JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 8842–8856, doi:10.1002/jgrd.50663, 2013
Seasonal tropical cyclone precipitation in Texas: A statistical
modeling approach based on a 60 year climatology
Laiyin Zhu,1 Oliver W. Frauenfeld,1 and Steven M. Quiring 1
Received 25 April 2013; revised 25 June 2013; accepted 18 July 2013; published 22 August 2013.
[1] Sixty years of tropical cyclone precipitation (TCP) in Texas has been analyzed because
of its importance in extreme hydrologic events and the hydrologic budget. We developed
multiple linear regression models to provide seasonal forecasts for annual TCP, TCP’s
contribution (percentage) to total precipitation, and the number of TCP days in Texas. The
regression models are based on three or fewer predictors with model fits ranging from 0.18
to 0.43 (R2) and cross-validation accuracy of 0.05–0.36 (R2). La Niña exhibits the most
important control on TCP in Texas. It is the major driver in our models and acts to reduce the
vertical shear in the Caribbean and the tropical Atlantic, thereby generating more
precipitating storms in Texas. Lower maximum potential velocity, the theoretical maximum
wind speed that storms can attain, in the Gulf of Mexico, and low-level vorticity in the
Atlantic hurricane main development region increased the modeled R2 by 20% or more.
Both variables have negative coefficients in the TCP models. Lower maximum potential
velocity and vorticity are associated with tropical cyclones with lower maximum wind
speed and slower translation speed. Such weak TCs produce the majority of TCP and
extreme TCP events in Texas. The quartiles of the TCs with strongest maximum wind speed
and fastest translation speed are not associated with the largest mean daily precipitation
based on observations in Texas. We have also shown that sea level pressure in the Gulf of
Mexico, sea surface temperature in the Caribbean, and the North Atlantic Oscillation are
potentially important predictors of seasonal TCP in Texas.
Citation: Zhu, L., O. W. Frauenfeld, and S. M. Quiring (2013), Seasonal tropical cyclone precipitation in Texas: A statistical
modeling approach based on a 60 year climatology, J. Geophys. Res. Atmos., 118, 8842–8856, doi:10.1002/jgrd.50663.
1.
Introduction
[2] Tropical cyclones (TCs) are a big threat to the Atlantic
and Gulf of Mexico coastlines in the United States. They
can cause loss of life and major economic damage due to
storm surge, strong winds, and inland flooding [Pielke and
Landsea, 1998; Landsea et al., 1999; Pielke and Landsea,
1999; Villarini and Smith, 2010; Emanuel, 2011]. Pielke
et al. [2008] demonstrated that storms from 1996 to 2005
caused the second-most damage related to TCs over the past
11 decades. In addition, hurricanes have cost the U.S. $150
billion during 2004 and 2005 seasons combined. The risk
of TC disasters has the potential to increase in the future
because TC systems are closely connected with global and
regional oceanic and atmospheric conditions. Observations
and models show a recent increase in TC destructiveness
and the number of intense TCs and predict this trend will
keep increasing in the future if the global sea surface
This article is a companion to L. Zhu and S. M. Quiring [2013]
doi:10.1029/2012JD018554.
1
Department of Geography, Texas A&M University, College Station,
Texas, USA.
Corresponding author: L. Zhu, TAMU 3147, Department of Geography,
Texas A&M University, College Station, TX 77843-3147, USA.
([email protected])
©2013. American Geophysical Union. All Rights Reserved.
2169-897X/13/10.1002/jgrd.50663
temperature (SST) continues to rise [Knutson et al., 1998;
Knutson and Tuleya, 2004; Emanuel, 2005; Oouchi et al.,
2006; Shepherd and Knutson, 2007; Knutson et al., 2010].
The relationship between tropical cyclone frequency and
climate change is a question under debate. There are studies
showing an increasing trend in the number of TCs in the
North Atlantic after 1950 [Henderson-Sellers et al., 1998;
Holland and Webster, 2007] and its association with the
increased basin wide SST [Goldenberg et al., 2001;
Holland and Webster, 2007; Vecchi et al., 2008]. On the
other hand, a contradictory view is that the recent increase
in TC activity is due to natural variability [Landsea et al.,
2006] or improvements in observing practices [HendersonSellers et al., 1998]. Some model simulations predict a global
and regional decrease in the overall frequency of TCs in the
21st century due to warming conditions [Knutson and
Tuleya, 2004; Bender et al., 2010; Knutson et al., 2010].
[3] Compared with research about TC frequency and
intensity, there are fewer studies focused on long-term TC
precipitation (TCP) on land and its relationship with different
oceanic and atmospheric forcings. This is mainly because the
TCP climatology includes nearly all information about TC
genesis, track, frequency, and structure. But there is a lack of
accurate long-term records. TCP is a complex process and
highly variable from event to event [Rodgers et al., 1994a;
Rogers et al., 2003; Villarini et al., 2011a]. Several studies
reported recent increases in both annual TCP (ATCP) and its
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ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
contribution to annual/extreme precipitation based on observations in the Atlantic and the U.S. coast [Lau et al., 2008;
Knight and Davis, 2009; Kunkel et al., 2010; Nogueira and
Keim, 2010]. Some studies also demonstrated that ATCP in
the Atlantic is connected to the El Niño-Southern Oscillation
(ENSO) [Rodgers et al., 2001], the North Atlantic Oscillation
(NAO), and the Atlantic Multidecadal Oscillation (AMO)
[Nogueira and Keim, 2010; Maxwell et al., 2012].
[4] While complexities exist in predicting both long-term
trends and high-frequency dynamics of TC systems, some
statistical models have good skill in forecasting seasonal
TC frequency. Seasonal forecasting of TC frequency in the
Atlantic by using multiple linear regression models has been
performed for decades [Gray, 1984a; 1984b]. ENSO, the
Pacific Decadal Oscillation (PDO), Quasi-Biennial Oscillation
(QBO), and West African rainfall were found to be important
variables for explaining seasonal variations in TC counts
in the Atlantic [Gray, 1984b; Gray et al., 1993, 1994;
Klotzbach and Gray, 2003]. Poisson series models have
also been applied in forecasting seasonal TC counts [Elsner
and Schmertmann, 1993; Elsner and Jagger, 2004, 2006;
Villarini et al., 2011b] because they potentially better fit the
distribution of hurricane variability.
[5] Although heavy precipitation is an important feature of
landfalling TCs [Konrad, 2001; Nielsen-Gammon et al.,
2005; Konrad and Perry, 2010; Barlow, 2011] and plays a
considerable role in both the hydrological budget and
extremes, few studies have constructed statistical models to
forecast seasonal TCP amount for the U.S. This is mainly
because the difficulties in accurately forecasting/modeling
TCP events and the lack of an accurate long-term records
of TCP. The characteristics and dynamics of a single TC
are highly complex, and TCP varies considerably from TC
to TC [Rodgers et al., 1994a; Rogers et al., 2003; Villarini
et al., 2011a]. Thus, it is more reasonable to establish statistical relationships between seasonal TCP at varying spatial
scales and based on different climatic and oceanic forcings.
[6] Texas is a state large in size and located on the western
side of the Gulf of Mexico; therefore, it is frequently
impacted by damaging TCs [Keim and Muller, 2007; Islam
et al., 2009]. A 60 year TCP climatology of Texas [Zhu and
Quiring, 2013] showed that TCP is a major contributor
to total and extreme precipitation in Texas and has caused
severe damage by inland flooding (e.g., tropical storm Alison,
2001 and Hurricane Ike, 2008).
[7] In this study, we will construct and evaluate a variety of
statistical models of TCP by employing a comprehensive
suite of forcing variables and climate indices at a variety of
spatial scales. Virtually all previous studies have centered
on predicting the frequency or intensity of TCs and have
focused on large scales. Instead, this study will focus on
one of the important impacts of TCs—their resulting
precipitation—and will identify the factors and processes
that control the seasonal TCP variations in Texas at the
regional scale at a number of temporal lags. We expect to
find that many of the same variables that have previously
been found to impact TCs at larger scales to also be important
in affecting TCP. However, we also expect to uncover variables that are specific to regional processes, and to TCP in
Texas. Those variables will be evaluated statistically, and
we will seek to establish their physical mechanisms based
on observations.
2.
Data and Methods
2.1. Dependent Variables
[8] Our TCP information is derived from the cooperative
(COOP) observation network operated by the National
Climatic Data Center. There are 1358 COOP stations in
Texas, but most of them do not have a complete record. We
therefore used only those 220 stations with 100% complete
daily precipitation records for the entire 60 year period
(1950–2009). This subset guarantees our models will not be
biased by any temporal inconsistencies. We used the 6 h
interval best track data of the Atlantic basin hurricane
database (HURDAT) from the National Hurricane Center to
record the daily TC positions. It should be noted that our use
of 1950–2009 is necessitated by a lack of reliable records of
precipitation, climatic/oceanic forcing variables, and hurricane
tracks prior to 1950 [Henderson-Sellers et al., 1998; Kunkel
et al., 1999; Landsea et al., 2006]. All tropical disturbances,
depressions, storms, and category 1–5 hurricanes are included
if they made landfall on the coast of Texas or passed within
500 km of the state line (including both landfalling and
nonlandfalling TCs). We chose this 500 km buffer distance
based on previous studies [Knight and Davis, 2009; Kunkel
et al., 2010]. A TCP day is defined here as a 24 h interval
between 11:59 pm CST (day 1) to 11:59 am CST (day 0)
when a storm passed through or near Texas. We reorganized
the time period because most COOP gages record precipitation in the morning. Therefore, we considered the TC
positions at 1:00 pm (day 1), 7:00 pm (day 1), 1:00 am
(day 0), and 7:00 am (day 0) CST to be part of the TCP day.
A moving boundary was generated for each TCP day by
connecting the radius of the outermost isobar (ROCI) corresponding to the four daily TC positions. All stations falling
within that boundary were considered to be contributing to
TCP that day. Thus, every TCP day is treated individually to
ensure the maximum selection accuracy. This methodology
is referred to as the moving ROCI buffer technique, and it is
described in more detail in Zhu and Quiring [2013]. Inverse
distance weighting [Shepard, 1968; Watson and Philip,
1985] was used to interpolate the station-based TCP data into
1233 0.25° × 0.25° (~28 km × 28 km) grids in Texas.
[9] Three dependent variables have been calculated to
describe the seasonal TCP in Texas. The ATCP is calculated
by summing the TCP within each grid cell throughout a
hurricane season and then averaging all grids with nonzero
seasonal TCP. This variable provides information about the
average amount of TCP in Texas within a year. The second
variable is the TCP percentage (TCP%). It utilizes the ratio
of seasonal TCP to total annual precipitation for each rain
gauge station and then averages the percentages for all
stations with nonzero seasonal TCP. The annual TCP events
(TCPE) variable summarizes the number of days with TCP in
Texas. All the dependent variables are kept in their original
units for the subsequent model evaluations.
2.2. Independent Variables
[10] The original NCEP/NCAR reanalysis [Kalnay et al.,
1996] provides global atmospheric and oceanic variables from
1948 to present. We downloaded the data from http://www.
esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html at
the 2° resolution and daily time step. Different potential
independent variables were derived from this data source.
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Table 1. Description of Spatial Averaging Areas
Abbreviation
NAT
NINO34
NINO3
NINO4
MDR
WMD and EMD
GMX
WGM and EGM
CAR
WCA and ECA
TEX
Description, Unit, and Domain
Domain
North Atlantic Ocean (100°W to 2.5°W, 0°N to 30°N)
Niño 3.4 (170°W to 120°W, 5°S to 5°N)
Niño 3 (150°W to 90°W, 5°S to 5°N)
Niño 4 (160°E to 150°W, 5°S to 5°N)
Atlantic Main Development Region (85°W to 20°W, 10°N to 20°N)
Western MDR and Eastern MDR, based on dividing the MDR into these two subregions at 52°W
Gulf of Mexico (95°W to 80°W, 20°N to 30°N)
Western GMX and Eastern GMX, based on dividing the GMX into two subregions at 87.5°W
Caribbean (87°W to 61°W, 9.5°N to 21.5°N)
Western CAR and Eastern CAR, based on dividing the CAR into two subregions at 74°W
Texas (94.5°W to 107°W, 25.5°N to 36.5°N)
Regional
Global
Global
Global
Regional
Regional
Regional
Regional
Regional
Regional
Local
Several climate indices were also obtained from the NCEP
Climate Prediction Center (http://www.cpc.ncep.noaa.gov/
data/indices/). The different spatial domains used to average
the predictors are defined in Table 1. Four time periods (1, 3,
6, and 12 months before the hurricane season) were used for
the temporal averaging, indicated as MAY (May), MAM
(March to May), DJFMAM (December of previous year to
May), and June of previous year to May. The independent
variables (Table 2) can be classified into global, regional,
and local predictors according to the spatial domain used
for averaging. A number of different regions in the oceans
were defined including the North Atlantic, main development
region (MDR), Caribbean, and Gulf of Mexico (Figure 1).
All possible spatial and temporal combinations of variables
that may influence the frequency and characteristics of TCs
(e.g., size, intensity, and translation speed) were considered,
resulting in a total of 400 potential predictors.
[11] The global scale predictors include indices representing
signals of ENSO, Sahel precipitation index, NAO, QBO,
PDO, and Arctic Oscillation (AO). ENSO influences the
global circulation and vertical shear in the Atlantic; therefore,
a variety of different measures of ENSO are included. These
include SST and relative SST (RSST) for the Niño 3, Niño
4, and Niño 3.4 regions in the Pacific, and the Southern
Oscillation Index (SOI). The Niño RSST was calculated by
taking the differences between the average SST in each of
the three Niño regions and the global tropical ocean. This
Niño RSST is based on the concept of Atlantic RSST defined
by Vecchi et al. [2008] and shares similar information as the
original Niño SST. The Sahel precipitation index is a standardized measure describing the rainfall in the Sahel region of west
Africa (http://jisao.washington.edu/data/sahel/), which affects
the TC genesis in the Atlantic [Goldenberg and Shapiro,
1996]. The NAO describes the sea level pressure (SLP) differences in the North Atlantic and influences hurricane tracks in
the North Atlantic [Elsner and Kocher, 2000; Kossin et al.,
2010]. The QBO is the quasi-biennial oscillation of upperlevel winds and was found to be highly correlated with
Atlantic hurricane activity [Gray, 1984a]. However, the relationship is now under debate because of its disappearance after
the 1990s [Camargo and Sobel, 2010]. The PDO is an
interdecadal SST pattern in the Pacific that can intensify
(attenuate) ENSO’s influence on Atlantic hurricane activity
when both patterns are in (out of) phase [Klotzbach and
Gray, 2003]. The AO influences the general circulation pattern and thus potentially the landfalling TCs in the Atlantic
[Larson et al., 2005].
[12] The regional variables consist of basic oceanic and
atmospheric variables and additional advanced variables
derived from them. SST is considered to be the most
important driver of TC activity because it is strongly related
to the genesis, track, and intensity of TCs [Gray, 1984b;
Emanuel, 1991]. The Atlantic RSST is defined as the SST
difference between the North Atlantic and the tropical mean
Table 2. Description of Potential Predictors Used in the Statistical Modeling
Abbreviation
Description and Unit
Predictor
Property
Usage in Model
ATP
SHUM
RHUM
SOM
SLP
U & V WIND
PREW
SST
RSST
Air temperature at the surface (°C)
Specific humidity (kg/kg)
Relative humidity (%)
Soil moisture (mm)
Sea level pressure (hPa)
Zonal wind and meridional wind (m/s)
2
Precipitable water (kg/m )
Sea surface temperature (°C)
Relative SST, difference between the target region SST
and tropical SST (°C)
850–200 hPa vertical shear (kt)
5
1
850 hPa vertical vorticity (× 10 s )
Maximum potential wind velocity (m/s)
Sahel Rainfall Index (unitless)
Southern Oscillation Index (unitless)
North Atlantic Oscillation (unitless)
Quasi-Biennial Oscillation (unitless)
Pacific Decadal Oscillation (unitless)
Arctic Oscillation (unitless)
Local
Local
Local
Local
Local, Regional
Local
Local
Regional, Global
Regional, Global
Basic
Basic
Basic
Basic
Basic
Basic
Basic
Basic
Basic
c
c
c
c
c,s
c
c
c,s,ss
c,s,ss
Regional
Regional
Regional
Global
Global
Global
Global
Global
Global
Basic
Advanced
Advanced
Basic
Basic
Basic
Basic
Basic
Basic
c,s
c
c
c, s, ss
c, s, ss
c, s, ss
c, s, ss
c, s, ss
c, s, ss
VSHR
VOR
MPV
SAPI
SOI
NAO
QBO
PDO
AO
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ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Figure 1. Spatial domains for all potential independent variables used in Table 1.
(30°N–30°S). There is a strong relationship between North
Atlantic RSST and the TC frequency in that basin [Vecchi
et al., 2008]. This original Atlantic RSST and RSST of the
other spatial averaging domains will be used as potential
predictors. Vertical shear is another important predictor
because reduced vertical shear is associated with enhanced
TC activity [DeMaria, 1996; Vecchi and Soden, 2007].
Vertical shear is calculated as the difference in the wind
speed between pressure levels at 200 mb and 850 mb.
Vorticity is a numerical description for the rotational characteristics of atmospheric movements [Hoskins et al., 1985].
Low-level vorticity may influence TCs’ destructive power
(related to the maximum wind speed) [Emanuel, 2007] and
the track [Flatau et al., 1994; Emanuel, 2003]. The TC vortices can alter their environmental vorticity distribution and induce a poleward and westward drift of the TC [Davies, 1948;
Rossby, 1949]. The background vorticity can interact with vertical shears and produce beta gyres with profound influences
on TC tracks [Shapiro, 1992; Wu and Emanuel, 1995; Smith
et al., 2000]. Low-level vorticity is frequently used in seasonal
TC genesis prediction [Camargo et al., 2009; Belanger et al.,
2010] and the power dissipation index estimation [Emanuel,
2005, 2007]. Here we use the low-level (850 mb) background
vorticity, averaged within each spatial domain. Maximum
potential velocity (MPV) has also been included because it
describes the theoretical maximum wind speed that storms
can attain [Emanuel, 1995; Holland, 1997]. It is calculated
from the interactions between SST and atmospheric profiles.
The Emanuel [1995] version of MPV in wind speed is used
in this study. A TC system is characterized by a low-pressure
convection center [Landsea et al., 1999]; therefore, SLP was
used in many seasonal TC count forecasting models and is
thus also included here.
[13] Since TCs can interact with the land surface after landfall, we evaluate local predictors including air temperature,
specific and relative humidity, precipitable water, and soil
moisture in Texas before the hurricane season [Bosart
et al., 2000; Wu et al., 2006; Matyas, 2008]. SLP and zonal
and meridional winds have also been included as potential
predictors since they may impact the movement and duration
of TCs. All local variables are averaged over Texas, and all
independent variables are standardized into z-scores [e.g.,
Frauenfeld et al., 2011] for subsequent use in the model
development. The z-scores are calculated as the difference
between individual samples and the sample mean divided
by the sample standard deviation.
2.3. Model Development
[14] Many different types of statistical models have been
employed for modeling TC activity. Linear models are used
in many studies for forecasting of seasonal TC counts [Gray,
1984a; Gray et al., 1993; 1994; Klotzbach and Gray, 2003]
and TC size [Quiring et al., 2011]. However, linear regression
model requires the response variables to be normally distributed, which is sometimes not the case for TC data sets.
Nonlinear models, such as Poisson series and regression trees,
have also successfully been applied in several TC modeling
studies. For example, Poisson models were used to predict
TC frequency and intensity [Jagger and Elsner, 2006;
Villarini et al., 2010] because of their ability in fitting extreme
value distributions such as hurricane occurrence. Regression
tree models have no prerequisites regarding the distribution
of data and sometime have very good predictive skills.
Konrad and Perry [2010] used a regression tree model to
describe impacts of TC characteristics (speed of movement,
size, and strength) and the synoptic features on the amount
of TCP from individual storms in the Carolina region.
[15] Both the linear and Poisson series models have been
tested for this study. This approach produced very similar
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ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Figure 2. Probability of ATCP, TCP%, and TCPE compared with probability of their associated normal distribution
(normalized to fit in the same scale).
predictive skills with same number of independent variables.
Regression tree models were also evaluated and were found
to yield better fits, but the models were very complex with
many independent variables. Pruning the regression trees
into physically meaningful interpretable models with fewer
predictors (~3) reduced the predictive skill significantly,
resulting in worse skill than the linear and Poisson series
models. In this article, we therefore only present the results
from the linear models because of their simpler structure
and the better interpretability regarding the underlying
physical mechanisms of the model parameters. It should be
noted that our data are normally distributed (Figure 2),
supporting this linear approach.
[16] The three response variables selected for this study are
the ATCP, TCP%, and TCPE. Because there are 400 potential predictors, a data mining approach was adopted to select
the most appropriate combinations of variables. Three classes of models (red, green, and blue lines, Figure 3) have been
constructed for each of the three TCP response variables
(Figures 3a, 3b, and 3c): one type of comprehensive model,
and two types of simple models. The model names are abbreviated with “n,” followed by the number indicating the group
of models (response variables), followed by an alphabetic
letter representing the class of model. For example, model
“n1c” is the first group of models for the ATCP (n1), and is
a comprehensive (“c”) type. The comprehensive models
(“c,” red line in Figure 3) are constructed based on considering all 400 variables as potential predictors (Table 2). The
independent variables are separated into basic and advanced.
The simple models are based on basic, well-established
predictor variables [Gray, 1984a; Gray et al., 1994; Elsner
and Jagger, 2006]. Those basic variables are directly observed
scalars and vectors (e.g., temperature, pressure, humidity,
wind speed, etc.). Two advanced variables are calculated
to represent dynamic interactions of the atmosphere (e.g.,
MPV) and the earth (vorticity) and are only included in the
comprehensive models. Two types of simple models were
considered for each dependent TCP metric: “s” models (green
line, Figure 3), based on one regional variable (shown in last
column, Table 2; e.g., SLP) and one global-scale signal (e.g.,
ENSO). Finally, “ss” models (blue line, Figure 3) are based
on only global-scale variables (shown in last column,
Table 2; e.g., NAO plus ENSO).
[17] We used the “leaps” function (freely available from
the R statistical package), which applies an efficient
branch-and-bound algorithm [Miller, 2002] to select variables that best fit the regression model. The rationale is to
exhaustively search combinations of variables attaining the
largest adjusted R2 for each model. The “c” series models
have a pool of 400 potential variables for selection; the “s”
models have 208 potential variables; the “ss” models have
48 potential variables. During the selection process, the physical meaning of the predictors was also taken into account.
Gray [1984b] used four or fewer predictors in his multiple
linear models for seasonal forecasts of Atlantic TC frequency.
Those seasonal forecast models have evolved over the years
to even fewer numbers of predictors [Klotzbach and Gray,
2003; Klotzbach, 2007]. In a more recent study, Klotzbach
[2008] constructed seasonal TC frequency models based on
three or fewer variables. Quiring et al. [2011] used two or
fewer variables to fit models for TC sizes in different basins.
We therefore allow a maximum of three independent variables,
to avoid overfitting and to obtain parsimonious relationships,
allowing us to better ascribe physical meanings to the final
models. The models were evaluated based on both statistical
performance and physical interpretations. Goodness of fit was
determined by calculating both modeled and cross-validation
(CV) mean absolute error (MAE), R2, and adjusted R2. The
Akaike information criterion (AIC) and Bayesian information
criterion (BIC) were also evaluated for each model. Finally, a
leave-one-out CV [Gray et al., 1992] was applied for all
selected models to verify their stability and predictive skill.
3.
Model Comparison
[18] Table 3 shows that the independent variables in most
of the models are statistically significant (P-values) at the
95%-level. The t-statistic is calculated as the coefficient
divided by the standard error. Most of the p-values in our
models are less than 0.05 if the corresponding t-statistic is
compared with values in the Student’s t distribution. Model
accuracy and CV statistics are shown in Tables 4a–4c. For
the leave-one-out CV approach, one of the 60 years’ observations was always left out and predicted based on the
remaining observations. This resulting set of CV estimations
was then compared to the true observations using MAE, R2,
and adjusted R2. AIC and BIC were also calculated to
compare penalty scores for the number of parameters in the
different models.
[19] The ATCP model n1c achieves the best skill of all
nine models, with an R2 of 0.43. Although the TCPE model
n3c has a relatively low R2 (0.32), it has the best CV accuracy
in terms of its mean CV MAE (47.6% of the observed mean).
In fact, the TCPE models are the most stable of the three TCP
metrics (with CV MAE <50% of the observed mean). The
models for the ATCP are most unstable in terms of their
CV MAE (52.7% to 73.3% of the observed mean). The R2
improves significantly from the simple models to the
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ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Figure 3. Observed and modeled TCP: a. ATCP (models with n1), b. TCP% (models with n2), c. TCPE
(models with n3). The black line is the observations, the red line is for the comprehensive model (“c”), and
the green and blue represent two simple models (“s” and “ss”).
comprehensive models for ATCP and TCP%, with ~0.20
larger R2. The comprehensive models have better fits than
the simple models in years with extreme values (1961 and
1979 in Figures 3a and 3b). In contrast, the comprehensive
TCPE models are not much better (<0.05 in R2) compared
to the simple models.
[20] The n1c model stands out as the best model for ATCP.
It has a better fit and predictive skill than the other simple
models in the same group (~7 mm less model/CV MAE,
>0.20 more model/CV R2). The n1c model also exhibits less
overfitting than n1s and n1ss based on the lower AIC (~18)
and BIC values (~20). Models n1s and n1ss have a much
smaller CV R2 (0.11 and 0.05) than the modeled R2 (0.18
and 0.18). The n1ss model has a negative CV minimum
( 438.7), which indicates potential overfitting and/or instability in that model when predicting the left-out years.
[21] TCP% combines information from both the seasonal
and total annual precipitation amount. The comprehensive
model (n2c) again shows the best fit, stability, and predictive
skill. The n2c is ~0.20 higher in model/CV R2 and ~6%
higher in model/CV MAE. The AIC and BIC show that the
n2c also exhibits the least overfitting compared to the two
simple models in the same group. However, the comprehensive and simple models show less difference in terms of the
model versus CV statistics (MAE, R2, and adjusted R2).
Models n2s and n2ss have less skill in fitting extreme
years (Figure 3b).
[22] TCPE represents how many TCs have generated precipitation in Texas every year. The two-predictor models
(n3c) have reduced fitting skills when compared to the threepredictor comprehensive models (n1c and n2c), but they have
simpler model structure. The n3c shows a slightly bigger
model/CV R2 (~0.05), slightly less model/CV MAE (~1%),
and close AIC and BIC values when compared with the two
simple models (n3s and n3ss). The n3ss has ~1% model/CV
MAE than the n3c. The n3c is still the group’s best model,
but the difference between it and the other models is trivial.
4.
Physical Interpretations of Signals in Models
[23] Seasonal TCP in Texas is a complex function of many
interacting factors. However, the complex information can be
divided into two basic parts. One is how many TCs have generated precipitation in Texas in each season. This information
8847
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Table 3. Model Parameters and Coefficientsa
Dependent Variable
ATCP
Model Name
Parameters
Coefficient
t-Statistic
Significance (P-Value)
n1c
CONSTANT
MAY_VOR_MDR
DJFMAM_MPV_GMX
MAM_SOI
CONSTANT
MAY_SLP_GMX
MAY_RSST_NINO34
CONSTANT
DJFMAM_SST_NINO4
MAY_RSST_NINO34
CONSTANT
MAY_VOR_MDR
DJFMAM_MPV_GMX
MAY_SOI
CONSTANT
DJFMAM_SST_CAR
MAY_RSST_NINO34
CONSTANT
MAY_NAO
MAY_RSST_NINO34
CONSTANT
DJFMAM_MPV_GMX
MAY_RSST_NINO34
CONSTANT
MAY_SLP_GMX
MAY_RSST_NINO34
CONSTANT
MAM_SST_NINO4
MAY_RSST_NINO34
86.1
23.1
42.3
18.7
86.1
23.9
36.7
86.11
18.67
34.75
4.25
1.29
1.40
0.72
4.25
0.89
1.33
4.25
0.87
1.23
2.55
0.60
0.76
2.55
0.45
0.73
2.55
0.60
1.16
11.43
2.85
5.41
2.24
9.80
2.48
3.80
9.60
1.89
3.52
12.76
3.78
4.12
2.10
11.07
2.26
3.40
11.06
2.24
3.16
14.36
3.32
4.21
14.14
4.62
3.65
13.67
2.16
4.16
<0.001
0.006
<0.001
0.029
<0.001
0.016
<0.001
<0.001
0.06
0.001
<0.001
<0.001
<0.001
0.04
<0.001
0.027
0.001
<0.001
0.029
<0.002
<0.001
0.02
<0.001
<0.001
<0.001
<0.001
<0.001
0.035
<0.001
n1s
n1ss
TCP%
n2c
n2s
n2ss
TCPE
n3c
n3s
n3ss
a
For a key to the Acronyms, Please see Tables 1 and 2.
is directly modeled (TCPE), and it also influences ATCP and
TCP%. Another important factor is how much precipitation
is generated by each individual storm. This is highly variable,
since each storm is different in terms of its type, size, translation speed, track, and interactions with the local environment. The constructed models have provided some useful
and interesting information on TCs in Texas and have revealed some of the major physical mechanisms that control
variations in TCP. For each of model, maps were generated
for the spatial distributions of the correlations between the response variables (TCP metrics) and important predictors (climatic forcings) in the final models (Figures 4, 5, 6, and 7).
4.1. ENSO
[24] Many studies [Gray, 1984b; Gray et al., 1993; 1994;
Elsner et al., 1999; Klotzbach and Gray, 2003; Klotzbach,
2011a] have demonstrated that ENSO has a major influence
on seasonal TC frequency in the Atlantic by altering the
Walker circulation. In typical ENSO warming events (Niño
3.4 SST warming), the weaker than normal Walker circulation makes an eastward shift, so there is an increased
upper-level westerly wind over the Caribbean and the tropical Atlantic. The strong westerly wind may combine with
lower-level easterly waves and generate a high vertical wind
shear environment, which is not favorable to TC formation
and movement [Gray, 1984a; DeMaria, 1996; Goldenberg
and Shapiro, 1996; Knaff et al., 2004; Klotzbach, 2011a].
Therefore, in the negative phase of ENSO (La Niña), the
environmental conditions are more favorable for TCs in the
Atlantic and Caribbean to develop, persist, and make landfall. More TCs make landfall in the U.S. during La Niña
years than El Niño or neutral years.
[25] ENSO is the most important variable in our models. In
particular, the La Niña (Niño 3.4 SST cooling) signal is the
major control of Atlantic TC frequency [Gray, 1984b; Wu
and Lau, 1992; Klotzbach, 2011b]. All models have at least
one predictor pertaining to the La Niña signal, but in different
forms, such as SST and RSST in the Niño regions, and the
SOI (Table 3). The La Niña signal here indicates lower
prehurricane season SST in the Niño 3.4 region, causing more
TC activity and hence TCP in Texas. Pearson correlations
were calculated between TCPEs and gridded SST in the
Niño 4 and Niño 3 regions (Figure 4). The spatial patterns of
the La Niña signal (negative correlation between SST and
TCPE) are quite strong and dominate in the eastern central
Pacific (Niño 3.4 region) before the Atlantic hurricane season.
[26] SOI is significant in the n1c and n2c models. SOI is
the atmospheric component of the ENSO cycle [Deser and
Wallace, 1987; Trenberth and Shea, 1987; Trenberth and
Hoar, 1996]. Previous modeling [Villarini et al., 2011b]
indicated that remote influences of SOI and tropical
mean SST can explain part of the U.S. landfalling hurricanes
counts. All SOI predictors have positive coefficients in our
models, which corresponds to the La Niña phase. Niño 3.4
RSST predictors have negative signs, meaning that there is
more TC activity in Texas when Niño 3.4 SST is cooling
relative to the tropical mean.
[27] Two of the simple models (n1ss and n3ss) are solely
based on ENSO signals. Besides the La Niña signal, the
positive sign of Niño 4 SST predictors indicates that the
higher SST in the western central Pacific region (5°S–5°N,
160°E–150°W) may be favorable to more TCP in Texas.
Several studies have already investigated the impacts from
the shifting patterns of Pacific Ocean warming on North
8848
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Table 4a. Observations and Statistical Measures of Model Fit and Leave-One-Out Cross Validation (CV) Model Statistics for ATCPa
n1c
Mean
SD
Max
Min
MAE
2
R
2
Adj R
AIC
BIC
n1s
n1ss
Observed
Model
CV
Model
CV
Model
CV
86.1
75.5
330.1
0
86.1
49.7
312.9
1.7
45.4(52.7%)
0.43
0.40
674.6
664.1
85.3
48.3
291.7
1.8
48.5(56.3%)
0.36
0.34
86.1
31.7
157
6.2
52.2(60.6%)
0.18
0.15
692.9
684.6
86.2
32.1
171.4
7.1
54.7(63.5%)
0.11
0.09
86.1
32.2
148.6
16.8
52.9(61.4%)
0.18
0.15
692.5
684.2
77.7
80.1
148.8
483.7
63.1(73.3%)
0.05
0.03
2
2
a
Statistical measures of model fit include mean absolute error (MAE), coefficient of determination (R ), adjusted coefficient of determination (adj. R ),
Akaike information criterion (AIC), and Bayesian information criterion (BIC).
Table 4b. Observations and Statistical Measures of Model Fit and Leave-One-Out Cross Validation (CV) Model Statistics for TCP%a
n2c
Mean
SD
Max
Min
MAE
2
R
2
Adj R
AIC
BIC
n2s
n2ss
Observed
Model
CV
Model
CV
Model
CV
4.25
3.28
13.53
0
4.25
2.10
12.04
0.21
2.05(48.2%)
0.41
0.38
292.5
300.8
4.22
2.03
10.41
0.24
2.19(51.5%)
0.34
0.31
4.25
1.48
7.08
0.72
2.31(54.4%)
0.20
0.18
306.0
314.3
4.27
1.49
7.11
0.81
2.42(56.9%)
0.14
0.12
4.25
1.47
7.52
0.77
2.32(54.6%)
0.20
0.18
302.4
312.9
4.26
1.51
8.26
0.99
2.44(57.4%)
0.13
0.12
2
2
a
Statistical measures of model fit include mean absolute error (MAE), coefficient of determination (R ), adjusted coefficient of determination (adj. R ),
Akaike information criterion (AIC), and Bayesian information criterion (BIC).
Table 4c. Observations and Statistical Measures of Model Fit and Leave-One-Out Cross Validation (CV) Model Statistics for TCPEa
n3c
Mean
SD
Max
Min
MAE
2
R
2
Adj R
AIC
BIC
n3s
n3ss
Observed
Model
CV
Model
CV
Model
CV
2.5
1.6
6
0
2.6
0.9
5.6
0.6
1.13(45.2%)
0.32
0.30
213.4
221.8
2.6
1
6.3
0.3
1.19(47.6%)
0.27
0.24
2.5
0.9
4.5
0.4
1.14(45.6%)
0.27
0.24
218.1
226.5
2.5
0.9
4.6
0.5
1.2(48%)
0.23
0.22
2.6
0.8
4.6
0.9
1.1(44%)
0.25
0.23
215.8
226.3
2.5
0.8
4.6
0.9
1.17(46.8%)
0.19
0.18
2
2
a
Statistical measures of model fit include mean absolute error (MAE), coefficient of determination (R ), adjusted coefficient of determination (adj. R ),
Akaike information criterion (AIC), and Bayesian information criterion (BIC).
Atlantic TCs [Kim et al., 2009; Lee et al., 2010; Larson et al.,
2012]. Kim et al. [2009] showed that the Gulf of Mexico
coast and Central America will have above average TC frequency and increased TC landfall probability under central
Pacific warming (the Niño 4 region).
4.2. MPV and Vorticity
[28] MPV and vorticity are two important advanced variables that improved the performance of the comprehensive
models significantly (by ~0.20 R2) when compared to the
simple models (Tables 4a–4c). Their coefficients are negative
in all comprehensive models (Table 3).
[29] MPV is a variable originally developed by Emanuel
[1995] and Holland [1997] to describe the limit for the
maximum wind velocity that is possible in TCs based on
the ocean and atmosphere energy conditions. Previous
studies indicated storms with stronger winds are associated
with larger amount of precipitation [Cerveny and Newman,
2000], especially in the inner core area [Rodgers et al.,
1994b]. Jiang et al. [2008] investigated rainfall ratios of 37
TCs from 1998 to 2004 based on the three-hourly TRMM
Multisatellite Precipitation Analysis product. They showed
a much weaker positive relationship between the maximum
wind speed and the rainfall rate over land than over ocean.
However, the relationships between MPV and TCP metrics
in our models are all negative, which indicates that greater
TCP may be the result of weaker storms. The negative correlations between MPV and the TCP metrics are quite spatially
8849
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Figure 4. Pearson’s correlations between SSTs in Niño 4 and 3 regions and annual TCPE: (a) May Niño 3
and 4 SST and TCPE, (b) March to May Niño 3 and 4 SST and TCPE, (c) December to May Niño 3 and 4
SST and TCPE; the black dots represent correlations significant at the 90%-level.
consistent in the Gulf of Mexico as shown in Figures 5b, 6b,
and 7a. Many TCs with relatively low maximum wind speeds
have generated large amounts of precipitation in coastal areas
of the U.S. For example, Tropical Storm Alison in 2001,
Hurricane Irene (Category 1–3) in 2011, and Hurricane Isaac
(Category 1) in 2012 are all recent examples of TCs with relatively low winds that produced large amounts of precipitation
and caused severe inland flooding.
[30] Low-level (850 mb) MDR vorticity in May is another
advanced predictor significant in the comprehensive ATCP
and TCP% models. Vorticity is a numerical description for
the rotational characteristics of the atmosphere [Hoskins
et al., 1985]. TCs are rotating systems themselves that are
embedded in the large-scale environmental rotations/vorticity
[Emanuel, 2003]. The environmental vorticity may influence
the TC genesis, tracks, and intensity [Davis and Emanuel,
1991; Flatau et al., 1994; Emanuel, 2003; Jones et al., 2003;
Emanuel, 2007] and is frequently used in seasonal TC genesis
prediction [Camargo et al., 2009; Belanger et al., 2010] and in
the power dissipation index estimation [Emanuel, 2005,
2007]. Emanuel [2005] also mentioned that the potential
intensity, low-level vorticity, and vertical wind shear are
highly correlated with each other. Therefore, enhanced lowlevel vorticity prior to the hurricane season may contribute to
higher TC wind speed during the season. Most studies have
shown that enhanced vorticity produces more convection,
higher wind, and more intense precipitation. However, MDR
May vorticity all exhibit negative coefficients in our TCP
models (Table 3). Spatially, those negative correlations are
mostly located in western MDR near the Gulf of Mexico
(Figures 5a and 6a). This could be explained similarly as
MPV: storms with weaker winds produce more precipitation,
since low vorticity may correspond to low TC wind speed.
In addition, less vorticity in the western MDR may result in
TCs with larger size and slower translation speed before they
enter the Gulf of Mexico. Indeed, it has been suggested that
a smaller TC radius is associated with larger values of vorticity
[May and Holland, 1998]. Vorticity can also have complex
impacts on TC movement based on the physical interaction
between TCs’ own vorticity and the environmental flow
[Holland, 1983; Shapiro, 1992; Flatau et al., 1994]. The track
and translation speed of a TC are important factors determining how much precipitation will result in Texas. Relatively
low environmental vorticity may produce slower spinning
storms travelling slower, with more accumulated precipitation.
[31] MPV and vorticity significantly affect TC characteristics
including the wind intensity, spatial coverage, and translation
speed. The models show negative relations between MPV/
vorticity and TCP metrics. Therefore, it is reasonable to test
Figure 5. Pearson’s correlations between regional predictors and ATCP: (a) May vorticity and ATCP, (b) December
to May MPV and ATCP, (c) May SLP and ATCP; the black
dots represent correlations significant at the 90%-level.
8850
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
speed. Thus, a majority of storms generating precipitation in
Texas have daily TC maximum speed less than 20 m/s and
translation speed less than 20 km/h. The highest mean TCP
is from the third quartile of daily TC maximum wind speed,
and there is no statistically significant difference in mean
TCP from all maximum wind speed quartiles at the 95%
significance level. Jiang et al. [2008] obtained a correlation
of 0.51 between the over land inner-core mean rain ratio
(mm h 1) and the maximum wind speed. The analyses in
Figures 8a and 8c are based on the daily precipitation volume
across the area covered by TCs. By using the TMPA data,
Shepherd et al. [2007] have shown that tropical depressions/
storms contribute more to the total seasonal rainfall (8–17%)
than major hurricanes in the coastal U.S., because of the higher
frequency of occurrence. This agrees with our results, depicted
in Figure 8a. The second and first quartiles of daily TC translation speed produce much higher mean precipitation than the
other two quartiles (Figure 8c). The mean precipitation of the
second quartile TC translation speed (blue, Figure 8d) is statistically significantly larger than the precipitation in the third
quartiles of TC translation speed (red, Figure 8d). The quartile
precipitation analysis demonstrates that there is no significant
difference in the mean TCP produced by TCs with different
maximum wind speed, but some differences in the mean
TCP produced by TCs with different translation speeds.
However, the strongest and the fastest moving storms are not
generating the most daily TCP in Texas.
Figure 6. Pearson’s correlations between regional predictors
and TCP%: (a) May vorticity and TCP%, (b) December to
May MPV and TCP%, (c) December to May SST and TCP%;
the black dots represent correlations significant at the
90%-level.
the relationships indicated by the statistical models: do storms
with weaker winds and slower translation speeds generate
more TCP in Texas historically? To further explore this, we
examine how the maximum wind speed, translation speed,
and TCP coverage are related to the amount of precipitation
generated by individual TCP days in Texas. Daily TC maximum wind speed and translation speed were averaged from
observations for each TCP day from the 6 hourly observations.
The daily TCP volume is calculated for each TCP day by
aggregating all precipitation amounts from the nonzero grids.
There are 30 TCP days (out of all 495 days) that had only
one observation of spatial position. These 30 days were therefore not used in the analysis because they had a very minor
precipitation impact in Texas, and treating their traveling
speed as 0 km/h will bias the analysis.
[32] The 465 days were divided into quartiles according
to their daily TC maximum wind speed (Figure 8a) and
daily TC translation speed (Figure 8b). The mean daily TCP
volume and its confidence limit were calculated for quartiles
of both daily TC maximum wind speed (Figure 8c) and translation speed (Figure 8d). We used a 95% significance level to
test the statistical difference between means from different
quartiles. Figures 8a and 8b indicate highly skewed distributions of daily TC maximum wind speed and TC translation
4.3. Other Predictors
[33] Besides ENSO, MPV, and vorticity, other climatic
variables also appear in some models. May SLP in the Gulf
of Mexico has negative coefficients in two simple models
for both ATCP (n1s) and TCPE (n3s). SLP is known to be
an important predictor for hurricane frequencies [Ray, 1935;
Landsea et al., 1998; Landsea et al., 1999; Goldenberg
Figure 7. Pearson’s correlations between regional predictors and TCPE: (a) December to May MPV and TCPE, (b)
May sea level pressure and TCPE; the black dots represent
correlations significant at the 90%-level.
8851
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Figure 8. Histograms and quartiles (red dashed lines) of TCP days based on (a) daily TC maximum wind
speed and (b) translation speed; and the mean daily TCP volume (circles) and its confidence limits (dashed
line) for quartiles of TC maximum wind speed (c), and quartiles of TC translation speed (d) for the 95%
significance level (colored dashed lines).
et al., 2001]. Gray et al. [1993] showed that low June to July
SLP correspond to increased TC activity in the Atlantic basin
after 1 August. Shapiro [1982] suggested a negative correlation
(~ 0.3) between the May–June–July SLP in the Gulf of
Mexico and the August–September–October hurricane
activity in the Atlantic Ocean based on historical records from
1899 to 1978. Gray et al. [1993] explained that the low MDR
SLP strengthens the intertropical convergence zone and is
more favorable for cyclogenesis [Gray, 1968]. Figures 5c
and 7b show that negative correlations for SLP are consistent
in the Gulf of Mexico and the northwest tropical Atlantic.
Knaff [1997] indicated that the low regional SLP is associated
with more moisture and higher temperature in the middle
levels and weaker vertical wind shear between the 200 mb
and 850 mb levels. Therefore, the low SLP in the Gulf of
Mexico prior to the hurricane season might be more favorable
to the formation and development of TCs in the Gulf of
Mexico and thus more TCP in Texas.
[34] The December–May SST in the Caribbean shows a positive sign in the n2s TCP% model (Table 3). Inoue et al. [2002]
argued that a strengthened easterly trade wind may create low
SST, high SLP, and more outgoing long-wave radiation in
the Caribbean in some years, which are unfavorable for
the development of TCs. Furthermore, higher SST in the
Caribbean is favorable for allowing TCs from the Atlantic to
enter the Caribbean [Vecchi and Knutson, 2008; Kossin
et al., 2010]
[35] Annual Atlantic and U.S. landfalling TC frequencies
are also related to the NAO [Emanuel, 2005; Kossin et al.,
2010]. The TCP% model n2ss (Table 3) shows a negative
coefficient for May NAO. Kossin et al. [2010] indicated that
the May–June NAO controls the position of the North
Atlantic subtropical high, which modulates the tracks of the
“straight moving” hurricanes during the season. The “straight
moving” hurricanes are defined as ones that formed in the
deep tropics, travel straight westward with little recurvature,
and finally make landfall in the Caribbean or the Gulf
coast [Elsner, 2003; Kossin et al., 2010]. Some TCs producing precipitation in Texas can be those “straight moving”
hurricanes. In addition, negative NAO is related to a winter
precipitation decrease in the southeastern U.S. [Hurrell,
1995]. Less winter precipitation may lead to less annual
precipitation, thus potentially more contribution from
TCPs. NAO was also found to be negatively correlated
with drought-busting TCs in the southeastern U.S. [Maxwell
et al., 2012].
8852
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
5.
Discussion and Conclusions
[36] Multiple linear regression models were built for
predicting ATCP, the percentage of TCP, and TCP events
in Texas. Three types of models were constructed for each
of the TCP metrics: comprehensive models including all
simple and advanced forcing variables, and two simple
models using only the basic forcing variables. The comprehensive models account for 32%–43% of the variance of
the seasonal TCP metrics, while the simple models account
for 18%–27% of the variance. Most of the variables in the
models are statistically significant (95%-level). Most models
are stable in term of modeled and CV errors.
[37] ENSO is the most important factor in the models. The
primary signal is related to La Niña: lower Niño 3.4 SSTs in
the Pacific reduce the upper tropospheric winds and the
vertical shear in the Caribbean and tropical Atlantic [Gray,
1984a, 1984b]. The reduced vertical shear is more favorable
to TC genesis and development, which increases the chance
of Texas being impacted by TCs.
[38] The addition of MPV in the Gulf of Mexico and
vorticity in the MDR substantially increased model fit and
CV accuracy of the comprehensive models for the ATCP
and TCP%. These variables affect the maximum wind speed,
translation speed, track, and size of TCs making landfall in
Texas. The quartile of TCs with the highest maximum wind
speed does not produce the highest mean daily precipitation.
For example, hurricane Emily on 20 July 2005 had a maximum wind speed of 53.3 m/s, but only produced 2.1 km3 of
TCP in Texas. The quartile of TCs with highest translation
speed produces much less daily precipitation than slow
moving TCs. For example, on 17 October 1989 hurricane,
Jerry had a translation speed of 50.7 km/h and only generated
0.05 in km3 TCP in Texas. In addition, the majority of TCP is
produced by TCs with relative lower maximum wind speed
(< 20 m/s) and slower translation speed (< 20 km/h) in
Texas. Those results support the negative signs of MPV
and vorticity.
[39] Low SLP in the Gulf of Mexico is favorable to the
formation and development of TCs in the Gulf of Mexico,
producing more TCP in Texas. Higher than normal SST in
the Caribbean enhances the local TC genesis and is also
favorable to TCs formed in the Atlantic that then move
through the region. Finally, negative NAO may produce
more westward “straight moving” TCs and less winter precipitation, therefore increasing TCP’s contribution to annual
precipitation of Texas.
[40] This is the first regional study using multiple linear
regression models to account for seasonal TCP in Texas.
The models are constructed based on ≤3 independent
variables (many just have two), with good statistical skill
and viable physical interpretations. No other studies have
evaluated seasonal TCP at any spatial scale. However, many
previous studies have focused on seasonal forecasting of TC
frequency, intensity, and size. Klotzbach [2011b] are able to
account for up to 70% of the variability in the post-August
TC frequency in the Atlantic by using three predictors. The
TCP event models in our study use two variables that account
for ~30% variability in the annual number of TCs generating
precipitation in Texas. This lower variance is likely due to the
different spatial scales. By using five predictors, Goh and
Chan [2012] constructed seasonal (July–November) forecast
models that account for 33–43% variance in TCs affecting
Japan and Korea, which is a more comparable spatial scale
as Texas. Multiple linear regression models are able to account
for 20% and 42% variance in the number of Caribbean
hurricanes, using two to three predictors at 3–5 month lead
times [Jury and Rodríguez, 2011]. Compared to those
regional-scale assessments for TC frequency and the additional confounding factors when investigating the impacts of
events (versus the occurrence of the events themselves), our
models can still account for 20–40% of the variance in TCP
by using <3 predictors.
6.
Limitations
[41] The multiple linear regression models are zero inflated
because of several years when no storms occurred within or
near Texas. We have tested the Poisson series of statistical
models [Jagger and Elsner, 2006; Villarini et al., 2010],
but this yielded little improvement in terms of model fit, skill,
and CV accuracy. There are only 6 years (10%) when Texas
had no landfalling TCs that generated precipitation; therefore, we retained those years to preserve the model integrity.
[42] Sixty years of TCP data may not be long enough to
represent the low-frequency variability and long-term trends
in TC activity. Thus, our models may not be able to capture
those low-frequency climatic and oceanic forcings related
to TCs. However, we are limited to the recent 60 years
because of a lack of relatively reliable records of precipitation, climatic/oceanic forcing variables, and hurricane tracks
[Henderson-Sellers et al., 1998; Kunkel et al., 1999; Landsea
et al., 2006] prior to 1950. Furthermore, there is a trade-off
between a high spatial density of observations versus
the temporal consistency. Our use of the subset of 220 out
of 1358 COOP stations that are serially complete over
1950–2009 therefore comes at the potential expense of fully
capturing the spatial variability.
[43] Although the spatial correlation patterns are mostly
consistent between the forcing variables and TCP metrics,
the magnitude of those correlations is relatively low (0.2–0.3,
significant at the 90%-level). This is likely due to uncertainty
in the locations of cyclogenesis, and the regional scale
employed in this study. There are also many other factors
possibly affecting the amount of rainfall in TCs, such as the
environmental water vapor [Jiang et al., 2008], topography
[Wu et al., 2002], and interactions with other synoptic systems
[Atallah et al., 2007; Andersen and Shepherd, 2013]. Those
additional mechanisms warrant further investigation using
both observational and modeling approaches.
[44] Acknowledgments. The authors would like to thank three
anonymous reviewers for their helpful comments and suggestions.
References
Andersen, T. K., and J. M. Shepherd (2013), A global spatiotemporal analysis
of inland tropical cyclone maintenance or intensification, Int. J. Climatol.,
n/a–n/a, doi:10.1002/joc.3693.
Atallah, E., L. F. Bosart, and A. R. Aiyyer (2007), Precipitation distribution associated with landfalling tropical cyclones over the eastern
United States, Mon. Weather Rev., 135(6), 2,185–2,206, doi:10.1175/
Mwr3382.1.
Barlow (2011), Influence of hurricane-related activity on North American
extreme precipitation, Geophys. Res. Lett., 38, L04705, doi:10.1029/
2010GL046258.
8853
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Belanger, J. I., J. A. Curry, and P. J. Webster (2010), Predictability of North
Atlantic Tropical Cyclone Activity on Intraseasonal Time Scales, Mon.
Weather Rev., 138(12), 4,362–4,374, doi:10.1175/2010mwr3460.1.
Bender, M. A., T. R. Knutson, R. E. Tuleya, J. J. Sirutis, G. A. Vecchi,
S. T. Garner, and I. M. Held (2010), Modeled Impact of Anthropogenic
Warming on the Frequency of Intense Atlantic Hurricanes, Science,
327(5964), 454–458, doi:10.1126/science.1180568.
Bosart, L. F., C. S. Velden, W. E. Bracken, J. Molinari, and P. G. Black
(2000), Environmental influences on the rapid intensification of
Hurricane Opal (1995) over the Gulf of Mexico, Mon. Weather Rev.,
128(2), 322–352, doi:10.1175/1520-0493(2000)128 < 0322:EIOTRI >
2.0.CO;2.
Camargo, S. J., and A. H. Sobel (2010), Revisiting the Influence of the
Quasi-Biennial Oscillation on Tropical Cyclone Activity, J. Climate,
23(21), 5,810–5,825, doi:10.1175/2010jcli3575.1.
Camargo, S. J., M. C. Wheeler, and A. H. Sobel (2009), Diagnosis of the
MJO Modulation of Tropical Cyclogenesis Using an Empirical Index,
J. Atmos. Sci., 66(10), 3,061–3,074, doi:10.1175/2009jas3101.1.
Cerveny, R. S., and L. E. Newman (2000), Climatological relationships
between tropical cyclones and rainfall, Mon. Weather Rev., 128(9),
3,329–3,336, doi:10.1175/1520-0493(2000)128 < 3329:CRBTCA >
2.0.CO;2.
Davies, T. V. (1948), LX. Rotatory flow on the surface of the earth.— Part I.
Cyclostrophic motion, Philos. Mag. Series 7, 39(293), 482–491, doi:10.1080/
14786444808521699.
Davis, C. A., and K. A. Emanuel (1991), Potential Vorticity Diagonostics of
Cyclogenisis, Mon. Weather Rev., 119(8), 1,929–1,953, doi:10.1175/
1520-0493(1991)119 < 1929:pvdoc > 2.0.co;2.
DeMaria, M. (1996), The effect of vertical shear on tropical cyclone intensity
change, J. Atmos. Sci., 53(14), 2,076–2,087, doi:10.1175/1520-0469
(1996)053 < 2076:TEOVSO > 2.0.CO;2.
Deser, C., and J. M. Wallace (1987), El Niño events and their relation to the
Southern Oscillation: 1925-1986, J. Geophys. Res., 92(C13),
14,189–14,196, doi:10.1029/JC092iC13p14189.
Elsner, J. B. (2003), Tracking Hurricanes, Bull. Am. Meteorol. Soc., 84(3),
353–356, doi:10.1175/bams-84-3-353.
Elsner, J. B., and T. H. Jagger (2004), A Hierarchical Bayesian Approach to
Seasonal Hurricane Modeling, J. Climate, 17(14), 2,813–2,827,
doi:10.1175/1520-0442(2004)017 < 2813:ahbats > 2.0.co;2.
Elsner, J. B., and T. H. Jagger (2006), Prediction Models for Annual
U.S. Hurricane Counts, J. Climate, 19(12), 2,935–2,952, doi:10.1175/
jcli3729.1.
Elsner, J. B., and B. Kocher (2000), Global tropical cyclone activity: Link to
the North Atlantic oscillation, Geophys. Res. Lett., 27(1), 129–132,
doi:10.1029/1999GL010893.
Elsner, J. B., and C. P. Schmertmann (1993), Improving Extended-Range
Seasonal Predictions of Intense Atlantic Hurricane Activity, Weather Forecast,
8(3), 345–351, doi:10.1175/1520-0434(1993)008 < 0345:ierspo >
2.0.co;2.
Elsner, J. B., A. B. Kara, and M. A. Owens (1999), Fluctuations in North
Atlantic hurricane frequency, J. Climate, 12(2), 427–437, doi:10.1175/
1520-0442(1999)012 < 0427:finahf > 2.0.co;2.
Emanuel, K. (1991), The Theory of Hurricanes, Annu. Rev. Fluid Mech., 23,
179–196, doi:10.1146/annurev.fluid.23.1.179.
Emanuel, K. (1995), Sensitivity of Tropical Cyclones to Surface Exchange
Coefficients and a Revised Steady-State Model incorporating Eye
Dynamics, J. Atmos. Sci., 52(22), 3,969–3,976, doi:10.1175/1520-0469
(1995)052 < 3969:sotcts > 2.0.co;2.
Emanuel, K. (2003), Tropical cyclones, Annu Rev Earth Pl Sc, 31, 75–104,
doi:10.1146/annurev.earth.31.100901.141259.
Emanuel, K. (2005), Increasing destructiveness of tropical cyclones over the
past 30 years, Nature, 436(7051), 686–688, doi:10.1038/Nature03906.
Emanuel, K. (2007), Environmental factors affecting tropical cyclone power
dissipation, J. Climate, 20(22), 5,497–5,509, doi:10.1175/2007jcli1571.1.
Emanuel, K. (2011), Global Warming Effects on US Hurricane Damage,
Weather Clim. Soc., 3(4), 261–268, doi:10.1175/Wcas-D-11-00007.1.
Flatau, M., W. H. Schubert, and D. E. Stevens (1994), The Role of
Baroclinic Processes in Tropical Cyclone Motion - the Influence of
Vertical Tilt, J. Atmos. Sci., 51(18), 2,589–2,601, doi:10.1175/15200469(1994)051 < 2589:TROBPI > 2.0.CO;2.
Frauenfeld, O. W., P. C. Knappenberger, and P. J. Michaels (2011), A reconstruction of annual Greenland ice melt extent, 1784–2009, J. Geophys.
Res., 116, D08104, doi:10.1029/2010JD014918.
Goh, A. Z.-C., and J. C. L. Chan (2012), Variations and prediction of the annual number of tropical cyclones affecting Korea and Japan, Int. J.
Climatol., 32(2), 178–189, doi:10.1002/joc.2258.
Goldenberg, S. B., and L. J. Shapiro (1996), Physical mechanisms for the
association of El Nino and west African rainfall with Atlantic major
hurricane activity, J. Climate, 9(6), 1,169–1,187, doi:10.1175/1520-0442
(1996)009 < 1169:PMFTAO > 2.0.CO;2.
Goldenberg, S. B., C. W. Landsea, A. M. Mestas-Nunez, and W. M. Gray
(2001), The recent increase in Atlantic hurricane activity: Causes and
implications, Science, 293(5529), 474–479, doi:10.1126/science.1060040.
Gray, W. M. (1968), Global View of the Origin of Tropical Disturbances and
Storms, Mon. Weather Rev., 96(10), 669–700, doi:10.1175/1520-0493
(1968)096 < 0669:gvotoo > 2.0.co;2.
Gray, W. M. (1984a), Atlantic Seasonal Hurricane Frequency .1. El-Nino and
30-Mb Quasi-Biennial Oscillation Influences, Mon. Weather Rev., 112(9),
1,649–1,668, doi:10.1175/1520-0493(1984)112 < 1649:ASHFPI > 2.0.
CO;2.
Gray, W. M. (1984b), Atlantic Seasonal Hurricane Frequency .2. Forecasting
Its Variability, Mon. Weather Rev., 112(9), 1,669–1,683, doi:10.1175/15200493(1984)112 < 1669:ASHFPI > 2.0.CO;2.
Gray, W. M., C. W. Landsea, P. W. Mielke, and K. J. Berry (1992), Predicting
Atlantic Seasonal Hurricane Activity 6–11 Months in Advance, Weather
Forecast, 7(3), 440–455, doi:10.1175/1520-0434(1992)007 < 0440:
PASHAM > 2.0.CO;2.
Gray, W. M., C. W. Landsea, P. W. Mielke, and K. J. Berry (1993), Predicting
Atlantic basin seasonal tropical cyclone activity by 1 August, Weather
Forecast, 8(1), 73–86, doi:10.1175/1520-0434(1993)008 < 0073:pabstc >
2.0.co;2.
Henderson-Sellers, A., et al. (1998), Tropical cyclones and global climate
change: A post-IPCC assessment, Bull. Am. Meteorol. Soc., 79(1),
19–38, doi:10.1175/1520-0477(1998)079 < 0019:TCAGCC > 2.0.CO;2.
Holland, G. J. (1983), Tropical Cyclone Motion - Environmental Interaction
Plus a Beta-Effect, J. Atmos. Sci., 40(2), 328–342, doi:10.1175/1520-0469
(1983)040 < 0328:TCMEIP > 2.0.CO;2.
Holland, G. J. (1997), The maximum potential intensity of tropical cyclones,
J. Atmos. Sci., 54(21), 2,519–2,541, doi:10.1175/1520-0469(1997)054
< 2519:TMPIOT > 2.0.CO;2.
Holland, G. J., and P. J. Webster (2007), Heightened tropical cyclone activity
in the North Atlantic: natural variability or climate trend?, Philos T R Soc
A, 365(1860), 2,695–2,716, doi:10.1098/rsta.2007.2083.
Hoskins, B. J., M. E. McIntyre, and A. W. Robertson (1985), On the use and
significance of isentropic potential vorticity maps, Q. J. Roy. Meteorol.
Soc., 111(470), 877–946, doi:10.1256/smsqj.47001.
Hurrell, J. W. (1995), Decadal Trends in the North Atlantic Oscillation:
Regional Temperatures and Precipitation, Science, 269(5224), 676–679,
doi:10.1126/science.269.5224.676.
Inoue, M., I. C. Handoh, and G. R. Bigg (2002), Bimodal Distribution of
Tropical Cyclogenesis in the Caribbean: Characteristics and Environmental
Factors, J. Climate, 15(20), 2,897–2,905, doi:10.1175/1520-0442(2002)
015 < 2897:bdotci > 2.0.co;2.
Islam, T., W. Merrell, W. Seitz, and R. Harriss (2009), Origin, Distribution, and
Timing of Texas Hurricanes: 1851–2006, Nat. Hazards Rev., November
2009, 136–144, doi:10.1061/(ASCE)1527-6988(2009)10:4(136).
Jagger, T. H., and J. B. Elsner (2006), Climatology models for extreme hurricane winds near the United States, J. Climate, 19(13), 3,220–3,236,
doi:10.1175/jcli3913.1.
Jiang, H. Y., J. B. Halverson, and E. J. Zipser (2008), Influence of environmental moisture on TRMM-derived tropical cyclone precipitation over land and
ocean, Geophys. Res. Lett., 35, L17806, doi:10.1029/2008gl034658.
Jones, S. C., et al. (2003), The extratropical transition of tropical cyclones:
Forecast challenges, current understanding, and future directions, Weather
Forecast, 18(6), 1,052–1,092, doi:10.1175/1520-0434(2003)018 < 1052:
tetotc > 2.0.co;2.
Jury, M., and E. Rodríguez (2011), Caribbean hurricanes: interannual variability and prediction, Theor. Appl. Climatol., 106(1-2), 105–115, doi:10.1007/
s00704-011-0422-z.
Kalnay, E., et al. (1996), The NCEP/NCAR 40-year reanalysis project, Bull.
Am. Meteorol. Soc., 77(3), 437–471, doi:10.1175/1520-0477(1996)077
< 0437:tnyrp > 2.0.co;2.
Keim, B. D., and R. A. Muller (2007), Spatiotemporal patterns and return
periods of tropical storm and hurricane strikes from Texas to Maine,
J. Climate, 20(14), 3,498–3,509, doi:10.1175/jcli4187.1.
Kim, H. M., P. J. Webster, and J. A. Curry (2009), Impact of Shifting
Patterns of Pacific Ocean Warming on North Atlantic Tropical Cyclones,
Science, 325(5936), 77–80, doi:10.1126/science.1174062.
Klotzbach, P. J. (2007), Revised prediction of seasonal Atlantic basin
tropical cyclone activity from 1 August, Weather Forecast, 22(5),
937–949, doi:10.1175/waf1045.1.
Klotzbach, P. J. (2008), Refinements to Atlantic basin seasonal hurricane prediction from 1 December, J. Geophys. Res., 113, D17109, doi:10.1029/
2008jd010047.
Klotzbach, P. J. (2011a), El Nino-Southern Oscillation’s Impact on Atlantic
Basin Hurricanes and U.S. Landfalls, J. Climate, 24(4), 1,252–1,263,
doi:10.1175/2010jcli3799.1.
Klotzbach, P. J. (2011b), A simplified Atlantic basin seasonal hurricane
prediction scheme from 1 August, Geophys. Res. Lett., 38, L16710,
doi:10.1029/2011GL048603.
8854
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Klotzbach, P. J., and W. M. Gray (2003), Forecasting September Atlantic
basin tropical cyclone activity, Weather Forecast, 18(6), 1,109–1,128,
doi:10.1175/1520-0434(2003)018 < 1109:FSABTC > 2.0.CO;2.
Knaff, J. A. (1997), Implications of Summertime Sea Level Pressure
Anomalies in the Tropical Atlantic Region, J. Climate, 10(4), 789–804,
doi:10.1175/1520-0442(1997)010 < 0789:iosslp > 2.0.co;2.
Knaff, J. A., S. A. Seseske, M. DeMaria, and J. L. Demuth (2004), On the
influences of vertical wind shear on symmetric tropical cyclone structure
derived from AMSU, Mon. Weather Rev., 132(10), 2,503-2,510,
doi:10.1175/1520-0493(2004)132 < 2503:Otiovw > 2.0.Co;2.
Knight, D. B., and R. E. Davis (2009), Contribution of tropical cyclones to
extreme rainfall events in the southeastern United States, J. Geophys.
Res., 114, D23102, doi:10.1029/2009jd012511.
Knutson, T. R., and R. E. Tuleya (2004), Impact of CO2-induced warming on
simulated hurricane intensity and precipitation: Sensitivity to the choice of climate model and convective parameterization, J. Climate, 17(18), 3,477–3,495,
doi:10.1175/1520-0442(2004)017 < 3477:IOCWOS > 2.0.CO;2.
Knutson, T. R., R. E. Tuleya, and Y. Kurihara (1998), Simulated increase of
hurricane intensities in a CO2-warmed climate, Science, 279(5353),
1,018–1,020.
Knutson, T. R., J. L. McBride, J. Chan, K. Emanuel, G. Holland, C. Landsea,
I. Held, J. P. Kossin, A. K. Srivastava, and M. Sugi (2010), Tropical
cyclones and climate change, Nat. Geosci., 3(3), 157–163, doi:10.1038/
Ngeo779.
Konrad, C. E. (2001), The most extreme precipitation events over the eastern
United States from 1950 to 1996: Considerations of scale, J. Hydrometeorol,
2(3), 309–325, doi:10.1175/1525-7541(2001)002 < 0309:tmepeo >
2.0.co;2.
Konrad, C. E., and L. B. Perry (2010), Relationships between tropical cyclones and heavy rainfall in the Carolina region of the USA, Int. J.
Climatol., 30(4), 522–534, doi:10.1002/Joc.1894.
Kossin, J. P., S. J. Camargo, and M. Sitkowski (2010), Climate Modulation
of North Atlantic Hurricane Tracks, J. Climate, 23(11), 3,057–3,076,
doi:10.1175/2010jcli3497.1.
Kunkel, K. E., K. Andsager, and D. R. Easterling (1999), Long-term trends
in extreme precipitation events over the conterminous United States and
Canada, J. Climate, 12(8), 2,515–2,527.
Kunkel, K. E., D. R. Easterling, D. A. R. Kristovich, B. Gleason, L. Stoecker,
and R. Smith (2010), Recent increases in U.S. heavy precipitation associated
with tropical cyclones, Geophys. Res. Lett., 37, L24706, doi:10.1029/
2010GL045164.
Landsea, C. W., G. D. Bell, W. M. Gray, and S. B. Goldenberg (1998), The
Extremely Active 1995 Atlantic Hurricane Season: Environmental Conditions and Verification of Seasonal Forecasts, Mon. Weather Rev.,
126(5), 1,174–1,193, doi:10.1175/1520-0493(1998)126 < 1174:teaahs >
2.0.co;2.
Landsea, C. W., R. A. Pielke, A. Mestas-Nunez, and J. A. Knaff (1999),
Atlantic basin hurricanes: Indices of climatic changes, Clim. Change,
42(1), 89–129, doi:10.1023/A:1005416332322.
Landsea, C. W., B. A. Harper, K. Hoarau, and J. A. Knaff (2006), Can we
detect trends in extreme tropical cyclones?, Science, 313(5786), 452–454,
doi:10.1126/science.1128448.
Larson, J., Y. P. Zhou, and R. W. Higgins (2005), Characteristics of
landfalling tropical cyclones in the United States and Mexico: Climatology
and interannual variability, J. Climate, 18(8), 1,247–1,262, doi:10.1175/
JCLI3317.1.
Larson, S., S. K. Lee, C. Z. Wang, E. S. Chung, and D. Enfield (2012),
Impacts of non-canonical El Nino patterns on Atlantic hurricane activity,
Geophys. Res. Lett., 39, L14706, doi:10.1029/2012gl052595.
Lau, K. M., Y. P. Zhou, and H. T. Wu (2008), Have tropical cyclones
been feeding more extreme rainfall?, J. Geophys. Res., 113, D23113,
doi:10.1029/2008jd009963.
Lee, S. K., C. Z. Wang, and D. B. Enfield (2010), On the impact of central
Pacific warming events on Atlantic tropical storm activity, Geophys.
Res. Lett., 37, L17702, doi:10.1029/2010gl044459.
Matyas, C. (2008), Shape measures of rain shields as indicators of changing
environmental conditions in a landfalling tropical storm, Meteorol Appl,
15(2), 259–271, doi:10.1002/met.70.
Maxwell, J. T., P. T. Soule, J. T. Ortegren, and P. A. Knapp (2012), DroughtBusting Tropical Cyclones in the Southeastern Atlantic United States:
1950-2008, Ann. Assoc. Am. Geogr., 102(2), 259–275, doi:10.1080/
00045608.2011.596377.
May, P. T., and G. J. Holland (1998), The role of potential vorticity generation in tropical cyclone rainbands, Symposium on Tropical Cyclone
Intensity Change, 95-98.
Miller, A. J. (2002), Subset selection in regression, 2nd ed., vol. xvii, p. 238,
Chapman & Hall/CRC, Boca Raton.
Nielsen-Gammon, J. W., F. Q. Zhang, A. M. Odins, and B. Myoung (2005),
Extreme rainfall in texas: Patterns and predictability, Phys Geogr, 26(5),
340–364, doi:10.2747/0272-3646.26.5.340.
Nogueira, R. C., and B. D. Keim (2010), Annual Volume and Area
Variations in Tropical Cyclone Rainfall over the Eastern United States,
J. Climate, 23(16), 4,363–4,374, doi:10.1175/2010jcli3443.1.
Oouchi, K., J. Yoshimura, H. Yoshimura, R. Mizuta, S. Kusunoki, and
A. Noda (2006), Tropical cyclone climatology in a global-warming
climate as simulated in a 20 km-mesh global atmospheric model:
Frequency and wind intensity analyses, J. Meteorol. Soc. Jpn., 84(2),
259–276, doi:10.2151/jmsj.84.259.
Pielke, R. A., and C. W. Landsea (1998), Normalized hurricane damages in
the United States: 1925-95, Weather Forecast, 13(3), 621–631,
doi:10.1175/1520-0434(1998)013 < 0621:nhditu > 2.0.co;2.
Pielke, R. A., and C. N. Landsea (1999), La Nina, El Nino, and Atlantic hurricane damages in the United States, Bull. Am. Meteorol. Soc., 80(10),
2,027–2,033, doi:10.1175/1520-0477(1999)080 < 2027:LNAENO >
2.0.CO;2.
Pielke, R., J. Gratz, C. Landsea, D. Collins, M. Saunders, and R. Musulin
(2008), Normalized Hurricane Damage in the United States: 1900–2005,
Nat. Hazards Rev., 9(1), 29–42, doi:10.1061/(ASCE)1527-6988(2008)
9:1(29.
Quiring, S., A. Schumacher, C. Labosier, and L. Zhu (2011), Variations in
mean annual tropical cyclone size in the Atlantic, J. Geophys. Res., 116,
D09114, doi:10.1029/2010jd015011.
Ray, C. L. (1935), Relation of Tropical Cyclone Frequency to Summer
Pressures and Ocean Surface-Water TemperatureS, Mon. Weather Rev.,
63(1), 10–12, doi:10.1175/1520-0493(1935)63 < 10:rotcft > 2.0.co;2.
Rodgers, E. B., J. J. Baik, and H. F. Pierce (1994a), The Environmental
Influence on Tropical Cyclone Precipitation, J. Appl. Meteorol., 33(5),
573–593, doi:10.1175/1520-0450(1994)033 < 0573:TEIOTC > 2.0.CO;2.
Rodgers, E. B., S. W. Chang, and H. F. Pierce (1994b), A Satellite Observational
and Numerical Study of Precipitation Characteristics in Western NorthAtlantic Tropical Cyclones, J. Appl. Meteorol., 33(2), 129–139, doi:10.1175/
1520-0450(1994)033 < 0129:ASOANS > 2.0.CO;2.
Rodgers, E. B., R. F. Adler, and H. F. Pierce (2001), Contribution of tropical
cyclones to the North Atlantic climatological rainfall as observed from
satellites, J. Appl. Meteorol., 40(11), 1,785–1,800, doi:10.1175/15200450(2001)040 < 1785:COTCTT > 2.0.CO;2.
Rogers, R., S. Y. Chen, J. Tenerelli, and H. Willoughby (2003), A numerical
study of the impact of vertical shear on the distribution of rainfall in
Hurricane Bonnie (1998), Mon. Weather Rev., 131(8), 1,577–1,599,
doi:10.1175//2546.1.
Rossby, C. G. (1949), O a Mechanism for the Release of Potential Energy in
the Atmosphere, J. Meteorol., 6(3), 164–180, doi:10.1175/1520-0469
(1949)006 < 0164:OAMFTR > 2.0.CO;2.
Shapiro, L. J. (1982), Hurricane Climatic Fluctuations. Part II: Relation to
Large-Scale Circulation, Mon. Weather Rev., 110(8), 1,014–1,023,
doi:10.1175/1520-0493(1982)110 < 1014:hcfpir > 2.0.co;2.
Shapiro, L. J. (1992), Hurricane Vortex Motion and Evolution in a 3-Layer
Model, J. Atmos. Sci., 49(2), 140–153, doi:10.1175/1520-0469(1992)
049 < 0140:HVMAEI > 2.0.CO;2.
Shepard, D. (1968), A two-dimensional interpolation function for irregularlyspaced data, in Proceedings of the 1968 23rd ACM national conference,
edited, pp. 517-524, ACM, doi:10.1145/800186.810616.
Shepherd, J. M., and T. Knutson (2007), The Current Debate on the Linkage
Between Global Warming and Hurricanes, Geography Compass, 1(1),
1–24, doi:10.1111/j.1749-8198.2006.00002.x.
Shepherd, J. M., A. Grundstein, and T. L. Mote (2007), Quantifying the
contribution of tropical cyclones to extreme rainfall along the coastal southeastern United States, Geophys. Res. Lett., 34, L23810, doi:10.1029/
2007gl031694.
Smith, R. K., W. Ulrich, and G. Sneddon (2000), On the dynamics of
hurricane-like vortices in vertical-shear flows, Q. J. Roy. Meteorol. Soc.,
126(569), 2,653–2,670, doi:10.1002/qj.49712656903.
Trenberth, K. E., and T. J. Hoar (1996), The 1990-1995 El Nino Southern
Oscillation event: Longest on record, Geophys. Res. Lett., 23(1), 57–60,
doi:10.1029/95gl03602.
Trenberth, K. E., and D. J. Shea (1987), On the Evolution of the Southern
Oscillation, Mon. Weather Rev., 115(12), 3,078–3,096, doi:10.1175/
1520-0493(1987)115 < 3078:oteots > 2.0.co;2.
Vecchi, G. A., and T. R. Knutson (2008), On Estimates of Historical North
Atlantic Tropical Cyclone Activity, J. Climate, 21(14), 3,580–3,600,
doi:10.1175/2008jcli2178.1.
Vecchi, G. A., and B. J. Soden (2007), Increased tropical Atlantic wind shear
in model projections of global warming, Geophys. Res. Lett., 34, L08702,
doi:10.1029/2006gl028905.
Vecchi, G. A., K. L. Swanson, and B. J. Soden (2008), CLIMATE
CHANGE Whither Hurricane Activity?, Science, 322(5902), 687–689,
doi:10.1126/science.1164396.
Villarini, G., and J. A. Smith (2010), Flood peak distributions for the
eastern United States. Water Resour. Res., 46, W06504, doi:10.1029/
2009wr008395.
8855
ZHU ET AL.: MODELING SEASONAL TCP IN TEXAS
Villarini, G., G. A. Vecchi, and J. A. Smith (2010), Modeling the
Dependence of Tropical Storm Counts in the North Atlantic Basin on
Climate Indices, Mon. Weather Rev., 138(7), 2,681–2,705, doi:10.1175/
2010mwr3315.1.
Villarini, G., J. A. Smith, M. L. Baeck, T. Marchok, and G. A. Vecchi (2011a),
Characterization of rainfall distribution and flooding associated with U.S.
landfalling tropical cyclones: Analyses of Hurricanes Frances, Ivan, and
Jeanne (2004), J. Geophys. Res., 116, D23116, doi:10.1029/2011jd016175.
Villarini, G., G. A. Vecchi, and J. A. Smith (2011b), U.S. Landfalling and
North Atlantic Hurricanes: Statistical Modeling of Their Frequencies and
Ratios, Mon. Weather Rev., 140(1), 44–65, doi:10.1175/mwr-d-11-00063.1.
Watson, D. F., and G. M. Philip (1985), A Refinement of Inverse Distance
Weighted Interpolation, Geo-Processing, 2(4), 315–327.
Gray, W. M., C. W. Landsea, P. W. Mielke, and K. J. Berry (1994),
Predicting Atlantic Basin Seasonal Tropical Cyclone Activity by 1 June,
Weather Forecast, 9(1), 103–115, doi:10.1175/1520-0434(1994)009
< 0103:PABSTC > 2.0.CO;2.
Wu, C. C., and K. A. Emanuel (1995), Potential Vorticity Diagnostics of
Hurricane Movement .2. Tropical-Storm-Ana (1991) and Hurricane-Andrew
(1992), Mon. Weather Rev., 123(1), 93–109, doi:10.1175/1520-0493(1995)
123 < 0093:PVDOHM > 2.0.CO;2.
Wu, G. X., and N. C. Lau (1992), A GCM Simulation of the relationship
between tropical-storm formation and ENSO, Mon. Weather Rev., 120(6),
958–977, doi:10.1175/1520-0493(1992)120 < 0958:agsotr > 2.0.co;2.
Wu, C. C., T. H. Yen, Y. H. Kuo, and W. Wang (2002), Rainfall simulation
associated with typhoon herb (1996) near Taiwan. Part I: The topographic
effect, Weather Forecast, 17(5), 1,001–1,015, doi:10.1175/1520-0434
(2003)017 < 1001:rsawth > 2.0.co;2.
Wu, L. G., S. A. Braun, J. Halverson, and G. Heymsfield (2006), A numerical study of Hurricane Erin (2001). Part I: Model verification and storm
evolution, J. Atmos. Sci., 63(1), 65–86, doi:10.1175/jas3597.1.
Zhu, L. Y., and S. Quiring (2013), Variations in Tropical Cyclone Precipitation
in Texas (1950 to 2009), J. Geophys. Res. Atmos., 118, 3,085–3,096,
doi:10.1029/2012JD018554.
8856