Automated detection of atmospheric rivers (ARs) has been heavily relying on
magnitude thresholding on either the integrated water vapor (IWV) or
integrated vapor transport (IVT). Magnitude-thresholding approaches can
become problematic when detecting ARs in a warming climate, because of
the increasing atmospheric moisture. A new AR detection method derived
from an image-processing algorithm is proposed in this work. Different
from conventional thresholding methods, the new algorithm applies
threshold to the spatiotemporal scale of ARs to achieve the detection,
thus making it magnitude independent and applicable to both IWV- and
IVT-based AR detection. Compared with conventional thresholding
methods, it displays lower sensitivity to parameters and a greater
tolerance towards a wider range of water vapor flux intensities. A new
method of tracking ARs is also proposed, based on a new AR axis
identification method and a modified Hausdorff distance that gives a
measure of the geographical distances of AR axes pairs.
Introduction
Many previous studies have demonstrated the dual hydrological roles played by
atmospheric rivers (ARs), both as a freshwater source for certain
water-stressed areas and a
potential trigger for floods .
Increasing attention towards ARs is seen not only among the research community
but also within water resource management agencies, risk mitigation managers
and policy makers . Some of the pressing research questions
that challenge the research community are how ARs will respond to global
warming and how changes in ARs will affect future hydroclimate projections.
Answers to these questions will require a set of robust AR detection methods
that consider the nonstationary nature of the atmospheric responses to global
warming.
The increased attention to AR research has led to the development of an array
of AR detection and/or tracking methods with considerable variability in their
design, complicity and targeted scientific questions. The Atmospheric River
Tracking Method Intercomparison Project (ARTMIP)
was initiated as a community effort to systematically estimate the
methodological uncertainties in AR detection. In the 1-month
“proof-of-concept” analysis , 15 different detection
methods were included to quantify various AR-related statistics from the North
American and European landfalling ARs. And the early start comparison work
included eight methods, some of which also came with
sub-catalogues with different parameter choices. All of these AR detection
methods are based on either integrated water vapor (IWV) or integrated vapor
transport (IVT), or a combination of both. For most of the algorithms compiled
by ARTMIP, a pre-determined value is used as the magnitude threshold for the
initial selection before subsequent geometrical considerations. For instance,
, , and identified ARs as
contiguous regions, where IWV ≥20 mm, at least 2000 km in length and
no more than 1000 km in width. A 250 kg m-1 s-1 IVT threshold was used by
in detecting landfalling ARs onto the North American
continent. These AR magnitude-thresholding methods have the advantage of being
easy to use and straightforward to interpret.
An implicit assumption with this magnitude-thresholding approach is that the
atmospheric moisture level stays unchanged throughout the analysis period, or
the temporal power spectrum remains constant across decadal or larger
timescales. As the threshold value used in the analysis is based on the
historical observations, a question arises of whether the constant threshold
value can be reliably used for AR detection under future warming climate as the
atmospheric moisture level is expected to increase.
For the estimate of present-day ARs, different choices of magnitude
threshold may also cause considerable uncertainties . For instance, when estimating the
number of landfalling AR events at Bodega Bay using the Modern-Era
Retrospective analysis for Research and Applications version 2 (MERRA-2),
raising the IVT magnitude threshold from 250 to 500 kg m-1 s-1
was found to reduce the total number of AR events during water years
of 2005–2016 from 185 (termed as “baseline ARs”) to 14 (termed as
“stronger ARs”), with the same detection method by .
An alternative to the absolute magnitude threshold is the use of a
chosen percentile of IVT or IWV at a given location as a threshold, such as the
85th percentile of local climatology used in some studies (e.g.,
). Such an approach grants the IVT or IWV
threshold the sensitivity to the possible basin, seasonal or latitudinal
differences. However, a prescribed percentile value may not have the
flexibility to adopt to the fast-changing synoptic conditions where ARs are
embedded. Furthermore, an additional 100 kg m-1 s-1 constant IVT threshold was
found to be necessary to complement detection in the polar regions
.
The prescribed threshold approach also requires different thresholds for
IWV-based and IVT-based applications (for instance, 2 cm for IWV and 250 kg m-1 s-1
for IVT), and in both cases, it is likely that different threshold
values are required for midlatitude systems and polar systems. As demonstrated
in , lower air temperature and the reduced water holding
capacity demand a separate set of threshold catered to the polar climate.
A possible solution to the problems is to avoid the usage of magnitude
threshold and instead apply the filtering process to moisture filamentary
structures. Instead of thresholding the IVT or IWV magnitudes which
show greater sensitivity to a cut-off value, we propose a method that
performs the filtering on the spatiotemporal “spikiness” of IVT or
IWV fields which are found to have lower sensitivity to
parameter choices. This reduced parameter sensitivity makes it
less prone to the problem of the nonstationary nature of the
atmospheric moisture level under the warming climate.
A reasonable AR axis definition is a necessary prerequisite to
accurate AR length estimate and a useful metrics for subsequent
tracking. The accuracy of axis estimation has not received
enough attention in literature, although sensitivities in
geometrical constraints have been highlighted .
The AR axis is typically defined as a simple curve that
follows the orientation of the AR, providing a summary of its
geographical location and extent. used the image-processing
skeletonization algorithm to find AR axes. This method has the
advantage of being able to handle complex shapes and the resultant
axis never goes out of the AR boundary. However, it lacks physical
correspondence and the identified axes do not always follow the
maximum intensities of the ARs.
Another method to identify the AR axis is to perform a curve fitting on the
coordinates of the AR region. For instance, fitted a
third-degree polynomial to the latitudes and longitudes of AR coordinates. For simple
shapes, this gives a satisfactory result, but for complex, curvy
shapes, polynomial fitting suffers from the inability to handle multiple
outputs (e.g., one longitude corresponds to more than one latitude)
and difficulties in finding a balance between overfitting and underfitting.
defined the AR axis by performing a perpendicular
line scan along the great circle between the furthest apart
pair of AR region coordinates and assigning axis points to the
largest IVT value along the scanning line. For complex shapes, the
identified axis is not guaranteed to be a continuous curve.
More recently, introduced another axis identification
method which uses a k-nearest neighbor method in the
forward/backward searches for a sequence of local centroids as the AR
axis. As will be shown later, this method is similar to our method in that
the IVT direction information is encoded into the identified axis;
therefore, the axis reflects not only the AR's location but its major
flow direction as well.
Along with the new AR detection algorithm, we propose a new method to identify
AR axis. By building a topological graph from AR region coordinates and the horizontal
moisture flux vectors, the axis-finding problem is transformed into a
path-searching problem. With moisture flux information encoded into the formulation,
the found AR axis has close physical correspondence, follows the major orientation
of the flows, stays close to the maximum flux values and never extends out of
AR boundary. It is also capable of handling very complex shapes.
Many previous studies performing AR detection are solely concerned with
determining AR presence at any given time/location. Only a few recent studies
(e.g., ) attempted to track ARs as unique
entities through their life cycle. In contrast, tracking of tropical
cyclones and extratropical storms has been a common practice. This is largely
because the circular symmetry in these systems permits their locations being
represented by a single coordinate pair, and inter-center vicinity being
measured by either the distance between coordinate pairs
e.g., or an areal overlap ratio with the help of
radii estimates e.g.,. The complex shapes of ARs and the
absence of circular symmetry deny such a convenience. In this work, we also
propose an AR tracking algorithm in which a modified Hausdorff distance, which
gives an effective measure of the geographical proximity of two ARs,
is used as an inter-AR distance estimate.
This work is mostly focused on the description and introduction of the new
detection and tracking methods, collectively named the Image-Processing-based Atmospheric River Tracking method (IPART), using the application on Northern Hemisphere IVT
data as an illustration. A more detailed comparison between ARs detected by
this new method and other conventional methods are reported in a separate
study. This paper is organized as follows: Sect. 2 gives a description of
the methods. Section 3 examines the parameter sensitives of the proposed
method by comparing the AR detection results against those by two conventional
detection methods. This is followed by an analysis of the tracking of ARs
in Sect. 4 and an illustration of applying the proposed method on IWV-based
detection in Sect. 5. Lastly, Sect. 6 summarizes the results and discusses
some limitations of these methods.
The Image-Processing-based Atmospheric River Tracking (IPART) methodAR detection using the top hat by reconstruction (THR) algorithm
The AR detection method is inspired by the image-processing
“top hat by reconstruction” (THR) technique , which consists of
subtracting from the original image a “greyscale reconstruction by
dilation” image. In the context of AR detection, the greyscale image in
question is the non-negative IVT distribution. The THR process starts by
defining a “marker” image, which in this case is obtained by applying a
greyscale erosion on the IVT data. Greyscale erosion (also known as minimum
filtering, e.g., ) can be understood by analogy with a
moving average. Instead of the average within a neighborhood, erosion replaces
the central value with the neighborhood minimum. Similarly, dilation replaces
with the maximum. And the neighborhood is defined by the structuring element
E, which is an important parameter in the entire THR process.
Then lateral spread (dilation) starts from the “marker” image. The dilation
is capped in pixel intensity by the original IVT distribution, giving the
greyscale reconstruction by dilation component (hereafter reconstruction),
which corresponds to the background IVT component. Finally, the difference
between IVT and the reconstruction gives the anomalous IVT, from which AR
candidates are searched. Intuitively, the THR algorithm consists of a search
for a “baseline” intensity level within a given neighborhood (the erosion
process), a creation of plateaus at this level (reconstruction) and a final
segmentation of baseline and anomalies. Non-zero regions in this anomaly
component are then selected, giving a collection of marked out regions in the
data domain denoting the boundaries of potential ARs. More details of the THR
algorithm are given in Sect. in the Appendix, and
Fig. gives some illustrations of this filtering process applied on
1-D and 2-D data.
Figure a shows a snapshot of the IVT field at an
arbitrary time point, and a horizontal line denotes the position of a zonal
cross-section, whose profile is shown in Fig. b. The blue curve in
Fig. b shows the two prominent peaks with IVT values above
1000 kg m-1 s-1. The dashed green curve shows the result of 1-D erosion
applied on this cross-section, where the structuring element E used is a line
segment with length 13: E=[1,⋯,1]︸13.
The result of the 1-D erosion is used as the “marker” image, from which
lateral spread (dilation) starts. The dilation is capped by the original IVT
profile, giving the reconstruction plotted as dashed red curve. Finally, the
difference between IVT and the reconstruction is defined as the anomalous IVT,
plotted as the dashed black curve. The lateral extent of these horizontal
plateaus across the local peaks is, by design, 13 pixels wide.
Given that the data used in this case have a
horizontal resolution of 0.75∘, this is equivalent to ∼1040 km,
which is also the upper bound of typical AR width (see later sections).
However, this is too strict a cut that the prominent Atlantic AR is largely
gone in the filtered curve. This is because this AR is zonally well oriented so
that only the very tip of the IVT profile can fit into this zonal lateral
extent. The other AR in Pacific has a much narrower zonal extent;
therefore, a larger portion of its peak is retained. For shallower peaks like
the one around 170∘ E, the filtering still gives a non-zero
anomaly but with a much smaller magnitude, properly reflecting their
shallowness.
To address the missing Atlantic AR, the erosion and reconstruction processes
are extended into 2-D (x and y dimensions), using a 2-D disk-like structuring
element (a 2-D mesh satisfying x2+y2≤6 pixels, 6 being chosen as
it gives a diameter of 13 after adding a central pixel). The profiles of the
results are plotted as solid curves in Fig. b. This time, about half
the two prominent IVT peaks are attributed to the reconstruction
component and the other half to anomalies. The shallow peaks stay about the
same.
Figure c and d show the maps of 2-D reconstruction and anomalies,
respectively. Again, plateaus are created in the reconstruction field, above
which are the anomalies. Exactly where in height a peak is cut depends on how
wide the peak's shape is, and it is the direction with the greatest gradient
that matters. For AR-like features, this corresponds to the cross-sectional
direction along which the 6-pixel radius takes
effect. This allows us to properly isolate plumes that are narrow in one
direction but elongated in the other. Shallow peaks can also be retained,
largely regardless of their smaller absolute magnitudes, as long as the peaks
stand out at the given spatial extent.
We then extend the processes of erosion and reconstruction to 3-D (i.e., time,
x and y dimensions), measuring “spatiotemporal spikiness”. The added
temporal dimension helps detect plumes that are transient at a given temporal
extent. The structuring element used for 3-D erosion is a 3-D ellipsoid:
E=(z,x,y)∈Z3∣(z/t)2+(x/s)2+(y/s)2≤1,
with the axis length along the time dimension being t, and the axes
for the x and y dimensions sharing the same length s. Both t and
s are measured in pixels/grids. Note that the axis length of an
ellipsoid is half the size of the ellipsoid in that
dimension. For relatively large-sized E, the difference resulted from
using an ellipsoid structuring element and a 3-D cube with size
(2t+1,2s+1,2s+1) is fairly small.
Considering the close physical correspondence between ARs and extratropical
storm systems , the “correct” parameter
choices of t and s should be centered around the spatiotemporal scale of
AR. Suppose the IVT data have a horizontal resolution of 0.75∘ and
a temporal resolution of 6 h. The typical width of an AR is within 1000 km
(e.g., , and results below); therefore, s=6 grids is
chosen. The typical synoptic timescale is about a week, giving t=4 d (recall
that t is only half the size of the time dimension).
An extra grid is added to ensure an odd numbered length: the number of
time steps is 4 steps d-1×4 d ×2+1 step =33 steps.
Lastly, a candidate AR is defined as a continuous region where THR
anomalies are above zero; however, the IVT accounted by this candidate is
the total IVT (i.e., the sum of reconstruction and anomaly, as shown in
Fig. a). Thus, detected candidates are then subject to some
geometrical filtering, as introduced next.
Illustration of 1-D and 2-D THR processes.
(a) Snapshot of IVT in kg m-1 s-1 on 23 January 1984 at 00:00 UTC. The horizontal
line denotes a zonal cross-section. (b) IVT profile along the zonal
cross-section defined in panel (a) as a blue curve.
Green curves are profiles of erosion, red ones the reconstructions,
and black ones the anomalies. Dashed lines show results obtained
via 1-D erosion/reconstruction and solid lines are results from 2-D
versions.
(c) A 2-D reconstruction of IVT, in kg m-1 s-1.
(d) IVT anomaly defined as the difference between IVT and 2-D reconstruction,
in kg m-1 s-1.
Geometric considerations
The identified AR candidates are then subject to
some geometric filtering to remove non-AR-like systems such as tropical
cyclones. The geometric requirements include the following:
Minimum length and minimum area. The length of an AR is defined as
the line integral of the AR axis, defined in the following section. A
typical 2000 km minimum length requirement is adopted to be
consistent with previous studies; however, a relaxed 800 km
threshold is also applied when we track ARs across time. This allows for
weaker systems, many of which occur during the genesis stage (the first
time point of the track of an AR)
of strong ARs, to be included and helps depict a more complete picture
of AR life cycle. However, it is required that the same AR reaches
2000 km or above at least one time step during its lifetime. A
500×103 km2 minimum area requirement is used to filter
out some miniature features.
Maximum length and maximum area. When setting too low a standard in detecting
AR candidates, the resultant region may cover too large an
area that no longer conforms to the definition of an AR. A
maximum length of 11 000 km and a maximum area of 10×106 km2
are imposed to screen out such cases. Some examples are given in
Sect. in the Appendix justifying
the choices of maximum length/area.
Isoperimetric quotient and length/width ratio. Isoperimetric quotient is defined as the ratio of the area enclosed
by an AR candidate's boundary and that of the circle having
the same perimeter of the AR: Q=4πA/L2, with
A being area in km2 and L being perimeter in km. This
serves the same purpose as the length / width ratio typically
used in previous studies, and more circular regions (such as
tropical cyclones) having isoperimetric quotients greater than 0.7 are
filtered out.
Note that when a tropical cyclone occupies a small partition of the AR
candidate (the concurrence of tropical cyclone and AR), the tropical
cyclone cannot be discarded by this criterion.
The reason for the preference
over length / width ratio is that length calculation is based on
finding an AR's axis, which in turn involves
solving an array of
optimal path-finding problems (see Sect. ). Therefore, the
easier solvable isoperimetric quotient can help bypass some
unnecessary computations.
After isoperimetric quotient filtering, passing candidates
are further filtered by a minimal length / width ratio of 2.
An arbitrary latitudinal range of 23–80∘. This is imposed on the centroid
of an candidate AR to select only
midlatitude systems. The use of centroid as the metrics implies that
some systems may have a tropical portion in their geographical region but
are primarily midlatitude as a whole.
Section in the Appendix gives further discussions on the choices and
related sensitivity tests on these geometrical criteria.
Passing candidates from the geometrical filtering are
regarded as ARs, their spatial regions are termed “AR regions”, and the
appearance at an instantaneous time point constitutes an “AR occurrence”,
which is equivalent to the term “AR object” in . The
contiguous occurrences through time of a single AR entity constitute an “AR
track”.
Finding the AR axis
Identifying an axis of an AR is important for tracking the movement of the AR.
Here, we describe a new procedure to identify the axis. The axis of an AR is
sought from the binary mask (Ik) representing the spatial region of the AR.
A solution in a planar graph framework is proposed here. The process of
defining the nodes and edges of the graph is given in
Sect. in the Appendix, and an
example of the axis-finding algorithm is given in Fig. .
The boundary pixels of the AR region are first found, labeled Lk. The
transboundary moisture fluxes are computed as the dot product of the gradients
of Ik and (uk,vk): ∇Ik⋅(uk,vk), where uk and vk
are the vertically integrated moisture fluxes in the zonal and meridional
directions, respectively. Then the boundary pixels with net input moisture
fluxes can be defined as Lk,in={p∈Lk∣(∇Ik⋅(uk,vk))(p)>0}; similarly, boundary pixels with net output moisture fluxes are
the set Lk,out={p∈Lk∣(∇Ik⋅(uk,vk))(p)<0}. These boundary pixels are colored in green and black, respectively, in
Fig. .
For each pair of boundary nodes {(ni,nj)∣ni∈Lk,in, nj∈Lk,out}, a simple path (a path with no repeated nodes) is sought
that, among all possible paths that connect the entry node ni and the exit
node nj, is the “shortest” in the sense that its path integral of weights is the lowest.
The weight for edge eij is defined as
wij=e-fij/A,
where fi,j is the projected moisture flux along edge ei,j (see
Sect. in the Appendix for
more details), and A=100 kg m-1 s-1 is a scaling factor. This formulation
ensures a non-negative weight for each edge and penalizes the inclusion of
weak edges when a weighted shortest path search is performed.
The Dijkstra path-finding algorithm is used to find this shortest path
pij*. Then among all pij* paths that connect all entry–exit pairs,
the one with the largest path integral of along-edge fluxes is chosen as the AR
axis, as highlighted in yellow in Fig. .
Note that, unlike
the skeletonization method, the axis
does not necessarily follow the center of the AR shape all the time.
Three more axis-finding examples are given in the Supplement.
It could be seen that various aspects of the physical processes of ARs are
encoded. The shortest path design gives a natural looking axis that is free
of discontinuities and redundant curvatures and never shoots out of the AR
boundary. The weight formulation assigns smaller weights to edges with larger
moisture fluxes, “urging” the shortest path to pass through nodes with
greater flux intensity. The found axis is by design directed, which in certain
applications can provide the necessary information to orient the AR with
respect to its ambiance, such as the horizontal temperature gradient,
which relates to the low-level jet by the thermal wind relation.
Application of the axis-finding algorithm on the AR in the North
Pacific on 1 December 2007 at 00:00 UTC. IVT within the AR is shown as colors, in
kg m-1 s-1. The region of the AR (Ik) is shown as a collection of grey
dots, which constitute nodes of the directed graph. Edges among neighboring
nodes are created. A square marker is drawn at each boundary node and is
filled with green if the boundary node has net input moisture fluxes (ni∈Lk,in) and with black if it has net output moisture fluxes (ni∈Lk,out). The found axis is highlighted in yellow. The inset image shows
the IVT distribution over the North Pacific with the selected AR highlighted in
black contour.
Tracking ARs across time steps
For each AR, we take seven (roughly) evenly spaced points along the AR axis as
“anchors” that collectively describe the approximate location of the AR.
To measure the inter-AR distances, we borrow the Hausdorff distance that is
commonly used in compute vision to measure the geometrical similarity between
2-D or 3-D objects (e.g., ) and modify it
as follows.
Denote the anchor points of an AR at time t as A={a1,a2,⋯,a7} and those of an AR at time t+1 as B={b1,b2,⋯,b7}.
The forward Hausdorff distance is defined as
hf(A,B)≡maxa∈A{minb∈B{dg(a,b)}},
namely, the largest great circle distance (dg) of all distances from a point in A to the
closest point in B. And the backward Hausdorff distance is
hb(A,B)≡maxb∈B{mina∈A{dg(a,b)}}.
Note that in general hf≠hb. Unlike the standard definition of
Hausdorff distance that takes the maximum of hf and hb, we take the
minimum of the two:
H(A,B)≡min{hf(A,B),hb(A,B)}.
The rationale behind this modification is that merging/splitting of ARs mostly
happens in an end-to-end manner, during which a sudden increase/decrease in the
length of the AR induces misalignment among the anchor points. Specifically,
merging (splitting) tends to induce large backward (forward) Hausdorff
distance. Therefore, min{hf,hb} offers a more faithful
description of the spatial closeness of ARs. For merging/splitting events in a
side-to-side manner, this definition works just as well.
This formulation effectively summarizes inter-AR closeness into a single
distance measure; therefore, tracking of ARs across time steps can be
achieved using similar techniques as in the tracking of tropical cyclones or
storms.
There are two possible manners in which such feature tracking can performed: (i) in a
“simple path scheme” where the track of a feature across time forms a
topological simple path, i.e., no merging nor splitting is allowed, and a system
can only appear at one location at any given time; and (ii) in a “network scheme” where
features are allowed to merge/split for arbitrary number of times, and their
combined tracks form a directed network. The former scheme is simple to
implement and suitable for occurrence statistics, as each occurrence is counted
only once. In the later scheme, an occurrence may be included in more than one track
if it is involved in a merging or splitting. Therefore, the latter scheme is more suitable for case
studies where the full lifetime of a system or interactions between systems are
of interest.
In this study, we focus on the simple path-tracking scheme. To achieve that, a
nearest neighbor method is used that the two AR axes found in consecutive time
steps with a Hausdorff distance ≤1200 km are linked, with an exclusive
preference for the smallest Hausdorff distance. The full algorithm is given in
Sect. in the Appendix. Two selected cases using the network tracking scheme are
given as an illustration.
Parameter sensitivity tests in the detection of ARsSensitivity of AR occurrence numbers to parameters
With the geometric metrics kept constant, the parameters that affect the
detection performance of the THR algorithm are the temporal (t) and spatial
(s) sizes of the structuring element. ARs found with a given parameter
combination are labeled as “THR-tx-sy”, where x (y) denotes the
value of t (s), in units of days (number of grid cells).
IVT anomalies (in kg m-1 s-1) from the THR process on
23 January 1984 at 00:00 UTC. Subplots are results obtained using different
combinations of the time (t) and space (s) parameters of the 3-D
structuring element in the THR process, and the subplots are labeled in
a format of (td, sp), with d being short for “days”
and p for “pixels”. From row 1 to row 6, t increases
from t=1 to t=9 d. From column 1 to column 5, s
increases from s=4 pixels to s=12 pixels, with a step of 2.
Axes' information has been omitted for brevity, and the domain is the
same as in Fig. a.
Shown in Fig. are the IVT anomalies from the THR process on
23 January 1984 at 00:00 UTC, obtained using 30 different combinations of t and s.
The IVT data are computed as IVT =u2+v2, where u and v are
the vertically integrated horizontal moisture flux components, with a 0.75∘
horizontal resolution and a 6-hourly temporal resolution. u and v
data are obtained from ECMWF's ERA-I
reanalysis product . It has been demonstrated that the choice of
reanalysis dataset contributes little to the resultant detection statistics
. It can be seen that the filtering process is
rather insensitive to the size/shape of the structuring element. All three
major ARs and the moderate one at the center of the map are isolated in each
combination, and notable differences only appear in the tropical reservoir and
around the edges of the isolated ARs. In particular, a larger structuring
element retains more tropical signals and gives larger AR regions. This is
because the spatiotemporal size of an enlarged structuring element starts to
deviate away from the transient nature of ARs and would tend to include larger
systems.
As a comparison, we also applied two conventional detection methods on the
same ERA-I data. For the constant IVT anomaly threshold approach, IVT anomalies are
first obtained by subtracting from the 6-hourly IVT data a low-frequency
component, which is the mean annual cycle (during January 2004 to December 2010)
smoothed by a 3-month moving average. The use of anomalous IVT instead of
absolute values helps remove slow-varying features and makes a fixed threshold
more applicable across basins, seasons and years . The only
parameter used in this method is the cut-off IVT
value; therefore, ARs found by an IVT anomaly threshold of,
for instance, 250 kg m-1 s-1, are labeled as “IVT250ano”.
To detect ARs using a percentile-based threshold, we first computed the
85th IVT percentile for each of the 12 months within all 6-hourly time
steps during the 3-month period centered on that month, within a
9-year moving time window. For instance, the months of June–July–August (JJA) during 1996–2004
are used to find the 85th percentiles for the month of July 2000. Then
the threshold used to detect AR candidates is the 85th IVT percentile,
or a fixed 100 kg m-1 s-1, whichever is larger, as in
. ARs found by this method are labeled as “IVT85%”.
As the parameters of THR and constant-IVT methods are of different natures
(spatiotemporal scales versus horizontal vapor flux), it is not obvious how to
design directly comparable perturbation ranges. Therefore, the perturbation
range of constant IVT threshold is arbitrarily chosen to be
200–300 kg m-1 s-1 – a 20 % perturbation around the
standard 250 kg m-1 s-1 value. The
perturbation of the t parameter is set to 1–8 d, and s to 3–10 grids,
about 50 %–75 % perturbation around the standard values of t=4 d
and s=6 grids. The percentile value serves the same role in
affecting detection results as the constant IVT threshold; therefore, only the
85th percentile result is presented as a reference.
The same set of geometric filtering is applied to results from the THR,
constant IVT thresholding and the IVT85% methods. The minimal length
requirement is set to 2000 km. It is important to keep in
mind that much of the sensitivity in the number of detected ARs comes from
the interplay between initial detection and subsequent geometric filtering
.
Figure shows the mean annual number of AR
occurrences over the North Pacific during 2004–2010 from different methods.
The numbers are the AR occurrences within all 6-hourly time steps, evenly
divided into calendar years. It could be seen that the annual mean detection number
displays lower sensitivity to the THR t parameter at fixed s
(Fig. a) and similarly to the s parameter at
fixed t (Fig. b), compared with the sensitivity
to IVT thresholds (Fig. d). Detection number
varies more when both t and s change simultaneously, as shown in
Fig. c, from 2208 at the smallest (t=1 d, s=3 grids)
scale to 2730 at the (t=6 d, s=8 grids) scale. The
tendency of increasing AR numbers with enlarging scales is due to the interplay
between initial detection and geometric screening. However, as long as the
parameters are set around the typical synoptic spatiotemporal scales, the
resultant AR occurrence numbers are more or less the same.
In comparison, the constant IVT threshold method produces fewer ARs as one
raises the threshold, creating a drop of 848 from the IVT200ano to the
IVT300ano setup. The effect from varying IVT thresholds is intuitive: as one
raises the threshold, smaller regions are retained. When coupled with a
minimal size requirement, more get filtered out.
Average annual number of AR occurrences over the North Pacific during
2004–2010. (a) AR occurrence numbers by the THR method with various
time (t) parameters and a fixed space parameter (s=6). (b) Similar
to panel (a) but for fixed time (t=4) and varying space (s) parameters.
(c) Results from the THR method with time (t) and space (s) varying simultaneously
from the lower bound of t=1 d, s=3 grids to the upper bound of
t=8 d, s=10 grids. (d) AR occurrences from the constant IVT
thresholding method with the threshold value ranging from 200 to 300 kg m-1 s-1
and the result from the IVT85% method as in the last column.
Also note that the IVT85% method reports more than double the number
of ARs of the highest THR method
(Fig. d). As will be shown in later
sections, this method tends to produce ARs with notably different
features compared to the other two and is likely because the geometric
metrics listed in Sect. are
insufficient in effectively filtering some weak plumes. Specifically, it is
likely that the requirement of a minimal mean poleward IVT component
and mean IVT direction being within 45∘ of the AR shape
orientation that are applied by but absent in this
study is making the greatest difference.
Results in Fig. suggest that the THR-t4-s6 method
reports 760 more AR occurrences per year than the IVT250ano method. By
applying a matching method based on areal overlap ratio, we are able to
look closer at the degree of agreement between these two methods in terms of AR
occurrences and their accounted IVTs.
Besides occurrence numbers, there are also some differences in the geographical
locations of the detected ARs by different methods, with different
implications in the seasonally accumulated meridional moisture
transport related to ARs.
Details of this are beyond the scope of
this study and are discussed further in .
Snapshots of IVT distributions on (a) 11 January 2006
at 06:00 UTC over the North Pacific,
(b) 13 January 2007 at 00:00 UTC over the North Pacific
and (c) 7 February 2009 at 06:00 UTC over the North Atlantic.
ARs found by the THR-t4-s6 method are drawn in solid green
contours, those by the IVT250ano method in solid black contours
and those by IVT85% in dotted black contours. Length (in km) and
area-averaged IVT (in kg m-1 s-1)
for the THR-t4-s6 (IVT250ano) ARs are labeled out in green
(black) boxes. Hatching indicates areas where the IVT anomalies
are above the 250 kg m-1 s-1 threshold.
Comparison of selected cases
Figure shows some selected cases where an AR occurrence is
detected by the THR-t4-s6 method but not by IVT250ano. ARs found by the former
are drawn in solid green contours and the latter in solid black contours. On
11 January 2006 at 06:00 UTC (Fig. a), both methods detect the stronger
AR over the northeastern Pacific; however, the weaker one at ∼160∘ E
is missed by IVT250ano. This is because the region where IVT
anomalies are above the 250 kg m-1 s-1 threshold is too small, as indicated by the
hatching. This AR is not detected by IVT250ano until 12 January 2006 at 12:00 UTC, at
which time it has migrated to ∼180∘ E. Then, 4 d later
(16 January 2006 at 12:00 UTC), it makes landfall onto the North American continent.
Figure S1 in the Supplement shows the entire life cycle sequence
of this AR.
Similarly, the northwestern Pacific AR on 13 January 2007 at 00:00 UTC is missed by the
IVT250ano method (Fig. b). The THR method identifies this AR
occurrence as one with a length of 3186 km and an average absolute IVT of
283 kg m-1 s-1. Then, 30 h later, IVT250ano detects this AR until
18 January 2007 at 06:00 UTC, at which time it is just about to make landfall in North America
(Fig. S2). Meanwhile, THR traces this particular AR
throughout this period until 1 d after it is last seen in the IVT250ano
detection (Fig. S2). Also shown in Fig. b is
another AR occurrence at ∼155∘ W that is solely detected by THR.
This AR is not detected by IVT250ano until 15 January 2007 at 06:00 UTC
(Fig. S2).
Figure c shows another case in the North Atlantic. The AR in
question is propagating over the eastern North America at the time of
7 February 2009 at 06:00 UTC. The life cycle sequence in Fig. S3
indicates that this AR never appears in the IVT250ano detection until its
dissipation on 13 February 2009 at 12:00 UTC just south of Iceland.
Figure c also shows another AR occurrence over the northeastern
Atlantic that is missed by the IVT250ano method but detected by THR.
It could be seen that the exclusive THR AR detection tends to correspond to the
genesis or dissipating stages of some well-defined AR tracks
(Fig. a, b) or in other cases the entire life cycle of some
weak systems as in Fig. c. also suggested that
discrepancies among methods are smaller in cold seasons than in warm seasons, in
more active years than in quieter years and during time steps with higher
observed IVT than those with lower IVT. In summary, sensitivity to
detection methods is much greater for weaker systems.
It was also observed that methods with more restrictive geometrical criteria tend to
report less detection compared with those with comparable magnitude
thresholds but are more permissive in the geometrical requirements
. In most of the existing detection methods,
geometrical filtering is applied as an extra step after the initial region
detection. However, these two steps are inherently closely coupled: once the
candidate region is determined, so is its geometry, and with the help of a
sensible length estimate, its length as well. Therefore, for a
magnitude-thresholding detection method, the choice of the threshold to some extent
already determines the expected geometrical extent of the passing candidates,
with largely predictable behavior as one adjusts the threshold: raising the
threshold level restricts the sizes of the detected ARs, and vice versa.
However, what is less predictable is the resultant AR statistics when applying
the same threshold to data across multiple decades when low-frequency drifts
may be present or to climate projections where different model biases are
to be expected.
The sensitivity and uncertainty embedded in geometrical constraints still exist
in the THR method but to a much lesser extent. Weaker systems as shown in
Fig. are more likely to be detected together with the most
intensive ones. It also implies that the geometrical filtering is more of an
independent criterion rather than closely coupled with the initial region
detection process. This allows for the inclusion of systems that are weaker (note
that in climate scale, or with different model biases, it is less obvious
how weak is weak) in intensity but sizable in geometry. As shown above and
will be discussed later, this often leads to the captured AR tracks having a fuller
life cycle. As the strength and size criteria are decoupled, the user can
still apply a subsequent magnitude filtering on the maximum and/or average IVT
to obtain the subset of a certain intensity level. Therefore, it offers greater
control power without completely breaking the compatibility with existing
methods.
As a reference, Fig. also shows as dotted black contours
the ARs detected by the IVT85% method. This method displays improved
sensitivity to weaker IVT signals, as in the case of the landfalling
AR in Fig. a and the one over the eastern North America
in Fig. c. However, it still misses the three ARs in
Fig. a and b.
Also note that the THR ARs on the eastern side of the map in
Fig. a and Fig. c enclose more than one
local IVT maxima in their region contours. This can happen when merging or
splitting creates two nearby transient plumes and can subsequently contribute
to the geometry-related uncertainties. A method has been developed to separate
such “multi-core systems” into “single-dome” ARs and will be introduced in a
future update of the algorithm.
Sensitivity of AR shapes and IVT intensities to parameters
Some geometrical features and IVT intensities of the ARs identified
by the three methods are summarized in Fig. .
Considering the low sensitivity to either t or s parameters with the
other one fixed in the THR method, only the parameter combinations when both
t and s vary simultaneously are included.
Distributions of (a) AR length (in km), (b) width (in km),
(c) area (in 106 km2), (d) length / width ratio, (e) mean IVT averaged
over AR region (in kg m-1 s-1) and (f) maximum IVT within the AR region (in
kg m-1 s-1) of ARs identified by different methods, during
the period of 2004–2010. Box ends denote the interquartile range
of the distribution, with the median as the line in the middle.
Box whiskers denote the 5th and 95th percentiles.
Figure shows that enlarging the THR structuring
element tends to produce ARs with larger sizes, and this can be seen in the
length (Fig. a), width
(Fig. b) and area
(Fig. c) distributions. (Note that width
is defined as the effective width, i.e., the ratio of area over length.)
However, the length / width ratio remains about constant (Fig. d).
Raising the constant IVT threshold has the opposite effect, where the resultant
ARs are progressively shorter (Fig. a),
narrower (Fig. b) and
smaller in size (Fig. c).
Figure e suggests that larger-sized ARs tend to
have lower mean IVT values, and this is true among THR and constant IVT
threshold methods. Although the maximum IVT follows a similar trend
(Fig. f), the differences are much smaller.
This is because when taking the average over the region of larger-sized ARs,
the mean values get “diluted” more during the spatial averaging process, yet
the maximum values are largely immune to this “dilution”. Therefore, the
lower mean IVT values of THR ARs are primarily due to their larger sizes than
due to the inclusion of weaker systems. The variation among constant IVT
threshold methods is also consistent with in that higher
threshold on IVT produces higher average IVT intensities.
Results of the IVT85% ARs are also displayed as a reference. ARs found by
this method display comparable size distributions as that by THR-t2-s4 method
(Fig. a–d) but with notably weaker mean
(Fig. e) as well as maximum IVT distributions
(Fig. f). Combined with the high number of ARs
found by IVT85% as shown in Fig. d, it could be
inferred that a good number of these are fairly weak systems that get ignored
by the other two.
The sizes of ARs constitute an important source of
uncertainty in many AR-related estimates . For
instance, showed that by lowering the IVT threshold from 300
to 200 kg m-1 s-1, the resultant landfalling AR frequency onto the North
American coast rises by ∼50 % (see their Fig. 5). A similar concern was
also raised in when quantifying North Pacific AR
frequencies. Currently, no metrics have been developed to objectively quantify
the appropriateness of the AR boundary definition. We offer some brief
discussions on this topic from a segmentation cost perspective in Sect. in the Appendix.
Tracking ARs across time
Besides the quantification of AR occurrences, prediction of ARs also requires
tracking ARs across time steps. Figure a shows an example of the
tracking algorithm applied on THR-t4-s6 ARs found on 2 December 2007 at 00:00 and 06:00 UTC,
drawn with dashed blue and red lines, respectively. A blue (red) arrow indicates
the forward (backward) Hausdorff distance between a pair of ARs that get
linked. It could be seen that for pairs that are well separated or relatively
clustered, the Hausdorff distance correctly measures the inter-AR closeness
and enables the nearest neighbor algorithm to make the correct associations.
Note that the minimal length requirement is relaxed to 800 km, but it is
required that the same AR reaches ≥2000 km for at least one time step during
its lifetime.
(a) Tracking of ARs across 2 December 2007 at 00:00 and 06:00 UTC using the
nearest neighbor algorithm. ARs on 2 December 2007 at 00:00 UTC are represented by
their anchor points joint by dashed lines and are drawn in blue, and
ARs on 2 December 2007 at 06:00 UTC are drawn in red. Blue (red) arrows indicate the
forward (backward) Hausdorff distance among paired ARs, and the
distances (in km) are labeled nearby. (b) Tracks of three selected ARs
represented by their axes. The life cycle of an AR is represented as the
black–yellow transition in the coloring. Other ARs during the same
period are omitted for brevity.
Figure b shows the tracks of three selected ARs
in November–December 2007 obtained using the simple path scheme. The axes of
the ARs are drawn with a black–yellow color scheme, with the transition
representing the stages of their life cycle. The two ARs originating from
Pacific (AR1, AR2) have experienced the association process as shown in
Fig. a. AR1 reaches a length of ∼4700 km shortly before its
landfall onto the western coast of the North America on 4 December 2007 at 06:00 UTC.
AR2 starts as an eastern Pacific system on 1 December 2007 at 00:00 UTC and survives the
cross-continent and cross-basin travel before its European arrival on
7 December 2007 at 06:00 UTC, at which point the AR has shrunk to a fairly short 960 km.
AR3 is initially fueled by a tropical cyclone in the Caribbean Sea and is
joined by another plume (not shown in this figure) coming from the eastern
Pacific during its eastward travel and dissipates halfway through its
North Atlantic propagation.
Tracks of two ARs obtained using the network scheme.
Each of the two ARs (AR1 and AR2) has two branches (branch a and
branch b) in their tracks, shown in panels (a) and (b), respectively.
The same color scheme as in Fig. is used to represent
their life cycles. The different branches of a single AR track
are highlighted in red ellipses.
Figure shows two selected AR tracks obtained using the network scheme,
where merging and splitting are captured. To achieve this, three
consecutive applications of the nearest neighbor algorithm are performed, with
different input arguments each time. More details are given in Sect.
in the Appendix. The first selected case (AR-1) starts from
the northwest Pacific on 21 December 2007 at 12:00 UTC and splits into a southern branch
(AR-1a, shown in Fig. a) and a northern branch (AR-1b,
Fig. b) during its eastward propagation. The two branches then merge
into one shortly before the North American arrival on 29 December 2007 at 12:00 UTC. In
fact, the life cycle
of this AR is further complicated by the joining of a
third branch originating from another tropical system. We have omitted the
third branch for the sake of clarity. AR-2 demonstrates a merging case in which a
system from the Gulf of Mexico (AR-2a; Fig. a) is joined by an
eastern Pacific one (AR-2b; Fig. b), and the combined track then
makes European landfall. It has been estimated that about 25 % of
wintertime extratropical cyclone tracks experience at least one merging and/or
splitting during their lifetime . The proposed method enables
similar analysis on AR tracks and their possible links with merging or
splitting cyclones.
The simple path scheme is then applied to all Northern Hemisphere
ARs found by the THR-t4-s6 method during the November–April seasons of November 2004 to
April 2010. Depending on the AR centroid at genesis time, those lying within
120∘ E–100∘ W are labeled “Pacific”, and those
within 100∘ W–20∘ E are labeled “Atlantic”. After
removing tracks lasting shorter than 24 h, it is found that, on average,
both the North Pacific and North Atlantic have about 80 AR tracks during the
November–April season. More notable difference is observed in track durations,
as shown in Fig. . The median of the Pacific track
durations is 78 h; that of the Atlantic is 66 h. Such a difference is
largely attributed to those tracks lasting for 150 h or beyond and is consistent
with the greater longitudinal span of the Pacific basin. Note that the
duration is defined as the lifetime of individual AR tracks and is distinct
from a per grid, Eulerian definition as in, for instance, ,
and , who measured the contiguous time spans when
a grid cell experiences AR occurrences.
Distribution of track durations (in hours) of AR tracks in the
North Pacific (cyan) and North Atlantic (orange). The “inf” label is
used to form the right bin edge for the last bin which includes all tracks
lasting longer than 150 h.
Figure displays the movements of all Northern
Hemisphere AR tracks during the November–April seasons of November 2004 to April 2010.
The geometrical centroid of the AR region is used as a proxy to location, and
coloring represents the maximum IVT within the AR region at each time step. It
could be seen that distributions of AR tracks overlap well with the storm track
regions of the North Pacific and North Atlantic basins,
with a southwest–northeast orientation . ARs of both ocean basins
can be traced back to the western boundary warm current regions – the
Kuroshio Current for the Pacific and the Gulf Stream for Atlantic. For the Atlantic, a
considerable number of ARs also originate from the Gulf of Mexico.
Keep in mind that an arbitrary 23∘ N latitude requirement has been
applied during the detection stage which to some extent prevents the
genesis locations to be traced back to the main moisture reservoir
within the tropics.
Movement of Northern Hemisphere AR tracks as indicated by the geometrical centroids during the
November–April seasons of November 2004 to April 2010. Color represents the maximum
IVT within the AR region.
Note that Fig. also shows an additional hot spot in the Middle East
around the Red Sea, one across north Africa–Mediterranean–eastern Europe
and another even weaker one over west Siberia. We would
refrain from naming them ARs, as they conflict with the conventional AR
definition in that they are weaker in strength, not ocean-originated and
likely driven by different physical mechanisms. However, these are well
organized (above 2000 km in length)
and relatively persistent (can
be tracked over 24 h) water plumes. The identification of such systems
speaks to the greater adaptability of the THR method and its ability to
encompass a wider range of transient water vapor plumes in a single
framework.
Application on IWV in polar regions
To support our claim that the proposed THR method can be extended
to IWV-based applications, we show only a selected case of
IWV-based AR detection here because of the length limitation of the paper.
Unlike IVT where the transition from tropical trades to extratropical
westerlies creates a natural separation in the tropical and extratropical IVT
distribution,
ARs represented by IWV are usually well connected with the tropical
reservoir. Therefore, some modification of the THR process is needed. The
detailed procedure is given in
Sect. in the Appendix. A selected case is
shown in Fig. .
(a) IWV in the Southern Hemisphere on 19 May 2009
at 00:00 UTC, in cm. (b) IWV anomalies in cm, obtained using a two-step THR,
which uses a structuring element E with size t=4 d, s=6 pixels.
The IWV data from ERA-I are first projected onto the polar Lambert azimuthal
projection before carrying out the two-step THR process, which uses the same
structuring element of size t=4 d, s=6 pixels. Shown in
Fig. a and b are the IWV and IWV anomalies, respectively, on
19 May 2009 at 00:00 UTC. The AR located at 60∘ E is moving towards
Antarctica. This particular case has been documented by
, in which the conventional 2 cm threshold value for
IWV has been corrected by an empirical formula to cater to the decreased
saturation capacity of the polar region. Note that although IVT is more than
2 orders of magnitude larger than the values of IWV, the THR method does not
require a separate threshold for the IWV applications, and no polar adjustment
is needed.
Conclusions
In this work, we propose a new set of automated AR detection and tracking
methods. The THR algorithm exploits the transient nature of ARs to segment IVT
signals. Compared with the intensities of AR-related vapor fluxes, the
inherent spatiotemporal scale of AR is a more stable attribute. This makes
the method less prone to the potential difficulties in reliably detecting ARs
in a warming climate, and results from different models are more directly
comparable when model biases may be present. It also demonstrates reduced
sensitivity to parameter choices and greater tolerance towards a wider range of
transient water vapor plumes and therefore has the potential of encompassing
water plumes with various strengths into a unified framework. Furthermore, as
strength is decoupled from the initial selection process, it is subject to the
user to later select only those that meet a given strength standard, giving
finer control power for different applications.
An intensity scale like those used to rank tropical cyclones has just been
established for the landfalling ARs . In the proposed scale,
five intensity categories were devised, covering the lowest “weak” category,
with observed IVT being 250–500 kg m-1 s-1, to the highest “exceptional”
category, whose IVT level is 1250 kg m-1 s-1 or above, with extra duration
factors taken into account in all categories. The difference in categories can
mean the difference from a mild, beneficial atmospheric freshwater delivery to
a hazardous extreme event that can cause damages measured in billions of
dollars . Therefore, it is advantageous for a detection method
to have a wider detection spectrum rather than solely focusing on the most
intensive events.
Besides the mostly commonly used magnitude-thresholding methods,
new AR detection techniques are continually being developed. For instance,
the ARTMIP project reported one machine-learning-based detection
method that is also threshold-free .
As the AR research matures, more inspirations from other disciplines like
machine learning, image processing or computer vision are brought into
the view of the AR community. Such inputs can offer some new perspectives
of looking at various AR-related questions and can often lead to new
discoveries that would have been obscured using conventional methods.
More physical information is encoded into the axis-finding method based on a
directed graph model, creating an effective summary of an AR in the sense of
geometry and physics. Problems of discontinuity, spurious branches,
weak physical correspondence and difficulties in handling complex shapes are
overcome in this method.
Lastly, tracking of ARs across time steps in a similar manner to the tracking
of tropical cyclones and storms is achieved using a modified Hausdorff distance
as the inter-AR proximity measure. Long-lived ARs spanning multiple days,
having cross-continent or cross-basin tracks can be reliably traced through
their tropical/subtropical origins to high-latitude landfall.
However, these methods come with their own limitations. Firstly, the THR method
is
considerably more complex than the constant thresholding method. Although it
has been shown to have lower parameter sensitivity, sensitivities in other
aspects still exist, particularly in the interplay between candidate region
detection and the subsequent geometric filtering. Some ARs may fail the detection
for their being just shy of a 2000 km length requirement or in
other cases being too long because two nearby water plumes are merged together.
Ambiguity in the shape of ARs still constitutes an important source of
uncertainty in many AR-related statistics. A more accurate and controllable
depiction of the AR shape is still in demand.
This appendix provides more technical details on AR detection using the THR
algorithm, AR axis definition, inter-AR distance measure and tracking algorithms.
A discussion on the AR sizes from a segmentation cost perspective is also given.
Some select AR life cycle sequences are shown at the end.
Top-hat reconstruction by dilation algorithm
Greyscale reconstruction by dilation can be defined as iterative applications
of elementary geodesic dilations of a marker image M
“under” a mask image I until convergence . An elementary
geodesic dilation is defined as
δI(1)(M)=(M⊕B)∧I,
where M⊕B is the dilation of M by a flat structuring element B,
and ∧ is the pointwise minimum operator. Intuitively, geodesic dilation
spreads a local high-intensity value in the marker image M to its neighbors so
long as it does not exceed values in the “mask” image I. The spread starts
from the given “marker” and stops until no change can be made:
δI(n)(M)=δI(1)∘δI(1)∘⋯∘δI(1)(M)︸ntimes,such thatδI(n)(M)=δI(n+1)(M),
where δI(n)(M) is the reconstruction by dilation.
The “marker” image used is the greyscale erosion of the image I by a
structuring element E:
M≡ϵE(I)=I⊖E.
The erosion and reconstruction by dilation computations are performed using the
scikit-image software package designed for imaging processing
in the Python programming language.
Schematic diagram illustrating the planar graph built from the AR
pixels and horizontal moisture fluxes. Nodes are taken from
pixels within region Ik and are represented as circles. Red vectors
denote IVT vectors. The one at node ni forms an angle θ
with the x axis and has components (u, v). Black arrows denote
directed edges between nodes, using an 8-connectivity neighborhood
scheme. The edge between node ni and nj is eij and forms
an azimuth
angle α with the y axis. wij is the weight attribute
assigned to edge eij, and fij is the along-edge moisture
flux.
Define the directed planar graph for axis finding
A directed planar graph is built from Ik, which is the binary mask defining
the AR region, using the coordinate pairs (λk,ϕk) as nodes (see
Fig. for an illustration). At each node, directed edges to its
eight neighbors are created, so long as the moisture flux
component along the direction of the edge exceeds a
user-defined fraction (ϵ) to the total flux. The along-edge flux is
defined as
fij=uisin(α)+vicos(α),
where fij is the flux along the edge eij that points from node ni
to node nj, and α is the azimuth angle of eij.
Therefore, an edge can be created if fij/ui2+vi2≥ϵ.
Here, a relatively small ϵ=0.4 is used, as the orientation of an AR
can deviate considerably from its moisture fluxes, and denser edges in the
graph allow the axis to capture the full extent of the AR.
Tracking ARs using the simple path scheme
To make an association between two ARs at consecutive time steps, a
“nearest neighbor” approach is used.
Formally, suppose n tracks have been found at t=t: A={a1,a2,⋯,an}, and t=t+1 has m new records: B={b1,b2,⋯,bm}. The Hausdorff distances between all pairs of possible
associations form a distance matrix:
M=H(a1,b1)H(a1,b2)⋯H(a1,bm)H(a2,b1)H(a2,b2)⋯H(a2,bm)⋮⋮⋮⋮H(an,b1)H(an,b2)⋯H(an,bm).
Nearest neighbor algorithm.
Then Algorithm is called with these arguments: (A=A,B=B,M=M,H*=1200 km, R-=[],C-=[]). The algorithm iteratively links two AR
records with the smallest distance, so long as the distance does not exceed a
given threshold H*. It ensures that no existing track connects to more than
one new record, and no new record connects to more than one existing track.
After this, any left-over records in B form a new track on their own. Then
the same procedure repeats with updated time t:=t+1. Tracks that do not
get any new record can be removed from the stack list, which only maintains
a few active tracks at any given time.
Therefore, the complexity does not scale with time.
Tracking ARs using the network scheme
Merging and splitting are allowed in this scheme, and the process consists of
three consecutive applications of the nearest neighbor algorithm described
above. Specifically, the process works as follows:
Make a copy A′ of the existing tracks A at time t=t,
and a copy M′ of the distance matrix M.
Apply the nearest neighbor algorithm as in Algorithm :
A,R1+,C1+=Algorithm A2(A=A,B=B,M=M,H*=H*,R-=[],C-=[]),
where
R1+ (C1+) contains the indices of tracks
(records) that are linked in this process.
Merging is handled by repeating the nearest neighbor process as follows:
A,R2+,C2+=Algorithm A2(A=A,B=B,M=M′,H*=H*,R-=R1+,C-=[]).
Note that the backed-up distance matrix M′ is used as it contains no
infinities, and the argument R-=R1+ masks out tracks
that have been linked in the previous step, giving other
tracks a chance to merge to the same new record.
Splitting is handled by repeating the nearest neighbor process as follows:
A,R3+,C3+=Algorithm A2(A=A,B=B,M=M′,H*=H*,R-=[],C-=C1+∪C2+).
This time, new records that have been allocated in the previous
steps are masked, giving other records a chance to split
an existing track. Note that when splitting, the new record
is appended to a back-up copy of the track from A′, and a
new track is added to A after the split, as described in lines
7–9 of Algorithm .
Any left-over records in B form a new track on their own. Then,
return back to step 1 with updated time t:=t+1.
It should be noted that this is not equivalent to a “link-all-neighbors”
strategy, which will deny the preference to the nearest neighbor and create
redundant links before (after) a merge (split). After a merge, merging tracks
will have identical tracks thereafter; and for every split, a new track
is created with its history retained. Therefore, there would be many duplicated
records in this scheme.
Segmentation cost estimates
The AR detection task can be viewed as a segmentation problem in the
image-processing framework that a segment of the image (AR) is identified as the
foreground image and thus getting separated from its background (the IVT
distribution). In this formulation, a cost function can be defined to
quantify the total intra-segment variances, as an evaluation of the
effectiveness of the AR detection method in isolating high AR-related IVT
values from its background:
C≡1IVTmax(Nf+Nb)∑Nf(If,i-If‾)2+∑Nb(Ib,i-Ib‾)2,
where Nf, Nb are the number of grids in the foreground and background
segments, respectively. If,i (Ib,i) denotes the pixel value of the
foreground (background) image at location i, and the average across the
segment is denoted If‾ (Ib‾). The summations in
square brackets quantify the total intra-segment variances. This is the same
definition as used by in determining the optimal segmentation
threshold. Either too small or too large an AR boundary definition would raise
the cost function and result in a less effective separation of high-intensity
values from the background. This is also equivalent to the cost function used
in the k-means clustering algorithm (e.g., chap. 7); in
this case, the number of clusters is k=2, where the minimization of the cost
converges to the solution. The normalization by maximum IVT (IVTmax) and
the total image domain size (Nf+Nb) enables intercomparisons among
different ARs. The total image domain is chosen as the bounding box of the AR
boundary expanded out in four directions by five grid cells.
IVT distribution on 30 June 2004 at 06:00 UTC over the northeastern
Pacific (in kg m-1 s-1). Boundaries of ARs detected by (a) THR-t1-s3,
(b) THR-t4-s6, (c) THR-t7-s9, (d) IVT200ano, (e) IVT250ano, (f) IVT300ano
and (g) IVT85% methods are drawn with black curves.
(i) The segmentation costs in all seven methods, in kg m-1 s-1.
Figure compares the segmentation costs of an AR
mutually detected by three THR methods, three constant IVT threshold methods
and the IVT85% method, on 30 June 2004 at 06:00 UTC over the northeastern Pacific.
Consistent with discussions in the main text, shrinking the THR structuring element has
a similar effect to raising the constant IVT threshold that a smaller
proportion of the transient IVT anomalies is segmented from the background.
This particular time step is chosen because the segmentation cost comparison as
shown in Fig. i is qualitatively consistent with the
long-term 2004–2010 average (not shown). Although not specifically designed to
minimize the segmentation cost, the THR-t4-s6 method that reflects the typical
spatiotemporal scale of ARs gives the lowest cost.
Explanations for the choices of the geometrical filtering criteria
The geometrical filtering criteria, including the maximum length/area, the
minimum length, the maximum isoperimetric quotient, the minimum centroid
latitude and the maximum Hausdorff distance in the nearest neighbor linkage
process, are all determined from the physical natures of ARs as well as
trial-and-error processes. The proposed method is mostly concerned with
relaxing the hard and sensitive IVT strength threshold; therefore, the
geometrical considerations are largely treated as controlled variables. Some
further details regarding the choices of these criteria are given here.
Maximum length/area
The maximum area/length requirements are set to fairly large
values. The maximum length is set to 11 000 km, which is longer than
the great circle distance (across the Pacific, ∼10 400 km) from Hong
Kong (∼22.3∘ N, 114.2∘ E) to Seattle (∼47.6∘ N,
-122.3∘ W). Assuming an average width of 700 km
(which is on the larger side for typical ARs), this multiplies to
an area of ∼7.3×106 km2, which is smaller than the
maximum area requirement set here (10×106 km2). These
requirements are far larger than what could be expected from
real-world AR sizes; therefore, they would only filter out erroneous detection.
Northern Hemisphere IVT distribution on 13 August 2004 at 18:00 UTC.
Black contours denote connected regions where the THR anomalies are greater than
zero. Panel (a) shows the result using THR-t7-s8 parameters; (b) shows the THR-t4-s6
parameters.
Regions with such large sizes only happen when two or more ARs are grouped
together in one contour, or some of the ARs are connected with the large and
continuous moisture plumes in the tropics to form a large continuous region.
This happens more frequently when the structuring element E is set too large,
as explained in Sect. . Figure gives one such example. In
Fig. a, the structuring element is set to t7-s8. This
merges the Pacific ARs with tropical plumes to form a big connected region that
later gets filtered out. Figure b is using the recommended
t4-s6 parameters; this time the midlatitude signals are better separated from
tropical ones so the Pacific AR is correctly retained. Those small noisy
contours will be filtered by the minimum area requirement.
A method is being developed to separate ARs that have been mistakenly
grouped together; once the new algorithm is fully ready, such maximum
length/area criteria are no longer needed.
Minimum length and maximum isoperimetric quotient
Some results regarding the sensitivities of
AR numbers to the minimum length and maximum isoperimetric quotient
criteria are given in Fig. .
(a) Average seasonal (November–April) AR numbers in the Northern Hemisphere
during November 2004 to April 2010 when different minimum length criteria are
applied. (b) Average seasonal AR numbers in the same time period when
different maximum isoperimetric quotient criteria are applied.
For minimum length (Fig. a), sensitivity around the
800–1400 km range is fairly small. Also keep in mind that the 800 km
threshold is used as a relaxed criterion to form a hysteresis thresholding
couple with the standard 2000 km criterion, so it does not work quite the
same as a single length threshold like in many other studies. This is an
attempt to introduce some fuzziness into the geometric criteria, and it allows
for a weaker feature (above 800 km in length) to be retained if and only if it is
associated with a strong feature (longer than 2000 km).
For maximum isoperimetric, sensitivity around the 0.7 threshold used
in this study is also fairly low (Fig. b).
Sensitivity tests on the lower latitudinal bound set to an AR's
centroid. (a) Average annual AR numbers in the Northern Hemisphere during
2004 to 2008 when different lower latitude bounds are applied. Cyan
(orange) bars show the number of ARs whose centroids are north (south) of
the given lower latitude bound. The dotted black line is the sum of the two.
(b) Distribution of the AR latitudinal centroids for ARs north (in blue) or
south (in orange) of the given lower latitude bound. (c) Similar to panel (b) but
for the distribution of the north-most axis point in ARs. (d) Similar to
panel (b) but for the AR lengths. (e) Similar to panel (b) but for the latitudinal span
of the ARs. (f) Similar to panel (b) but for the average zonal component of
vertically integrated moisture flux (<UQ>, in kg m-1 s-1).
Minimum centroid latitude
Figure gives some sensitivity tests regarding the choice of the
lower latitudinal bound imposed on AR region's centroid. After detecting all
ARs north of 10∘ N during 2004–2008, they are separated into two
groups depending on their centroid being north or south of a given lower
latitudinal bound. Values of this bound range from 11 to
31∘ N with an increment of 2∘. Detection north of this
bound is represented in blue color in Fig. ; detection south of
this bound (but north of 10∘ N) is colored in orange.
It can be seen that ∼19–23∘ N is the range where the detection
number shows reduced sensitivity to the latitudinal bound
(Fig. a). The same is also true for the centroid latitude
(Fig. b) and the latitude of the north-most axis point
(Fig. c). This low-latitude detection has comparable or
even larger lengths than the midlatitude ones (Fig. d) but
with notably smaller latitudinal span (Fig. e). Furthermore,
such low-latitude detection has primarily westward moisture fluxes, in
contrast to the midlatitude counterparts (Fig. f).
Therefore, they are mostly zonally oriented, large continuous vapor plumes
carried by the tropical trades and incompatible with the midlatitude,
storm-related AR definition taken in this study. This is also the primary
reason for imposing a lower latitudinal bound.
Maximum Hausdorff distance
The choice of 1200 km as the maximum Hausdorff distance during the
track stage is based on references to similar maximum distance
requirements used in extratropical cyclone tracking practices
and trial-and-error processes. Choices of 600,
800 and 1000 km (for 6-hourly intervals) are included in the
Supplement Table A of . We chose the largest one and
gave it an extra margin to make it 1200 km, because in addition to
movement, length variations also contribute to Hausdorff distance.
The choice of this length has very low sensitivity and can be easily
adjusted for data with different temporal resolution (e.g., scaled to
600 km for 3-hourly data or 2400 km for 12-hourly data).
Two-step THR for IWV polar application
The 3-D erosion process is the same as for IVT, but instead of performing the
reconstruction in three dimensions simultaneously, reconstruction on IWV is
split into two consecutive steps. The first one uses a structuring element B
that has only non-zero values along the time dimension. This constrains the
geodesic dilation to the time dimension. Formally, this step involves
δ(IWV)t=δIWV(n)(IWV⊖E)Δ(IWV)t=IWV-δ(IWV)t.
The second step takes Δ(IWV)t as input and performs a THR process
in which geodesic dilation only expands in x and y dimensions.
δ(IWV)s=δΔ(IWV)t(n)(Δ(IWV)t⊖E)Δ(IWV)=Δ(IWV)t-δ(IWV)s.
Recall that the THR algorithm achieves segmentation according to the
spatiotemporal “spikiness” of the data. As ARs in IWV are only
spatially connected to the tropical reservoir which is
temporally much more persistent, they can be separated in the time
dimension THR. Then the second THR is concerned with spatial dimensions and
helps retain spatially transient features.
As an alternative to the two-step THR approach, a temporal
filtering can be used to suppress the tropical signals. Then a similar 3-D THR
process can be applied on the high-pass component of IWV.
Code and data availability
The ERA-I reanalysis data used in the paper are publicly
available.
The implementations of the algorithms used in this work in the Python
programming language are posted in the Zenodo repository (10.5281/zenodo.3864592; ).
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-13-4639-2020-supplement.
Author contributions
GX and XM contributed to the development of the
algorithms and data analyses. GX contributed to the writing
of the manuscript, and all authors made significant contributions to its multiple revisions.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This is a collaborative project between the
Ocean University of China (OUC), Texas A&M University (TAMU) and the National
Center for Atmospheric Research (NCAR) and completed through the International
Laboratory for High Resolution Earth System Prediction (iHESP) – a collaboration
by the Qingdao National Laboratory for Marine Science and Technology
Development Center, Texas A&M University and the National Center for
Atmospheric Research. The authors also give thanks to Chris Patricola from the
Lawrence Berkeley National Laboratory, and Christine A. Shields
from National Center for Atmospheric Research for their comments and
suggestions for the manuscript.
Financial support
This research has been supported by the National Key Research and
Development Program of China (grant nos. 2017YFC1404000, 2017YFC1404100 and
2017YFC1404101) and the National Science Foundation of China (NSFC) (grant nos.
41490644, 41490640 and 41776013).
Review statement
This paper was edited by Paul Ullrich and reviewed by two anonymous referees.
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