Tropical Cyclone Precipitation Risk in the Southern
United States
MASSACHuSET-r' INSTITI ITF
OF TECHNOLOLV,
by
Sandra Michael Shedd
JUN 08 2015
B.A., Williams College, 2013
LIBRARIES
Submitted to the Department of Earth, Atmospheric, and Planetary
Science
in partial fulfillment of the requirements for the degree of
Master of Science in Climate Physics and Chemistry
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
@ Massachusetts Institute of Technology 2015. All rights reserved.
Signature redacted
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A u thor ...................................
Department of Earth, Atmospheric, and Planetary Science
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Mqv o
9015
Signature redacted
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Certified by.............. .................
Kerry A. Emanuel
Cecil & Ida Green Professor of Atmospheric Science
Thesis Supervisor
Signature redacted
Accepted by ........
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_
_
Robert D. van der Hilst
Chairman, Department Committee on Graduate Theses
2
Tropical Cyclone Precipitation Risk in the Southern United
States
by
Sandra Michael Shedd
Submitted to the Department of Earth, Atmospheric, and Planetary Science
on May 09, 2015, in partial fulfillment of the
requirements for the degree of
Master of Science in Climate Physics and Chemistry
Abstract
This thesis works to evaluate the new rainfall algorithm that is used to simulate longterm tropical cyclone precipitation (TCP) climatology throughout the southeastern
United States. The TCP climatology is based on a fleet of synthetic tropical cyclones developed using National Center for Atmospheric Research/National Centers
for Environmental Prediction reanalysis data from 1980 to 2010 and the Coupled
Hurricane Intensity Prediction System (CHIPS) model. The climatology is compared
to hourly rainfall estimates from the WSR-88D Next Generation Weather Radar
(NEXRAD-II) system. In general the synthetic TCP estimates show good agreement
with radar-based observations. The rainfall algorithm appears to perform better at
coastal locations versus inland ones, and in general has better agreement in the eastern locations considered in this study. In addition, the spatial dependence of radar
rainfall estimates was addressed, and in general more extreme TCP-events exhibited
a greater degree of event total precipitation variation at grid box-scale. Finally, preliminary work incorporating streamflow measurements as a metric for assessing TCP
risk using the synthetic rainfall climatology was begun. Correlation between both
grid box-specific and basin-average radar-based event TCP and surface streamflow
measurements (from the U.S. Geological Survey National Water Information System)
varied greatly, and was generally moderate, and future work should incorporate more
thorough streamflow modeling in order to evaluate these comparisons.
Thesis Supervisor: Kerry A. Emanuel
Title: Cecil & Ida Green Professor of Atmospheric Science
3
4
Acknowledgments
The Next Generation Weather Radar (NEXRAD) data from this study are from
the National Center for Atmospheric Research (NCAR) Earth Observing Laboratory
(EOL) data archive, managed by NCAR and the University Corporation for Atmospheric Research (UCAR). NCAR is sponsored by the National Science Foundation
(NSF). The dataset in its entirety can be accessed at
http://data.eol.ucar.edu/codiac/dss/id=21.089.
The surface water data used in this study are from the National Water Information
System (NWIS), part of the U.S. Geological Survey (USGS), and are officially referred
to as "USGS Surface-Water Data for USA." The USGS is a part of the U.S. Department of the Interior. This data can be accessed at http://waterdata.usgs.gov/nwis/sw.
I have made extensive use of the Atlantic hurricane database (HURDAT2) best
track data maintained by the National Hurricane Center (NHC), part of the National
Oceanic and Atmospheric Administration.
This study also used the Coupled Hurricane Intensity Prediction System (CHIPS)
developed by Professor Kerry Emanuel of the Massachusetts Institute of Technology.
Documentation for the model can be found at http://wind.mit.edu/emanuel/CHIPS.pdf
and in Emanuel [2004].
I sought the assistance of Dr. Seyed Hamed Alemohammad, PhD, postdoctoral
associate in the Massachusetts Institute of Technology Department of Civil and Environmental Engineering, for help in preprocessing the NEXRAD-II base data, transforming it from its compressed GRIB files to usable data.
Dr. Alemohammad's
assistance has been invaluable to this thesis.
This thesis would not have been possible without the guidance and support of
Kerry Emanuel, whose advice and assistance in planning and refining this work were
invaluable throughout the duration of my two years at MIT. I must thank Professor
Emanuel for taking me on as a student and helping me through the twists and turns of
my graduate career, albeit brief. My group of friends in the department and the MIT
Muddy Charles Pub, including Michael McClellan, Erik Lindgren, Andrew Davis,
5
Jared Atkinson, Luis Alvarez, Andrew Dhykius, Sarvesh Garimella, Ben Mandler,
and many others have also provided the moral support necessary to have done any of
this at all. The students in this department form an outstanding community. Thanks
also to the PAOC faculty for the diverse training I've been provided during my time
here. Finally, tremendous thanks to PAOC and the entire EAPS department for
creating a profoundly curious, stimulating, and motivating environment for scientific
research.
This work was funded in part by the Whiteman Fellowship, provided graciously
by Dr. George Elbaum (AA '59, SM AA, NU '63, PhD NU '67), and Ms. Mimi
Jensen in the spring of 2015. I am profoundly grateful for this sponsorship, which
allowed me the freedom to pursue varied research interests during my time at EAPS.
6
Contents
1
1.1
2
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1.1.1
Scientific motivation
. . . . . . . . . . . . . . . . . . . . . . .
11
1.1.2
Societal motivation . . . . . . . . . . . . . . . . . . . . . . . .
16
1.2
Tropical cyclone activity trends in the past several decades . . . . . .
18
1.3
Overview of tropical cyclone risk assessment
. . . . . . . . . . . . . .
19
23
Data, Models, and Methods
2.1
Next generation weather radar (NEXRAD) . . . . . . . . . . . . . . .
23
2.2
USGS National Water Information System . . . . . . . . . . . . . . .
24
2.3
Synthetic hurricane model . . . . . . . . . . . . . . . . . . . . . . . .
25
2.4
Statistical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2.5
3
11
Introduction
2.4.1
Calculating return periods using probability density functions
29
2.4.2
Calculating return periods using Weibull ranking method . . .
29
2.4.3
Correlation between streamflow return periods and radar return
periods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
. . . . . . . . . . . . . . . . . . . . . . . .
31
Cross-correlation function
33
Results
3.1
Comparison between NEXRAD-II observations and synthetic tropical
. . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.1.1
Return period analysis . . . . . . . . . . . . . . . . . . . . . .
34
3.1.2
Spatial sensitivity of return period analysis . . . . . . . . . . .
50
cyclone precipitation
7
3.2
3.3
Introducing streamflow measurements as a metric for TCP . . . . . .
59
3.2.1
Basin-average precipitation v. streamflow measurements
. . .
65
3.2.2
Cross-correlation function analysis . . . . . . . . . . . . . . . .
69
Discussion and Conclusions
. . . . . . . . . . . . . . . . . . . . . . .
A Truncated TC records: correlation with streamflow records
8
70
73
List of Tables
2.1
USGS NWIS monitoring stations location metadata . . . . . . . . . .
25
3.1
Coastal POI v. inland POI: return period analysis summary
. . . . .
42
3.2
Coastal POI v. inland POI: spatial variability analysis summary . . .
58
3.3
Cross-correlation function analysis results . . . . . . . . . . . . . . . .
69
9
10
Chapter 1
Introduction
1.1
Background
1.1.1
Scientific motivation
How much rain will a hurricane produce? A question that is very simply and succinctly phrased, but it remains by and large unanswered in the field of tropical meteorology.
Though much progress has been made over the past several decades in
determining the dynamics of tropical cyclones (TCs), predicting the location and
quantity of their precipitation remains an elusive concept. The fundamental cause of
TCs, the instability of the air-sea interaction in the tropics, has been identified [2].
Hurricanes have been conceptualized as energetically similar to a simple Carnot heat
engine ibid. Their interactions with the environment around them, such as with vertical wind shear, background flow, and Coriolis-based gradients, have been explored
in depth [121.
Vertical wind shear and its effects on the intensity development of
tropical cyclones has then been incorporated into the heat engine understanding of
TC structure [26]. The effect of background flow on storm track variability has been
shown to be latitudinal shifting and pulsating variations in strength of storm tracks
associated with both waves in the atmosphere interacting with the mean flow, and
interannual and decadal oscillations like the North Atlantic Oscillation (NAO) and
the Southern Annular Mode (SAM) [28]. The beta effect on TC movement has long
11
been understood to cause a westward and poleward motion of vortices relative to
the overall mean flow, and shapes the poleward-curving storm tracks that are predominantly observed [14]. These advances in the understanding of the kinematic and
thermodynamic characteristics of TCs are accompanied by subsequent developments
in the theory for tropical cyclone precipitation (TCP). However, despite a thorough
understanding of the physics and thermodynamics of mesoscale convective features,
the ability to assess TCP risk for a given area over a given time period is still inadequate.
The reasons for this lack of a good risk analysis of tropical cyclone precipitation
are many, but fundamental to the problem is the lack of a comprehensive analysis of
TC rainfall data. Coupled to this issue is the fact that precipitation is an exceedingly
localized phenomenon even within the structure of the TC itself. Convective features
of TCs are unlike those any other cloud formation in the atmosphere. Precipitation
intensity changes can occur rapidly as a cyclone's cloud features continually reorganize
[15]. Scientists have measured and developed some theory for portions of these intraTC mesoscale features, including spiral characteristics and deep convection.
It is
known that clouds and precipitation are often (but not always) organized into spiral
structures outside the eye wall, known as spiral rainbands, as shown in Figure 1-1
[3]. These are difficult for models used to simulate or forecast hurricane rainfall to
resolve, nor are the dynamics of their formation fully understood [15, 21]. Indeed, it
is becoming clear that rainbands themselves come in multiple varieties [21]. Further,
cloud processes in TCs are themselves diverse: there are a great many cloud structures
involved in the formation, maintenance, and dissipation of these cyclones, and each
has its own propensity for precipitation [15]. Moreover, the timescales of the evolution
of clouds and mesoscale TC features are rapid and nonuniform, leading to a complex
problem to understand, model, and eventually predict. However, as high-resolution
models become more widely used and computationally efficient, forecasting the risk
of extreme tropical cyclone precipitation at specific times and locations becomes more
and more feasible.
As a brief motivating example, Figure 1-2 shows a 5-hour sequence of reflectivity
12
40
Primary eyewall
Secondary eyewall
e#40
OW*
Environment
Inner
core
I
I
50km
> 20 dBZ
U > 32 dBZ
I
*0
Figure 1-1: Figure 30 from Houze [2010] showing a schematic diagram of principal,
secondary, and tertiary trainbands in a mature tropical cyclone.
measurements in horizontal cross sections of Hurricane Bill, from the 2009 Atlantic
hurricane season. These cross sections show an analog of precipitation features changing over the period of observation, and also illustrates the complicated mesoscale
features that rapidly evolve, leading to variegated precipitation amounts over any
13
given location within the storm radius. These features are difficult for models and
simulations to resolve due to their small spatial and temporal scales, contributing to
the difficulty of the question at hand: how much rain will a given tropical cyclone
produce.
14
60
300
60
300
55
55
60
200
200
50
100
40
0
30
45
40
100
35
35
301
0
2S
25
20
-100
20
-100
15
16
10
-200
10
-200
5
S
-200
-100
0
100
0
200
*...
a
soo
-200
-10
0
0
b
X"tul
R4W*Wv z-3.2km 20MO0[dz
0
==so
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200
55
40
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40
25
-100
20
ZD%
-100
-200
20
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16
15
10
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50
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60
46
145
100
40
100
40
35
30
0
20
-100
15
10
-200
5
-0
0
-200
-100
x
0
"
e
-0
100
200
300
36
30
25
20
15
10
6
0
f
Figure 1-2: Figure 7 from Moon & Nolan 120151 showing horizontal cross sections of
Hurricane Bill at 3200m at (a) 0600, (b) 0700, (c) 0800, (d) 0900, and (e) 1000 UTC,
and (f) the average reflectivity of all 2-min scans between 0600 and 1000 UTC. The
dashed lines are concentric circles every 50km. 1211
15
1.1.2
Societal motivation
Tropical cyclones are an important source of precipitation and a leading cause of
extreme weather (wind and rain) in the southern United States [30, 16]. They are
also among the most lethal and costly natural disasters affecting mankind. The single
most deadly natural catastrophe in United States history is the Galveston, Texas
hurricane of 1900, with a death toll estimated between 6,000 and 12,000 persons.
In very recent history, the U.S. experienced its most costly natural disaster yet in
Hurricane Katrina of 2005, which left more than $125 billion in damage and losses
[23]. Thus, TC activity in recent years has garnered a great deal of interest due to
their high risk of damage and loss of life. This risk is particularly salient as much of the
U.S. population continues to favor coastline habitation and brings with them increased
wealth [4]. Pielke et al [2008] showed by analyzing normalized damage associated with
lower 48 states TC landfalls through the twentieth century that largely due to the
continued aggregation of population to coastlines and vulnerable areas, risk of up to
hundreds of billions of dollars in damage from TCP and its aftereffects in the next
few decades becomes increasingly likely.
Further, the effect of a warming climate on TC activity remains not fully understood [9, 16].
There exists ongoing debate about these trends, observed and fore-
casted, in TC activity due to the exceedingly short observational record, coupled
with large interannual variability [13]. Work on the detection of trends in hurricane
activity [1, 18] at the end of the twentieth century focused mainly on frequency and
found any trend at all hard to detect. A shift in focus to seeking trends in tropical
cyclone intensity and risk, or the potential of loss of or damage to something of value
due to tropical cyclones, has allowed for the tracking of trends in TC activity over
the past several decades, and for the formulation of theories about the relationship
between global climate change and TC frequency and intensity.
As observed trends continue to develop and theories for the formation and evolution of tropical cyclones continue to expand, the salient question is then, what is
the anticipated future impact of tropical cyclones on society? Fluctuations in trop-
16
ical cyclone activity are of obvious importance to the global community. With the
increased availability of consistent wind and precipitation observations in the tropics,
combined with the development of computationally efficient modeling methods, researchers aim to develop models of tropical cyclones in order to gain insight into the
potential impact of climate change on TC activity.
It is in this realm of research that this thesis finds its niche. This thesis aims
to continue the work on verifying an existing model for hurricane intensity using
observations of TC activity through the past decade in the southeastern United States.
Existing weather and climate models simulate tropical cyclones at a variety of scales
in space and time. This paper analyzes the approach developed by Emanuel et al
12008] that generates large quantities of "synthetic tropical cyclones" that can be used
to quantify tropical cyclone precipitation (TCP). Where previous work has considered
only gage-based observations of precipitation [301, this work aims to combined rain
gage, radar, and streamflow observations in order to evaluate the rainfall algorithm
in the synthetic hurricane model in question.
The synthetic tropical cyclones, in
conjunction with radar, gage, and streamflow observations, are then used to assess
TC risk across a series of locations in the southern United States.
Hurricanes and tropical storms are the most lethal and costly natural disasters
that impact society today, and as has been discussed in previous sections, their destructiveness has been predicted to increase in the coming decades.
Bettering the
ability to predict hurricane risk is thereby a critical goal for socioeconomic planning
and for the preservation of life and the lived environment, especially in hard-hit regions like the southeastern United States.
This thesis contributes to this goal by
comparing and verifying synthetic tropical cyclone precipitation climatology as produced in Emanuel et al [2006] and others with NEXRAD radar products and USGS
NWIS streamflow measurements.
17
1.2
Tropical cyclone activity trends in the past several decades
Previous studies have shown that in the 21st century TC frequency and intensity have
increased over the past several decades, and these trends are slated to continue [4,
16, 30]. Knight and Davis [2009] showed that extremes in precipitation in the United
States have been increasing due to both higher incidence of TCs making landfall and
increased amounts of precipitation associated with each TC. By examining the relative
contribution of TC-associated precipitation to overall extreme weather precipitation
in the southeastern United States, they found that the TC precipitation contribution
has increased 5-10% per decade since the 1970's. A positive trend in the number of
TC days that contribute to the top ten wettest days of the year was identified in
three different datasets [16]. One major finding of their study was that the number of
TC events increased over the four decades of their study, but there was no change in
the frequency of all extreme events (both measured in wind and precipitation) over
the period of record.
Overall the contribution of TC events to extreme rainfall is
increasing in the southern United States.
These observations were also encapsulated in the definition of an index of potential destructiveness developed by Emanuel [20051: the power dissipation index (PDI),
which depends on the maximum sustained wind speed at the conventional measurement altitude of 10m over the lifetime of the storm. Detailed descriptions of this
statistical analysis technique is available in Emanuel 12005] and its supplementary
material. Applying the PDI to best track tropical cyclone datasets for both the Pacific and the Atlantic ocean basins, a near doubling in the power dissipation over the
period of record (~
1950 - 2010) was detected. This indicates increased frequency
and strength of hurricanes over the past several decades.
There still exists substantial debate about any trend in TC activity in recent
history, however. Landsea et al [2006] noted that gaps and biases in tropical cyclone
data for the 20th century, combined with operational changes in the satellite processes
used to identify and track TCs cast doubt on any trends detected therein. Trends
18
are also questioned based on the proven sensitivity of TC activity to interannual and
decadal climate oscillations [13] and on the disappearance of these trends if the time
period in question is doubled to the past century [5, 171.
Model results tend to support the hypothesis that frequency and intensity of
hurricanes has been increasing and will continue to increase in the coming decades
[Knutson et al 2010; Emanuel et al 2010]. Due to the heavy debate surrounding the
limited observations that have been studied thus far, the task of refining the models
to fit current TC activity observations is an important one. This situates this thesis's
research in the role of assisting in the verification of tropical cyclone models' accuracy
with the existing TC data record and thereby improving their ability to anticipate
TC risk.
1.3
Overview of tropical cyclone risk assessment
TC risk, as above, is defined as the potential for loss of or damage to something
of value due to TC activity.
The means by which damage and loss to the human
constructed environment occurs due to tropical storms and hurricanes are many,
including high winds, heavy precipitation, and flooding. Understanding of hurricanerelated precipitation, especially over mountainous orography, had not progressed to
the point of producing accurate precipitation risk forecasts.
Because historic records of hurricane wind speeds are more complete, there have
been many efforts to assess hurricane risk based on wind. Watson and Johnson [2004]
provide a thorough examination of wind-based TC risk and loss modelling practices
up until their date of publication[271, but here will be provided a brief overview of
past methods of TC wind risk assessment.
All estimation techniques begin with complications of hurricane tracks and intensities throughout the period of record. The "best track" data sets compiled and
maintained by forecasting groups like the National Oceanic and Atmospheric Administration's (NOAA's) National Hurricane Center (NHC) or the United States Navy's
Joint Typhoon Warning Center (JTWC) are examples of this. These records track the
19
cyclone center position at some temporal resolution, usually 6-12 hours, and attach
each time point to a single estimate of hurricane intensity (e.g. maximum wind speed,
pressure at storm center). In most hurricane risk assessment models, these data are
used as input for a wind model, a boundary layer model that incorporates surface
conditions and topography, a damage assessment model given wind and boundary
conditions, and a frequency of occurrence model [27].
The first type of TC risk assessments assigned standard probability distribution
functions to the distribution of maximum intensities of all storms on record within a
certain radius of a location of interest. These distributions were then randomly sampled, and risk assessors used standard models of radial structure of storms, combined
with geographical data of the region to assess the maximum wind achieved at the
point of interest. Already we can identify major drawbacks to this approach, one of
paramount importance being that the most damaging, most extreme high-intensity
hurricanes necessarily occur in the tails of the assigned distribution, for which there
is little data [22, 27].
This limitation was addressed in the 1990s via a variety of approaches, with additional methods outlined in greater detail in Emanuel [20061; this thesis derives its
base methodology from Vickery et al [2000] through Emanuel [2006]. The approach
developed by Vickery et al 12000] involves modeling the entire track of a tropical
storm (whereas previous methods focused only on landfall and decay of TCs). The
approach involves sampling input databases (i.e. the HURDAT database) for starting
positions, date, time, heading, central pressure, and translation speed of all TCs in
the observational record. Given these sampled synthetic proto-tropical storms, the
simulation estimates the storm's track (speed and direction) and its central pressure
(a metric for storm intensity) every six hours as a linear function of previous values,
allowing the track to evolve, change speed and intensity in a continuous fashion, in a
way that previous models did not. The advantage of this method of generating large
numbers of synthetic hurricanes is that it eliminates the problems associated with
predetermining statistical distributions of TC characteristics in an area of interest.
The model used in this thesis (Emanuel [2006], detailed in chapter 2, section 3)
20
expands upon these methods of using statistical properties of hurricane tracks to
generate large numbers of storm tracks, and runs a deterministic, coupled numerical
model to simulate storm intensity along the entire track.
21
22
Chapter 2
Data, Models, and Methods
This chapter describes the data and models used in this study, in addition to the
methodology used to carry out the verification. Section 2.1 details the radar-based
data product, Section 2.2 details the surface water streamflow measurements, Section
2.3 outlines the rainfall algorithm used to produce precipitation along the synthetic
hurricane tracks produced by the model, and Section 2.4 discusses the metrics and
statistics used to perform the validation of the model to the observed data.
2.1
Next generation weather radar (NEXRAD)
Rainfall estimates were collected from the radar- and rain gage-based product referred
to as the National Center for Environmental Prediction (NCEP)/Environmental Modeling Center (EMC)4 km GRIB multi-sensor analysis ("MUL") data. This is a realtime, hourly, multi-sensor National Precipitation Analysis (NPA) that was developed
at NCEP in cooperation with the Office of Hydrology (OH). This dataset is the result of the merging of two data sources with hourly observations collected by NCEP
and OH: first, the approximately 3000 automated, hourly raingage observations over
the 48 contiguous United States available through the Geostationary Operational
Environmental Satellite (GOES) Data Collection Platform (DCP) and the National
Weather Service (NWS) Automated Surface Observing System (ASOS); and second,
the hourly digital precipitation (HDP) radar estimates obtained from the WSR-88D
23
Next Generation Weather Radar (NEXRAD) system over the contiguous states. The
HDP estimates are created by the WSR-88D Radar Product Generator on a 131 x
131 4-km grid centered over each radar site. Bias correction of the initial radar estimates occurs using the gage data and a routine developed by NCEP on a contiguous
states 4-km grid from algorithms developed by OH. The grid conforms to the NWS
HRAP grid. This dataset is NEXRAD "Stage II" data, and this thesis adopts the
same terminology.
The data were retrieved from the Earth Observing Laboratory (EOL) part of
NCAR and UCAR [11] in hourly rainfall rate observations from Jan 1, 2002, to Dec
31, 2013. The data were converted directly from NEXRAD GRIB stereographic grid
to a lat-lob grid using nearest neighbor interpolation. The data are in mm/hr, and the
range is 25'N to 440 N and -125'W to -65'W, which are the coordinates of the center
of the boundary grids. The resolution is 0.05deg for both latitude and longitude.
2.2
USGS National Water Information System
The surface water data were collected by the U.S. Geological Survey (USGS) National
Water Information System (NWIS) in the form of daily historical data at a number
of monitoring stations throughout the southern United States. The metric used was
mean daily streamflow/discharge in ft3 /s. This metric was selected over daily peak
discharge due to its wider availability and greater observational consistency over the
spread of monitoring stations. The data were collected for single location observations, so no grid establishment or interpolation was used in this study. Table 1 below
lists the locations under consideration in this thesis and their relevant USGS NWIS
metadata. The given latitudes and longitudes below determined the locations under
consideration for both the NEXRAD data and the synthetic hurricane model as well,
so as to allow meaningful comparison between the calculated statistics for each.
Figure 2-1 situates these points on a map; Google Earth free software was used
24
Table 2.1: USGS NWIS monitoring stations location metadata
Location name
Miami
USGS Site
02289500
lat(N)
25.8
Ion (W)
80.3
drainage area (mi2
N/A
FL
FL
FL
FL
FL
Tampa
Cape Canaveral
Daytona Beach
Tallahassee
Jacksonville
02306654
02232400
02247510
02329000
02246500
28.0
28.4
29.2
30.6
30.3
82.6
80.9
81.1
84.4
81.7
N/A
1331.0
76.8
1140.0
8850.0
)
State
FL
GA
Savannah
02202500
32.3
81.4
2650.0
GA
Atlanta
02203655
33.7
84.4
22.5
GA
Athens
02217500
33.9
83.4
398.0
GA
Albany
02352500
31.6
84.1
5310.0
AL
Mobile
02471078
30.5
88.2
16.5
AL
Montgomery
02419890
32.4
86.2
4646.0
AL
Tuscaloosa
02465000
33.2
87.6
4820.0
AL
Birmingham
02423380
33.4
86.7
140.0
MS
Landon
02481510
30.5
89.3
308.0
MS
Jackson
02486000
32.3
90.2
3171.0
MS
Grenada
07285500
33.8
89.8
1550.0
MS
Fulton
02431000
34.3
88.4
612.0
LA
Baton Rouge
07374000
30.4
91.2
1125810.0
LA
New Orleans
07381000
29.8
90.8
N/A
LA
Lafayette
07386880
30.2
92.0
N/A
LA
Shreveport
07349860
32.4
93.6
N/A
TX
Corpus Christi
08211200
27.9
97.8
16611.0
TX
Houston
08074000
29.8
95.4
336.0
TX
Waco
08096500
31.5
97.1
29559.0
TX
Beaumont
08041780
30.2
94.1
9789.0
TX
Dallas
08056500
32.8
96.8
8.0
TX
Fort Worth
08048000
32.8
97.3
2615.0
TX
San Antonio
08178000
29.4
98.5
41.8
TX
Austin
08158000
30.2
97.7
39009.0
metadata sourced from http://waterdata.usgs.gov/nwis/dv/?referredmodule=sw
to create this map. This helps visualize the spread of the case study points, chosen
to provide a mixture of coastal, inland, Atlantic, and Gulf Coast states.
2.3
Synthetic hurricane model
Synthetic TCs were generated following a manner detailed in Emanuel [2008], which
involves providing an'environment from thermodynamic and kinematic statistics to
25
Figure 2-1: Satellite map of points of interest in the southeastern United States/Gulf
Coast region used as case studies in this thesis.
randomly seed and subsequently track a large number of synthetic TCs. The simulation begins with seeding weak (12 ms') vortices randomly over all ocean basins.
These initially weak vortices were tracked and identified as tropical cyclones if the
vortex reached wind speeds of 21 ms 4 . Following Marks [19921, storm tracks for the
identified TCs were developed using a beta and advection model, which prescribes
cyclone motion via the nonlinear combination of 1) an interaction between the vortex
and its environmental current (known as the steering concept), and 2) an interaction
between the vortex and the Earth's vorticity field [191.
The latter causes a west-
ward deviation from the steering flow taken by itself. Along the tracks, the intensity
of the TC winds is calculated by the Coupled Hurricane Intensity Prediction System (CHIPS) model[6].
The simulation of the tracks and their intensity is based
on atmospheric and oceanic conditions from the National Center for Atmospheric
Research/ National Centers for Environmental Prediction (NCAR/NCEP) reanalysis
from 1980 to 2010, and the climatology is independent of historical hurricane statistics, thereby bypassing the drawbacks associated with those methods as described in
the previous chapter. The climatology has also been shown to have good agreement
26
with both high-resolution global simulations of TCs [8] and with observations [10].
The following algorithm takes the synthetic TC tracks and intensities and estimates precipitation that could be expected from such a storm.
The algorithm
estimates vertical velocity in the lower troposphere, combining estimates based on
the vorticity evolution recorded in the CHIPS model output with topographic and
baroclinic effects. The vertical velocities were then coupled with estimates of the
environmental saturation specific humidity to estimate rainfall. Though this method
cannot be expected to produce reliable estimates for single storm events owing to the
presence of individual convective cells and other mesoscale features, the fact that the
statistics are being generated over a large collection of synthetic TCs leads to more
optimism that the ensemble averages will be accurate.
The algorithm incorporates the following contributions to storm-scale vertical velocity (outlined in greater detail in Zhu et al [2013]):
o Velocity due to axisymmetric overturning from vortex spin-up and spin-down
o Ekman pumping/suction
o Orography
o Baroclinic effects
The algorithm begins by using the curl of the wind stress estimated from the
gradient wind and background flow to generate vertical velocity at the top of the
boundary layer. Note that background flow and irregular surface drag will cause this
component to not be axisymmetric.
Next the topographic component is added, estimated as the vector product of
the horizontal wind with the gradient of topographic heights on a 0.25 x 0.25 degree
topographic data set'.
The model fits a standard radial profile of gradient wind to the recorded radius
of maximum winds and outer radius at each output time, and the time evolution
'This approximation is functional due to the longer time scales used in this simulation, which
cause cloud microphysical and stratification effects timescales to vanish [30]
27
of the gradient wind is estimated. This is used to estimate the stretching term in
the vorticity equation, as the difference between vertical velocities in the middle
troposphere and the boundary layer must produce enough stretching to account for
the time rate of change of the vorticity of the gradient wind.
The baroclinic component is composed of four effects of the interaction of a vortex
with environmental shear: isentropic ascent/descent due to interaction of the vortex
flow with background isentropic slope; isentropic ascent/descent owing to the interaction of background shear with vortex-born isentropic surface slopes; time-dependent
changes in vortex-born isentropic surfaces; and self-reinforcing distortions in the vortex flow and its associated isentropic field.
The total vertical velocity, composed of the sum of all the above components,
multiplied by saturation specific humidity at a given level (here 900hPa) estimates
the vapor flux through that level 2 It is assumed that a fixed fraction (0.9) of vapor
flux calculated thereof falls to the surface as precipitation.
2.4
Statistical methods
Tropical cyclone precipitation (TCP) for synthetic and observed TCs were compared
at 30 locations in the southeastern United States, described in Table 2-1. For consistency, the coordinates of the streamflow measurement sites were the ones used to
parse the radar-based precipitation data as well. Rainfall data were aggregated for the
grid box in the NEXRAD-II grid with latitude/longitude coordinates nearest to each
USGS streamflow measurement site. The reasons for selecting these locations were
the broad spatial extent of the regions that encompassed coastal and inland areas,
their positions as population centers for the states in question, and the completeness
of both their associated NEXRAD Stage II hourly precipitation data and their daily
mean streamflow data throughout the period of interest, which is January 1, 2002,
through December 31, 2013.
2
The effect of a warm TC core is not accounted for, as the specific humidity is estimated based
on ambient temperature at 600hPa and extrapolated downward on a moist adiabat. [30]
28
Comparison between both sets of observational TCP data and the syntheticallyproduced TCP was done through calculating return periods for each storm total
precipitation at the point of interest. Return periods in this thesis are calculated in a
manner after the approach of Emanuel and Jagger [2010]. Emanuel and Jagger [2010
found that return periods calculated in this manner, using empirical probability density functions, are fully consistent with those calculated using extreme-value theory
and a peaks-over-threshold model [7].
2.4.1
Calculating return periods using probability density functions
The procedure for calculating TCP return periods within a stated radius of a given
point of interest (POI) is detailed below [7]:
1. Define an exceedence frequency for a given TCP amount x as Fx= fl',
where
x = given total storm rainfall in mm, n = number of storms intersecting POI
with TCP greater than x, and m = total number of TCP-producing storms
intersecting the POI.
2. The probability that a storm produces rainfall in excess of x mm at the POI is
then P(X > x) = 1 - e-Fx
3. The return period of a storm with TCP in excess of x is then T = 1/P
2.4.2
Calculating return periods using Weibull ranking method
Following Water Resources Engineering 2005, the conventional method of calculating
return period for surface water discharge, or streamflow, is detailed below [20]:
1. The mean daily stream discharge from each TC coming within the specified
radius of the streamflow measurement site is recorded
2. The data are ranked from highest to lowest flow value
29
Return period =
"
3. The inverse Weibull formula is used to calculate the return period of each TC:
m = rank, n = number of years in the dataset
This method is used on the USGS NWIS streamflow data in this thesis, and additionally on radar observed TC rainfall, in order to evaluate the comparison between
streamflow-based and radar-based return periods.
2.4.3
Correlation between streamflow return periods and radar
return periods
The final section of this thesis begins introducing the possibility of comparing streamflow measurements as a metric for assessing hurricane risk. I begin by evaluating the
correlation between observed precipitation and maximum streamflow measurements
at each of the POI in the study. The maximum streamflow measurements were chosen
to be the highest streamflow (ft3 /s) values observed within a five-day time period
from the arrival of the TC in question at the POI. Though precipitation due to the TC
will have begun before the eye reaches the POI, this method is serviceable because
the radius of "intersection" is large (350km).
Return periods for these streamflow
values were calculated using the inverse Weibull formula as in Mays [20051. A linear
model was fit between the return periods calculated from streamflow measurements
taken in this way and from radar observations for each intersecting tropical cyclone
observation at the POI, and the correlation coefficient, R2 , was calculated for each
linear model.
Since rainfall is highly localized, and streamflow depends on rainfall over a whole
basin, in an effort to try to improve the fit of these linear models, the basin average
rainfall around four POI was calculated for each of their intersecting TCs, and a
new linear fit between the return periods of these values and their respective streamflow return periods was calculated. The basin boundaries were determined using the
mapping tool[24, 25] for the watershed boundary dataset from the USGS National
Hydrography Dataset (NHD). The NHD represents the drainage network with fea-
30
tures such as rivers, streams, canals, ponds, coastlines, dams, and stream gages, and
the watershed boundary dataset represents drainage basins as enclosed areas. The
latitude and longitude coordinates of the boundaries of the watersheds for Austin,
TX; Mobile, AL; and Tampa, FL were located, and the radar grid boxes included
within those boundaries were identified. The NEXRAD-II precipitation observations
for each TC event in each of the three sites' TC records over their entire basins so
defined were recorded and averaged. These basin average TC event rainfall values
were used to calculate return periods, which were compared via linear model fitting
to streamflow measurements for these sites.
2.5
Cross-correlation function
One more method to examine the correlation of the streamflow and radar TCP time
series was conducted, using the cross correlation function[29].
Cross-correlation is
defined as the similarity of two series as a function of the lag of one relative to the
other. In this analysis, since we are concerned with determining the similarity of the
series for distinct TC events, we consider the correlation of the series with zero lag,
measured using the following equation:
(f * g)[n]
=
EO f*[m]g[m + n]
Thus for our analysis, n = 0. The correlation of the streamflow event TCP return
periods and the radar-estimated event TCP return periods are compared using this
method.
31
32
Chapter 3
Results
This chapter presents and discusses the results of the statistical analysis of the synthetic hurricane precipitation climatology versus observed tropical cyclone precipitation climatology for the southern and southeastern United States.
was conducted using the R Statistical Computing Environment.
All analysis
Section 3.1 uses
NEXRAD-II radar observations to evaluate the synthetic hurricane model results.
Section 3.2 delves into the problem of the highly-localized nature of precipitation. Section 3.3 explores the possibility of future work using streamflow models and streamflow analysis to further refine and/or validate the synthetic hurricane model approach.
Section 3.4 concludes.
3.1
Comparison between NEXRAD-II observations
and synthetic tropical cyclone precipitation
Statistical analysis compared return periods of storm total precipitation at the 30
locations described in Table 2-1. Event total TCP was aggregated from the twohourly synthetic rain rate and compared with observed event total TCP, aggregated
from hourly radar rainfall estimates (Figures 3-1 through 3-6). Section 3.1.1 carries
out the analysis of the return periods as calculated from radar data from 2002-2013,
and section 3.1.2 explores the spatial sensitivity of these return periods at the case
33
study points of interest.
3.1.1
Return period analysis
Synthetic storm total TC rainfall is compared to NEXRAD-II radar-measured TC
rainfall aggregated from hourly observations in figures 3-1 through 3-6. In general,
over the entire range of study locations we see a moderate amount of both over and
underestimation by the synthetic hurricane statistics, which indicates no categorical
bias in the modeling parameters.
Event TCP generally shows good agreement for
short return period events (0-2 years, we call these "frequent" events), the synthetic
and observed TCP are in good agreement for nearly all locations. Because of the
temporal brevity of the available radar measurement period of record, calculations
for radar-based return periods are necessarily limited to that duration of time (12
years); however, it remains reassuring of synthetic TCP's risk estimation capabilities
that the records in large part line up'.
'The blue error bars, representing a 90% confidence interval on the NEXRAD-II observations, end
well to the right of the maximum observations due to the formula used to calculate the bootstrapped
confidence intervals: necessarily any rain values greater than the maximum observed in the 13-year
period of record has an infinite return period.
34
Storm Total Rainfall: Miami
1
5
10
50 100
500
Storm Total Rainfall: Tampa
5000
1
5
10
50
1W
500
5000
1
5
10
50
100
500
50 100
500
5000
5
10
50 100
500
5000
Storm Total Rainfall: Jacksonvlle
Storm Total Rainfall: Tallahassee
1
10
Storm Total Rainfall: Daytona Beach
Storm Total Rainfall: Cape Canaveral
1
5
5000
1
5
10
100
50000
retuw
period (y)
Figure 3-1: Comparison of storm total TC precipitation based on observed (blue dots)
and synthetic (black line) tropical cyclones at six locations in Florida: (a) Miami, (b)
Tampa, (c) Cape Canaveral, (d) Daytona Beach, (e) Tallahassee, and (f) Jacksonville;
the error bars represent a 90% confidence interval on the NEXRAD-II return period
observations
The Florida POIs Tampa, Tallahassee, and Jacksonville all show significant differences between radar-based return periods and the synthetic TC return periods; for
much of the trends plotted here (return periods of less than 10yr), the synthetic TC
trend line lies outside the 90% confidence intervals of the radar-based observations.
Cape Canaveral and Daytona Beach both exhibit good matching between the two
datasets, and Miami exhibits deviations only for return periods of larger than 10yr.
35
Skwrm Total Raknf": Altanta
Storm Total Rainfall: Savannah
8OD
i
1
5
10
50 100
5W
5000
1
5
10
50 100
500
5000
Storm Total Rainfall: Albany
Slrm, Total Rabiva: Aihona
8CO
E
1
5
10
50 100
rMka,
pariod
500
1
5000
5
10
50 100
500
5000
return period (y)
(y)
Figure 3-2: Comparison of storm total TC precipitation based on observed (blue dots)
and synthetic (black line) tropical cyclones at four locations in Georgia: (a) Atlanta,
(b) Savannah, (c) Athens, and (d) Albany; the error bars represent a 90% confidence
interval on the NEXRAD-II return period observations
All Georgia POIs show strong agreement between observed radar-based TC climatology and synthetic TC climatology; the synthetic TC trend is within the 90%
confidence interval at all points in all four POI.
36
Storm Total Rainfall: Montgomery
Storm Total RainaM: Birmingham
E
I
I
j
A
Q
-
0
5
10
50 100
50D
50
0to
1
6
10
50 100
500
5000
Storm Total Rainfall: Tuscaloosa
Storm Total Rainfa: Mobile,
I
I
1
-
MEOW5
10
50 100
50(
1
5
10
50 100
500
5000
return period (y)
rattm penod ty)
Figure 3-3: Comparison of storm total TC precipitation based on observed (blue dots)
and synthetic (black line) tropical cyclones at four locations in Alabama: (a) Birmingham, (b) Montgomery, (c) Mobile, and (d) Tuscaloosa; the error bars represent a
90% confidence interval on the NEXRAD-II return period observations
Montgomery and Mobile, Alabama, both show strong agreement between synthetic TC return periods and observed radar-based TC return periods. Birmingham
and Tuscaloosa, Alabama, both show underestimation of TC return periods by the
synthetic TC rainfall algorithm; in both POIs the synthetic TC trend line lies below and outside the 90% confidence interval for the observed radar-based TC return
period trend, showing a significant difference between the synthetic TC climatology
and that which we observe.
37
Storm Total Rainfall: Landon
Storm Total Rainfall: Jackson
1
5
10
50 100
500
5000
1
5
10
so 100
500
5000
Storm Total Rainfall: Fulton
Storm Total Rainfall: Grenada
E
J
1
5
10
50 100
500
5000
1
5
10
50 100
500
5000
retur period (y)
mmum period (y)
Figure 3-4: Comparison of storm total TC precipitation based on observed (blue
dots) and synthetic (black line) tropical cyclones at four locations in Mississippi: (a)
Jackson, (b) Landon, (c) Grenada, and (d) Fulton; the error bars represent a 90%
confidence interval on the NEXRAD-II return period observations
All Mississippi POIs show strong agreement between observed radar-based TC
climatology and synthetic TC climatology; the synthetic TC trend is within the 90%
confidence interval at all points in all four POI except for common TC events (return
periods < 2yr) in Fulton, MS, for which the synthetic algorithm underestimates TC
rainfall.
38
Storm
Storm Total RaInfall: New Orleans
E
1
5 10
50 100
50t
5000
I
I
i
;
5
10
Total Rainfall:
Baton
50 100
Rouge
500
5000
Storm Total Rainfall: Shreveport
Storm Total Rainfall Lafayette
E
1
5
10
50
100
500
5000
1
5
10
50 100
500
5000
return period (y)
roturn period (Y)
Figure 3-5: Comparison of storm total TC precipitation based on observed (blue dots)
and synthetic (black line) tropical cyclones at four locations in Louisiana: (a) New
Orleans, (b) Baton Rouge, (c) Lafayette, and (d) Shreveport; the error bars represent
a 90% confidence interval on the NEXRAD-II return period observations
The synthetic rainfall algorithm did a markedly poor job replicating observed TC
climatology in Louisiana. TC rainfall for a given return period is overestimated in
New Orleans, Lafayette, and Shreveport for all return periods over 2yrs. All synthetic
TCs with return periods greater than 1-2yrs in Baton Rouge have rainfall that is well
below that which we observe, so the synthetic algorithm underestimates rainfall in this
location. At this time there is no obvious geographical theory that can satisfactorily
explain this poor performance by the rainfall algorithm in Louisiana.
39
Storm Total Rainfall: Corpus Christi
Stonn Total RaInfaW Austin
Go8
1!
1
5
50100
10
044u
500
5
1
5000
10
50 100
500
5000
return period (y)
perS (Y
Storm Total Rainfall: Dallas
Slam, Total Rainfall: San Antonio
8
E
4
5
10
5000
500
5000
1
5
10
50 100
500
-swm
period
return period (y)
Stan Total Rainfall: Houston
Storm Total Rainfall: Waco
(
1
MEM
S
5000
MINOR
1
!~
S
ci
5
10
50
100
500
1
5000
5 10
50 100
500
retu perlod (y)
return period (y)
Storm Total Rainfall: Fort Worth
Storm Total Rainfall: Beaumont
5000
I
01
1
5
10
50 100
500
1
5000
5
10
50 100
500
00
retum period (y)
retur period (y)
Figure 3-6: Comparison of storm total TC precipitation based on observed (blue dots)
and synthetic (black line) tropical cyclones at eight locations in Texas: (a) Austin,
(b) Corpus Christi, (c) San Antonio, (d) Dallas, (e) Houston, (f) Waco, (g) Fort
Worth, and (h) Beaumont; the error bars represent a 90% confidence interval on the
NEXRAD-II return period observations
40
The synthetic rainfall algorithm overestimates TC rainfall for much of Texas, based
on the 8 POI in this study. Corpus Christi, Dallas, Houston, Waco, Fort Worth, and
Beaumont, TX, all show observed TC rainfall return periods to have much lower
rainfall measurements than those predicted by the synthetic algorithm. Austin and
San Antonio, TX, show decent matching between observed TC return periods and
synthetic TC return periods; the synthetic trend line is within the 90% confidence
interval for all points in both locations. San Antonio and Austin are geographically
near each other in central Texas, so it is possible that some geographical feature
they share is responsible for their similar degrees of success in the rainfall algorithm's
reproduction of observed TC climatology.
There are two ways that all the POIs can be categorized easily with respect to
each other: is the POI coastal or inland, and is it on the eastern or western side of
the Gulf of Mexico. One notable difference between the eastern and western POIs in
the study is that, based on Table 3.1, the eastern locations are much more likely to
have the synthetic algorithm successfully reproduce observed hurricane return period
climatology than western locations. It also appears that TC rainfall at inland locations are more often overestimated or underestimated by the synthetic TC algorithm
than coastal locations. There is no discernable trend with respect to the direction in
which (overestimation or underestimation) this departure from observations occurs.
The following graph presents a summary of the return period analysis for the entire
region, using five representative locations: Miami, FL; Albany, GA; Grenada, MS;
New Orleans, LA; and Corpus Christi, TX. These locations were chosen primarily
to get a spread of the region such that the same tropical cyclone did not necessarily
affect two of these locations at once, and secondarily to represent both coastal and
inland locations. The event TCP of all synthetic events and radar observations was
collected, and these data were used to construct radar-based and synthetic TC return
periods for the region as a whole.
We notice a good matchup for return periods of less than 20 years, but a systematic
underestimation of the return period for a given rainfall amount by the synthetic
rainfall algorithm (i.e. the synthetic algorithm overestimates the amount of rain for
41
Table 3.1: Coastal POI v. inland POI: return period analysis summary
'
'
'-
C
State Location name
a
d
Type
b
FL
Miami
Coastal 30
141.7
Fay 2008
None
FL
Alberto 2006
Coastal 31
Tampa
100.5
Overestimates
FL
Cape Canaveral
Coastal 29
294.4
Fay 2008
None
FL
Daytona Beach
Coastal 28
208.2
2008
Fay
None
FL
Tallahassee
Coastal 25
264.3
Overestimates
Fay 2008
FL
Jacksonville
Coastal 27
235.6 Underestimates
Fay 2008
GA
Savannah
110.9
Coastal 26
None
Tammy 2005
GA
Atlanta
Jeanne 2004
Inland
15
91.2
None
GA
Bill 2003
Athens
114.2
Inland
17
None
GA
Albany
140.0
Inland 24
2008
None
Fay
AL
Isaac 2012
Mobile
298.4
Coastal 28
None
AL
Montgomery
Inland
20
116.5
None
Fay 2008
AL
Dennis 2005
Tuscaloosa
18
125.3 Underestimates
Inland
AL
Birmingham
Ivan 2004
18
133.0 Underestimates
Inland
MS
Isaac 2012
Landon
245.3
Coastal 25
None
MS
Lee 2011
Jackson
22
Inland
122.7
None
MS
Isidore 2002
Grenada
Inland
18
162.2
None
MS
Isidore 2002
Fulton
Inland
16
117.7 Underestimates
LA
Baton Rouge
Gustav 2008
272.1 Underestimates
Inland 21
LA
New Orleans
Lee 2011
164.9
Coastal 23
Overestimates
LA
24
Rita 2005
Lafayette
Inland
159.3
-Overestimates
LA
Shreveport
Rita 2005
Inland 13
115.4
Overestimates
TX
Corpus Christi
117.8
Coastal 13
Overestimates
Dolly 2008
TX
Ike 2008
Houston
Inland
15
127.0
Overestimates
TX
Hermine 2010
Waco
Inland 11
108.4
None
TX
Beaumont
Coastal 18 Humberto 2007 120.6
Overestimates
TX
Hermine 2010
Dallas
8
Inland
96.9
Overestimates
TX
Fort Worth
Hermine 2010
7
87.5
Inland
Overestimates
TX
San Antonio
173.1 Underestimates
Inland
10
Fay 2002
TX
Hermine 2010
Austin
122.2
Inland
13
None
(a) number of TCs observed in period of record, 2002-2013; (b) name and year of TC that
produced the most rain in period of record; (c) rain produced by max TC (mm); (d) tendency
of systematic TC return periods to overestimate or underestimate radar-based return periods
a given return period TC).
The six figures below are partially a reproduction of figures 3-1 through 3-6, but
3-7 through 3-12 have incorporated TC return periods for the 30 POIs as calculated
using the inverse Weibull formula applied to the radar-based storm total TCP observations, and also includes 90% confidence intervals thereof. These were included
in order to evaluate the comparison between empirical cumulative density function
42
Synthetic TCs v. Observations: Summary
0
e*S
LO
N
.*0
e*0
e*0
.
.e
-
E
E
0
0
.
e*
e'
e*
E)
e.*
L0
Co.
L0
0
E
.0000
0
-
C.,
C.,
2
5
20
10
50
100
2
200
return period (y)
Figure 3-7: Comparison of storm total TC precipitation based on observed (red dots)
and synthetic (black dots) tropical cyclones aggregated for the entire region using five
representative POIs: Miami, FL; Albany, GA; Grenada, MS; New Orleans, LA; and
Corpus Christi, TX.
return period calculations and inverse Weibull formula return period calculations,
which is the conventional method of calculating flood return periods in surface water
hydrology. The Weibull return period data accurately reproduces the return periods
calculated using empirical CDFs in all cases, and in fact matches the synthetic return
periods more accurately in the following points of interest: Tampa, FL; Tallahassee,
43
FL; Jackson, MS; New Orleans, LA; Lafayette, LA; Corpus Christi, TX; Houston,
TX; and Beaumont, TX.
Storm Total Rainfal: Mai
Storm Total Rainfall: Tampa
E
1
5
10
50 100
500
1
5000
5 10
50 100
500
5000
5
Storm Total Rainfall: Tall *aham15
1
5
10
50 100
500
10
50 100
500
50(
Storm Total Rainfall: Daytona Beach
Storm Total Rainfalt Cape Canaveral
1
5
10
50 100
500
5000
Storm Total Rainfall: Jacksonville
5000
1
5
10
50 100
500
5000
Figure 3-8: Comparison of storm total TC precipitation based on empirical CDF
calculation (blue dots), Weibull formula return periods (red dots) and synthetic (black
line) tropical cyclones at six locations in Florida: (a) Miami, (b) Tampa, (c) Cape
Canaveral, (d) Daytona Beach, (e) Tallahassee, and (f) Jacksonville; the error bars
represent a 90% confidence interval on the NEXRAD-II return period observations
The inverse Weibull formula-calculated return periods for all POIs in Florida
precisely replicate those calculated using the empirical CDF method. It is notable
that the synthetic hurricane return periods more precisely match the Weibull method
return periods for radar rainfall in Miami, Tampa, and Tallahassee; however, no
44
geographical trend satisfactorily explains this tendency.
Storm Total Rainfall: Savannah
Storm Total Ralinfal Adanta
E
8
S
1
5
10
50 100
500
5000
1
5
10
50 100
500
5000
Storm Total Rainfall: Albany
Storm Total RaInall: Athens
E
T
8
1
5
10
50 100
500
5000
1
retumn period (y)
5
10
50 100
500
5000
return period (y)
Figure 3-9: Comparison of storm total TC precipitation based on empirical CDF
calculation (blue dots), Weibull formula return periods (red dots) and synthetic (black
line) tropical cyclones at four locations in Georgia: (a) Atlanta, (b) Savannah, (c)
Athens, and (d) Albany; the error bars represent a 90% confidence interval on the
NEXRAD-II return period observations
Relative to the empirical CDF-calculated return periods for all POIs in Georgia,
the inverse Weibull formula-based return periods appear to overestimate rainfall per
return period by a very slight amount.
However, both sets fall into each others'
respective 90% confidence intervals, so we can conclude that both methods produce
statistically similar return periods for each POI.
45
Storm Total Rainfall: Montgomery
Storm Total Rainfall: Birmingham
8
-
.0
1
5
10
50 100
500
5M -1
1
5
10
50 100
500
5000
Storm Total Rainfall: Tuscaloosa
Storm Total Rainfall Mobtile
LO
M
1
5
10
50 100
500
1
r"00
5
10
50 100
500
5000
retun peiiod (y)
return priod (y)
Figure 3-10: Comparison of storm total TC precipitation based on empirical CDF calculation (blue dots), Weibull formula return periods (red dots) and synthetic (black
line) tropical cyclones at four locations in Alabama: (a) Birmingham, (b) Montgomery, (c) Mobile, and (d) Tuscaloosa; the error bars represent a 90% confidence
interval on the NEXRAD-II return period observations
We observe the same precise replication of the empirical CDF return periods in all
POIs in Alabama, and improved accuracy of the synthetic hurricanes in Montgomery
and Mobile. The same overestimation observed in the empirical CDF return periods
for TCs in Tuscaloosa, AL, is also observed (and perhaps worsened) in the inverse
Weibull formula-based return periods.
46
Storm Total Rainfall: Landon
Stonr Total RaWinal: Jackson
E
LO
1
5
10
50 100
500
5000
1
5
10
50 100
500
50( 0
Storm Total Rainfall: Fulton
Storm Total Rainfal: Grenada
i~.
.5
S
1
5
10
50 100
501 10
retu- psdod (y)
1
5
10
50 100
500
50 0
return period (y)
Figure 3-11: Comparison of storm total TC precipitation based on empirical CDF
calculation (blue dots), Weibull formula return periods (red dots) and synthetic (black
line) tropical cyclones at four locations in Mississippi: (a) Jackson, (b) Landon, (c)
Grenada, and (d) Fulton; the error bars represent a 90% confidence interval on the
NEXRAD-II return period observations
All Mississippi POIs exhibited good matchup between return periods calculated
using both methods, and accurate replication of the observed TC climatology by the
synthetic TCs.
47
Storm Total RalnfaIk
New Orleans
Storm Total Rainfall: Baton Rouge
P
1
5
10
50 100
500
1
5000
Storm Total Rainfal- Latay el
5 10
50 100
500
to
50(
Storm Total Rainfall: Shreveport
a
1
5
50 100
10
relu
500
1
5000
pedod (y)
5
10
50 100
retum
500
50(to
peod (y)
Figure 3-12: Comparison of storm total TC precipitation based on empirical CDF
calculation (blue dots), Weibull formula return periods (red dots) and synthetic (black
line) tropical cyclones at four locations in Louisiana: (a) New Orleans, (b) Baton
Rouge, (c) Lafayette, and (d) Shreveport; the error bars represent a 90% confidence
interval on the NEXRAD-II return period observations
For New Orleans, LA, and Lafayette, LA, we note a better match between the
inverse Weibull formula-based return periods and the synthetic TC return periods as
compared to the empirical CDF-calculated return periods, and relatively poor precision between both sets of radar-based return periods in Baton Rouge, LA. Accuracy
is high in Shreveport, LA, and both sets of radar-based return periods align with
synthetic TC climatology satisfactorily.
48
Storm Total Rainfall: Corpus Christi
Storm Total Rainfal: Austin
1
5
10
50 100
retur
500
5000
1
5
10
50 100
500
5000
return period (y)
period (y)
Storm Total RabnfanL San Antonio
Storm Total Rainfall: Dallas
E
S
5
1
10
50 100
500
5000
1
5
10
50 100
500
5000
return period (y)
return period (Y)
Storm Total Rainfall: Waco
Storm Total Rainfall: Houston
E
S
0
1
5
10
50 100
retur
500
5000
1
5
10
50 100
500
5000
return period (y)
period (Y)
Storm Total Rainfall: Beaumont
Storm Total Rainfall: FortWorth
E
r
1
5
10
50 100
500
5000
1
5
10
50 100
500
5000
return period (y)
return period (Y)
Figure 3-13: Comparison of storm total TC precipitation based on empirical CDF
calculation (blue dots), Weibull formula return periods (red dots) and synthetic (black
line) tropical cyclones at eight locations in Texas: (a) Austin, (b) Corpus Christi, (c)
San Antonio, (d) Dallas, (e) Houston, (f) Waco, (g) Fort Worth, and (h) Beaumont;
the error bars represent a 90% confidence interval on the NEXRAD-II return period
observations
49
In all sites in Texas, the inverse Weibull formula-based radar rainfall return periods reproduce precisely the return periods calculated from radar rainfall using the
empirical CDF method. The same over- or underestimation in that method is replicated in the Weibull method return periods.
3.1.2
Spatial sensitivity of return period analysis
In order to explore and illustrate the high spatial sensitivity of rainfall and its extremely localized nature, the rainfall for all intersecting tropical cyclones was also
recorded for the surrounding eight grid boxes around each POI. Each grid box is a
0.05 degree latitude/longitude square, and so encompasses an area of ~ 25km 2 . The
return periods for this observed rainfall were also calculated and compared to those
of the POI. These plots are included below, as figures 3-13 through 3-18, and the
results are summarized in Table 3.2.
50
Storm Total Rainfall: Miami and SurrouitlingGuidpoint
Storm Total Rainfall: Tampa and Surrounding Grldponts
E
t
E
0.5
1.0
5,0
2.0
relum peod
Storm Total Rainfall: Cape Canaveral
0.5
1.0
Storm Total Rainfal
1.0
2.0
5.0
100
retum period (y)
and Sunounm*,g Gridpo
Storm Total Rainfall: Daytona Beach and Surrounding Gridpoin
05
50
20
retum
0.5
1O.0
(y
1
20
50
10.0
return penod (y)
pediod (yI
Tallahassee and Surrounding GrIdpolin
Storm Total Rainfall: Jacksonville and Surrounding Gridpointa
E
0.5
1.0
2.0
5.0
0.5
10.0
1.0
2.0
5.0
10.0
Figure 3-14: NEXRAD-I observed TCP return periods for POI and its 8 surrounding
gridboxes at six locations in Florida: (a) Miami, (b) Tampa, (c) Cape Canaveral, (d)
Daytona Beach, (e) Tallahassee, and (f) Jacksonville
The only Florida points of interest with major deviations between adjacent grid
points are Miami and Tallahassee; these POIs also happen to be the most southerly
and the most northerly POI in the state, respectively. For all POIs we note that the
common TCs, those with return periods of less than 2 years, are in better agreement
among all adjacent grid boxes. The overall shape of the return period plots is well
defined for all 9 grid boxes under consideration.
51
Storm Total Rainfal: Atlanta and Surroumding Gutdpoints
Storm Total Rainfall: Savannah and Surrounding Gridpoints
top lft
E
at ight
bMafn tddle,_$R
bdat l~ih
Ea
E
0
0
05
1.0
20
5b
0.5
00
1.0
2.0
5.0
10.0
return period (y)
Storm Total Rainfall: Attette an SurrainingGdidpolnta
I
Storm Total Rainfall: Albany and Surrounding Guldpoints
p idde_
bo71widl
boll,M, left
0.5
1.0
20D
50
0.5
10.0
relAM porid (y)
1.0
2.0
5.0
10.0
retur period (y)
Figure 3-15: NEXRAD-II observed TCP return periods for POI and its 8 surrounding
gridboxes at four locations in Georgia: (a) Atlanta, (b) Savannah, (c) Athens, and
(d) Albany
Savannah, GA, and Athens, GA show similarly high-quality matching of calculated
return periods between the 8 grid boxes adjacent to the location of interest, with only
minor spread for TCs of return periods near 7 or 8 years. Atlanta, GA, exhibits the
gradual increase in deviations from the calculated return periods for the grid box of
interest for its adjacent grid boxes as TC rainfall/return period increases. Albany,
GA, only exhibits decent agreement between adjacent grid boxes for very common
TCs and the most uncommon TCs, or return periods less than 2 years or greater than
12 years.
52
Storm Total Rainfall: Binmingham and Suvroumdlng Gridpoknt
Storm Total Rainfall: Montgomery and Surrounding Gridpoinkt
top left
top mile
top lghltE
left
E
tp milS
Poften left
beloem ee&1
boteto "Ohl
05
1.0
2-0
5.0
0.5
10.
1.0
relfnperiod
Storm Total Rainfall: Mobile and Surrounding Grldpolnts
2.0
return
5.0
penod
10.0
(y)
Tue104alou
topt lft
top meddle
E
1.0
5&0
Storm Total Rainfall: Tuscaloosa and Surrounding Gridpokts
E
0.5
20
return period
10.0
httolee mdiddle
bnelle igt
0.5
ty)
1.0
2.0
5.0
10.0
return period (y)
Figure 3-16: NEXRAD-II observed TCP return periods for POI and its 8 surrounding
gridboxes at four locations in Alabama: (a) Birmingham, (b) Montgomery, (c) Mobile,
and (d) Tuscaloosa
All Alabama POIs show no major deviation between grid boxes adjacent to the
four POIs.
53
Storm Total Rainfall: Jackso and Sewouning Gridpoints
Storm Total Rainfall: Landon and Surrounding Gridpoints
lo lepIft
botorn Wg
toItm t
0.5
1.0
20
5a
10.0
0.5
1.0
2.0
50
100
return Period (Y)
Storm Total Rainfall: Grenada and Surrounding Gridpoints
Storm Total Rainfall: Fulton and Surrounding Gridpolints
to 04001I
bottom, ffddle
hetorn
Ig~
I,
0.5
1.0
2,0
50
10,0
0.5
return period (y)
1.0
2.0
5.0
10.0
return period (y)
Figure 3-17: NEXRAD-II observed TCP return periods for POI and its 8 surrounding
gridboxes at four locations in Mississippi: (a) Jackson, (b) Landon, (c) Grenada, and
(d) Fulton
The only Mississippi POI that begins to exhibit major differences in the return
periods of TCs calculated for adjacent grid boxes is Landon, MS. Landon is the only
coastal POI considered in the state of Mississippi in this study. It is possible that
the coastal nature of this POI contributes to the different TC climatology of the area
and the greater rainfall variability on a local (individual grid box) scale.
54
Storm Total Rainfall: New Orleans and Surrouncldg GridpointE
-New
Storm Total Rainfall: Baton Rouge and Surrounding Gridpokib
Ordeats
0 Woftotg
tog ith
-
05
10
2i
5d
0.0
botitolft
bottom middle
bottom right
1.0
0.5
retub oteiod Wyt
Storm
2.0
5.0
100
return period (y)
Total RaInfall: Lafayette and Surromndbg Grtdpo
nta
Storm Total Rainfall: Shreveport and Surrounding Gridpoints
top let
toPmiddleo
bottom Is"
bottom middle
bottom light
0.5
1.0
2.0
50
10.0
0.5
retur POW y)
1.0
2.0
5.0
10.0
return period (y)
Figure 3-18: NEXRAD-II observed TCP return periods for POI and its 8 surrounding
gridboxes at four locations in Louisiana: (a) New Orleans, (b) Baton Rouge, (c)
Lafayette, and (d) Shreveport
Both New Orleans and Shreveport exhibit increasing spread between return period observations with increasing return period, with deviations in excess of 60mm of
rainfall between adjacent grid boxes. The other two Louisiana POIs have fairly consistent and much milder deviations between adjacent grid boxes. In sum, Louisiana
POIs serve to illustrate quite well the problem of extreme locality of rainfall.
55
Storm Total Rainfall: Austin and Surrounding Gddpobfts
Storm Total Rainfall: Corpus Christi and Surrounding Gridpoin
top Iant
t00 middle
rightn
1
bot
Wi
botm8d
E0
0.5
1.0
2,0
ret
5.
0,5
100
1'0
2.0
5.0
10.0
retum priod (y
period (0
Storm Total Rainfall: San Antonio and SurroundingGrIdpoin
Storm Total Rainfall: Dallas and Surrounding Gridpoints
8
upleft
midlef
umiuddle
uprigt
a
og
8.
bott left
btster middle
U
bodomn leftt
bottom
fight
S
0 --
(3
0.5
1.0
60
2.0
0.5
100
1.0
2.0
5.0
10.0
r-tu podod (Y
retum period (Y)
Storm Total Rainfall: Houston and Surrounding Gridpoints
Storm Total Rainfall: Waco and Surrounding Gridpoints
i
I
S
Hutoo
8
igt
uop left
uop mud"1
udle
up midle
ok
baftt
5
00000 ltt
8
idt
0
0.5
1.0
5.0
2,0
retun
0.5
100
I
up
.5
right
bottom Wt
-~bottorn ogot
U
torn rniddle
torn rigt
I
8
05
1.0
10.0
top
topmiddle
8.
5.0
Storm Total Rainfall: Beaumont and Surrounding Gridpointa
-FortWotht
uop left
I
2.0
return period (y)
Storm Total Rainfall: Fort Worth and Surrounding Gridpoint
8.
1.0
period (y
2,0
5,0
0.5
10,0
10
1
2.0
5.0
10.0
returm period (y)
retum period (y)
Figure 3-19: NEXRAD-II observed TCP return periods for POI and its 8 surrounding
gridboxes at eight locations in Texas: (a) Austin, (b) Corpus Christi, (c) San Antonio,
(d) Dallas, (e) Houston, (f) Waco, (g) Fort Worth, and (h) Beaumont
56
All Texas POIs show very good agreement between adjacent grid boxes for TCs
with return periods less than 4 years. Beaumont, TX, and San Antonio, TX show
deviations on the order of 50mm for TCs with return periods much larger than 57 years, with increasing imprecision with increasing return periods.
Reassuringly,
behavior between Dallas, TX, and Fort Worth, TX, is quite similar, which makes
sense due to their spatial adjacency; the two cities are mere miles apart. The Texas
POI with greatest precision between all 9 grid boxes under consideration is Waco.
Dallas and Fort Worth also show high precision. All'three of these locations are the
most inland POIs being considered in this study; it's possible that some aspect of
this inland climatology is the reason for the increased similarity between the POIs
and their adjacent boxes with respect to radar observed rainfall.
57
Table 3.2: Coastal POI v. inland POI: spatial variability analysis summary
State Location name
Type
a
b
c
d
FL
Miami
Coastal
SE
NW
47.4mm
6.6yr
FL
Tampa
Coastal
SE
W
20.7mm
3.3yr
FL
Cape Canaveral Coastal None None > 100mm 6.7yr
FL
Daytona Beach
Coastal
N
S
30.3mm
6.5yr
FL
Tallahassee
Coastal
S
NW
42.9mm
3.2yr
FL
Jacksonville
Coastal NW None
28.0mm
4. lyr
GA
Savannah
Coastal
N
NE
27.8mm
7.lyr
GA
Atlanta
Inland
E
W
45.3mm
12.9yr
GA
Athens
Inland
N
SW
32.9mm
6.8yr
GA
Albany
Inland
NE
SE
44.4mm
7.Oyr
AL
Mobile
Coastal
W
NW
32.2mm
4.3yr
AL
Montgomery
Inland
NE
NE
20.1mm
13.Oyr
AL
Tuscaloosa
Inland
W
NW
26.4mm
6.4yr
AL
Birmingham
Inland
E
None
17.8mm
6.5yr
MS
Landon
Coastal NW
E
> 100mm 12.9yr
MS
Jackson
Inland
None None
12.4mm
2.4yr
MS
Grenada
Inland
None None
22.5mm
4.3yr
MS
Fulton
Inland
SW
E
21.1mm
2.2yr
LA
Baton Rouge
Inland
SE
NW
25.5mm
5.1yr
LA
New Orleans
Coastal
NE
E
53.8mm
6.5yr
LA
Lafayette
Inland
SE
SW
27.7mm
4.1yr
LA
Shreveport
Inland
NW
SW
81.9mm
13.Oyr
TX
Corpus Christi
Coastal NW
NW
36.3mm
13.Oyr
TX
Houston
Inland
SW
S
31.4mm
7.0yr
TX
Waco
Inland None None
11.4mm
6.5yr
TX
Beaumont
Coastal
E
W
> 100mm 12.9yr
TX
Dallas
Inland
SW None
18.0mm
13.Oyr
TX
Fort Worth
Inland None NW
32.5mm
13.Oyr
TX
San Antonio
Inland
SW
NE
> 100mm 13.Oyr
TX
Austin
Inland
NW
E
41.6mm
12.9yr
(a) location of maximum over-deviation from POI; (b) location of maximum under-deviation
from PCI; (c) maximum spread; (d) return period of maximum spread. N = north, NE =
northeast, NW = northwest, etc. for locations of surrounding grid boxes. If "None", this
implies good agreement throughout grid boxes.
Table 3.2 summarizes the analysis of the spatial sensitivity of NEXRAD-II storm
total TC precipitation observations, and emphasizes the highly transient and local
nature of rainfall.
58
3.2
Introducing streamflow measurements as a metric for TCP
This section presents the results of the preliminary work aiming at developing surface
water measurements, particularly streamflow (also referred to as discharge) measurements, to quantify tropical cyclone destructive potential and thereby be used for TC
risk assessment purposes in the same manner as radar precipitation observations and
rain gage precipitation observations. Figures 3-19 through 3-24 present the results
of directly comparing POI NEXRAD-II-based return periods with peak streamflow
measurement-based return periods.
Appendix A contains similar figures for linear
models that exclude the most extreme (by return period) tropical cyclones from the
trends in the fit.
59
Streamflow v. Radar Retuir Periods: Miami
Streamflow v. Radar Retum Periods: Tampa
R-2 -00038
E
E
X
C-4
;
2
4
8
6
USGS streamniw
10
2
12
relir, peWd (y)
10
4
6
8
10
12
USGS streamflow return period (y)
Streamflow v. Radar Return Periods: Cape Canaveral
Streamflow v. Radar Return Periods: Daytona Beach
R-2 -
le-04
I
OD
0
L
8
So
8
AFF.. S
2
4
6
10
0
12
2
pedrod (JO
USGS streamtlow rMW
4
6
8
10
12
USGS streamflow retum period (y)
Streamflow v. Radar Reurm Periods: Talslhasue.
Jacksonville not included
due to Incompleteness of
streamflow measurement
record.
00
C4
2
4
6
a
10
12
Figure 3-20: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data at five locations in Florida: (a)
Miami, (b) Tampa, (c) Cape Canaveral, (d) Daytona Beach, and (e) Tallahassee.
The POI at Jacksonville was excluded from this analysis due to incompleteness of
streamflow record.
Of the Florida POIs, the correlation between streamflow-based and NEXRAD-IIbased observed TC return periods for a single grid box is only significant for Miami,
FL, and Tallahassee, FL (R 2 values of 0.33 and 0.58, respectively). The other three
sites considered show no correlation between return periods calculated from streamflow versus radar. This is likely due to major outliers in the trends. The longest
return period TCs are vastly different between the two measurement techniques; e.g.
60
over the period of record in Tampa, FL, radar-based return periods indicate that
Hurricane Alberto in 2006 was the most severe storm (return period maxed out at
13 years, the length of the period under consideration), whereas streamflow-based
return periods indicated that this hurricane has a return period of only 2.26 years;
conversely, the most severe (max return period 13yr) TC in Tampa over the period
of record based on streamflow measurements was Hurricane Frances in 2004, but this
storm's radar-based return period was only 2.9 years. These vast differences in return
period calculations dramatically skew the linear fit, leading to a near-zero correlation
coefficient.
Streamflow v. Radar Return Periods: Albany
Streamflow v. Radar Return Perdods: Athens
~OO
R~2 - 0,27
E
IX
W
Z
2
4
6
USGS streamow
8
10
12
2
retsM pOdd (y)
4
6
8
10
12
USGS streamflow retum period (y)
Atlanta, Savannah not included due to incompleteness of streamflow record
Figure 3-21: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-I radar data at two locations in Georgia: (a)
Athens, and (b) Albany. The POI at Atlanta and Savannah were excluded from this
analysis due to incompleteness of the streamflow record.
Athens, GA, showed moderately significant correlation (R 2 = 0.427) between
streamflow and the radar precipitation observations for the grid box directly over
the stream site. Albany, GA, showed no correlation (R 2 = 0.011), partially due to
mismatches of the most extreme TCP/streamflow cyclones in this POI's TC record.
In Albany, the radar observations indicated that Hurricane Fay, 2008, was by far
the most severe and uncommon cyclone event, whereas streamflow measurements
indicated that Hurricane Dennis in 2005 was the most extreme cyclone in the period
61
of record.
However, removing these two TCs from the analysis and repeating the
2
linear model fit only improved the correlation to R = 0.08, indicating that this
single grid box's observations are inadequate to explain much of the variability in
streamflow values at this site.
Streamflow v. Radar Return Periods: Montgomery
Streamflow v. Radar Return Porteds: Bumkigham
33 _f
_ Ie __4
E
Go
Lo
c,
to
X
N.V
6
4
2
a
10
2
12
4
6
8
10
12
USGS streamflow reftm pekid tyl
USGS streamfiow return period (y)
Streamflow v. Radar Return Periods Mobile
Streamflow v. Radar Return Periods: Tuscaloosa
W~2
W72 -&,AM
E
0 023
E
aD
X
4
2
6
8
10
2
12
4
6
8
10
12
USGS sireamrfow return period (y)
USGS streamfiow retumn pmod (y)
Figure 3-22: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data at four locations in Alabama: (a)
Birmingham, (b) Montgomery, (c) Mobile, and (d) Tuscaloosa
Of the Alabama POIs, only Birmingham, AL, showed significant correlation for
this model design (R 2 = 0.334). Montgomery, Mobile, and Tuscaloosa, AL, had no
correlation, with R2 values of 0.063, 0.010, and 0.023, respectively. For Montgomery
and Mobile, the lack of correlation is due to extreme TC mismatch between the
datasets; by excluding the two extreme TCs as measured by each dataset, correla2
tion coefficients for these two POI improved to R = 0.362 and 0.546, respectively.
2
Tuscaloosa's lack of correlation did not improve by removing outliers (R only in-
creased to 0.08).
62
Streamflow v. Radar Return Periods: Landon
Streamflow v. Radar Return Perods: Jackson
W2 - 0 IM
I
S
2
4
6
8
10
I
2
12
4
6
8
10
12
USGS strearnIow rek"' pWdod (y)
USGS streamflow return period (y)
Streamflow v. Radar Return Periods: Grenada
Streamflow v. Radar Return Periods: Fulton
R^2 - D.8254
E
LB
X
W
2
4
6
0
10
2
12
4
6
8
10
12
Figure 3-23: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data at four locations in Mississippi:
(a) Jackson, (b) Landon, (c) Grenada, and (d) Fulton
The matchup between the observed TC records in streamflow and radar in Mississippi did comparably quite well. Fulton, MS, showed remarkably high correlation
between these two datasets (R 2 = 0.825).
correlation (R 2 = 0.512).
Grenada, MS, also exhibited significant
Much of the linear fit success for these two sites can be
attributed to the matchup of the most extreme TC for their respective records. Landon, MS, showed mild correlation (R2 = 0.190), but did not improve by excluding
extreme TCs (R 2 decreased to 0.023). Jackson, MS initially showed no correlation
(R 2 = 0.018) between the datasets for the TC record, but improved slightly by excluding outliers (R2 = 0.213).
63
2
4
6
8
10
Baton
4 2-.0016
Streamfnow v. Radar Rettun Pedod.: New Odrens
Streamfnow v. Radar Return Periods:
2
12
4
6
10
8
Rouge
12
USGS streamoew Nrn Veftd (1)
USGS streamflow return period (y)
Streamfnow v. Radar Return Periods: Lafayete
Streamfnow v. Radar Return Periods: Shreveport
02281
R^2 -
00
to
2
4
6
8
10
2
12
USGS streanlow re"au pewd 4y)
4
USGS
6
8
10
12
streamflow return period (y)
Figure 3-24: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data at four locations in Louisiana: (a)
New Orleans, (b) Baton Rouge, (c) Lafayette, and (d) Shreveport
Of the Louisiana POIs in this study, only Shreveport exhibited some correlation
between the TC records for radar versus streamflow (R 2 = 0.228).
Interestingly,
Shreveport is the only inland location considered in Louisiana. The other three sites
in LA were uncorrelated in the initial analysis (New Orleans: R 2 = 0.037, Baton
Rouge: R 2 = -0.017,
and Lafayette: R 2 = 0.030). None of the three sites improved
markedly by excluding outliers.
This indicates a fairly severe lack of correlation
between observed streamflow in the three coastal Louisiana sites. This could possibly
be due to the complex surface hydrology situation created by the Mississippi River
Delta.
64
Streamflow v. Radar Return Periods: Corpus Christi
Streamflow v. Radar Return Periods: Austin
..........
E
~05X
X
2
4
6
10
a
2
12
4
USGS strearniow retum peiod(y
4
6
10
12
USGS streamrfow return period (y)
Streamflow v. Radar Return Periods: Beaumont
Streamflow v. Radar Return Porlode: Fort Worth
'V
8
6
1;;-;*695
C
a
W
8
10
12
2
4
6
8
10
12
USGS streemow return period (y)
USGS streamnow retun perloI ty)
San Antonio, Dallas, Houston, Waco not included due to
incompleteness of streamflow measurement record
Figure 3-25: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data at four locations in Texas: (a)
Austin, (b) Corpus Christi, (c) Fort Worth, and (d) Beaumont. San Antonio, Dallas,
Houston, and Waco were excluded from this analysis due to incompleteness of their
streamflow records.
Correlation between streamflow observations and radar observations in Fort Worth
and Beaumont, TX, were remarkably high (R 2 = 0.714, 0.695, respectively) considering the paucity of intersecting TCs at these locations. Austin and Corpus Christi
showed little to no correlation in the initial analysis (R 2 = 0.053, 0.154, respectively).
Austin, TX, did not improve correlation by excluding outliers (R 2 = 0.05), but Corpus
Christi exhibited great improvement with the abridged linear model (R 2 = 0.844).
3.2.1
Basin-average precipitation v. streamflow measurements
In order to develop a more nuanced picture of the relationship between radar-based
precipitation observations and recorded streamflow measurements on the ground, a
65
basin average TC event precipitation was calculated for the entire TC record for three
of the sites in this study: Athens, GA; Mobile, AL; and Tampa, FL.
Streamflow v. Basin Avg Radar Return Periods: Athens
RA2 = 0.3536
LO
Cq.
0
0
(D
0)
LO
C
T_
00
4
LO
i
2
4
8
6
10
12
USGS streamflow return period (y)
Figure 3-26: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. basin-averaged NEXRAD-II radar data in Athens, GA.
Comparing the basin-averaged rainfall observed in the NEXRAD-II radar dataset
for the entire watershed located around the streamflow measurement site at Athens,
GA, actually resulted in a worsening of the correlation between streamflow-based
TC return periods and radar-based TC return periods for the recorded TCs at this
66
site (R 2 = 0.353 versus R2
-
0.427). This is somewhat unexpected, as we would
expect that including more of the basin features in the radar analysis would better
capture streamflow variability. It is coincidental that a single grid box's precipitation
observations better match a streamflow measurement than those over the whole basin
that feeds into the surface water measurement site.
Streamflow v. Basin Avg Radar Return Periods: Mobile
RA2 =
0.0134
LO
04J
0
C
.C
LO
C
cc
C-
CU
1
2
4
1
1
8
6
10
12
USGS streamflow return period (y)
Figure 3-27: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. basin-averaged NEXRAD-II radar data in Mobile, AL.
Mobile, AL, also exhibited no significant improvement in correlation (R 2
=
0.013
versus R 2 = 0.010) between basin-averaged precipitation and streamflow measure-
67
ments for the TCs in its record than it had when only a single grid box was used.
Again, this is unexpected; because streamflow depends on rainfall over a wide area,
it is surprising that naively averaging rainfall over the entire basin did not result in
any improvement in correlation.
Streamflow v. Basin Avg Radar Return Periods: Tampa
R^2 = 0.2951
0)
CO
LO_
0
CL
0
C
CDJ
CD
V-
C
CU
CO
1
2
4
8
6
10
12
USGS streamflow return period (y)
Figure 3-28: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. basin-averaged NEXRAD-II radar data in Tampa, FL.
Averaging the NEXRAD-II observed precipitation over the basin around the Tampa,
FL measurement site led to a much improved correlation with streamflow measure-
68
ments (R2 = 0.295 versus R2 = 0.004). This is the result we expect based on surface
water dynamics[20].
3.2.2
Cross-correlation function analysis
The following table presents the results of using the cross-correlation function with a
lag time of zero to examine the similarity of the radar-based precipitation TC return
periods and streamflow TC return periods, and the significance of this correlation is
tested at p = 0.05.
Table 3.3: Cross-correlation function analysis results
State
FL
FL
FL
FL
FL
FL
GA
GA
GA
GA
AL
AL
AL
AL
MS
MS
MS
MS
LA
LA
LA
LA
TX
TX
TX
TX
TX
TX
TX
TX
Location name
Miami
Tampa
Cape Canaveral
Daytona Beach
Tallahassee
Jacksonville
Savannah
Atlanta
Athens
Albany
Mobile
Montgomery
Tuscaloosa
Birmingham
Landon
Jackson
Grenada
Fulton
Baton Rouge
New Orleans
Lafayette
Shreveport
Corpus Christi
Houston
Waco
Beaumont
Dallas
Fort Worth
San Antonio
Austin
Significance p=0.05
significant
not significant
not significant
significant
significant
NA
NA
NA
significant
significant
not significant
significant
significant
significant
significant
significant
significant
significant
not significant
not significant
significant
significant
not significant
NA
NA
significant
NA
significant
NA
significant
69
CCF zero lag
0.341
0.170
0.188
0.657
0.864
NA
NA
NA
0.802
0.476
0.057
0.324
0.605
0.759
0.678
0.495
0.840
0.948
0.144
0.023
0.528
0.376
0.029
NA
NA
0.505
NA
0.909
NA
0.558
3.3
Discussion and Conclusions
This thesis contributes to work aimed at evaluating the rainfall algorithm in Emanuel's
[20081 approach to tropical cyclone risk assessment that uses large sets of synthetic
tropical cyclones in order to estimate tropical cyclone climatology that can be used
to estimate risk. This method of TC risk assessment is important because it allows
for the generation of a large number of cyclones from which, given the validity of the
statistics and climatology they produce, TC risk can be more accurately estimated.
Because the synthetic TCs provide greater spatial and temporal resolution of tropical cyclone precipitation risk, it enables the estimation of severe storm events with
extremely long return periods ( > 100 years).
Tropical cyclone precipitation risk estimated using the synthetic TCs was evaluated using 12 years of NEXRAD-II radar observations for sites across the southern
United States, circumscribing the Gulf of Mexico and including both coastal and
inland sites. The metric used to compare synthetic TCP to NEXRAD-II TCP observations is the return period of aggregated storm total precipitation. In most locations,
the synthetic TCP climatology aligned with observations to a very reasonable extent.
Both overestimation and underestimation of the observed TCP record occurred in
roughly equivalent amounts, which suggests a lack of inherent bias in the algorithm
with respect to creating too much or too little rainfall for a given TC. There appeared
to be some degree of spatial dependence on tendencies of the synthetic TC climatology
to over- or underestimate TCP risk: sites on the western side of the Gulf of Mexico
exhibited greater instances of synthetic TCP inaccuracy (Table 3.1). Of the inland
sites, a majority exhibited synthetic TCP inaccuracy; of the coastal sites, fewer than
half were over- or under-estimated. Therefore, the synthetic rainfall algorithm as it
stands is more successful at reproducing observed TC climatology on the coast.
Some of the spatial dependencies of the synthetic rainfall algorithm's ability to
generate valid TCP trends for a given point of interest are due to insufficiencies in the
observed TC record at that POI. Agreement between the two methods is influenced
by scarcity of the TC record, so agreement is stronger at coastal locations.
70
This
implies that, once a careful synthetic TC climatology is produced for inland locations
(by refining the the rainfall algorithm in these areas), the synthetic approach for
estimating TCP risk could be a critical tool in developing accurate risk assessments
for inland locations, since the observational record in these areas is sparse.
The locations in this study that exhibited the most extreme TCP risk in both the
synthetic estimation and observational record are Miami, FL; Tampa, FL; Tallahassee,
FL;, Landon, MS; and New Orleans, LA. All of these POIs are considered coastal. The
larger regions with widespread high TCP risk according to synthetic climatology are
the Florida peninsula, southern Mississippi and Louisiana, and southeastern Texas.
These assessments from the synthetic TC climatology align with previous analyses of
TC risk in the United States [10, 30].
The extreme local variability of precipitation was also investigated in this thesis,
via the evaluation of radar-based TCP return periods for each POI grid box and
its eight adjacent grid boxes, each of which covering an area of ~ 25km2 .
This
is an important avenue of research because of the dependence of flood hazards on
precipitation over a wide area.
The high degree of variability between grid boxes
make wide area total event precipitation difficult to predict. My work showed that
coastal locations typically have greater variability in event TCP at grid box scale than
inland locations. The most dramatic instances of event TCP variability (evidenced
by wide spread between return period/total rainfall amounts between adjacent grid
boxes) primarily occurred for TCs with return period longer than 8 years, which can
be considered the most extreme events in the 13 year record used for this study.
Finally, I began the work of incorporating surface water streamflow measurements
as a method for assessing TC risk in the southern United States. The viability of
this method was explored by examining the correlation between radar observations
of event TCP and maximum streamflow observed over the event TC dates for a given
tropical cyclone. Some sites showed mild correlation between these two metrics, but
on the whole, precipitation calculated at just a single grid box failed to fully capture
the streamflow dynamics observed in the period of record. To attempt to improve
the correlation, basin-average event TCP for each intersecting cyclone was calculated
71
at three different POI, and this value was compared to streamflow measurements.
This led to moderate improvement of the correlation between radar observations and
streamflow measurements in some locations, but unexpectedly worsened the correlation at others.
The cross-correlation function analysis showed better similarity
between the streamflow TC return periods and the NEXRAD-II TC return periods
than did the linear model analysis. All but 5 POIs showed significant correlations
between the two datasets with a lag time of zero.
There are a great many more
variables at play in generating surface streamfiow, and much more work remains to
be done in this vein before streamflow estimates can be used to assess TC risk in the
synthetic method. Future work should consist of developing a means to drive a surface
hydrological model using rainfall estimates produced by the synthetic algorithm. The
hydrology model can then produce streamflow estimates, the statistics of which can
be compared to the observational record. An advantage of this method over radarbased comparisons would be that the streamflow record is much longer, allowing for
the risk of greater magnitude and longer return period events to be assessed. One disadvantage, however, is the decreased spatial resolution of streamflow measurements;
though, since characteristics and precipitation of the whole basin/watershed must be
considered in a hydrological model that produces streamflow estimates, this issue may
be found to be minimal.
72
Appendix A
Truncated TC records: correlation
with streamflow records
This appendix contains the figures for the secondary analysis that compares streamflow TC return period measurements to radar TCP return period measurements for
single grid boxes, while excluding the most extreme TCs in the record for each POI.
73
Streamflow v. Radar Return Periods: Miami
0 1925
RI2
R-2
=0
Streamflow v. Radar Return Periods: Tampa
Z23
E
X
2
1
4
5
streamrifow rekim period (y)
1
3
USGS
USGS
-
3
4
Streamflow
return period (y)
5
6
Streamflow v. Radar Return Periods: Daytona Beach
Streamfiow v. Radar Return Periods: Cape Canwveral
R-2
2
Ri2 -0441
0,0814
I
j
1
2
3
4
5
1
6
USGS streamfow rekum period tyt
2
3
4
5
6
USGS streamflow returm period (y)
Streamflow v. Radar Return Periods Tlahaasee
R^2 -0 0066
Of-
1
Jacksonville, FL, not
included in this analysis
due to incompleteness of
streamflow record
2
3
4
5
6
USGS streamfiow return period (y)
Figure A-1: Linear correlation of 2002-2013 TCP return periods as measured by USGS
streamflow data v. NEXRAD-I radar data, excluding the most extreme TCs by each
dataset, at five locations in Florida: (a) Miami, (b) Tampa, (c) Cape Canaveral, (d)
Daytona Beach, and (e) Tallahassee. The POI at Jacksonville was excluded from this
analysis due to incompleteness of streamflow record.
74
Streamflow v. Radar Return Periods: Athens
Streamflow v. Radar Return Periods: Albany
2 0.1534
R2________________________-
15
2.0
25
3.0
35
40
45
1
USGS streamflow return period (y)
2
3
4
5
6
USGS streamflow return period (y)
Atlanta, Savannah, GA not included in this analysis due to
incompleteness of streamflow records.
Figure A-2: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data, excluding the most extreme TCs
by each dataset, at two locations in Georgia: (a) Athens, and (b) Albany. The POI
at Atlanta and Savannah were excluded from this analysis due to incompleteness of
the streamflow record.
75
Stainfmow v. Radar Return Periods: Montgomery
Streamflow v. Radar Return Periods: SBiiOnsarw
RIW
0 7805
ff
X
4J
2
3
EL.
2
3
4
5
5
6
Sirsamifow v. Radar Return Periods: Tuscaloosa
5359
E
1
4
USGS streamnfow return period (y)
Strearnflow v. Radar Return Pereds: 1Me
2 .0
3
2
4
USGS streamliw retun ped (y)
______
9*2 .40X
E
2
6
3
4
5
6
USGS streamflow return period (y)
USGS streamlow return period (Y)
Figure A-3: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data, excluding the most extreme TCs
by each dataset, at four locations in Alabama: (a) Birmingham, (b) Montgomery, (c)
Mobile, and (d) Tuscaloosa.
76
Streamflow v. Radar Return Periods: Jackson
W2 - 01125
Streamflow v. Radar Return Periods: Landon
W2 0 02
I
2
1
3
4
5
6
2
1
USGS strearnfow return period (y)
-
0 0346
5
4
Streamnflow retumn verwo
Strearnflow v. Radar
Streamfiow v. Radar Return Periods: Grenada
RV
3
USGS
6
MV
Return Periods: Fufton
a
I
2
3
USGS
4
streamfiow return
5
6
2
3
4
5
a
USGS strearmftow return period (y)
period (y)
Figure A-4: Linear correlation of 2002-2013 TCP return periods as measured by USGS
streamflow data v. NEXRAD-II radar data, excluding the most extreme TCs by each
dataset, at four locations in Mississippi: (a) Jackson, (b) Landon, (c) Grenada, and
(d) Fulton.
77
Streamnflow
v. Radar Return Periods: Ilew Orkwons
Streamfiow v. Radar Return Periods: Baton Rouge
R^1 - 0 0894
R*2 z 00
IL
E
X
I
2
1
3
USGS
4
5
6
2
-
1
5
streamfiow retum period (y)
Streamflow v. Radar Return Periods: Shreveport
0 338
R^2
Streamflow v. Radar Return Period: Lafayette
R^2
4
3
USGS
streamfow retum periad (y)
0.0017
I
I
I
I :1
2
3
USGS
4
5
2,0
6
2.5
3.0
3-5
USGS streamflow return period (y)
streamaiow retumn peiod (y)
Figure A-5: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data, excluding the most extreme TCs
by each dataset, at four locations in Louisiana: (a) New Orleans, (b) Baton Rouge,
(c) Lafayette, and (d) Shreveport.
78
Strearnflow v.
R^2
II
Streamfilow v. Radar Return Periods: Corpus Christi
Radar Return Periods: Austin
0 0784
RI2
- DU442
I.
431*
Ni
6Q
,
,
,
i
-
2
3
4
5
6
2
3
4
5
S
USGS streamflow retum period (y)
USGS streamflow return period (y)
Streamflow v. Radar Return Periods: Fact Woeth
Streamflow v. Radar Return Periods: Beaumont
RI2 - 0.0061
I
I
I
3
2
4
USGS streamfow retun period (y)
3
4
5
6
USGS streamftow retum period (y)
Figure A-6: Linear correlation of 2002-2013 TCP return periods as measured by
USGS streamflow data v. NEXRAD-II radar data, excluding the most extreme TCs
by each dataset, at four locations in Texas: (a) Austin, (b) Corpus Christi, (c) Fort
Worth, and (d) Beaumont. San Antonio, Dallas, Houston, and Waco were excluded
from this analysis due to incompleteness of their streamflow records.
79
80
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