AICS TECHNICAL REPORT
N0. 2016-001

A simple method for detecting the lifecycle ofdeep moist convection from discretized data

By

Yoshiaki Miyamoto1,2, Tsuyoshi Yamaura2, Ryuji Yoshida2,
Hisashi Yashiro2, Hirofumi Tomita2,3,
and Yoshiyuki Kajikawa2
1, Rosenstiel School of Marine and Atmospheric Science, The University of Miami
2,RIKEN Advanced Institute for Computational Science
3,Seamless Environmental Prediction Research, Japan Agency for Marine Earth

Science and Technology

Submitted on 05/04/2016
Accepted on 08/07/2016
Published and copyrighted by
RIKEN Advanced Institute for Computational Science (AICS)
7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, 650-0047, JapanA simple method for detecting the lifecycle of deep
moist convection from discretized data
Yoshiaki Miyamoto1,2 , Tsuyoshi Yamaura2 , Ryuji Yoshida2 ,Hisashi Yashiro2 , Hirofumi Tomita2,3 , and Yoshiyuki Kajikawa2
1: Rosenstiel School of Marine and Atmospheric Science, The University of Miami
2: RIKEN Advanced Institute for Computational Science
3: Seamless Environmental Prediction Research, Japan Agency for Marine–Earth Science and Technology

Abstract
Deep moist convection plays a crucial role in transporting energy and momentum
in the Earth’s atmosphere. Examining the convection is fundamentally importantfor better understanding of various atmospheric phenomena, e.g., typhoons, as wellas the convection itself. We developed a simple methodology for detecting thelifecycle of convection from discrete spatiotemporal data such as output of model
simulations or reanalyses, which are often used in the Atmospheric Science research.
The method includes only a few thresholds and hence it can be applied to data ofglobal atmosphere in which environmental conditions for the convection are largely
diﬀerent in space and time. We tested and verified the method on a global simulation
with high spatiotemporal resolution.

1

Introduction

The Earth’s atmosphere is characterized by rotational motion and stratification due togravity, and the majority of flow motion is well approximated as being horizontally two–
dimensional. However, convection plays a key role in vertically transporting energy in theatmosphere. Convection is active in the troposphere where there is a near balance between heating due to solar radiation, re-radiation from the atmosphere itself, and verticaltransport of heat by convection.
A defining characteristic of the Earth s atmosphere is the large abundance of water
present. In the range of pressures and temperatures found in the atmosphere, water canchange its phase (e.g., Houze 1993, Emanuel 1993). Consider an air parcel that contains
a certain mass of dry air and a certain amount of water vapor. As this air parcel is lifted1

upwards, the pressure and temperature of the parcel decrease. If the mixing ratio of water
vapor in the parcel exceeds the saturation mixing ratio (which decreases with decreasing
temperature), the vapor condenses, changing from gas to liquid. If the air parcel continues
moving upward and passes the 0–deg temperature level, the water will change its phase
to ice. This condensation heats the air surrounding the water droplet due to the vapors decrease in molecular kinetic energy. Hence, the following positive feedback may occur.
The heated air parcel will tend to be less dense than the surrounding air (i.e., it will bepositively buoyant). This positive buoyancy causes the air parcel to move upward more
quickly, allowing a larger amount of water to condense. This condensation then further
increases the temperature of the air parcel. This positive feedback process can continue
until the air parcel is no longer positively buoyant. The strongest convection can reach
altitudes of 10 – 15 km because of this positive feedback process. It should be noted that
we have neglected the presence of rain, which would tend to accelerate the vertical motion
and remove water mass from the air parcel.
Convection transports mass and energy in the vertical direction (e.g., LeMone et al.
1984, Tung and Yanai 2002a,b). Synoptic scale atmospheric motion is characterized by
two horizontal dimensions, but even in that case, convection plays a fundamental rolein transporting physical quantities in the vertical direction. The troposphere, which is
the lower–most layer in the atmosphere extending from the ground up to altitudes ofapproximately 10–15 km, is characterized by continuous convective heating and radiative
cooling (Manabe and Strickler 1964, Manabe and Wetherald 1967). At any given moment,
the atmosphere contains a number of convective cells spanning the entire vertical extent
of the troposphere with water in liquid and/or ice phases.
Figure ?? depicts a schematic view of the lifecycle of deep moist convection (cf. Byers
and Braham 1948). Condensation occurs in the updraft region as a result of low-level air
converging in the early development phase. In the mature stage, liquid and solid waterphases are present in the entire troposphere and strong updrafts and downdrafts co-exist
within a single convection cell. Thereafter, the downdraft produced by precipitation
dominates, and the convection decays. The typical timescale from genesis to dissipationis 20–30 minutes. Both inside and near the convection cell, the fluid motion is highly
perturbed, which causes significant mixing at the outer edge of the convection cell (e.g.,
Dawe and Austin 2013). Whereas positive buoyancy due to condensation will tend to keep
the convection cell narrow (Bjerknes 1938), this diﬀusion tends to expand the horizontal
scale of the cloudy convective region.
Convection produces a large amount of precipitation throughout the phase-change
process. Localized convection can sometimes be the source of local downpours, potentially leading to local disasters. The timescale for convection is short compared with thetimescales of larger weather systems, such as mid-latitudinal lows or fronts. Additionally,2the physical process of convection is highly nonlinear; this is due mainly to the moist processes (phase change) and partly to the smallness of flow scale1 . This makes forecasting
convection diﬃcult, and the accurate prediction of convection is necessary for disasterprevention.
Convection can be regarded as cloudy, organized disturbances such as the MaddenJulian oscillation, tropical cyclones (typhoons), or mid-latitudinal lows. Modeling studies(Miyamoto et al. 2015 and Kajikawa et al. 2016) used global simulations to show thatconvective features are remarkably diﬀerent among these disturbances: the vertical extent
of convection is higher in tropical disturbances such as the Madden-Julian oscillation or
tropical cyclones, but the intensity (vertical velocity) is stronger in the Madden-Julian
oscillation. These researchers concluded that convection intensity depends on whether theconvection forms with or without strong flow forcing and background stability, whereas
the vertical extent simply depends on latitudinal variations in static stability. Their conclusions indicate that the detailed eﬀects of convection need to be properly accounted forto simulate or predict cloudy disturbances. In other words, more eﬀort to comprehensively
examine the diﬀerences among the disturbances is needed to better understand and moreaccurately predict cloudy disturbances that can cause local disasters.
Due to the importance of convection and the popularity of gridded (discretized)
data, previous studies have proposed methodologies for detecting deep convection using
discretized data sets. Dawe and Austion (2012) developed a technique for tracking cloud
cells in the spatiotemporal dimension using very high-resolution data. This techniquedetects conditions ranging from dry phases (plumes)to moist shallow cumulus clouds.
Plant (2009) proposed a sophisticated method for tracking clouds in model simulations;this method is also applicable to high-resolution data that resolves convection cores overmultiple grid points. Additionally, both methods can capture cloud cell mergers andsplitting events. Although these methods are useful and highly accurate, they require
a number of steps to implement within numerical models or to apply to online model
calculation programs.
In this report, we propose a simple method for extracting the lifecycle of convection
from a data set that is discretized in spatiotemporal dimensions (such as data or resultsfrom numerical models). This method enables researchers to address the physics of convection using conventional data sets. The method developed here can be used to perform
detailed statistical analyses of convection. Given the observed spatial scale of convection,
the data grid spacing might need to be coarser than several hundred meters; beyond thisthe convection core can fluctuate in time in a single convection cell. This methodology
has been used by Miyamoto et al. (2013, 2015) and Kajikawa et al. (2016).
1

The nonlinear advection terms are large compared with the others.

3(1) development (2) mature(3) decay

time

Figure 1: Schematic of the lifecycle of deep moist convection. The abscissa and ordinate
are the horizontal and vertical directions, respectively. The topmost altitude of the panels
approximately corresponds to the tropopause height. The shaded area represents a large
amount of hydrometeors, while the gray blurred region in (3) represents the presence ofrainfall. The yellow arrows indicate the flow direction. The left, center, and right panels
respectively show the genesis/development, mature, and decay phase.

2

Proposed methodology of extracting the convection

The method proposed here mainly consists of two processes: (1) detecting the convection
core grid points and (2) producing the lifecycle of convection. We first detect convective
and convection core grid points by applying simple definitions at each time step. Then,the temporal connections between convection core grid points are diagnosed to determine
the convection lifecycle.

2.1

Convective and convection core grid points

First, the atmosphere is vertically divided into N z layers starting from the top of theboundary layer (∼ 1 km) up to the tropopause. Here we have chosen N z = 5; weconducted several sensitivity tests varying N z, and we found that 5 appears to produce themost reasonable results. For this value of N z, each layer has a depth of a few kilometers.
Next, to identify convective grid points in each layer at every time step (cf. the graypoints in Fig. ??), we select grid points that satisfy the following conditions:
1. layer–averaged qt is larger than 0.2 g kg−1
2. layer–averaged w exceeds 0 m s−1 ,4where qt is the total hydrometeors and w is the vertical velocity. The layer average
represents the mean value in the layer (cf. Fig. ??), and the averages are weighted bydistance.
We then examine the following two conditions:3. ∇h w averaged inside and below the layer is larger than 0 s−1 in all directions
4. no neighboring grid points are convective grid points.
Girds satisfying all four conditions are defined as convection-core grid points (cf. thewhite point in Fig. ??). Note here that ∇h ≡ ∂/∂xi represents the horizontal diﬀerential
in the xi direction, where i is the number of grid points adjacent to the current grid point.
At this point, the following information:– horizontal grid points at which convection is detected,– layer at which the convection is present, and– time,is stored as a convective grid point.

2.2

Lifecycle

We define the lifecycle of convection in discretized data as a time sequence of convection
grid points in a certain area and time-range that are detected using the method above.
The detected convection-core grid points are tracked in time using the following method
to extract candidates for convection lifecycles. To determine whether convection core
C001ta (where ‘001

represents the ID of the convection core grid point) at t = ta isconnected to core C001ta +∆t at t = ta + ∆t (where ∆t is the temporal resolution of thedata), we consider the following conditions:
1. C001ta +∆t is located within N x grid points of C001ta ,2. C001ta +∆t is in the same layer or is one layer higher than C001ta , and3. C001ta +∆t has not yet been identified as the survivor of other cores at t = ta + ∆t.
After performing some sensitivity tests, we set N x = 2, so grid points within two grid
points of C001ta are searched at the next time step ta + ∆t; this condition can be changed
depending on the spatiotemporal resolution of the data set, as we discuss later.
Let us now consider that a candidate satisfying all the conditions (C001ta ) is found.
If it is a survivor of a core at t = ta − ∆t, the lifetime of that core is increased by one
5

(a)
(a)

(b)
(b)
(a)

(c)
(a)
(c)

(b)
(c)

(b)

grid which satisﬁes
grid satisfying thethe condition
condition
gridwhicheight
has eight
grid having
surrounding
gridsgrids
surrounding

grid which
the cond
grid whichsurroundconvection center

convection

area of convection

area of con

estimate
gradient
searching radiusestimate gradius of convection

radius of coconvection core grid

Searching area at thenext step
gradient of w

(c)grid which satisﬁes
the condition
Figure 2: Schematic of the convection detecting method in the horizontal space. The
grid which has eightgray points are the grid points satisfying all the conditions of convective grid points.
surrounding grids
The gray points surrounded by the black line are the grid points at which the surround-convection
ing 8 grid points also satisfy the convective–grid conditions.
Thecenter
white points with theblack line indicates the convection core grid points. The light–gray circle centered at thearea of convection

convection–core grid point represents the area in which the convection–core grid points
will be searched at the next step. The dashed arrowestimate
indicates gradient
the horizontal gradient ofradius of convection

the vertically averaged vertical velocity.

time step. Otherwise the lifetime is 0; all the convection cores initially have a lifetime of
0 when they are first detected. The vertical layer of C001ta is updated to the value att = ta from that at t = ta − ∆t. When C001ta is not a survivor of a core t = ta − ∆t6Layer 5
Layer 4Layer 3Layer 2
Layer 1
Detected step:layer:

1
1

N-2
3

N-1
4

N
5

not
detected

time

Figure 3: Schematic of the convection detecting method for the time–height section. The
abscissa and ordinate are time and height, respectively. The bottom shows the time stepand layer at each life stage.
(when it is first detected at t = ta ), the layer of C001ta is set to 1 (all new convection
cores form in the lower–most layer). By completing this series of tests for all the detected
convection core grid points at all time steps, we obtain samples of temporally connected
convection cores (i.e., the lifecycle of convection). The convection samples contain thefollowing information:– horizontal grid points,– vertical layer, and– timeat each time step in the sample s lifetime.
Finally, we define a full convection lifecycle to be a convection sample that satisfies
the following conditions:4. the vertical layer reaches N z = 5 at the final time step, and5. the total lifetime (over all steps) is equal to or longer than N z × ∆t s.
7

We record the following information for each instance of detected convection at eachtime step:– horizontal grid points– vertical layer– time– longitude and latitude– land surface information (land/ocean)– maximum vertical velocity wmax at the convection core grid point– height of wmax
– combined average of the vertical velocity inside and below the layer– combined average of the longitudinal and latitudinal velocity inside and below thelayer– combined average of the mixing ratio of hydrometeors inside and below the layer– vertically averaged mass divergence below the 500–m level– precipitation– Convective Available Potential Energy (CAPE)– Convective Inhibition (CIN)– Lifted Condensation Level (LCL).
2.2.1

Horizontal motion

The present method for detecting the convection lifecycle determines whether convection
is still present in the time step following the initial detection. For accurate detection,
we must consider the horizontal motion due to convection during a time step ∆t. For
a constant velocity Vc over a time step, the distance moved can be written as Vc ∆t.
The velocity of convection is typically of the same order as the horizontal velocity in the
troposphere, so Vc = O(10 m s−1 ). Therefore, after a time step ∆t, if there is a convection
core grid point within a radius Vc ∆t of a convection core detected in the previous timestep,that convection core is diagnosed as a survivor of the one from the previous step. Notethat if the search distance is too large, this could result in the mis-detection of other,8unrelated convection cores; However, if the search distance is too small, a quickly moving
convection core could be missed.
As an example, we can consider a data set with a grid spacing of 1000 m and a time
step ∆t of 60 s. If we consider a search radius of 2000 m, this corresponds to allowing a
convection core to move two grid points (N x = 2) from ta to ta + ∆t. This corresponds
to an average speed over one time step of 33.33 m s−1 . Note here that a speed of 33.33
m s−1 is very fast, but not unrealistic. It appears, however, that most convective cells do
not move even one grid point (1000 m) in ∆t = 60 s. This argument would be diﬀerent
depending on the resolution of the data, so the horizontal search for convection cores must
be optimized for various cases. Here we have several options.
a) search for grid points within a specified distanceThis option is to simply search for grid points within a given distance (N x) from thegrid point at which the convection core is present at t = ta without taking the search
direction into consideration. Hence, the search sequence only depends on the specified
search distance.
b) search grid points after adding a background velocity
Because the convection cell is expected to move at the background velocity, Vc , of thevertical level where the convection is present, this option is to conduct the search after theconvection core grid point is moved by the distance it is expected to travel. In particular,
the convection is assumed to move a distance Vc ∆t during a time step, and then thegrid points located within a specified distance of the newly defined (moved) convection
core grid point are searched. This option appears to be powerful, especially when thehorizontal wind speeds are large. However, it is not certain that this option always yields
better results than option a), because it is not always clear which level plays a dominantrole in moving the convection core.
c) search from nearby grid points at the present time (t = ta )This option changes the sequence of the search. First, the convection core grid point
at t = ta is searched, then the grid points directly adjacent to the core grid point are
searched, and finally the grid points within two grid points of the core grid point are
examined. This option is useful when the probability of a convection core existing after atime step is highest at the grid point location from t = ta and decreases with increasing
distance from this grid point.
2.2.2

Vertical development

As discussed earlier, we divide the troposphere into N z layers (cf. Fig. ??); as shown
above, when N z = 5 the depth of each layer is a few kilometers. To meet our definitionof convection, the convection core needs to start from Layer 1 and go through all layers

9

up to Layer 5. Here we discuss why convection must sequentially progress through thelayers one by one.
The maximum vertical velocity that an air parcel can obtain (i.e., potential verticalvelocity) is derived from the non-diﬀusive vertical momentum equation,dw
Tp − Te=g = B,dt
Te(1)

where Tp , Te , and g are the temperature of the parcel, the environmental temperature, andthe gravitational acceleration, respectively. We note that the vertical motion is accelerated
only by buoyancy in this system. We now introduce the convective available potential
energy (CAPE), which is the vertically integrated buoyant energy of an air parcel. Thisis defined as
CAPE ≡

∫ EL

Bdz,

(2)

LFC

where LFC and EL represent the level of free convection and the equivalent level at which
the buoyancy is zero, respectively. If one assumes that all CAPE is converted to kinetic
energy, the potential vertical velocity wmaxp is obtained:
1

wmaxp ≈ (2CAPE) 2 .

(3)For example, when CAPE is 800 J kg−1 (a typical value), wmaxp is 40 m s−1 . However,
the true vertical velocity is rarely observed to reach wmaxp ; this implies that it is rare forthe entire CAPE to be consumed, which is mainly due to the presence of diﬀusion. Note,however, that vertical velocities larger than 30 m s−1 are observed in the tropics.
If we assume that the maximum vertical velocity in a numerical model is 30 m s−1 ,it takes 100 s (= 3000 m / 30 m s−1 ) to rise by one layer in the strongest convection.
Because the timestep for the data used here is 60 s, it is rare for the peak altitude toskip a layer (i.e., move two layers) in a single time step; thus we apply the condition thatconvection must proceed through the atmosphere layer by layer.

3

Results

We analyze the data of Miyamoto et al. (2013, 2015, 2016) and Kajikawa et al. (2016),
which consists of output from global model simulations with 870 m grid spacing in thehorizontal direction, 94 layers in the vertical direction (up to 30 km in altitude), and aone-minute output interval. Due to the huge computational cost of global analysis, here
we only focus on the West Pacific region with lon × lat = [0,9] × [200,270]; global results
can be found in Miyamoto et al. (2013, 2015, 2016) and Kajikawa et al. (2016).

10

3.1

Threshold of vertically averaged mixing ratio of hydrometeors

One of the benefits of the method presented in this work is that it requires fewer specified
thresholds, so it can be applied to data sets in which the atmospheric conditions varyin space or time (such as data sets covering the entire globe). The only threshold that
explicitly needs to be set for our present analysis is the vertically averaged hydrometeors
qt ; we set the threshold of qt to be 0.2 g kg−1 . The vertically averaged vertical velocity
also has a threshold value, which is 0.0 m s−1 , as shown earlier. However, this is obviously
required to detect convection and should not be changed greatly; thresholds less than 0
would cause especially severe errors.
To examine the sensitivity of our method to the assumed threshold of averaged qt ,we tested our method using a threshold of 0.0 g kg−1 . Figure ?? shows histograms of qt
at the convection core grid points detected by applying that threshold. The number ofconvection cores having qt in the range 0.0 – 0.1 g kg−1 is two orders of magnitude larger
than in any other range and the number decreases exponentially with the mixing ratio.
This simply indicates that more convection cores can be obtained when the threshold issmaller. The average convection structure obtained using the 0.0 g kg−1 threshold is,
however, unlike either the observationally obtained structure or the structures obtainedusing the 0.2 g kg−1 threshold. Thus, a low threshold for qt is desired in terms of detecting
a large number of convection cores, but a non–zero threshold is needed to obtain realistic
convection structures. The present method applies a threshold of 0.2 g kg−1 .

3.2

Vertical profiles of quantities at convection core grid points

In our detection method, we require that convection cores traverse all the layers of theatmosphere during its lifetime; this enables us to extract a reasonable lifecycle for theconvection from discretized data. To verify the method, it is necessary to examine verticalprofiles of physical quantities related to convection, such as the vertical velocity or mixing
ratio of hydrometeors at the convection core grid points.
Figures ?? and ?? show composite vertical distributions of the vertical velocity andthe hydrometeor mixing ratio of the convection cores detected in each layer; the originallydefined altitudes of each layer are also indicated at the right boundary of each panel. The
distributions of vertical velocity and hydrometeor mixing ratio both have a single peakwhich increases as the layer increases. The peak altitudes of vertical velocity correspondwell with the originally defined layers, with some exceptions (Layer 2 and 5). In particular,
the composite vertical velocity profile detected in Layer 5 has its peak at the altitude ofLayer 4. This does not represent an error of calculation, however, because the method11

5convection number

10

4

10

3

10

2

10

1

10

0

2
−1
q (g kg )4tFigure 4: Histogram of qt of the detected convection in the western north Pacific when
the threshold of qt is 0.0 g kg−1 . The bin is 0.5 g kg−1 .
does not require the convective cells to have a peak at the defined altitudes. Overall, ourresults indicate that the method properly detects the layer of convection height. We alsofind that the peak hydrometeor mixing ratio appears at lower altitudes than that of thepeak vertical velocity.

4

Discussion and concluding remarks

We developed a simple methodology for detecting deep moist convection in a discretizeddata set. Our method requires fewer thresholds and can thus be applied to data in which
the atmospheric conditions vary widely in space and time. Applying this method toa global data set with very high spatiotemporal resolution, we found that the method
reasonably detects the convection lifecycle.
The proposed method is optimized for data in which the convection core is resolved
by a single grid point. Because the method detects the convection core at one timestep
and tracks the core in time, the core grid point needs to be clearly distinguishable fromother grid points. Miyamoto et al. (2013) showed that once the horizontal grid spacing issmaller than 3.5 km, convection cores are represented by multiple grid points rather than

12

ww

15

z (km)

10

L1
L2
L3
L4
L5

L5
L4
L3
L2

5

L1
0
−0.5

0
−1
ww (m s )0.5

Figure 5: Vertical profiles of composited vertical velocity of convection samples detected
at each layer. The bold gray lines at the right edge of panel indicate the height of original
definition in the method.
a single one. This implies that our method can reasonably be applied to data with a grid
spacing of a few kilometers.
There are some diﬃculties in applying our method to very high-resolution data, suchas large-eddy simulations with resolutions of the order of 100 m. This is because theconvection core location can significantly vary in time. This diﬃculty could be removed
for certain ranges by decreasing the time interval of the output data. This does not,however, assure that there will be only a single core in the convection, and there isa possibility of multiple updraft cores. Therefore, for such a high-resolution data, themethod is most likely to properly work after a spatial filter on convection distance scales
is applied to smooth the data.

Acknowledgement
The numerical calculations for the analyses in this report have been conducted on the K
computer.

13

qt

15

z (km)

10

L1
L2
L3
L4
L5

L5
L4
L3
L2

5

L1
0
−0.5

0
−1
q (g kg )0.5

tFigure 6: Same as Fig. ??, but for composited mixing ratio of hydrometeors.

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