 觀測的特徵，並進一步改進 MJO 的預報。
關鍵詞：馬登-朱利安振盪(MJO)、混合層加深、海表溫度冷卻、COARE 3.0、風 應力
Abstract
During the boreal winter, Madden–Julian Oscillations (MJOs) as organized deep
convections and intra-seasonal weather systems propagate eastward along the equator,
starting from the west of the Indian Ocean. Two EM-APEX, two ALAMO floats, and an
FIO buoy were deployed in the northwest coast of Australia, which captured the ocean
responses of temperature, salinity, and horizontal current velocity during the passage of
one MJO in the middle of December 2018. The four floats captured a rapid deepening of
mixed layer depth (MLD) from 25 m to 50 m since 14th Dec in five days. At the same
time, strong westerly wind associated with MJO was mostly > 9 m s-1. The wind-induced
a strong current up to 0.4 m s-1 for destabilizing the upper ocean. The gradient Richardson
number (Ri) was computed for identifying the instability. Because the low Ri < 0.25 was
frequently observed, instability and strong turbulence might occur in the upper ocean
under the strong wind forcing. Using the Thorpe-scale method, the turbulent dissipation
rate was approximately 10-7 to 10-6 W kg-1 in the MLD, which was larger than those within
the typical thermocline. Strong turbulent mixing might occur via shear instability under
the consecutive days of wind forcing, thereby MLD deepening. MLD deepening
contributed to cooling sea surface temperature (SST) by about 1.1 °C. The heat fluxes
were modulated by SST variation from 100 to 400 W m-2. The heat flux variation might
affect the development of MJOs. Because MLD deepening may contribute to the cooling
of SST, the simulation of MLD variation is critical in models. In the study, model results
demonstrate that the computation of the wind stress using the COARE 3.0 algorithm may
be underestimated under MJO. Therefore, with correct wind stress based on the float
measurements, several features of the observations can be better captured in models and further improve MJOs’ forecasts.
Keywords: Madden–Julian Oscillations, Mixed layer deepening, SST cooling, COARE
3.0 algorithm, wind stress.
Content
致謝……….………i
摘要……….……….………...ii
Abstract ... iii
Content ... v
List of Figures ... viii
List of Tables ... xiii
1 Introduction ... 1
2 Measurements under the MJO in 2018 ... 4
2.1 Profiling floats and buoy measurement ... 4
2.2 Other datasets in the study ... 7
2.3 Madden-Julian Oscillation in 2018 ... 8
3 Upper ocean structure and atmosphere responses to the MJO ... 11
3.1 Surface wind, ocean responses, and SST cooling ... 11
3.1.1 Surface wind on the buoy ... 11
3.1.2 Upper ocean structure ... 12
3.1.3 Current velocity ... 15
3.2 Heat fluxed variations ... 16
3.3 Summary to MJO in 2018 ... 17
4 Wind-induce mixed layer deepening ... 19
4.1 Mixed layer depth deepening ... 19
4.2 Gradient Richardson number ... 21
4.3 Thorpe scale method and dispassion rate ... 23
4.4 Summary of mixed layer depth deepening ... 25
5 Effect of Turbulent Mixing under MJOs ... 26
5.1 Model description ... 26
5.2 Simulating mixed layer depth deepening ... 28
5.3 Effects on vertical resolution in the upper ocean ... 29
5.4 Parameters in the KPP mixing scheme ... 31
5.5 Summary of MLD simulation by using KPP ... 33
6 Momentum and Buoyancy Response during MJOs ... 35
6.1 Wind drag coefficient ... 36
6.2 Wind-induce current ... 37
6.3 Linear momentum budget method and wind stress ... 40
6.3.1 Linear momentum budget method ... 40
6.3.2 Wind stress ... 41
6.4 Buoyancy flux effect ... 45
7 Conclusion and discussion ... 47
Reference ... 51
List of Figures
Fig. 1: The trajectories of AL9207 (black), AL9209 (cyan), EM8487 (green), and
EM8488 (purple) from 11th Dec to 21st Dec 2018. The position of the FIO buoy is
displayed as a white point. Geostrophic current (black arrows) derived Sea surface
height anomalies (shading) from NOAA altimetry data of 14th Dec. ... 6
Fig. 2: (a) Daily OLR anomalies from NOAA and (b) TRMM precipitation rates
averaged over 10°S–10°N from 50°E–130°E during Oct–Dec 2018. The dashed
lines are the location longitude of the buoy. (c) Mean OLR and Mean precipitation
rates averaged over 10°S–10°N at 115.1°E. ... 9
Fig. 3: RMM1 and RMM2 index through 8 different areas. The index outside this center
circle is regarded as an MJO moving from west to east. Contrastingly, MJO is
considered weak when this is within the center circle. ... 10
Fig. 4: (a) Wind speed at 4 m height on the buoy above the sea surface (b) east-west
component (c) north-south component of wind speed. ... 12
Fig. 5: Temperature profiles of (a) AL9207, (c) AL9209, (d) EM8487, and (g) EM8488.
Salinity of (b) AL9207, (d) AL9209, (f) EM848, and (h) EM8488. ... 14
Fig. 6: (a) SST of AL9207 (blue line) and AL9209 (orange line) and (b) Himawari-8
satellite measurements of skin-SST at AL9207 (blue line), AL9209 (orange line)
Fig. 7: (a) East-west components and(b) north-south components of measurements of
current velocity taken by EM8487. (c) East-west and (d) north-south components
of measurements of current velocity taken by EM8488. The missing data are expressed with gray dots. ... 16
Fig. 8: (a) Latent heat plus sensible heat flux (orange line: AL9207; green line:
AL9209). (b) Shortwave radiation (yellow line) and longwave radiation (pink line)
on buoy. (c) Surface air temperature (blue line), and SST (orange line: AL9207;
green line: AL9209) (d) Relative humidity on buoy measurement. ... 18
Fig. 9: (a)–(d) Surface MLD (magenta lines) and buoyancy frequency N2 (shading)
derived from two ALAMO floats and two EM-APEX floats measurements
AL9207, AL9209, EM8487, and EM8488, respectively. The negative values of N2
are expressed with pink dots. The missing data are expressed with gray dots. ... 20
Fig. 10: (a) and (d) are the buoyancy stratification N2 (shading) derived from EM8487
and EM8488. The negative values of N2 are expressed with pink dots. (b) and (e)
are vertical sheer square of EM8487 and EM8488 (c) and (f) are (1/Ri) – 4 and
surface MLD (black lines) of EM8487 and EM8488. The missing data are
expressed with gray dots. ... 22
Fig. 11: (a) and (b) are TKE dispassion rate and MLD (black lines) estimated by Thorpe
scale method. The value below 10-11 are denoted with gray dots. (c) and (d) are
(1/Ri) – 4 and surface MLD (black lines)... 24
Fig. 12: (a)–(c) Simulations of MLD deepening at the different initial conditions of
three floats in KPP (blue line), with the comparison to the float observation (black
line). ... 29
Fig. 13: Different vertical resolutions on simulations of MLD (a)–(c) at AL9207,
AL9209, and EM8487 (blue: 4 m; orange: 2 m; yellow: 1 m), with the comparison
to the float observation (black line). ... 30
Fig. 14: Different gradient Richardson number on simulations of MLD (a)–(c) at
AL9207, AL9209 and EM8487 (blue: Ri0 = 0.4; orange: Ri0 = 0.7; yellow: Ri0 =
1), with the comparison to the float observation (black line). ... 32
Fig. 15: Different bulk Richardson number on simulations of MLD (a)–(c) at AL9207,
AL9209 and EM8487 (blue: Ric = 0.3; orange: Ric = 0.5; yellow: Ric = 0.7), with
the comparison to the float observation (black line). ... 33
Fig. 16: Current velocity averaged from 0 m to 20 m depth of EM8487 (blue line) and
ROMS (orange line). ... 35
Fig. 17: Different magnitude of wind stress on simulations of MLD (a)–(c) at AL9207,
AL9209 and EM8487, (blue: wind stress estimated from COARE 3.0; orange: 1.2
times; yellow: 1.5 times; purple: 1.8 times of wind stress), with the float
observation (black line). ... 37
Fig. 18: Power spectrum density of (a) east-west current and(b) north-south current. .. 38
Fig. 19: East-west components of (a) current velocity, (b) semi-diurnal-tide, and (c)
inertial current; north-south components of (d) current velocity (e) semi-diurnal-
tide, and (f) inertial current. The missing data are expressed with gray dots. ... 39 Fig. 20: (a) East-west and (b) north-south component of EM8487 measurement
excluding semi-diurnal tides and background current (c) East-west and (d) north-
south component of ROMS results which have been adjusted with time lags. ... 40
Fig. 21. Depth-integrated comparisons of float observations (black line with one
standard deviation error bars) and KPP simulations (orange: COARE 3.0
estimated; blue: 1.5 times; green: 1.8 times of wind stress) during the MJO. (a) and
(c) is the time rate change momentum of U and V components, respectively. (b)
and (d) is Coriolis force terms of U and V components, respectively. ... 44
Fig. 22: The drag coefficient Cd as a function of wind speed at 10 m above the sea
(yellow: Large and Pond,1981; green: COARE 3.0 estimated; blue: derived from
observation; orange: derived from 1.35 times of wind with one standard deviation
error bars) ... 44
Fig. 23: The heat flux input in MLD simulation of COARE 3.0 estimated (blue line);
estimated value + 50 W m-2 (orange line); estimated value – 50 W m-2 (yellow line)
compare to the float observation (black line) at (a)–(c) at AL9207, AL9209 and
EM8487. ... 46
List of Tables
Tab. 1: Floats measured properties and resolution. ... 7
1 Introduction
Madden‐Julian oscillations (MJO, Madden & Julian, 1972), an intraseasonal
planetary‐scale weather system, propagate eastward through the tropical warm pool. MJO
convection typically consists of large-scale coupled patterns in atmospheric circulation
associated with surface westerly wind bursts and heavy precipitation (Zhang 2005).
Strong oceanic responses to the westerly wind bursts result in a cooling of the ocean
mixed layer and SST (Hendon et al., 1998; Vialard et al., 2008; Moum et al., 2014).
Several model studies have illustrated that air-sea heat and moisture fluxes can be
modeled significantly by upper ocean structure and SST variation. The change of air-sea
heat and moisture fluxes involve the MJOs convection evolution and propagation (Bernie
et al., 2008; DeMott et al. 2015; Ruppert and Johnson, 2015). Owing to this, exploring
the interaction between atmospheric features of MJOs and the upper ocean responses can
aid the model prediction on intraseasonal weather systems.
The ocean mixed layer (ML) is commonly considered the layer from the sea surface
to the top of the seasonal thermocline where features vertically quasi-homogeneous in
temperature or density due to well mixed by turbulence (Kara et al., 2000, Lorbacher et
al., 2006). Surface mixed layer depth (MLD) is important in the heat budget because it
determines heat content and the water column to which net surface heat flux is distributed.
(Chen et el., 1994). The temperature within MLD decrease during MJO through the
entrain of colder water, which is caused by turbulent mixing at the base of ML. As
previous studies and observations in the stratified ocean suggested (Vialard et al., 2013;
Moum et al., 2014; Marshall and Hendon, 2014), the shear of horizontal current due to
direct wind influences is the principal factor for rapid upper ocean cooling, while the wind
is effective. Because significant westerly wind bursts often occur during the active phase
of MJOs, studying the effect of wind is critical for understanding the momentum
transported into the ocean in the MJO-ocean interaction.
Note that the westerly wind associated with the MJO (Wyrtki, 1973; Nagura and
McPhaden, 2008; Schott et al., 2009) may generate significant vertical shear in the surface
mixed layer. Once the ratio of buoyancy frequency squared to vertical shear squared, i.e.,
the gradient Richardson number, is less than 0.25, it may induce the shear instability
(Miles and Howard, 1961). Strong turbulence due to the shear instability may then
destabilize the stratified oceans to deepen the surface mixed layer (Yusuke Ushijima et
al., 2020). Model studies on the wind-driven deepening of ML demonstrate the factors
regarding turbulence process, which include buoyancy and energy source to vertical shear
for instability (Price et al., 1986; Large et al., 1994). Thus, quantitating the MLD
deepening rate as well as the momentum transport into the ocean is essential to better
understanding and simulating such upper ocean processes on MJOs.
In November 2018, the Centre for Southern Hemisphere Oceans Research (CSHOR)
and China’s First Institution of Oceanography conducted a collaborative field campaign
to explore the air-sea interaction in the Indonesian Australian Basin (Feng et al. 2020).
The observations of an MJO event were documented in this study. The surface wind speed
was measured up to 10 m s-1 during the MJO active phase. At the same time, the MLD
deepened rapidly from 25 to 50 m in five days, which is more rapidly than the response
to the mature stage of the Indian summer monsoon (Liu et al., 2021). In the first two days
following the arrival of MJO, the SST was cooling > 1 °C. Because the temperature
between SST and air temperature rose, the heat flux into the ocean is increased to 400 W
m-2. In the following, the observations and data will be described in section 2. The upper
ocean responses and flux variation between air-sea is discussed in section 3. Then, the
dynamic of MLD deepening will be presented in Section 4. The comparison of the
observations with the model results using the K-profile parameterization (KPP) as well
as the momentum budget estimated will be highlighted in Sections 5 and 6, respectively.
2 Measurements under the MJO in 2018
2.1 Profiling floats and buoy measurement
Six Air Launched Autonomous Micro Observer (ALOMO, AL9205, AL9206,
AL9207, AL9208, AL9209, AL9210) profiling floats and two Electromagnetic
Autonomous Profiling Explorer (EM-APEX, EM8487 and EM8488) floats were
deployed at 115.3 °E and 16.8 °S on 22nd Nov, 2018 (Feng et al. 2020). Four floats
(AL9207, AL9209, EM8487 and EM8488) remained and profiled the upper ocean
structure until the middle of December. An anti-cyclonic eddy trapped the floats during
December, 2018. AL9207, AL9209, and EM8487 were located in the south and drifted
eastward; whereas the EM8488 was situated on the east side and drifted northward (Fig.
1). A mini-version of the Bailong buoy system from the FIO lab (Cole et al. 2011) was
deployed at 16.5°S, 115.1°E on 21st Nov (Fig. 1). This Bailong buoy system was engaged
in measuring the surface air temperature, pressure, humidity, surface winds, shortwave
and longwave radiations at 10 min intervals. With satellites, the real-time data which
recorded from the buoy were transmitted to the FIO lab. The wind is ~ 5 to 6 m s-1 from
14th to 17th Dec 2018.
The two ALOMO floats and two EM-APEX floats were equipped with different
types of CTD sensors (SBE-41 on AL9207, EM8487, EM8488 and RBR on AL9209),
making the discrepancy on vertical and temporal resolution, as well as the SST estimating.
AL9207 and AL9209 profiled from sea surface down to 300 m and 500 m, respectively.
EM8487 and EM8488 profiled from about from 10 m to 300m. The vertical resolution of
temperature and salinity on SBE-41 mounted on ALOMO floats (AL9207) and EM-
APEX (EM8487, EM8488) was 1 m and 3.5 m, respectively. For the CTD measurements
taken by the RBR at AL9209, the vertical resolution was 0.1 m in the upper 5 m and 1 m
below 5 m. ALOMO floats profiled during the ascending phase, and the temporal
resolution between each profile is 8 h at AL9207 and 3 h at AL9209 (Feng et al. 2020).
EM-APEX profiled during ascending and descending phases. The temporal resolution of
a cycle of ascending and descending was 2 hours. (Sanford et al., 2005; Hsu et al., 2017).
For the estimation of SST, ALAMO floats record the temperature during ascending,
corresponding to the measured pressure less than 0.2 dbar. Because the SBE-41 CTD
sensor at AL9207 did not measure in the upper 1 m, after the float entered the mission of
surface phase, the first value of temperature measurements at about 0.1 or 0.2 bar was
used as SST. The estimated SST was several degrees higher than those at pressures < 0
dbar, similar to the typical difference between the SST and air temperature in the region
(Hsu et.al 2022). On the AL9209, SST was found by the highest temperature where at
around 0.2 m depth in the upper 1 m, after excluding air temperature which salinity
measurements were < 32 psu in the samples.
Except temperature and salinity, two orthogonal pairs of electrodes on the EM-
APEX floats can measure the voltage. The horizontal current was obtained from EM-
APEX floats which measured the electric and magnetic fields in the ocean (Sanford et al.
2005). The electromagnetic currents, induced by seawater motion, is measured and used
to estimate the oceanic current velocity based on the principle of motional induction
(Sanford et al. 1978). The vertical resolution of horizontal current velocity was around
3.1 m.
Fig. 1: The trajectories of AL9207 (black), AL9209 (cyan), EM8487 (green), and
EM8488 (purple) from 11th Dec to 21st Dec 2018. The position of the FIO buoy is
displayed as a white point. Geostrophic current (black arrows) derived Sea surface height
anomalies (shading) from NOAA altimetry data of 14th Dec.
Tab. 1: Floats measured properties and resolution.
2.2 Other datasets in the study
Several other datasets are utilized for describing atmospheric and oceanic states
during the passage of the MJO. The satellite altimetry data is provided by the NOAA
Laboratory, which can be used for computing the geostrophic current. Daily outgoing
longwave radiation (OLR) data from NOAA (https://psl.noaa.gov) and precipitation data
from the near-real-time legacy product of Tropical Rainfall Measuring Mission (TRMM)
Multi satellite Precipitation Analysis (Huffman and Bolvin 2018) is used to identify the
propagation of MJO convection. The fifth generation European Centre for Medium-
Range Weather Forecasts (ECMWF) reanalysis (ERA5; Hersbach et al. 2020) with
horizontal resolution of 0.25° × 0.25° is used to compare the atmosphere data measured
by the buoy. Himawari-8 satellite measurements of SST were used to compare with the
SST on floats (https://registry.opendata.aws/noaa-himawari). Because the floats only Float name Measurements Profiling depth Vertical resolution Temporal resolution
AL9207 Temperature, Salinity 500 m 1 m 8 hours
AL9209 Temperature, Salinity 350m Upper 5 m: 0.1 m Below 5 m: 1 m
3 hours
EM8487 Temperature, Salinity, current velocity
10m-300m CTD: 3.5 m Current: 3.1 m
~2 hour
EM8488 Temperature, Salinity, current velocity
10m-300m CTD: 3.5 m Current: 3.2 m
~2 hour
profile the temperature and salinity in the upper around 300 m on three floats and 500 m
on a float, HYCOM GOFS 3.1 (https://www.hycom.org/dataserver/gofs-3pt1/analysis) is
used for the initial condition of deep ocean in the model’s run in section 5.
2.3 Madden-Julian Oscillation in 2018
The MJO active phase is characterized with the presence of a deep convective
anomaly (Wheeler and Hendon 2004). Therefore, the remote-sensing measurements of
precipitation and outgoing longwave radiation (OLR) from 10 °N to 10 °S are used to
identify the convective events due to the MJOs. The anomalies with the eastward
propagation of the convective systems are regarded as activate phase of MJO events (Fig.
2). We also use the RMM1 and RMM2 indexes (Real-time Multivariate MJO series 1, 2;
Wheeler and Hendon, 2004), provided by Australia Bureau Meteorology (BoM), to
describe the evolution of the MJO along the equator. RMM1 and RMM2 are mathematical
methods which combine cloud amount and winds at upper and lower levels of the
atmosphere. The index provides MJO strength and location in 8 different areas (Fig. 3).
In the middle of December, an eastward propagating signal arrived at the longitude
of the buoy and floats. Despite the rain did not increase significantly, the mean OLR
which was from 10 °N to 10 °S, started to decline from 230 W m-2 to 190 W m-2 on 14th
Dec. Meanwhile, the RMM1 and RMM2, which combined cloud amounts and winds at
upper and lower atmosphere levels, demonstrated an MJO event that went through the
north of Australia (http://www.bom.gov.au/climate/mjo/). The arrival time of MJO
convection explained why the wind speed measurements at the buoy were > 6 m s-1 since
14th Dec. Therefore, these five days were defined as the MJO activity phase in the study.
Fig. 2: (a) Daily OLR anomalies from NOAA and (b) TRMM precipitation rates averaged
over 10°S–10°N from 50°E–130°E during Oct–Dec 2018. The dashed lines are the
location longitude of the buoy. (c) Mean OLR and Mean precipitation rates averaged over
10°S–10°N at 115.1°E.
Fig. 3: RMM1 and RMM2 index through 8 different areas. The index outside this center
circle is regarded as an MJO moving from west to east. Contrastingly, MJO is considered
weak when this is within the center circle.
3 Upper ocean structure and atmosphere responses to the
MJO
Based on satellite data, MJO passed the location of floats and buoy from 14th to 17th
Dec 2018. During the MJO passage, ocean temperature, salinity, current velocity profiles,
and several atmosphere parameters were recorded. Below, we will use these data sets to
explore the upper ocean response to the MJO and corresponding oceanic feedback to the
MJO’s deep convection.
3.1 Surface wind, ocean responses, and SST cooling
3.1.1 Surface wind on the buoy
During the MJO active phase, the wind direction was mainly toward northeast (Fig.
4), and consistent with the ECMWF wind data. The wind speed increased up to around
10 m s-1 when MJO convection arrived. The meridional wind did not change significantly
in the MJO period and maintained about 6 m s-1. On the other hand, the westerly wind
increased from approximately 3 m s-1 to 6 m s-1 from 12th Dec to 14th Dec. The wind speed
is ~ 5 to 6 m s-1 until the end of MJO. The increasing wind may enhance the mixing in
the upper ocean.
Fig. 4: (a) Wind speed at 4 m height on the buoy above the sea surface (b) east-west
component (c) north-south component of wind speed.
3.1.2 Upper ocean structure
The float measurements were used for exploring the upper ocean response to the
MJO. The temperature in the upper 20 m of three floats was greater than 28 °C from 13th
to 14th Dec 2018 before the MJO and generated a warm layer. When the MJO convection
arrived at the float positions, the temperature dropping was found with the four floats in
the upper 20 m and extended to the upper 40 m due to the vertically mixed (Fig. 5). The
mean temperature in the upper 20 m decreased by 1.0 °C in three days at AL9207 and
AL9209. It was similar to the change of the SST, cooled by about 1.0 °C (AL9207) and
1.2 °C (AL9209) within the same period. Because EM8487 and EM8488 did not measure
the temperature above 15 m, the temperature was averaged from 15m to 20 m, and both
values were 0.5 °C drop in the same period. Since the SST is the uppermost temperature
of the ocean layers, the SST cooling and decrease of upper-ocean temperature should
result from the entrainment of colder water below the mixed layer during the MJO.
Studying dynamics for inducing the entrainment of cold water during the MJO active
phase is crucial.
On the other hand, the salinity was around 34.5 psu in the upper 30 m at AL9207 and
EM8487, which was 0.1 higher than AL9209 on 14th Dec when MJO arrived. In the
following five days, the salinity increased by about 0.5 psu. At EM8488, the salinity was
homogenous about 34.4 psu in the upper 50 m during the concerned period. The decrease
in salinity might be caused by rising evaporation due to the increase in wind speed. On
these four floats, a lower salinity layer was found within 40 m to 60 m, and the difference
came by 0.15 psu with the upper layer. These led to a strong stratification at that depth.
Besides the floats measurements for exploring the vertical change of upper ocean
structure, satellite data were also used to discuss the spatial variations of SST cooling (Fig.
6). The spatial variation of skin SST data were obtained from Himawari-8 satellite
measurements, which removed the low-quality data and averaged the nearest eight data
points (0.5°×0.5° region) from the float position. The comparison demonstrated that the
skin SST had the same cooling trend than the floats’ SST, despite it was 2 °C larger than
floats. Therefore, even the SST measurement at the floats was the sea state at the single
points, the change of SST was still consistent with the general trend of SST within this
region. The skin-SST of EM8488 was around 1 °C higher than the other floats in that
EM8488 was located farther north than the others (Fig. 1).
Fig. 5: Temperature profiles of (a) AL9207, (c) AL9209, (d) EM8487, and (g) EM8488.
Salinity of (b) AL9207, (d) AL9209, (f) EM848, and (h) EM8488.
Fig. 6: (a) SST of AL9207 (blue line) and AL9209 (orange line) and (b) Himawari-8
satellite measurements of skin-SST at AL9207 (blue line), AL9209 (orange line) and
EM8487 (green), and EM8488 (magenta).
3.1.3 Current velocity
Horizontal current velocity was measured from EM8487 and EM8488, which
provided information on current magnitude and variation under the MJO westerly wind
(Fig. 7). Before the passage of MJO’s deep convection, horizontal current at EM8747 was
less than 0.2 m s-1 in the upper 100 m. When the MJO convections arrived, the eastward
current accelerated to 0.4 m s-1 in the upper 60 m, whereas north-south did not change
apparently. The accelerated eastward current might be caused by the strong westerly wind
(Fig. 4). It might induce strong vertical shear of horizontal current and vertical mixing via
shear instability mixing. On EM8488 east-west current decreased from 0.2 m s-1 to -0.1
m s-1, consistent with the variation of the magnitude of geostrophic current from sea
surface height anomalies (Fig. 1).
Fig. 7: (a) East-west components and(b) north-south components of measurements of
current velocity taken by EM8487. (c) East-west and (d) north-south components of
measurements of current velocity taken by EM8488. The missing data are expressed with gray dots.
3.2 Heat fluxed variations
Air-sea heat fluxes were computed by using the atmospheric measurements from the
buoy and float measured SST, based on the COARE 3.5 algorithm (Fairall et al. 1996a;
Fairall et al. 2003) (Fig. 8). Because the SST was cooled by 1.1 °C in three days, the
difference between air temperature and SST increased from 1 to 2.5 °C during the active
phase. The increase of wind speed can also favor the evaporation, thereby latent heat
changing. Additionally, the dry southerly winds from the Australian continent might
influence the humidity drop at the air-sea interface from 16th to 20th Dec (Feng et al. 2020).
The decline in humidity also favored the evaporation. The latent (LH) plus sensible heat
flux (SH) therefore rose from 100 to 400 W m-2 between 14th and 18th Dec. The downward
shortwave radiation decreased by about 50 W m-2 on 13th Dec and 16th Dec. The flux
variation affected the convection development. During the MJO active phase, SST
cooling caused by probable vertical mixing resulted in heat flux variation, which affected
convection development. In other words, the dynamics that control the SST change
magnitude in the upper ocean are essential in MJO evolution.
3.3 Summary to MJO in 2018
During the MJO convection from 14th to 18th Dec, a buoy, two ALAMO floats, and
two EM-EPAX floats recorded the ocean and atmosphere variations. After the arrival of
MJO convection to the floats, the wind raised to 10 m s-1. The horizontal current increased
0.4 m s-1 at EM8487 in upper 40 m simultaneously. The stronger current might destabilize
ocean stratification via shear instability. As a result, the colder water below entrained to
the mixed layer, resulting in the upper ocean and SST cooling at about 1.1 °C. The heat
flux was modified from 100 W m-2 to 400 W m-2 by the SST variation and might
significantly affect the convection system development.
Fig. 8: (a) Latent heat plus sensible heat flux (orange line: AL9207; green line: AL9209).
(b) Shortwave radiation (yellow line) and longwave radiation (pink line) on buoy. (c)
Surface air temperature (blue line), and SST (orange line: AL9207; green line: AL9209)
(d) Relative humidity on buoy measurement.
4 Wind-induce mixed layer deepening
Based on the buoy and floats measurement, the increase of wind and the acceleration
of horizontal current in the upper 40 m occur simultaneously. The stronger current may
destabilize ocean stratification via shear instability. This section will therefore explore
factors for causing the change in surface MLD.
4.1 Mixed layer depth deepening
Multiple MLD criteria are proposed, including temperature and density-based criteria
such as temperature difference near the ocean surface (Wyrtki 1964) or density gradient
criteria (Lukas and Lindstrom 1991). Here, we compute the MLD by exploring the
difference of potential density between MLD and reference depth z0 that exceed a
constant. The z0 is choose arbitrarily to exclude the unknown spikes on density gradient
caused by turbulence near the sea surface. In this study, the MLD is estimated by fulfilling
density difference larger than 0.15 kg m-3 that is Δρ = ρ(MLD) – ρ(z0) > 0.15 kg m-3
where z0 = 15 m. The z0 chosen in the study is to avoid the warm layer in the upper 10 m
to 12 m formed on the 13th, which may be associated with sudden wind precipitous fall.
The Brunt-Väisälä frequency (N2) is often used for discussing the density
stratification and express as:
N2 =−g ∂ρ ρ0∂z
N2 was estimated by temperature and salinity measurements of four floats. High N2
from 25 m to 50 m was consistent with the change of MLD in the concerning period (Fig.
9). During the MJO active phase from 14th to 17th Dec 2018, the MLD was deepened
rapidly from 25 m to 50 m in five consecutive days which was captured by the four floats
simultaneously. Strong vertical turbulent mixing might cause the rapid decline of MLD,
thereby the upper ocean cooling. According to the negative N2 ubiquitous above MLD,
i.e., the inversion of seawater density, the upper ocean was under the unstable conditions.
The major forcing for the instability will be discussed in the next part.
Fig. 9: (a)–(d) Surface MLD (magenta lines) and buoyancy frequency N2 (shading)
derived from two ALAMO floats and two EM-APEX floats measurements AL9207,
AL9209, EM8487, and EM8488, respectively. The negative values of N2 are expressed
with pink dots. The missing data are expressed with gray dots.
4.2 Gradient Richardson number
The study discusses the stability within the stratified shear flow by computing the
gradient Richardson number (Ri), which also aims to find where the probable turbulent
mixing happened. It is defined as
Ri = 𝑁2 𝑆2 =
−g ∂ρ ρ0∂z (𝜕𝑈
𝜕𝑧)2+ (𝜕𝑉
𝜕𝑧)2
where N2 is buoyancy frequency, g is the gravity acceleration, ρ is the situ density, ρ0 is
the reference density, S is the vertical shear term, U is eastward components, V is
eastward component of current, and z is the vertical coordinate. Ri is the proportion of
stratified layer and shear flow. If the shear flow supplies sufficient kinetic energy,
turbulence can overcome the stratified barrier, and mixing occurs. Miles (1961) and
Howard (1961) demonstrated that Ri, of 0.25, is a linear stability threshold. Weak
stratified or strong shear within the stratified shear flow can result in Ri < 0.25 and
generate shear instability. The enhanced shear production term in the TKE budget will
favor the growth of turbulence and thereby turbulent mixing. Contrastingly, when Ri >
0.25 everywhere in the fluid, flows are stable.
Ri was computed by EM8487 and EM8488 velocity and density measurements (Fig.
10). When the MJO convective arrived, Ri less than 0.25 occurred frequently above the
MLD on EM8487 and EM8488. Within the MLD, the horizontal current was accelerated
by stronger wind MJO brought, making the shear term in Ri large enough to reach the
threshold of 0.25. Namely, due to the stronger current and night time surface cooling,
instability occurred above the MLD. The instability might contribute to the density
inversion in the ML, and the deepening of MLD should result from the corresponding
turbulent mixing.
Fig. 10: (a) and (d) are the buoyancy stratification N2 (shading) derived from EM8487
and EM8488. The negative values of N2 are expressed with pink dots. (b) and (e) are
vertical sheer square of EM8487 and EM8488 (c) and (f) are (1/Ri) – 4 and surface MLD
(black lines) of EM8487 and EM8488. The missing data are expressed with gray dots.
4.3 Thorpe scale method and dispassion rate
Based on the observed N2 and small Ri at the floats, strong turbulent mixing occurred
and related to the passage of MJO’s deep convection. Here, we will estimate the turbulent
kinetic energy (TKE) dissipation rate to quantify the magnitude of turbulent mixing.
Thorpe (1977) assumes the kinetic energy of turbulent eddy transfers to potential energy,
resulting in the displacement of a fluid particle. Explaining more, the density
measurements profile is reordered to a gravitationally stable profile in which density
increase with depth. The fluid particles' vertical distance must be moved adiabatically in
this process, and the density displacement is Thorpe displacement. The Thorpe scale is
computed by using the root mean square of Thorpe displacement. The turbulent
dissipation rate is estimated by Thorpe scale (Fig. 11), using EM8487 and EM8488
density profiles. The estimation of turbulent dissipation rate is approximately between
10-8 to 10-6 W kg-1 above the MLD during the MJO active phase. The number is more
significant than the estimated value of low wind conditions in the area, which was about
10-11 to 10-10 W kg-1 within the thermocline.
When current shear is strong enough or stratification is weak enough, the Ri will
decrease to reach the threshold of < 0.25. It will result in Kelvin-Helmholtz instability.
Because of the westerly wind (Section 3), the vertical shear of horizontal current could
be 3 × 10-4 s-2. Despite strong stratification within the thermocline, Ri lowered by the
strong vertical shear was typically below 0.25 in the upper ocean. The shear instability
associated with the low Ri might enhance turbulence kinetic energy, which would
ultimately become potential energy or heat. The momentum from wind stress contributed
to current shear that countered the stabilizing effect of density stratification, thereby
generating the shear instability. To sum up, the change of MLD during our experiments
was forced by the momentum transition from wind to current flow. The entrainment of
cold water might then cool the SST.
Fig. 11: (a) and (b) are TKE dispassion rate and MLD (black lines) estimated by Thorpe
scale method. The value below 10-11 are denoted with gray dots. (c) and (d) are (1/Ri) –
4 and surface MLD (black lines).
4.4 Summary of mixed layer depth deepening
When the MJO convection event arrived, the wind accelerated the horizontal current
to around 0.4 m s-1. The enhanced vertical shear due to the significant current velocity
will decrease Ri to less than 0.25 in the ML. In other words, the enhanced vertical shear
should be the major factor causing the deepening of ML by inducing the shear instability.
Thorpe scale method was used to estimate the turbulent dissipation rate during this
turbulent mixing event. The estimated turbulent dissipation rate within the MLD was
about 10-8 to 10-6 W kg-1, more significant than that within the typical thermocline of
about 10-10 to 10-9 W kg-1. Strong turbulent mixing might be the major factor leading to
the MLD deepening from 25 m to 50 m via the shear instability in this event.
5 Effect of Turbulent Mixing under MJOs
The rapid deepening of MLD by more than 25 m in five days was observed at two
ALAMO floats and two EM-APEX floats. According to the float measurements, the MLD
deepening may affect the SST cooling magnitude. Because the SST variation to model
forecast is crucial, this study will simulate the MLD deepening caused by wind-induced
mixing. Previous studies have demonstrated the critical effect of vertical resolution and
mixing parameters on the simulation of turbulent mixing (Large et al. 1994), thereby the
variations of SST. These two factors will be discussed in the following. Because EM8488
far away from the buoy may not have the similar wind field as that at buoy, the ocean
response at EM8488 will not be discussed.
5.1 Model description
Large et al. (1994) developed the K-profile parameterization (KPP) ocean boundary
layer (OBL) parameterizations model to study turbulent mixing within the ocean. The
turbulent vertical velocities of unresolved eddies within OBL are expressed as the vertical
divergence of the turbulence kinematic fluxes, leading to the time evolution of properties,
such as temperature, salinity, and momentum. In KPP, vertical turbulent mixing is
parameterized using the gradient Richardson number (Rig) and the bulk Richardson
number (Rib).
Rib is expressed in:
𝑅𝑖𝑏 = (𝐵𝑟− 𝐵(𝑑))𝑑 (𝑉𝑟2− 𝑉2(𝑑)) + 𝑉𝑡(𝑑)
Br and Vr are mean buoyancy and velocity, d is depth and Vt include other effects such as
convection or non-local entrainment. The depth of OBL is at where Rib equals to critical
value Ric. Due to the strong eddy diffusivity, the vertical structure in OBL is almost
homogeneous
We use KPP in one-dimensional Regional Oceanic Modeling System (ROMS;
Shchepetkin and McWilliams 2005) to simulate the evolution of the upper ocean structure.
Float measurements in the upper 200 m are averaged from 12th Dec 1:00 p.m. to 13th Dec
6:00 a.m. as the initial conditions. Below 200 m, the missing measurements of
temperature, and salinity and horizontal current are compensated with Hycom data.
AL9207 and AL9209 do not have the current data so the initial conditions are completely
filled with Hycom data. The forcing term utilize buoy measurements, including wind, air
temperature, humidity, air pressure, shortwave, and longwave radiation. The run starts on
the 13th Dec when was one day before the arrival of MJO. The temporal resolution is 600
s. The default setting of mixing parameters critical gradient Richardson number equal 0.7
and critical bulk Richardson number equal 0.3. The vertical resolution is about 1 m from
110 m depth to the ocean surface.
5.2 Simulating mixed layer depth deepening
The simulation of surface MLD is compared to the observation (Fig. 12). To avoid
the impact of eddy which is located at the south of floats after 15th Dec, the comparison
focuses on 13th to 14th when the westerly wind rose up. The model does not predict the
MLD deepening during the MJO active phase as that observed by the three floats. On
AL9207 and EM8487, the result of MLD deepening rate is underestimated with a
difference of 5 m to the observations. Because the change of MLD is affected by the
turbulence simulating, some previous studies suggested some factors, including
resolution and KPP parameter (Critical Bulk Ri, Critical Gradient Ri), affect MLD
performance in KPP. Therefore, the sensitive test of the resolution, KPP parameter will
be described in the following section.
Fig. 12: (a)–(c) Simulations of MLD deepening at the different initial conditions of three
floats in KPP (blue line), with the comparison to the float observation (black line).
5.3 Effects on vertical resolution in the upper ocean
Vertical resolution is required to capture a small scale, such as vertical mixing
features in the equatorial ocean (Jia et al., 2021). Woolnough et al. (2007) and Bernie et
al. (2008) have proposed that increasing vertical resolution to around 1 m is critical for
simulating SST variations during the MJOs. In this study, the vertical resolution of 1 m,
2 m, and 4 m in upper 110 m are used in MLD deepening simulation (Fig. 13). In the
model, the MLD of AL9207 shallows about 5 m on Dec 13th at 12 p.m., and the MLD
maintains about the same depth in the following days. The MLD does not change
significantly in the three floats during the MJO. Furthermore, there is no significant
difference between high resolution and coarse resolution on MLD. The results
demonstrate that the vertical resolution apparently does not act on MLD performance in
this case.
Fig. 13: Different vertical resolutions on simulations of MLD (a)–(c) at AL9207, AL9209,
and EM8487 (blue: 4 m; orange: 2 m; yellow: 1 m), with the comparison to the float
observation (black line).
5.4 Parameters in the KPP mixing scheme
In the KPP, the parameters Ri0and Ric directly affect the vertical diffusivity Kρ within
and below the OBL, and these may result in difference of turbulence simulating. The
effects of these two parameters are studied.
Ri0 is increased from 0.7 to 1, resulting in stronger turbulence induced by shear at
the base of OBL (Fig. 14). However, the KPP still fails to simulate the MLD deepening
depth. The values of Ri0 are tested to make the simulated MLD similar with the
observation depth. The model results are not similar to the observation unless Ri0 of 5
was used. Although strengthening and extending the turbulent mixing at the base of OBL
can obtain a similar result to observation, the value is too large and not real in general
ocean conditions. Moreover, when Ri0 decreases from 0.7 to 0.3, more challenged to
induce shear instability. The MLD is not significantly variable, either.
On the other hand, increasing the Ric from 0.3 to 0.7 forces the KPP to simulate a
thicker OBL (Fig. 15). That is, increasing the Ric value may enhance wind effect on
destratifying all stratification to a deeper layer. When wind forcing became stronger at
about 13th 12 pm UTC, different Ric used in the model will cause the variations of
simulated MLD. When Ric equals 0.5, MLD is similar to the observation on AL9209. On
AL9207 and EM8487, the results by tuning Ric to 0.7 can also make simulation of MLD
close to the observation MLD when the wind field increases. In short, by modifying the
parameters Ric can reach a deeper KPP boundary layer and simulate a similar MLD
variation of observation when the wind started. However, the value between 0.5 or 0.7
does not correspond to typical ocean conditions (Geernaert 1990). Because the observed
change of MLD is due to the wind-driven shear instability, the momentum flux during the
model simulation can also significantly affect the ocean current. Therefore, the next
section will discuss the sensitive test of momentum flux.
Fig. 14: Different gradient Richardson number on simulations of MLD (a)–(c) at AL9207,
AL9209 and EM8487 (blue: Ri0 = 0.4; orange: Ri0 = 0.7; yellow: Ri0 = 1), with the
comparison to the float observation (black line).
Fig. 15: Different bulk Richardson number on simulations of MLD (a)–(c) at AL9207,
AL9209 and EM8487 (blue: Ric = 0.3; orange: Ric = 0.5; yellow: Ric = 0.7), with the
comparison to the float observation (black line).
5.5 Summary of MLD simulation by using KPP
We use KPP in one-dimensional ROMS to simulate the MLD deepen under the buoy
wind measurement. With the default parameters set in KPP, the MLD deepening depth do
not simulate well on MLD deepening. In the model, MLD does not change significantly
in the first two MJO days. Because the vertical resolution, critical gradient Ri, and critical
bulk Ri can affect MLD performance in KPP, the sensitive tests are performed to explore
these factors' effects on MLD simulations. The vertical resolution and critical gradient Ri
do not affect apparently on the MLD. Although tuning critical to 0.7 bulk Ri can obtain
similar MLD, this high value of 0.7 does not correspond to typical ocean conditions.
Therefore, adjusting the parameters in the KPP may not be appropriate for simulating the
observed MLD deepening during the MJOs. Other factors will be discussed in the section.
6 Momentum and Buoyancy Response during MJOs
According to the adjustment on the parameters in KPP, the critical bulk Richardson
number can affect the MLD simulation significantly. However, when we tune Ric to match
the MLD of observation, the value must be larger than typical ocean conditions (~ 0.3).
Because the MLD deepening is caused by shear instability, the simulated horizontal
current velocity will affect the MLD deepening significantly.
Here, we compare the model results with the observed current velocity at EM8487.
The observed current in the upper 20 m is larger around 0.05 m s-1 than ROMS result (Fig.
16). In other words, the simulation of momentum flux may be underestimated, which will
lead to the different current velocity on simulation. Below, we will discuss the effect of
the drag coefficient Cd, which will affect the computation of surface wind stress.
Furthermore, because buoyancy flux can affect the MLD deepening, the effect of heat
flux will be discussing in this section, too.
Fig. 16: Current velocity averaged from 0 m to 20 m depth of EM8487 (blue line) and
6.1 Wind drag coefficient
Surface wind stress (τ), generated by wind momentum, forces ocean current. It is
commonly parameterized with a drag coefficient (Cd) and expressed as τ = CdρairU10|U10|
where ρair is the air density, and U10 is wind velocity at 10 m above the sea surface. In
ROMS, COARE 3.0 algorithm (Fairall et al. 2003) is used to estimate wind stress.
However, momentum flux in the model is probably underestimated, resulting in current
and shear failing to simulate well (Fig .16). Thus, wind stress estimated from COARE 3.0
in ROMS is multiplied 1.2, 1.5, and 1.8 times and then simulated the MLD deepening
again. That is, the transferred wind momentum from the atmosphere into the ocean is
artificially increased. When the wind stress was increased by larger Cd, MLD deepening
simulated well on MLD depth on the three floats (AL9207, AL9209, EM8487). Therefore,
whether the wind stress estimated by COARE 3.0 is underestimated that leads to the
underestimated deepening of MLD needs to be studied. In the next part, the wind-induced
current will be extracted from float measurement to quantify the observed momentum
flux during the field experiment.
Fig. 17: Different magnitude of wind stress on simulations of MLD (a)–(c) at AL9207,
AL9209 and EM8487, (blue: wind stress estimated from COARE 3.0; orange: 1.2 times;
yellow: 1.5 times; purple: 1.8 times of wind stress), with the float observation (black line).
6.2 Wind-induce current
For the purpose of computing the current momentum obtained from the surface wind
stress, non-wind-driven currents must be excluded from the raw measurements. Fast
Fourier Transform (FFT) is applied to the current velocity measurement, in order to find
the dominant current components from 1st to 31th Dec in the upper 50 m. Two peak signals
are found, including a 43.5 h period and a 12.5 h period which is regarded as inertial
motion and semi-diurnal M2 tide, respectively (Fig. 18). As a result, the primary
constituent of float measurement current is written in:
V = Vinertial + Vsemi-diurnal + Vbackground
With the bandpass filter, the magnitude of Vsemi-diurnal is extracted (Fig.19). The semi-
diurnal tides are extracted with a period between 11 h and 14 h, and the magnitude is up
to 0.1 m s-1. Previous model studies and observations in the region also found the same
stronger semi-diurnal tides (Holloway et al. 2001; Rayson et al. 2011). The inertial
motions are extracted with a period between 41 h and 46 h. The magnitude is generally
less than 0.05 m s-1.
Fig. 18: Power spectrum density of (a) east-west current and(b) north-south current.
Fig. 19: East-west components of (a) current velocity, (b) semi-diurnal-tide, and (c)
inertial current; north-south components of (d) current velocity (e) semi-diurnal-tide, and
(f) inertial current. The missing data are expressed with gray dots.
The inertial motions in the upper ocean are regarded as generated by the local wind.
The wind-induced current is estimated using the float measurement, after excluding the
semi-diurnal tide and the background current that averages the current velocity before the
MJO. The result is compared to the model result with no current as the initial condition
(Fig. 20). A 43.5 h period current is found in both observation and model results in the
upper ocean. By lag-correlation, 14 h lags on east-west and 12 h lag north-south
components (not shown) are discovered between the model and observation. The spatial
variation of wind between the floats and buoy may cause the difference in the occurrence
time of MLD deepening, so we shift the phase of model results slightly. This observation
of wind-induced current and model results will be used to compute wind stress by the
linear momentum budget method.
Fig. 20: (a) East-west and (b) north-south component of EM8487 measurement excluding
semi-diurnal tides and background current (c) East-west and (d) north-south component
of ROMS results which have been adjusted with time lags.
6.3 Linear momentum budget method and wind stress
6.3.1 Linear momentum budget method
The surface wind stress is estimated following Sanford et al. (2011) and Hsu et al.
(2017). Using the EM8487 wind-induce current velocity profiles computes the depth-
integrated on linear momentum balance equation that is:
∂V
∂t + V ⋅ ∇V + fk̂ × V = − 1
ρ0∇p + 1 ρ0
∂τ
∂z− ρ ρ0gk̂
where V is the ocean current velocity, f is Coriolis frequency (around rad s-1 at 16°S), ρ
is the situ density, ρ0 is Boussinesq density, and τ is the stress vector. The depth-integrated
horizontal momentum equation from sea surface to depth -z is:
∫ (∂vh
∂t + vh∇h⋅ vn+ vh⋅ ∇hvh+ fk̂ × vh+ 1
ρ0∇hp) ⅆz
0
−z
= (τ0− τ−z)
ρ0 + w−zV−z
where the horizontal current (Vh = uî + vĵ) and gradient operator (∇h= ∂ ∂x⁄ î + ∂ ∂y⁄ ĵ),
τ0 is the surface wind stress, τ-z is turbulence stress. V-z is horizontal velocity. Here
assuming τ-z and w-z V-z are zero. During the forcing stage of wind (Sanford et al. 2011),
nonlinear and pressure gradient terms may be negligible. Due to this assumption for
neglecting the nonlinear and pressure gradient terms, there will be an error in estimated
(Δτ). Thus, surface wind stress (τ0) derived from depth-integrated linear momentum
equation:
τ0 = τ + Δτ = ρ0∫ (∂vh
∂t + fk̂ × vh) ⅆz
0
−z
6.3.2 Wind stress
According to depth-integrated linear momentum equation, the time rate change on
horizontal momentum and Coriolis force is estimated by float’s wind-induced current and
model results via integrating to 100 m depth (Fig. 21). The observation error bar is one
deviation with different time-averaging background currents and extracting semi-tide.
Coriolis force terms of observation are adjusted with the offset 0.35 N m-2 on east-west
momentum and 0.15 N m-2 on north-south momentum that is contributed by the eddy of
which current velocity is about 0.2 m s-1 and 0.08 m s-1, respectively. We focus on the
wind stress variation on the first day of MJO to avoid unknown momentum transfer.
During the wind forcing period, the time rate change of velocity in the model results
is less than the observation. The value of observation is up to 0.3 N m-2 and -0.25 N m-2
on northward and eastward components, respectively. Contrasting to the observation, the
model result is about 0.1 N m-2 on the original wind stress. The difference comes to 0.2
N m-2 between observations. The result shows that the wind stress does not efficiently
input to the ocean in the model. Because the wind stress is the function of Cd and wind
speed, Cd may be underestimated, or the wind speed on the float position is larger than
the buoy. When Cd multiple to 1.8 times, the value is similar to observation. The result
demonstrates that increasing the wind stress can obtain a similar momentum flux to the
observation. On the other hand, the Coriolis force on the model is also less than the
observations. The meridional and zonal components are both about 0 N m-2 at Dec 13th
12 p.m. During the MJO, Coriolis force changes to 0.175 N m-2 in the first inertial current
period on both northward and eastward components. By contrast, the model results are
about 0.1 Nm-2. The multiple of the Cd to 1.5 times can be similar to the magnitude of
observation. Namely, the wind stress difference can significantly affect the acceleration
rate of horizontal current. MLD simulation may be affected by the underestimated wind
stress.
Note that there are two aspects of underestimated wind stress. Firstly, the drag
coefficient used in the model simulations is from the COARE 3.0 algorithm. The
underestimated momentum flux due to an inappropriate drag coefficient may affect the
MLD and SST simulation during the MJO active phase. However, the 1.8 times Cd may
be larger too large (Fig. 22). Secondly, the wind stress is estimated by 10-m height wind
magnitude. The wind stress as a function of wind speed square. When the wind speed
increases by 1.35 times, the wind stress will increase by about 1.8 times simultaneously.
Due to the different locations of the buoy and the three floats (AL9407, AL9409,
EM8487), the wind above the sea surface of the float may be an anomaly to the buoy. The
possible wind speed difference leads to an underestimate of the wind stress. To sum up,
compared to the observation, the wind stress was underestimated in the model, resulting
in the failure of MLD simulation. This may cause by the inappropriate drag coefficient,
or the wind forcing term cannot represent those above the float. In the next section,
because the buoyancy flux affects the deepening of MLD, the buoyancy will be
considered in the simulation.
Fig. 21. Depth-integrated comparisons of float observations (black line with one standard
deviation error bars) and KPP simulations (orange: COARE 3.0 estimated; blue: 1.5 times;
green: 1.8 times of wind stress) during the MJO. (a) and (c) is the time rate change
momentum of U and V components, respectively. (b) and (d) is Coriolis force terms of U
and V components, respectively.
Fig. 22: The drag coefficient Cd as a function of wind speed at 10 m above the sea (yellow:
Large and Pond,1981; green: COARE 3.0 estimated; blue: derived from observation;
orange: derived from 1.35 times of wind with one standard deviation error bars)
6.4 Buoyancy flux effect
During the nighttime, ocean heat transfer to the atmosphere leads to sea surface
cooling. Due to the cooling, the sea surface water density increases and sink. The process
results in turbulent convection, and MLD may deepen during this. Thus, the value of the
heat flux, which considers the sea surface cooling magnitude, may affect the MLD. The
latent and sensible heat flux is associated with the air temperature difference and the wind
speed. To find the possible effect of the temperature and wind speed anomaly, the ± 50 W
m-2 of the estimated heat flux as these anomalies effect and be simulated again. The result
demonstrated that increasing 50 W m-2 of heat flux allows the MLD to deeper, around
2 m. Contrastingly, the MLD of decreasing 50 W m-2 is 2 m shallower than the original
heat flux input. This means the heat flux affects the MLD simulation. As a result, the
buoyancy effects are required to consider in the simulation. However, the possibility
effect of buoyancy flux, around ± 2 m, is not much more significant than the wind stress
effect (Fig. 22). The model results are not similar to the observation unless more than 400
W m-2 is used (not shown). The value is too large and irrelevant in this area (Marshall and
Hendon, 2014). To conclude, the model study finds that critical Richardson numbers,
wind stress, and heat flux may result in the MLD deepening simulation accuracy during
MJO. Among them, appropriate wind stress input is much more crucial in simulating
