# Simulating the influence of sea-surface-temperature (SST) on tropical
cyclones over South-West Indian ocean, using the UEMS-WRF regional climate
model

Chibueze N. Oguejiofor
African Institute for Mathematical Sciences
AIMS, Rwanda.
Rwanda, PA 15213
<EMAIL_ADDRESS>
&Babatunde J. Abiodun
University of Capetown
Capetown, South Africa.
South Africa,7700
<EMAIL_ADDRESS>
Use footnote for providing further information about author (webpage,
alternative address)— _not_ for acknowledging funding agencies.

###### Abstract

Tropical cyclones remain a major threat to the lives, property and economy of
communities around the South West Indian ocean, notably Southern Africa and
Madagascar. Tropical cyclones occur quite frequently around this region, hence
the need to be adequately prepared for the impact of climate variability and
climate change on them. Previous studies have shown that global warming due to
anthropogenic forces may lead to an increase in the frequency of occurrence of
tropical cyclones within the region. However, there is little work done
regarding the impact of this on the intensity of tropical cyclones formed.
This study uses the weather research forecast (WRF) model to perform a series
of simulations for tropical cyclone Enawo with the aim of investigating the
effect of an increase or decrease (by 2${}^{\circ}C$) in sea surface
temperature (SST) on the intensity of the tropical cyclone (using windspeed,
precipitation and pressure as measures of cyclone intensity). The experiment
uses the data from European Centre for Medium-Range Weather Forecasts (ECMWF)
ERA5 re-analysis dataset to validate the results of the WRF model which was
ran using boundary conditions data from climate forecast system reanalysis
(CFSR).

The results indicate that the WRF model performs reasonably well in simulating
the track and windspeed of the tropical cyclone, when compared to
observational data. In simulating the tropical cyclone, the WRF model shows
that an increase in the SST by 2${}^{\circ}C$ generally increases the
intensity of the tropical cyclone formed. This is evident in the increasing
maximum precipitation rate as well as windspeed, and decreasing minimum
pressure. An increase in SST also causes the emergence of a second low
pressure system. On the other hand, a decrease in the SST by 2${}^{\circ}C$
leads to a minute effect in the intensity but generally acts to decrease it.
This results in a smoother track path for the tropical cyclone, a decrease in
the maximum precipitation rate and windspeed, and an increase in the surface
pressure.

The results of this study have shown that increasing the global temperature by
around 2${}^{\circ}C$ \- violation of the Paris Accord \- would lead to more
violent and unpredictable tropical cyclones within the South West Indian
ocean, and hence more destruction and loss of lives.

_K_ eywords Tropical cyclone $\cdot$ South West Indian Ocean $\cdot$ Weather
Research Forecast (WRF) $\cdot$ Re-analysis $\cdot$ Sea Surface Temperature
(SST)

##  1 Introduction

###  1.1 Background

Tropical cyclones are one of the most catastrophic natural phenomena in
occurence today. They are a deadly force of nature, wrecking havoc to coastal
cities as well as inland. The ripple effect of tropical cyclone activities
range from severe and destructive wind, flooding, landslides/mudslides,
pollution of fresh water with sewage, storm surges, enhancing mosquito-borne
diseases, amongst others. Tropical cyclones account for nine of the ten most
costly inflation-adjusted insurance natural disaster losses (200m dollars)
between 1970 and 2009 [1]. This is is because strong windspeed from tropical
cyclones have been known to destroy overhead powerlines (leading to
electrocution), drown vehicles and complete overrun of low-rise building
structure. Of particular concern, is the effect of tropical cyclones on tall
buildings/skyscrapers in which it has been well known to distort the
foundation of skyscrapers, hence, leading to a tilt in buildings structures
and a domino effect of a series of skyscrapers on one another. In original
loss values, tropical cyclones account for two of the five most costly
economic losses and four of the five most costly insurance losses from natural
disasters over the period 1950 to 2009 [2].

Apart from the loss of property, the loss of lives due to tropical cyclones
have been increasingly alarming over the last decade. A total of about 10,000
people have died each year as a direct result of tropical cyclones or other
destructions emanating from it [3]. The deadliest tropical cyclone ever
recorded was the cyclone Bhola which occurred in the 1970. This cyclone had an
estimated death toll of between 300,000 and 500,000 lives. The most recent of
such destructive nature of tropical cyclones occurred between 4th to 21st of
March 2019 as a tropical cyclone named Idai made landfall twice and affected a
total of 4 countries (Madagascar, Mozambique, Malawi and Zimbabwe) with a
death toll of over 1000 people and several thousands more still missing. This
was one of the most deadliest cyclones in the South-West Indian ocean with a
damage of >1billion US dollars [4]. Countries around the South-West Indian
ocean (notably Madagascar and Mozambique) are particularly vulnerable to
cyclones. One of the most critical factors needed for the formation of
tropical cyclones is a warm sea temperature. Hence, there is need for a proper
understanding of the effect of climate change (notably sea-surface-temperature
increase) on tropical cyclogenesis and variation of it’s intensity and
frequency with increasing sea surface temperature.

The intensity and frequency of natural disasters have generally increased in
recent decades more than humans are able to adjust to. This has largely been
associated with anthropogenic forces. Natural disasters possess an inherent
unpredictability that makes preparation and planning an elusive task for
countries. One of these natural disasters are Tropical cyclones also known as
Hurricanes, Typhoons or Tornado’s. The choice of name is dependent on the
location (North-West Pacific – Typhoon, Atlantic and North-East Pacific –
Hurricanes, South Pacific – Cyclones).

Tropical cyclones are basically strong spiraling mass of wind about a low
pressure core in the South Pacific (Figure 1). They have been known to cost
billions of dollars in damages around various regions around the world. They
exist as a warm-core, self-sustaining spiral of wind with surface wind
reaching up to 110$mph$. Tropical cyclones usually originate in warm sea
waters (temperature >26.5${}^{\circ}C$) before moving and generating strong
winds which are usually most destructive when they make landfall.

Tropical cyclones are categorized on a scale of 1 to 5 based on the amount of
damage caused due to wind gush and speed - category 5 being the most
destructive with wind gusts greater than 280$kmh^{-1}$ and category 1 being
the least destructive with wind gusts between 90-125 $kmh^{-1}$. Apart from
classification based on destruction, cyclones are classified into stages
characterized by wind force. These include tropical disturbance, tropical
depression, moderate tropical storm, severe tropical storm, tropical cyclone,
intense tropical cyclone and very intense tropical cyclone with wind-force of
< 28$kt$ (<5 $kmh^{-1}$), 28-33$kt$ (51-63 $kmh^{-1}$), 34-47$kt$ (63-88
$kmh^{-1}$), 48-63$kt$ (89-117 $kmh^{-1}$), 64-89$kt$ (118-165 $kmh^{-1}$),
90-115$kt$ (166-212 $kmh^{-1}$) and >115$kt$ (>212 $kmh^{-1}$) respectively.

Figure 1: Cross section of the structure of a cyclone showing the flow of air
and the location of the cyclone eye and eye wall

###  1.2 Statement of problem

The effect of anthropogenic forces in altering the climate has been profound,
warranting the Paris accord in 2016. This agreement signed by over 196 state
parties had a goal to keep the increase in global average temperature to well
below 2${}^{\circ}C$; and to limit the increase to 1.5${}^{\circ}C$.

The result of sea surface temperature (SST) variation on the frequency of
cyclone is not as consistent as it’s effect on the cyclone intensity [5].
Observational data shows that the ideal temperature for the formation of
cyclones is >26.5∘C, hence, the need to investigate how increasing/decreasing
SST could affect the intensity of cyclones formed, especially in the South
Western Indian ocean. The parameters used in the quantification of cyclone
intensity includes rainfall, pressure, wind and precipitation rate.

###  1.3 Aim and objectives

The aim of this research is to understand and compare the effect of
increasing/decreasing sea surface temperature (SST) on the intensity of
tropical cyclones formed around the South-West Indian ocean using the WRF
model. This will help identify our expectation on the effect of global warming
around this region, if the Paris agreement fails to be reached.

The objectives of the study is:

  * •

Identify the rainfall, pressure and wind pattern of cyclone Enawo just as it
was about to make landfall in Madagascar.

  * •

Simulate the influence of increased temperature on the rainfall, pressure
andwind speed on cyclone Enawo.

  * •

Simulate the influence of decreased temperature on the rainfall, pressure and
wind speed on cyclone Enawo.

  * •

Make a detailed comparison on the effect of sea surface temperature change on
the intensity of tropical cyclones formed.

###  1.4 Description of study area

####  1.4.1 Location of study area

The South-West Indian basin is one of seven known tropical cyclone basins in
the world today Figure 2. Others include the North Atlantic basin, the North-
East Pacific basin, the North-West Pacific basin, the North Indian ocean
basin, the South-East Indian ocean basin (Australian basin) and the South
Pacific Australian basin.

The South-West Indian basin extends from longitude (30∘E to 90∘E) and latitude
ranging from the equator to a little below the tropic of Capricorn. It is
bounded to the north by India, to the East by Southern Africa and to the West
by Australia.

Figure 2: Global distribution of cyclone basin in the world and the statistics
of average annual number of tropical storms and cyclones, average annual
number of tropical cyclones and percentage of the population recorded between
1968 and 1990 [6].

####  1.4.2 Climatology of study area

The spatial distribution of tropical cyclones over the South-West Indian ocean
is usually between latitude 35∘E to 95∘E, cutting across Madagascar and
touching some parts of southern Africa.

Moving with respect to the easterly trading wind, tropical cyclones in this
ocean basin follow a southwestward track before curving about their initial
track in a southward direction where they transcend from tropical to
extratropical cyclones [7]. The curve in track by cyclones in this region can
also follow a south eastward track as shown in Figure 3

Figure 3:  Map showing the tracks of tropical systems in the South-West Indian
ocean with a VMAX observation during the 1999–2016 period. Tropical systems
which reached a VMAX of greater than 64kt are spotted in red colours . Letters
SA, Mo, T, and K indicate South Africa, Mozambique, Tanzania, and Kenya,
respectively. Letters Co, My, Ma, F, T, S, Re, Mr, Ag, Sb, Ro, and Ch indicate
the islands of Comoros, Mayotte, Madagascar, Farquhar, Tromelin, Seychelles,
La Réunion, Mauritius, Agalega, Saint Brandon, Rodrigues, and the Chagos
Archipelago, respectively [8]

More intense cyclone activities occur between 10∘S and 20∘S for the South-West
Indian ocean basin (Figure 3). However between longitude 30∘E and 45∘E (with
the channel separating Mozambique and Madagascar), there is a shift in the
location of the more intense tropical cyclone activities to between 15∘S and
30∘S. This displacement in the position of the more intense cyclones could be
associated to higher sea surface temperatures within the Mozambique channel,
as it has known that tropical cyclones require warm SST (from Figure 3) to
originate and be sustained.

The intensity of tropical cyclones over the South-West Indian ocean is quite
similar to those of hurricanes and typhoons found in the North-East and North-
West Pacific ocean which have a cooler SST as shown in Figure 5

Figure 4: . Climatology of mean SSTs exceeding 22∘C in the meridional part of
the SWIO basin for the active cyclone seasons from September to June during
the 1999–2016 period. Temperatures are extracted from the 6-h-resolution
global EI dataset at 0.75∘ latitude–longitude resolution [9]. Letters indicate
the various islands or countries as in Figure 1 The total sample size is 170
months.

##  2 Literature Review

###  2.1 Characteristics of cyclones over South West Indian ocean

The nature of tropical cyclogenesis over the South-West Indian ocean has not
received enough attention as that of the North Atlantic basin or any other
basin [10]. Tropical cyclones in this region appears to be the least studied
in peer-reviewed literature [11]. This is because, the relative absence of
land around this region would imply that tropical cyclones systems which
originate in this region would rarely make landfall, and in the rare ocassion
that they do, the countries affected (Madagascar, Mozambique) do not have a
vibrant meterological scientific community. Most tropical systems which occur
in this region affect vulnerable islands such as Madagascar (>22 million
inhabitants) known for it’s agro-based economy or the Mascarene Islands, which
include La Réunion (870,000 inhabitants) and Mauritius (1.3 million
inhabitants).

In the Southern Hemisphere, a single season of tropical cyclone goes from the
1st of July through to 30th of June. This corresponds with the season of the
Northern Hemispheric equivalent [11]. However, historical data emphasizes that
the activities of tropical cyclones in the South-West Indian Ocean (0–40∘S,
30–90∘E), tropical storms (including tropical cyclones) occur mainly from late
November to April, with on average 10 per season which usually reaches a peak
during the months of January and February [12, 13].

Over the past decade, much emphasis on modelling perspectives has been given
to the process in which tropical cyclones intensify and the factors
influencing this. However, there is still a lack of understanding of the
intensification and hence forecasting of cyclone intensity has been relatively
uncertain compared to forecast of cyclone tracks [14]. Tropical cyclones Eline
and Favio are examples of known cases which occured in the last decade around
the South West Indian ocean where there was a sudden intensification of the
storms, causing severe damage in property and loss of lives in Madagascar and
Mozambique [15, 16]. Intensifications of this nature usually occurs when the
cyclone passes over regions of positive upper-ocean thermal anomalies [17,
18].

####  2.1.1 Cyclone Enawo

Cyclone Enawo was an intense tropical cyclone which struck Madagascar in March
2017. It was identified as the strongest cyclone to ever hit Madagascar after
cyclone Gafilo in 2004. Cyclone Enawo killed a total of 81 people amongst
other property that were destroyed.

The cyclone started off as a moderate tropical depression on the 3rd of March
after which it drifted slowly while intensifying. On the 5th of march, it
intensified into a tropical cyclone and on the 6th of march, it transcended
into an intense tropical cyclone. On the 7th of march, cyclone Enawo made
landfall over the Sava region in Madagascar just after attaining it’s peak
intensity with a 10 minute sustained windspeed of 205$kmh^{-1}$ (Figure 5). On
the 9th of march, it re-emerged from the land back into the Indian ocean as a
tropical depression moving South West - South, over central and Southern
Madagascar, weakening into a Tropical Depression, but still damaging
infrastructures, causing floods and landslides in several areas of the country
[19]. The damage caused by cyclone Enawo was was felt by several
municipalities of Madagascar, mainly Antalaha and Maroantsetra.

In the United nations (UN) Situation Report nr. 5 on 14 of April 2017,
estimated, economic losses conducted by the CPGU (Cellule de Prevention et de
Gestion des Urgences) and the World Bank was: $400 million (about 4% of annual
GDP of Madagascar).

Figure 5: Tropical cyclone Enawo at peak intensity just before it makes
landfall over Madagascar on the 7th of March 2017[20] Figure 6: The track
followed by tropical cyclone Enawo from it’s origin till it’s dissipation [21]

###  2.2 Impact of climate change on tropical cyclones

The importance of fluctuations in the intensity and frequency of tropical
cyclone activities can not be over emphasized, especially since the affected
population have been on a steady increase [22]. Amongst other natural
disasters, tropical cyclones has been estimated to be one of the costliest in
terms of loss of lives and property in the United states [23]. Furthermore,
recent research proposes the importance of the activities of tropical cyclones
in the regulation of thermohaline circulation in the oceans [24]. This has an
important feedback effect on regional and global climate.

One of the major challenges in attributing activities of tropical cyclones
with climate change is to establish whether or not the changes in cyclone
behaviour is not due to short term climate changes known as climate
variability [5]. Only after this, can we attribute this to climate change.

According to previous theoretical research and practical observations done in
the past, the intensity of tropical cyclones have been forecasted to increase
with increasing global mean temperature [25, 26]. However, these trend-
detection in cyclone activities with temperature has been more focussed on the
frequency. The theoretical intensity that tropical cyclones could attain was
modelled and hence proposed that the presence of a climate affected by
greenhouse gases would impact tropical cyclones by increasing their potential
intensities [25]. Since then, alternative potential intensity theories has
provided some support to this perspecive [27].

The most commonly used metric for essessing the intensity of tropical cyclones
is its power. This is expressed as the cubed cumulative wind speed of each
storm over track it traverses. Tracks followed by cyclones differ across
models, hence the power estimated. Figure 7 displays the effect of climate
change on the power of tropical cyclones in different basins as described by
four different climate models. Notice that the power in most basins show an
alternating increase and decrease except in the North-Pacific basin which
shows a consistently increasing power.

Figure 7:  Effect of climate change on the power of tropical cyclones as shown
by four climate models [5]

###  2.3 Modelling of tropical cyclones

Tropical cyclones are described as mesoscale scale structures with a synoptic
scale powerplant [28]. This implies that they are controlled by a variety of
atmospheric processes. A fairly accurate model of tropical cyclones needs to
account for cloud convection, sea surface temperature, wind speed amongst
other processes. As such, general climate models are not suitable for
modelling of tropical cyclones because fine processes are not well captured in
it’s coarse grids. This is in contrast with regional climate models whose
higher resolution allows for these.

In modelling the potential risk of tropical cyclones, more attention is payed
to it’s tendency to make landfall. Therefore statistical models are built
using exlusive historial data where tropical cyclones made landfall [29].
However, comparatively there are few such cases where hurricanes made
landfall, thus risk assessment is somewhat difficult. This limitation of data
scarcity is overcome by using historical data for cyclone which never made
landfall as well, thus increasing the amount of data to be used in the
contruction of the statistical model.

One of the most important considerations in modelling a tropical cyclone
across a basin is it’s track from genesis to dissipation. Apart from the
track, cyclone intensity are also studied on a basin-wide scale. Models like
the autoregressive model uses increments for direction and speed forecast with
random error terms [30]. Autoregressive model that works quite differently by
using latitude and longitude increments as opposed to velocity can also be
explored [31].

Other modelling paradigm exists such as the three-dimensional hurricane
modeling studies using regional nested modeling approaches. However, an
identified limitation of this model is that it makes use of the current
climate conditions as input, obtained from single global climate model—the
Geophysical Fluid Dynamics Laboratory (GFDL) R30 coupled model [26].

##  3 Dataset and Methodology

###  3.1 Model description

The model used for this study is the Unified Environmental Modeling System
(UEMS) - Weather Research Forecast (WRF) model regional climate model. It is a
complete, full-physics, state-of-the-science numerical weather prediction
(NWP) package that incorporates the the National Oceanic and Atmospheric
Administration’s (NOAA) and WRF systems into a single user-friendly, end-to-
end forecasting system.

Figure 8 shows the components of the WRF regional climate model and it’s data
processing/forecasting workflow. The WRF framework includes components for
dynamical solvers, initialization, WRF-Var, WRF-Chem amongst others. The two
options for dynamical solvers in the WRF model includes: the Advanced Research
WRF (ARW) solver developed primarily at National Center for Atmospheric
Research (NCAR), and the Nonhydrostatic Mesoscale Model (NMM) solver developed
at National Centers for Environmental Prediction (NCEP).

Figure 8: Components of the WRF system. [32]

The Weather Research and Forecasting (WRF) model is a numerical weather
prediction (NWP) and atmospheric simulation system designed for both research
and operational applications [32]. It’s developement was a collaborative
effort by NCAR, Atmospheric Administration’s (NOAA), the Department of
Defense’s Air Force Weather Agency (AFWA) and the Center for Analysis and
Prediction of Storms (CAPS) to develop a mesoscale forecasting system capable
of predicting mesoscale weather and drive research opportunities into it’s
operations.

The ARW is one of two dynamical solvers which are a subset of the WRF model.
The ARW solver combines with the NMM solver shown in Figure 8 and all other
WRF components within the framework. It includes real-data and idealized
simulations, various lateral boundary condition options, full physics options,
non-hydrostatic and hydrostatic (runtime option) amongst others. There are no
significant differences between the designs of the NMM and ARW dynamical cores
except for the output of model physics [32]. The NMM core is a fully
compressible, hydrostatic NWP which was later extended to include non-
hydrostatic options. On the other hand, the ARW is a fully compressible,
Eulerian, non-hydrostatic model with run-time hydrostatic option.

For the purpose of interpretability in the equations below,ignoring the
Coriolis effect alongside variables which account for the earths curvature and
diffussion,the WRF model can be configured to solve the following equations:

$\displaystyle\frac{d\mathbf{v}}{dt}=-\frac{1}{\rho}\nabla p-g\mathbf{k}$ (1)

$\displaystyle\frac{d\rho}{dt}=-\rho\nabla\cdot\mathbf{v}$ (2)

$\displaystyle\frac{d\theta}{dt}=\frac{Q}{C_{p}\pi}$ (3)

$\displaystyle p=\rho RT$ (4)

The above equations represents the momentum equation (Navier-Stokes),
continuity equation, thermodynamic equation and the equation of state
respectively. Where v is the wind vector representing $(u,v,w)$ as the
velocity components in the $(x,y,z)$ directions, g is the acceleration due to
gravity, $R$ represents the molar gas constant for dry air, $Q$ is the heating
due to adiabatic process, $C_{p}=\left(\frac{7}{2}\right)\times R$ represents
the specific heat capacity of dry air, while k represents the unit vector in
the vertical direction. $\pi$ and $\theta$ denotes the exner function and the
potential temperature respectively and are defined as:

$\displaystyle\pi=\left(\frac{p}{p_{0}}\right)^{R/Cp}\text{ and
}\theta=\frac{T}{\pi}$ (5)

When solved, these equations estimate the state of dry air/atmosphere
expressed in terms of temperature $(T)$, pressure $(p)$, density $(\rho)$ and
the windspeed components $(u,v,w)$. However, the run-time hydrostatic option
for the ARW assumes hydrostatic balance for the momentum equation in the $w$
direaction and thus represents motion in the vertical direction as a balance
between the pressure gradient force (PGF) and the gravitational pull,
described mathematically as:

$\displaystyle\frac{\partial p}{\partial z}=-\rho g$ (6)

The formulation of the model equations adapts a mass-based terrain coordinate
system solved in Arakawa-C grid using Runge–Kutta third-order time integration
techniques. ARW modeling system supports horizontal nesting that allows
resolution to be focused over a region of interest by introducing an
additional grid (or grids) into the simulation with the choice of one-way and
two-way nesting procedures. [33]

###  3.2 Model configuration & data description

The ARW domain for the model simulation was defined as shown in Figure 9 below
using the Lambert Conformal Grid projection type for mid-latitudes centered
over 0∘ longitude (GMT) with a centerpoint latitude of -20.211∘ and a
centerpoint longitude of 59.798∘. The number of horizontal (NX) and vertical
(NY) grid points chosen was 100 with an initial grid spacing of 45km and a
terrestial data resolution of 10 minute.

The domain bounded by the yellow box in Figure 9 spans latitude 40∘E to 80∘E
and longitude 0∘N to 40∘S.

Figure 9: Primary domain for WRF simulation

After defining the domain, localization process of set domain was initialized.
This serves to extract the terrestrial data over the area covered by the
domain(s) from the large global files at the resolution(s) specified during
your domain creation.

Following the localization of the domain, boundary conditions were downloaded
from the National Center for Environmental Prediction (NCEP’s) Climate
Forecast System Reanalysis for my domain at a 6 hour frequency for 10 days
(March 2nd 2017 - March 11th 2017). The boundary conditions serve as input to
the ARW solver in model simulation. The output of simulations were exported as
NetCDF files. These consited of a total of 37 simulation results (4
simulations per day, for 10 days).

The choice of the domain for localization and dates in which boundary
conditions were obtained was guided by the choice of the tropical cyclone to
be studied.

###  3.3 Experiment design

Figure 10 shows the experiment design workflow for investigating the influence
of increasing/decreasing sea surface temperature (SST) on tropical cyclone
Enawo over the set domain. The experiment hinges on the increase and decrease
of SST in the boundary condition dataset which serve as the input data for the
ARW dynamical core of the WRF model.

Figure 10: Experiment design and workflow for observing the effect of sea
surface temperature (SST) changes in boundary data on the track and intensity
of tropical cyclone Enawo.

After defining the domain for simulation, as well as the duration (2nd March
2017 to 11th March 2017) and frequency (4 hours per day) in which the boundary
conditions are to be obtained, the following procedures were followed in this
order for the purpose of observing the influence of temperature increase on
the intensity of tropical cyclones within the domain.

  * •

The boundary condition was used as input into the UEMS-WRF model in three
phases:

    * –

Unaltered boundary condition (Control) was inputed into the WRF model for
simulation and the simulation was saved as the control output of the model.
This boundary condition was labelled (A) as shown in Figure 10

    * –

The sea surface temperature for the unaltered boundary condition above was
increased by 2${}^{\circ}C$, then inputed into the UEMS-WRF model. This
boundary condition was labelled (B) as shown in Figure 10.

    * –

The sea surface temperature for the unaltered boundary condition was then
decreased by 2${}^{\circ}C$ before inputed into the UEMS-WRF model for
simulation. This boundary condition was labelled (C) as shown in Figure 10.

  * •

The output of the model from the three boundary conditions (A, B and C) were
analysed comparatively to see if there was an increase/decrease in the
intensity of the tropical cyclone Enawo with increased sea surface
temperature. Comparison of the intensity of the tropical cyclone was based on
the following variables: the maximum precipitation rate, maximum windspeed,
minimum surface pressure etc.

These variables were chosen amongst existing output variables from the WRF
model simulation because they are variables that best identify intensity of
tropical cyclones. Theoretically, the pressure and windspeed in the eye of a
tropical cyclone should be lower than the surrounding. Hence, we could perform
a comparative analysis of the minimum pressure for all three of our simulation
scenerios.

##  4 Results and Discussion

This section discusses the result of all of experiments ran using the UEMS-WRF
model for the simulation of cyclone Enawo. The first section describes the
validation of WRF model results with observed data from European Centre for
Medium-Range Weather Forecasts (ECMWF) ERA5 re-analysis dataset, while the
second section illustrates the sensitivity of various climatological
parameters to increasing/decreasing SST.

###  4.1 Model validation

####  4.1.1 Validating the Track of the Tropical Cyclone

Figure 11 (a) and (b) shows a comparison between the observed track (by meteo-
france) for cyclone enawo with the track simulated by the WRF model. This
shows that the WRF model reasonably reproduces the track for cyclone Enawo

Figure 11 (b) shows the path followed by the tropical cyclone Enawo. This was
simulated by monitoring the coordinates of the lowest sea-level pressure point
as it drifts over time. The simulation shows the low pressure core of tropical
cyclone following an initial southward direction, before it changes to a
western direction on the 4th of March 2017, where it pressure was about 970
HPa. The cyclone continues on this western direction until the 7th of March,
where the lowest pressure was recorded (957.624 HPa) just before it makes
landfall.

After making landfall, the pressure gradually increases to about 988 HPa as
it’s intensity decreases and it moves through cities like Antisabe,
Fiamarantosa and Toasmania. The low pressure core of the cyclone moves in a
southward direction through the land until it emerges at latitude 25∘S where
it’s intensity decreases as it’s pressure increases till it dissipates.

Figure 11: A comparison of the observed track (a) for cyclone Enawo with the
simulated track (b) by the WRF model. The WRF simulation of the track for
cyclone Enawo uses it’s low pressure vortex as parameter for 10 days (2nd
March - 11th March, 2017). The NCL tool was used to locate the low pressure
vortex used in identifying the track mapped from genesis of lysis.

####  4.1.2 Validating the Windspeed Vector

Figure 12 (a) and (b) shows a validation of the output of windspeed vector
from the WRF model simulation with the European Centre for Medium-Range
Weather Forecasts (ECMWF) ERA5 reanalyses dataset by the Copernicus climate
change services. This shows the similarity between the model output and
observed data.

By comparison, we notice that two curls for velocity vector fields are located
at longitude 52∘E and 75∘E on the European Centre for Medium-Range Weather
Forecasts (ECMWF) ERA5 re-analysis data. However, these two vector curl fields
are located at longitude 30∘E and 90∘E.

The magnitude of the velocity field simulated by the WRF model is seen to be
larger than for the observed European Centre for Medium-Range Weather
Forecasts (ECMWF) ERA5 re-analysis data reanalysis data. Maxiumum windpspeed
of about 40$ms^{-1}$ is identified in the WRF simulation of the cyclone
location before it makes landfall. However, a maximum windspeed of about
26$ms^{-1}$ is noticed from the European Centre for Medium-Range Weather
Forecasts (ECMWF) ERA5 re-analysis data. This suggests the WRF model
exaggerated the windspeed during simulation. Also, in both the re-analysis
data and simulated dataset, there is a noticeable low velocity core in the
location for the tropical cyclone. This is consistent with the structure
expected for tropical cyclones.

Figure 12: Validation of the windspeed vector generated by the WRF model (b)
with the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5
Reanalyses dataset (a) by the Copernicus climate change services, showing
similarity in curl of vector fields.

###  4.2 Sensitivity analysis

####  4.2.1 Sensitivity of Cyclone Track

Figure 13 (a), (b) and (c) below shows the effect of SST on the track followed
by cyclone Enawo from it’s genesis (2nd of March) to it’s lysis (11th of
March). We notice by comparing Figure 13 (a) and (c), that decreasing the SST
does not have a significant effect on the track followed by the cyclone,
except for a more smoother trajectory.

On the other hand,comparing figure 13 (a) and (b), there is a more noticeable
distortion in the track of the cyclone with increased SST. Between the 2nd and
4th of March, there are minute haphazard tracks in the cyclone. The most
noticeable phenomena is between the 10th to 11th of March, where a lower
pressure system was identified towards the East. This is due to the fact that
an increase in SST creates a another cyclone which occurs simultaneously as
the previous one.

This suggests that an increase in SST has a potential of increasing the number
of cyclone occurences within a given time frame.

Figure 13:  Figure showing the track followed by cyclone Enawo from the 2nd of
March to the 11th of march 2017. (a.) Control simulation, (b.) Simulation with
SST increased by 2${}^{\circ}C$. (c.) Simulation with SST decreased by
2${}^{\circ}C$.

####  4.2.2 Sensitivity of Total Precipitation

Figure 14 below shows how the increase in SST temperature causes an increase
in the total accumulated precipitation and it’s spatial distribution, as
compared to when the SST was unaltered and when it was decreased by
2${}^{\circ}C$. Figure 14 (a) shows the sum of the total precipitation for the
beginning of the simulation period (2nd of March,2017) to the end of the
simulation period (11th of March,2017).

Figure 14:  The total accumulated precipitation on the 6th of March 2017, for
the cyclone location in (a) Control simulation, (b) Simulation with SST
increased by 2${}^{\circ}C$, (c) Simulation with SST increased by
2${}^{\circ}C$, (d) Simulation with SST increased by 2${}^{\circ}C$ \- Control
simulation , (e) Simulation with SST decreased by 2${}^{\circ}C$ \- Control
simulation

It is observed by comparing Figure 14 (a) and (b),that an increase in SST
causes an increase in the spatial distribution of precipitation pattern over
the entire domain. Whereas, a comparison of Figure 14(a) and (c) illustrates
that a decrease in SST leads to a reduction in the spatial distribution of
precipitation coverage. It is also noticed by comparing Figure 14 (a), (b) and
(c), that an increase in SST leads to an increase in the cummulative total
precipitation over the entire period, while a decrease in SST leads to a
decrease.

It is observed from Figure 14 (d) that there is a predominant positive spatial
value in the difference between the simulation with SST increased by
2${}^{\circ}C$, implying that an increase in SST leads to an overall increase
in the total precipitation as well as it’s spatial distribution. On the other
hand, from Figure 14 (e), there is a predominant zero to negative spatial
value in the difference between the simulation with SST decreased by
2${}^{\circ}C$. This would imply that a decrease in SST has an effect of
decreasing the total precipitation in some areas, but on a larger scale, it
has minimal effect on the precipitation.

####  4.2.3 Comparative Analysis of Variations in Selected Climatological
Variables (Maximum Precipitation Rate, Minimum Surface Pressure and Maximum
Windspeed)

Figure 15 illustrates the effect of sea surface temperature (SST) on the
maximum precipitation rate, minimum surface pressure and maximum windspeed
(velocity at 10m) for the entire domain within the simulation period which the
hurricane lasts (2nd - 11th March 2017).

Figure 15:  Figure showing that (a) The maximum precipitation rate for the
simulation with increased SST (black) is higher than the control simulation
and simulation with decreased sea surface temperature (SST). (b) The maximum
value velocity component (u at 10m) for the simulation domain is much higher
for the simulation with increased sea surface temperature(SST) (black), but
lower for the control simulation and simulation with decreased SST. (c) The
minimum surface pressure of domain is much lower for the simulation with
increased sea surface temperature (SST) (black), and is higher for the control
simulation and simulation with decreased SST.

Figure 15 (a) shows the fluctuation of the maximum precipitation rate over the
entire simulation domain in which the tropical cyclone was tracked by on
Figure 11.

We notice the maximum precipitation rate for the control simulation (red line)
has a value of about 0.020$mms^{-1}$. This value is less than the maximum
precipitation rate for the simulation whose SST was increased by
2${}^{\circ}C$ (0.026$mms^{-1}$). This is shown by the black line. Finally, a
decrease in the sea surface temperature (SST) of the simulation (shown by
green line) illustrates a decrease in the maximum precipitation rate to a
value of 0.016$mms^{-1}$.

From these images, we can deduce that an increase in the sea surface
temperature (SST) affects the intensity of the tropical cyclone by increasing
it’s maximum precipitation rate. Also, we can deduce that a decrease in the
SST has a negative effect on the tropical cyclone by decreasing it’s maximum
precipitation rate.

Figure 15 (b) shows a variation in the maximum windspeed (velocity at 10m) for
the entire domain within the simulation period which the hurricane lasts (2nd
- 11th March 2017).

We notice a much more increased value in the vertical windspeed for the
simulation with increased SST as opposed to the control simulation and that
with decreased SST. For the control simulation (red line), the maximum in
windspeed is at about 34$ms^{-1}$. On the other hand, for the simulation with
increased SST, there is a maximum windspeed value of 38$ms^{-1}$. Finally, a
decrease in the SST produces a maximum windspeed of about 28$ms^{-1}$.

The trend shows that the red-line (simulation with increased SST), is
consistently higher than the control simulation (black-line) and the
simulation with decreased SST (green-line), illustrating that increasing the
SST has an overall effect of increasing the maximum windspeed (velocity at
10m) for the entire domain.

Figure 15 (c) shows a variation in the minimum pressure for the entire domain
within the simulation period which the hurricane lasts (2nd - 11th March
2017).

We clearly see that an increase in sea surface temperature (shown by the black
line) impacts the tropical cyclone by decreasing the minimum surface pressure.
However, decreasing the sea surface temperature (SST) has an effect of
increasing the minimum pressure measured for the entire domain simulated. This
is observed by comparing the green-line and the red-line showing that the
green-line is consitently above the black and red lines. Tropical cyclones are
characterized as a low pressure system, thus, the decrease in pressure caused
by increasing the SST is indicative of it’s positive effect on the intensity
of the tropical cyclone.

A combination of the results from Figure 15 (a), (b), (c) shows that
increasing the sea surface temperature (SST) causes an overall increase in the
intensity of the simulated tropical cyclone which manifests in form of
increased maximum precipitation rate, decreased surface pressure and increase
in the magnitude of the windspeed.

####  4.2.4 Comparing the Vertical Profiles of the Cyclone Structure

Figures 16 (a) - (e) and Figures 17 (a) - (e) shows a vertical profile of the
windspeed and pressure for the tropical cyclone indicating variations in
intensity for the control simulation, simulation with increased SST and
simulation with decreased SST.

Figure 16:  Vertical profiles showing variation in vertical windspeed of the
tropical cyclone for: (a) The control simulation (b) The simulation with
increased sea surface temperature (SST) by 2${}^{\circ}C$, (c) The simulation
with decreased sea surface temperature (SST) by 2${}^{\circ}C$, (d) Simulation
with SST increased by 2${}^{\circ}C$ \- Control simulation, (e) Simulation
with SST decreased by 2${}^{\circ}C$ \- Control simulation

A comparison of Figures 16 (a) and (b) shows that there is a decrease in the
windspeed at the eye of the tropical cyclone (30∘) for the simulation with SST
increased by 2${}^{\circ}C$. Also, Figures 16 (d) shows a negative difference
at the eye of the tropical cyclone, also indicative of a decreasing windspeed
with increased SST.

On the other hand, by comparing Figures 16 (a) and (c), there is no major
difference in the magnitude of windspeed at the eye. However, there is a
decrease in the magnitude of the windspeed at the eye wall. This is indicative
of a decreasing strenght in the strenght of the tropical cyclone. Also,
Figures 16 (e) shows a zero to positive difference at the eye. This indicates
that a decrease in SST has little or no effect on the intensity of the this
tropical cylone.

Figure 17: Vertical profiles showing variation in pressure of the tropical
cyclone for: (a.) The control simulation, (b) The simulation with increased
sea surface temperature (SST) by 2${}^{\circ}C$, (c) The simulation with
decreased sea surface temperature (SST) by 2${}^{\circ}C$, (d) Simulation with
SST increased by 2${}^{\circ}C$ \- Control simulatio , (e) Simulation with SST
decreased by 2${}^{\circ}C$ \- Control simulation

A comparison of Figures 17(a) and (b) shows that there is a decrease in the
pressure at the core of the tropical cyclone for the simulation with increased
SST. Figures 17 (d) shows a negative difference at the cylone core,indicative
of a decreasing core pressure with increased SST.

Whereas, Figures 17 (a) and (c), there is barely any noticeable difference in
the core pressure. Figures 17 (e) shows a zero to minute positive difference
at the eye. This indicates that a decrease in SST has little effect on the
intensity of the tropical cyclone, acting to increase the core pressure.

####  4.2.5 Sensitivity of Windspeed Vector

Figure 18 shows the vector of windspeed component on the 6th of March for the
location in which the tropical cyclone was tracked by Figure 11 to be located.

Figure 18 (a) indicates maximum windspeed component of about 38$ms^{-1}$ for
the control simulation. However, Figure 18 (b) shows maximum windspeed
component of about 46$ms^{-1}$ for the simulation with increased sea surface
temperature (SST) of 2${}^{\circ}C$, while Figure 18 (c) shows maximum
windspeed component of about 30$ms^{-1}$ for the simulation with decreased sea
surface temperature (SST) of 2${}^{\circ}C$.

The wind vector also shows a much more stronger curl vector field in Figure 18
(b), as compared with Figure 18 (a) and Figure 18 (c), indicating that an
increase in sea surface temperature (SST) affects the intensity of tropical
cyclone by increasing it’s windspeed.

Figure 18: (a) The velocity vector field for the control simulation (b) the
velocity vector field for simulation with increased sea surface temperature
(SST) (c) the velocity vector field for simulation with decreased sea surface
temperature (SST).

##  5 Conclusion and Recommendation

###  5.1 Summary

In a bid to understand the possible effect that global warming and a violation
of the Paris accord could have on tropical cyclogenesis and it’s
intensification around the South West Indian ocean, this study investigated
the influence of sea surface temperature (SST) variations in simulated
tropical cyclones from the WRF regional climate model. The objective of this
study was to observe the sensitivity of tropical cyclone Enawo to increase of
2${}^{\circ}C$ in sea surface temperature (SST), as well as decrease of
2${}^{\circ}C$. The characteristics of the tropical cyclone Enawo which was
observed for sensitivity analysis include the cyclone track, precipitation,
surface pressure, wind speed vector and the vertical cross-section/struture of
the tropical cyclone.

In order to achieve these objectives, the simulations from the WRF model was
initially validated using the European Centre for Medium-Range Weather
Forecasts (ECMWF) ERA5 re-analysis dataset for the active period of tropical
cyclone Enawo (2nd - 11th March 2017). The effectiveness of the WRF model in
representing the actual properties of the tropical cyclone was obtained by
comparing it’s output with that obtained from European Centre for Medium-Range
Weather Forecasts (ECMWF) ERA5 re-analysis dataset . To investigate the role
of sea surface temperature (SST) on the WRF simulations of the cyclone, the
SST from the boundary conditions for the WRF model was increased by
2${}^{\circ}C$ before simulation. The same procedure was repeated but with a
decrease in SST of 2${}^{\circ}C$ as well.

The result of the study is summarized below:

  * •

The simulation of cyclone Enawo using the WRF model is sensitive to
increase/decrease in the sea surface temperature (SST) of the boundary dataset
used in the simulation. However, it is more sensitive to temperature increase
than a decrease.

  * •

Increasing the SST by 2${}^{\circ}C$ has an overall increase in the intensity
of the tropical cyclone. This increase is manifested as:

    * –

Increase in the maximum precipitation rate.

    * –

Increase in the magnitude of the maximum windspeed.

    * –

Decrease in the magnitude of the minimum surface pressure.

  * •

Decreasing the SST by 2${}^{\circ}C$ has an overall decrease in the intensity
of the tropical cyclone. This increase is manifested as:

    * –

Decrease in the maximum precipitation rate.

    * –

Decrease in the magnitude of the maximum windspeed.

    * –

Increase in the magnitude of the minimum surface pressure.

  * •

Decreasing the SST by 2${}^{\circ}C$ has a less pronounce effect on the track
followed by tropical cyclone Enawo. The decrease has an overall effect of
smoothening the track followed by the cyclone. On the other hand, increasing
the SST by 2${}^{\circ}C$ has a more cospicuous effect on the track followed
by cyclone Enawo. This is evident in the emergence of a second low-pressure
system on the 10th of March. This indicates that an increase in SST leads to
an increase in the number of occurences of tropical systems.

###  5.2 Further work

The robustness of results obtained from this study can be improved by
providing multiple simulations of tropical cyclone Enawo using different
regional climate models. This would help to reinforce the confirmation of the
sensitivity of tropical cyclones to sea surface temperature (SST). Further
more, while the current study focusses on a single resolution, we could
observe the effect of various model resolution on the results obtained.

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# Slide, Constrain, Parse, Repeat:
Synchronous Sliding Windows for Document AMR Parsing

Sadhana Kumaravel , Tahira Naseem 11footnotemark: 1 , Ramon Fernandez
Astudillo,
Radu Florian, Salim Roukos
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
IBM Research AI Co-first author

###### Abstract

The sliding window approach provides an elegant way to handle contexts of
sizes larger than the Transformer’s input window, for tasks like language
modeling. Here we extend this approach to the sequence-to-sequence task of
document parsing. For this, we exploit recent progress in transition-based
parsing to implement a parser with synchronous sliding windows over source and
target. We develop an oracle and a parser for document-level AMR by expanding
on Structured-BART such that it leverages source-target alignments and
constrains decoding to guarantee synchronicity and consistency across
overlapping windows. We evaluate our oracle and parser using the Abstract
Meaning Representation (AMR) parsing 3.0 corpus. On the Multi-Sentence
development set of AMR 3.0, we show that our transition oracle loses only 8%
of the gold cross-sentential links despite using a sliding window. In
practice, this approach also results in a high-quality document-level parser
with manageable memory requirements. Our proposed system 111Code and model
available here https://github.com/IBM/transition-amr-parser performs on par
with the state-of-the-art pipeline approach for document-level AMR parsing
task on Multi-Sentence AMR 3.0 corpus while maintaining sentence-level parsing
performance.

##  1 Introduction

Pre-trained Transformer embedding representations Devlin et al. (2018); Liu et
al. (2019) have shown unparalleled predictive power at sentence-level, but are
not built for document encoding and are also not interpretable. Symbolic
representations such as Abstract Meaning Representation (AMR) parses Banarescu
et al. (2013), explicitly consider document-structure O’Gorman et al. (2018)
and human-understandable concepts, e.g. entities, subject-object relations and
actions, and thus can be expected to be complementary to sentence Transformer
embedding representations.

Document-level parsing involves both long texts and parses. When only the
source (text) or the target (parse) is long, a single sliding window approach
is a simple and effective solution Dai et al. (2019); Zaheer et al. (2020);
Beltagy et al. (2020). However, when both have long sizes, the sliding windows
must be synchronous, i.e. words and parse in the overlapping222Note that
parsing requires overlap to predict cross-window relations. part of the source
and target windows should correspond to each other. The black-box nature of
Transformers prevents us from determining this mapping in a simple manner,
precluding the application of sliding windows.

Here we propose an effective solution to apply this approach utilizing recent
progress in transition-based parsing. Structured-BART Zhou et al. (2021)
builds the parse graph incrementally and aligns the input tokens with parse
nodes. The alignment information allows us to make the sliding window on the
target side synchronous with the source window. Further, we can constrain the
decoding on the overlapping part of the window to obey the previous parse
while utilizing position embeddings consistent with the current window.
Combining these two observations, we build a document-level Structured-BART
parser and oracle.

Our oracle shows that a small window is enough to retain $92\%$ of gold inter-
sentential relations333This statistic was computed on the double-annotation
portion of the MS-AMR corpus in the Multi-Sentence AMR Dataset (MS-AMR)
O’Gorman et al. (2018). Further, we match the previous doc-AMR state-of-the-
art pipeline Naseem et al. (2022) while also matching Structured-BART on the
sentence level. To our knowledge, this is also the first parser to apply
synchronous sliding windows for document-level parsing, an approach that seems
both simple and effective.

##  2 Synchronous Sliding Window Parser

Given the quadratic cost of the attention mechanism in Transformers, many
efficient versions have been proposed Gu et al. (2021). Tay et al. (2022,
2020) presents a review of such Transformers and their performance on long-
range tasks. One emerging pattern is the use of a sliding window, which
provides an ingenious method to handle long-range. Previous works leveraging a
sliding window Zaheer et al. (2020); Beltagy et al. (2020), focus on modeling
long-range encoder context, while the decoder stays unaware of its own history
Ivgi et al. (2022). Modeling the decoder history is particularly important for
document-parsing since target history is not just a source of contextual
information for the future generation – it is in fact needed in its full
detail for 1) making long-distance co-reference links and 2) keeping the
future structurally consistent with the past.

Below, we present our transition-based parsing system (DocParser) with an
encoder-decoder transformer architecture able to use a sliding window both in
source and target. Our parser is a modification of the transition-based
Structured-BART Zhou et al. (2021). This model fine-tunes a pre-trained
sequence-to-sequence transformer to imitate the actions of an oracle given an
input text. These actions, when executed into a state machine, processes the
sentence left-to-right and incrementally predict the target graph. We first
discuss how we adapt the sentence-level state transition system for document-
level parsing (section 2.1) and then move on to the core of our proposal – the
idea of synchronous source and target side sliding windows with constrained
decoding (section 2.2).

###  2.1 Modified State Machine and Oracle

We utilize the state transition system and oracle defined in Zhou et al.
(2021) with modifications to handle inter-sentence relations. The oracle
traverses the input tokens from left to write performing one of the following
actions at each step:

> shift: move cursor to the next token.
> <node>/copy: create a node or copy input token under the cursor as node.
> $\textsc{[la/ra]}({\textup{j},\textsc{lbl}})$: create an arc with label lbl
> from the most recent node to the node at the $j_{th}$ step for la and
> reversed for ra.
> root: declare the most recent node the root. This can happen once in a
> sentence.
> close: close the state machine; attach unconnected components to the root.

Note, that the above state machine can handle only pairwise relations.
However, coreference chains in the MS-AMR corpus are annotated over clusters
of nodes. To model these chains, we break them into pairwise links. Another
aspect that differs in document-level parsing is the notion of the root node.
Document graphs do not have a semantic or syntactic root, they only provide
relations between a set of sentence-level graphs. In fact, the root node in
DocAMR is a dummy node connecting to all sentence-level roots. Considering
this, we modify the state transition system in two ways:

  1. 1.

We introduce a close_sentence action that allows to relax the one root
constraint to one root per sentence. More importantly, any unconnected sub-
graphs get attached to the sentence-level root, not the overall graph toot.

  2. 2.

We introduce a special same-as relation label that connects consecutive node
pairs belonging to the same coreference chain. The proximity of the chain
nodes is determined by the distance between their aligned tokens. Graph node
to tokens alignments are created using the approach given in Naseem et al.
(2019); Fernandez Astudillo et al. (2020).

With these changes, the state machine, along with the original alignment-based
oracle of Zhou et al. (2021), can seamlessly handle both document and
sentence-level AMR graphs. Any actions performed by this state machine are
associated with the source token under the cursor; furthermore, the tokens are
visited in order from left to right. These two properties come in handy when
implementing the sliding window and constrained decoding explained in the next
section.

Figure 1: Sliding window mechanism for DocParser. Green squares (left)
represent input tokens and blue rectangles (right) represent actions. Node-
making actions have white fill. Actions have token alignments that readily
decide which actions to copy over to the next window. Any actions that refer
to the past beyond the overlap are not copied over (Greyed-out). After
merging, the actions can produce long-ranging co-reference chains.

###  2.2 Sliding Window and Constrained Decoding

We base our synchronous parsing approach on the structure-aware BART model of
Zhou et al. (2021) to learn this task. The major modifications to the original
BART architecture are a specialized hard cross-attention head Aharoni and
Goldberg (2017) to align input tokens to nodes and a dedicated decoder self-
attention pointer network Vinyals et al. (2015). This model (similar to other
encoder-decoder transformers) can handle source/target lengths of up to 1024
word pieces. The MS-AMR training data has documents that are up to 4277 tokens
with an average length of 540 tokens. The source token length typically
translates into a target action sequence about 3 times longer – thus, inputs
longer than 300 tokens become unmanageable.

To handle long documents, we chunk the input text into overlapping windows,
the window boundary is aligned with the sentence boundary whenever possible.
We parse one window at a time. Each subsequent window must agree with its
preceding window regarding the parse of the overlapping portion. This
requirement can only be met if we know which parts of the parse belong to the
overlapping text. Our transition-based model incrementally builds the AMR
parse by executing transition actions – these actions are monotonically
aligned to the source tokens. This makes it easy to keep the graphs of shared
portions coherent. We just have to copy over the actions aligned with the
overlapping part to the next window and then force decode that portion. When
copying over the actions, any connections to the non-overlapping parts of the
first window need to be removed and the pointer values in la and ra actions
need to be adjusted according to the new action positions.

Overlapping forced prefixes not only provides a smooth transition between
consecutive windows but also makes cross-window links possible – the actions
in the non-forced region of a window (following the prefix) are free to create
attachments with the nodes in the forced prefix444An alternative to force
decoding the shared portion could be to repeat the decoder block from the
overlapping part as a pre-computed prefix for the next window. This would be
more efficient in practice but will make the positional embedding information
inconsistent.. Figure 1 shows how the sliding window approach works.

|  | DocSmatch (Coref)
---|---|---
Window | Overlap | Oracle | DocParser
400 | 200 | 97.8 (92.3) | 64.3 (38)
400 | 100 | 97.6 (91.5) | 64.4 (39)
300 | 200 | 97.7 (91.8) | 65.1 (38)
300 | 100 | 97.4 (90.6) | 65.1 (38)
200 | 100 | 96.7 (87.7) | –
DocParser w/o sliding decoding | 52.35
Table 1: Oracle and DocParser Smatch and coreference scores with various window and overlap sizes on the double-annotation portion (dev) of MS-AMR 3.0 corpus.  |  | Multi-Sentence AMR 3.0 | Sentence AMR 3.0
---|---|---|---
System | Train Data | Smatch | DocSmatch (Coref) | Smatch
Naseem et al. (2022) | amr3.0+conll | 71.3 | 72.0 (50) | –
Zhou et al. (2021) | amr3.0 | – | – | 82.3
DocParser | ms-amr | 65.9 | 66.3 (45) | 71.6
DocParser | +amr3.0+conll | 71.8 | 72.1 (50) | 82.3
Table 2: Comparison of DocParser with the previous SoTA pipeline approach
Naseem et al. (2022) on the test set of the document level MS-AMR corpus and
with Zhou et al. (2021) on the AMR3.0 sentence level test set.

#### What falls off the window?

While the sliding window approach makes long text parsing possible, it has the
potential to lose long-range inter-sentence connections. As mentioned in
section 2.1, we break coreference chains into pairwise links between
consecutive participant nodes. The full chain can be reconstructed by putting
together the pairwise links. To assess the amount of cross-sentence
information lost due to window size restriction, we analyze the double-
annotation devset of MS-AMR corpus at different window sizes. We first convert
document-level AMR annotation into pairwise edges. Then for a given window
size and window overlap value, we only retain those gold pairwise edges that
are seen in the same window when sliding over the document. We then combine
the pairwise edges to reconstruct the document-level AMR graph. We convert
this trimmed graph as well as the original gold graph into DocAMR
representation and compute the DocSmatch to assess the information loss.
DocSmatch is an efficient implementation of smatch for documents and also
provides inter-sentence coreference subscore (see Table 1). To our surprise, a
window size as short as 200, loses only 3 points in Smatch and 12 in
coreference subscore. Our transition-based parser typically has a target
length of up to 3 times the source length. We, therefore, stick to a window
size of 300 tokens in our experiments with a 200 tokens overlap.

##  3 Experiments and Results

We evaluate DocParser on AMR 3.0 corpus – We use its Multi-Sentence O’Gorman
et al. (2018) test set for document-level evaluations and the standard AMR 3.0
test set for sentence-level evaluation. For training, we use all of AMR 3.0
dataset including the 50k sentences and 242 document annotations. In addition,
we parse the CoNLL 2012 coreference dataset Pradhan et al. (2012) at the
sentence level and project coreference information to graph nodes using the
parser-generated alignments (similar to Naseem et al. (2022)). This results in
a silver AMR corpus with gold coreference annotations (1405 documents). We
also include this silver data in our training set. We used a maximum learning
rate of $5e-4$ for the DocParser trained with MS-AMR data and $1e-5$ for the
full training set, 4000 warm-up steps, a dropout rate of 0.2 and trained up to
120 epochs. For prediction, we used a beam of size 10 to decode the double-
annotation part of MS-AMR (dev set) and used DocSmatch to find top 5
checkpoints and averaged over them. All experiments used a single NVIDIA V100
GPU. We use the publicly available implementation of Zhou et al.
(2021)555https://github.com/IBM/transition-amr-parser.

We compare against state-of-the-art document AMR parser of Naseem et al.
(2022) – a pipeline consisting of Zhou et al. (2021) parser and Joshi et al.
(2020) coreference resolution. Joshi et al. (2020) splits input text into non-
overlapping windows of length up to 512. We also compare with Zhou et al.
(2021) for sentence-level parsing. We report both the standard Smatch Cai and
Knight (2013) and the more efficient DocSmatch. We convert the graphs into
DocAMR 666https://github.com/IBM/docAMR representation before computing the
Smatch scores.

Table 2 shows our main result. DocParser, when trained on our full training
set, performs on par with the SoTA Naseem et al. (2022) while maintaining the
sentence-level performance of the underlying Zhou et al. (2021). We also
ablate the training data, by removing the CoNLL silver data and the sentence
level AMR 3.0 gold data – which degrades the performance substantially. We
also test DocParser with various window sizes (Table 1) to gauge the impact on
performance. It is clear that the use of sliding windows greatly improves the
parsing performance. The best setup is the window size of 300 tokens with 200
overlap – likely because this is the largest size for which the target actions
can safely fit within the 1024 length.

##  4 Conclusions

We propose synchronous source and target side sliding windows for document-
level AMR parsing. We show that the left-to-right incremental parser of Zhou
et al. (2021) is well suited for the effective implementation of this
approach.

## Limitations

Since we circumvent the problem of long documents using constrained windows,
some cross-sentential coreference information might fall through the cracks .
We show how much of this information is lost in Table 1. The process of
constructing these windows also involves breaking down coreference chains into
pairwise edges between contiguous mentions in the chain. In doing so, the
first mention of the chain which is often the most informative mention, goes
unseen when predicting the next mention in the chain.

## Ethics Statement

We do not anticipate any ethical concerns regarding our model or use of data.
The data we use in this experiment is publicly available and/or from a shared
task.

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