1. ANALYSIS OF EL NIÑO SOUTHERN OSCILLATION (ENSO) SIGNAL
STRENGTH ON PRECIPITATION STATISTICS, NORTH CAROLINA, USA
By
Sonia K. Sanchez Lohff
Senior Honors Thesis
Appalachian State University
Submitted to the Department of Geology
in partial fulfillment of the requirement for the degree of
Bachelor of Science
December, 2014
Approved by:
____________________________________________________________________
Dr. William P. Anderson, Jr., Ph.D, Thesis Director
____________________________________________________________________
Dr. Ryan E. Emanuel, Ph.D, Second Reader
____________________________________________________________________
Dr. Chuanhui Gu, Ph.D, Departmental Honors Director
2. i | Sanchez-Lohff
ABSTRACT
With the fast approaching climate change, knowledge concerning the tendencies and
patterns of climatic processes such as El Niño-Southern Oscillation (ENSO) and the effect that
these processes have on reservoirs, is essential for better optimization of water resources.
Numerous studies have examined the effect ENSO has on net precipitation depth, however, no
study to date has examined its effect on other precipitation parameters. In this study, five
precipitation statistics were produced—storm arrival, storm depth, storm duration, storm intensity,
and storm interval— and wavelet coherence analysis was used to evaluate varying significance
with ENSO. Three separate figures were produced: Continuous Wavelet Transform (CWT), Cross
Wavelet Transform (XWT), and Wavelet Coherence (WTC). This study uses the XWT figures to
visualize and also quantify significance as they show cross-correlations between the ENSO and
each precipitation parameter.
The XWT plots were derived from Multivariate ENSO Index (MEI) time series and winter
bi-monthly means. Each produced wavelet was assessed individually and comparatively with
neighboring sites; in addition, relevant ENSO-linked magnitudes for each site were evaluated and
plotted. Through this method, a strong decay in correlation moving further inland was observed
in storm depth, as is consistent with previous studies. In contrast, a strong increase in correlation
was noted with increasing distance from the Atlantic coast in storm arrival and storm interval. No
conclusive trends were observed in either storm duration or intensity. With no strong variability
in storm duration or intensity, all observations support themselves, as a longer time between storms
in the Blue Ridge would explain an increased storm depth along the coast.
Key Words: ENSO, Coherence Wavelets, Cross Wavelet Transform, Precipitation Statistics
3. ii | Sanchez-Lohff
ACKNOWLEDGEMENTS
First and foremost, I would like to thank Dr. Bill Anderson for advising me during the
process of my undergraduate research and writing my thesis. I could not have done it without your
help with data manipulation, as well as overall guidance, enthusiasm, and suggestions throughout
the whole process. I enjoyed our weekly meetings and “Eureka” moments accompanied with our
small victories over Matlab. Many thanks to Dr. Scott Marshall for all of the help using Matlab,
and for your patience with my constant questions. Your class helped me immensely and I hope to
use the skills I have learned in the near future. I would also like to thank Dr. Ryan Emanuel for
his help with the project, and also for being the second reader for my thesis. To Professor Robin
Hale, thank you for your help with the production of the GIS maps and your knowledge of the
program. Thanks also to the College of Arts and Sciences and the Appalachian Geology
Department for funding me for research as an Undergraduate Research Assistant.
Finally, I would like to thank all of the faculty in the Appalachian Geology Department for
all your support throughout the years, and all of the valuable knowledge I have gained from each
of you. Special thanks to Laura Mallard for your emotional support throughout the process, and
your ability to bring everything into perspective. Thanks also to Frank Thomas and Cameron
Batchelor for their constant moral support throughout the process of producing my thesis.
4. iii | Sanchez-Lohff
TABLE OF CONTENTS
Section Page
ABSTRACT..................................................................................................................................... i
ACKNOWLEDGEMENTS............................................................................................................ ii
LIST OF FIGURES .........................................................................................................................v
1. INTRODUCTION.....................................................................................................................1
1.1: Background................................................................................................................2
1.2: Literature Review ......................................................................................................3
2. METHODS................................................................................................................................8
2.1: Data...........................................................................................................................8
2.2. ENSO Indices............................................................................................................9
2.3: Data Manipulation ..................................................................................................10
2.4: Wavelets..................................................................................................................12
2.5: GIS..........................................................................................................................14
2.6: Quantification ........................................................................................................15
3. RESULTS ................................................................................................................................18
3.1: Site Description.....................................................................................................18
3.2: Wavelet and Magnitude Analysis.........................................................................18
3.2.1. Storm Arrival ...................................................................................................20
3.2.2. Storm Depth.....................................................................................................25
3.2.3. Storm Duration.................................................................................................29
3.2.4. Storm Intensity.................................................................................................33
3.2.5. Storm Interval ..................................................................................................33
3.3: Error Analysis......................................................................................................41
4. DISCUSSION..........................................................................................................................43
4.1: Teleconnection within MEI Time Series..............................................................43
4.2: Wavelet Breakdown Example ..............................................................................43
7. 1 | Sanchez-Lohff
1. INTRODUCTION
Hydrology is becoming an increasingly important field due to the growing demand for
water resources both globally and within developed countries such as the United States. With the
rapid rise in global population, water resources all over the world are being tapped and exploited
to their natural limits or beyond. Unlike other natural resources, however, there is no replacement
for water, which is essential to both the life and productivity of human culture. These increases in
water demand come from a variety of sources from agriculture to industrial uses to drinking water
resources. Because of the high level of exploitation and our limited knowledge of storage and
fluxes within the Hydrologic Cycle, it is important to study all aspects of the water cycle as well
as the processes that affect it. For example, research has demonstrated that the El Niño-Southern
Oscillation (ENSO) affects seasonal climate fluctuations in many parts of the globe; these effects
have considerable implications for humans. One relevant study of this phenomenon was
conducted to examine the benefits of using ENSO-related climate forecasts to optimize agricultural
decisions in Argentina [Podestá et al., 2007]. It was found that the production of maize, soybeans
and sorghum were higher in the warm phases induced by ENSO than those in the cold phases
[Podestá et al., 2007]. With observations like this one, agricultural decision-making can mitigate
the negative effects and optimize on the positive influences of the cycle [Podestá et al., 2007]. As
exemplified in this study, with a broader knowledge in the tendencies and patterns of climactic
processes such as ENSO and the effect that these processes have on water resources, better
management of water resources will result.
This is a hydrologic study of interannual controls on precipitation in the southeastern
United States. North Carolina is the main area of focus. A deep understanding of hydrologic
8. 2 | Sanchez-Lohff
processes is particularly important in North Carolina, because the economy relies heavily on
industrial and agricultural products such as tobacco, cotton, soybeans, peanuts, sweet potatoes, and
apples [North Carolina—Department of Agriculture and Consumer Services]. ENSO may have a
strong effect on the seasonal delivery of water, thereby affecting this agricultural production. Here,
a number of rainfall parameters—storm arrival, storm duration, storm depth, storm intensity, and
storm interval— are examined statistically in order to assess their correlation with ENSO.
1.1. Background
ENSO refers to a coupled atmosphere-ocean variance of sea surface temperatures and
surface air pressures in the tropical Pacific Ocean [Trenberth and Stepaniak, 2000]. During El
Niño cycles, weaker trade winds blow westward in the Pacific basin, allowing warm water to flow
towards the east. This influx of warm water ceases the upwelling of cold, deep water on the
western coast of South America. El Niño is characterized by positive anomalies in sea surface
temperatures (SST) in the central and eastern equatorial Pacific Ocean [Kurtzman and Scanlon,
2007]. It represents the warm phase of the ENSO cycle. Conversely, La Niña is characterized by
negative anomalies and basin-wide cool SST [Kurtzman and Scanlon, 2007]. Each El Niño event
is unique in itself with individual characteristics. ENSO occurs in regularly occurring bi-annual
events lasting 9-12 months [Rasanen and Kummu, 2012]. An average cycle lasts 3 to 4 years, but
extreme cases can last up to 6 years [Wolter and Timlin, 2011;Trenberth, 1997]. The evolution of
each cycle is distinctive also, and is dependent on climatological factors [Trenberth and Stepaniak,
2000]. Due to a sudden shift in Pacific Ocean circulation in the tropics in 1976/77, there was an
associated change in the development of ENSO cycles [Trenberth and Stepaniak, 2000].
Rasmusson and Carpenter [1982] found that past ENSO cycles matured along the coast of South
9. 3 | Sanchez-Lohff
America and, from there, spread westward. However, in more recent years after the abrupt climate
shift, effects were first felt in the central pacific and then spread eastward [Trenberth abd
Stepaniak, 2000] to locations including North Carolina [Anderson and Emanuel, 2008].
1.2. Literature Review
Previous studies have suggested that ENSO has a major impact on global and regional
climate variability. A significant number of global patterns of oceanic and atmospheric anomalies
are repeated every 4 to 6 years, which is consistent with El Niño oscillation [Rajagopalan and
Lall, 1998]. For example, temperature variations are felt around the world in response to these
cycles. Some of these include below-normal temperatures in regions surrounding the Indian Ocean
and Africa [Diaz and Kiladis, 1989]. During the winter season, these below-average temperature
anomalies expand to southeastern China and the Philippines [Diaz and Kiladis, 1989]. Regional
sea level fluctuations have been documented in various parts of the world as a result of ENSO.
For example, ENSO induces interannual changes in the East China Sea; specifically, a ±2 cm sea
level fluctuation is felt [Lin et al., 2010]. ENSO has even been shown to have a major influence
in such large events as tropical cyclones [Camargo et al., 2007]. These huge storms have a great
impact on flooding in coastal areas, which is especially problematic with the rapid rise in sea level
[Camargo et al., 2007]. Although ENSO invokes many climatological changes, an even wider
range of hydrological anomalies have been studied and correlated to the cycles including
precipitation, floods and droughts, river discharge and recharge, groundwater flow, baseflow, soil
moisture, coastal water quality, and groundwater flow [Glantz, 2001].
Precipitation is perhaps one of the most studied areas in correlation to ENSO. Robelewski
and Harplet [1987] did a global analysis through harmonic vectors to determine areas with positive
10. 4 | Sanchez-Lohff
correlation between ENSO and precipitation. They found a number of areas to have coherent
relationships specific to this study; these include the western and central equatorial Pacific Ocean
basin, northern South America, eastern equatorial Africa, parts of the United States, Central
America, Caribbean, southern Europe, and southern India [Robelewski and Harplet 1987].
Although precipitation variance is a very well-known effect of ENSO, this change in influx of rain
has many subsequent effects on other hydrologic processes. Furthermore, the global influence of
ENSO is well recognized. The local effects are much less understood, and many studies have been
devoted to examining smaller-scale variations confined to specific areas.
There have been many studies done specific to areas within the zones that Robelewski and
Harplet [1987] found to be correlative. For example, Richey et al. [2005] conducted a study in
Brazil in the Amazon River basin centered on river discharge. In the study, river discharge
anomalies were compared to atmospheric pressure anomalies, which are used to identify ENSO.
It was found that interannual fluctuations in the hydrograph could be explained by ENSO. More
specifically, high discharge rates were associated with the warm El Nino cycles [Richey et al.,
2005]. Another important topic of study is water quality, which is extremely important as it has a
major impact on human life. Lipp et al. [2001] examined the influence of ENSO on coastal water
quality in Tampa Bay, Florida (USA). As is consistent with the common trend, precipitation and
stream flow are augmented in south central Florida in the warm phase of ENSO [Lipp et al., 2001].
This amplified influx causes a deterioration in water quality; therefore, the study concluded that
ENSO and degraded water quality were in phase with one another [Lipp et al., 2001]. An
important aspect that was observed in this study as well was that water quality decreased even
more during the winter season [Lipp et al., 2001]. This was quantified by an overall increase in
fecal pollution that were able to be transported due to the increase in rainfall [Lipp e. al., 2001].
11. 5 | Sanchez-Lohff
Many of the hydrologic effects of ENSO can be linked to each other. For example, Dai et
al. [1998] studied the effect of ENSO on dry and wet areas around the globe by examining soil
moisture. The Palmer Drought Severity Index (PDSI), a proxy for soil moisture content, was used
in the study. PDSI was evaluated with available stream flow and soil moisture to determine
moisture conditions on the ground in the area of question. They found that variations in severe
drought and severe moisture surplus were often induced by ENSO events. The precipitation
anomalies associated with ENSO prompt the temporal and spatial patterns of the PDSI [Dai et al.,
2004]. Rasanen and Kummu [2012] did a similar study focusing on interannual variations
between cumulative flow causing severe floods and droughts in South East Asia. The study was
done in a largely monsoon-dominated area in the Mekong River Basin. In this case, however,
ENSO was found to have a mitigating effect on precipitation of these monsoons [Rasanen and
Kummu, 2012]. The local climatological variations due to ENSO also had a lagged effect on the
hydrologic processes in the area [Rasanen and Kummu, 2012]. As exemplified by these two
studies, ENSO has many different effects on a variety of elements.
Although the effects of ENSO are felt globally, influences are unique to different areas of
the globe. There have been many studies centered on the analysis of signal strength of ENSO in
the United States. These studies have shown that even within the United States there are different
influences specific to certain regions. Ropelewski and Halpert [1986] first introduced the method
of 24-month harmonic analysis to discover regions that had similar hydraulic responses. There
were only four main regions that showed a coherent ENSO precipitation response: Gulf of Mexico
(GM- Texas to Florida), High Plains (HP), Mid-Atlantic, and Great Basins (GB) [Kurtzman and
Scanlon, 2007]. The rest of North America was not found to have a clear ENSO-related
precipitation response [Kurtzman and Scanlon, 2007]. Some of the four high-correlative areas
12. 6 | Sanchez-Lohff
showed a higher coherence than others [Kurtzman and Scanlon, 2007]. For example, time series
of the October to March months in the GM region showed a 50% increase in precipitation in the
18 out of 22 ENSO events analyzed [Kurtzman and Scanlon, 2007]. Analysis of GB times series
yielded an above average precipitation rate in 9 out of the 11 ENSO events analyzed.
Countless studies reiterate the common trend of higher average precipitation in the United
States during the warm phase of the ENSO cycle. Two studies specific to North Carolina focused
on the effect of this augmented precipitation influenced by ENSO—these include groundwater and
submarine groundwater discharge. These studies are especially relevant as their methods and
procedures are very similar to the ones done in this study. In their first study, Anderson and
Emanuel [2008] found El Nino winter to produce an average of 67% more rainfall than during La
Nina conditions. Another important observation is that the intensity of the correlation steadily
decayed inland [Anderson and Emanuel, 2008]. This augmented precipitation was felt in
baseflow, but had a lagged effect, which ranged between zero to three months [Anderson and
Emanuel, 2008]. During the winter season, ENSO influence was most strongly felt in the
groundwater system two months after the event peaked; there was twice as much baseflow in effect
of a strong El Niño cycle [Anderson and Emanuel, 2008]. In another study, Anderson and
Emanuel [2010] confirmed that the ENSO signal is transmitted to submarine groundwater
discharge as well. The coastal aquifer of Hatteras Island in eastern North Carolina was analyzed
in the study. Through spectral analysis of seasonal recharge and precipitation, high variance
around a period of 2 to 7 years was significant and interpreted as ENSO oscillations. When taking
the lag into account there was a very significant correlation between submarine groundwater
discharge/recharge and ENSO.
13. 7 | Sanchez-Lohff
Previous studies of the Southeastern United States, and North Carolina in particular, have
documented the effects of ENSO on precipitation and groundwater resources. No study to date
has looked at connections between ENSO and specific precipitation characteristics. Here, we
analyze bulk storm related statistics with ENSO to try and predict precipitation tendencies along
the Southeastern coast of the United States. Being able to anticipate rainfall trends for specific
regions one or two seasons in advance would be invaluable knowledge that could be put to
optimizing water management decisions. This is especially true in a place like North Carolina,
which relies so heavily on the resource, both agriculturally and industrially.
14. 8 | Sanchez-Lohff
2. METHODS
This study uses precipitation data to generate bi-monthly and seasonal averages from a
number of bulk statistics. As mentioned above, the hydrologic parameters analyzed are: storm
arrival, storm duration, storm depth, storm intensity, and storm interval. These calculated time
series are then evaluated against Multivariate ENSO Index, MEI (reference: Methods, 2.2). The
precipitation data come from observations at a large number of weather stations distributed evenly
between the three physiographic provinces of North Carolina: Coastal Plain, Piedmont, and Blue
Ridge. These individual regions within the state are analyzed by generating cross coherence
wavelets for each site using a script written by Grinsted [2004]. The wavelets are correlation
figures that compare time-to-frequency representations of both MEI values and each filtered storm
characteristic [Holman et al., 2011]. From these methods, we will present an in-depth quantitative
analysis of ENSO-related parameters in North Carolina.
2.1. Data
As this is a very data-intensive project, there were many steps that had to be taken to
prepare these data before any correlation analyses could be done. Initially, rainfall measurements
were requested from the State Climate Office of North Carolina [http://www.nc-
climate.ncsu.edu/cronos]. Each site represents a dense log of daily precipitation measurements
that range back to December 1949 and finish at the end of December 2013. This is the largest
possible data set available as 1949 was the first year that daily rain measurements were recorded.
It is important to note that our study only analyzes years ranging from 1950 to 2013; December
15. 9 | Sanchez-Lohff
1949 was needed to calculate the initial date for the bimonthly value, which is explained further
below.
Because our study is centered on cross-correlating to evaluate ENSO influence, a large and
dense data set is very important as it allows for the interannual variations of ENSO to be effectively
recognized, while also avoiding aliasing of the oscillations. An identical number of site data were
requested for each physiographic province to accomplish an even site distribution throughout the
state. However, upon data manipulation some of the sites had to be deleted from the study, so the
total number of stations within each region is not exactly the same in the correlation part of the
study. The Blue Ridge region has 17 total sites, while the Coastal Plain has 16 total sites, and the
Piedmont has 13 total sites.
2.2. ENSO Indices
There are a variety of indices for determining the phase of ENSO. An evaluation of all of
these was done to determine the most accurate index to utilize in this study. One of the indices is
compiled by the Japan Meteorological Agency (JMA). This index is a mean of SST in the tropical
Pacific Ocean during a 5-month period in 2 ̊ x 2 ̊ grids [Hong et al.; Trenberth, 1997]. The JMA
index categorizes periods into three phases: cold phase, neutral phase, and warm phase [Trenberth,
1997]. The warm phase, which represents El Niño events, is defined as 6 consecutive months with
an average SST anomaly greater than 0.5 ˚C [Trenberth, 1997]. A cold phase, which represents
La Niña events, is similarly categorized as an area with SST anomalies less than -0.5 ˚C for a six
consecutive month period [Trenberth, 1997]. Anywhere that lies in between these two bounds is
defined as a neutral phase [Trenberth, 1997]. The Southern Oscillation Index (SOI) is another
indicator of the ENSO state. It is based on the difference between surface air pressure anomaly
16. 10 | Sanchez-Lohff
between Tahiti and Darwin, Australia [Hong et al.; Trenberth, 1997]. The SOI, however, is
relatively noisy; indices based on SST are much less noisy [Hong et al.].
The method of monitoring ENSO used in this study is Multivariate ENSO Index (MEI).
Due to its analysis of six different parameters, MEI is considered one of the best indices for
characterizing ENSO [Wolter and Timlin, 1998]. The components of MEI are sea-level pressure,
sea-surface temperatures, zonal and meridional components of surface wind, surface-air
temperature, and cloudiness in the South Pacific Ocean [Wolter and Timlin, 1998; Wolter and
Timlin, 1993]. MEI offers an all-encompassing, multi-variable way of expressing ENSO more
accurately and with less vulnerability to error; for these reasons, we use it in our study.
2.3. Data Manipulation
There were many steps that had to be taken towards data processing after the raw data was
acquired. Initially, the task was to convert precipitation observations to a similar format as MEI.
There were a number of inconsistencies in the data that had to be addressed along the way, all of
which are explained below. As this is a very data-intensive project, much of the process was
accomplished through automated methods in the interest of efficiency and appropriate
manipulation criteria.
Once daily precipitation values for the years in question were attained for each station,
missing dates within the measurements were evaluated. Almost all of the sites had measurements
that were missing. Heterogeneity in respective site data presents a large problem as each site much
present an identical range of dates for proper analyses to be executed. Each site was made linearly
continuous by using Excel to ensure the exact same number of measurements per site. Each of the
missing dates was replaced with “NaN” (meaning “Not a Number”) in anticipation of processing
17. 11 | Sanchez-Lohff
through Matlab. It is also important to note that as well as non-linear records, there was also
another inconsistency in the data that had to be addressed, that is non-continuous observations.
There were a number of measurements at each site that were not recorded for certain days. These
missing measurements were also replaced with “NaN”, and were dealt with using Matlab later on
in the process. Since this is such a huge range of data, with each site containing 23,407 daily
precipitation measurements, some missing data points can be overlooked. However, to avoid
inaccuracy, all sites missing more than 1000 measurements were omitted from the study.
The majority of the data were processed through automation. A series of scripts were
executed to manipulate data to the desired output. To begin, the daily precipitation observations
for each site had to be converted into each individual parameter. Each specific precipitation
characteristic was calculated differently and was produced by the function ‘StormStat.m’
(reference: Appendix I, 6.1). Storm arrival is the time between the beginning of storms in data
units. Storm interval is the length of time between storms (end of one to the beginning of the next
in data units). Storm duration is the duration of storm in data units. Storm depth is the depth of
rainfall during each storm in data units. Finally, storm intensity is the average depth of storm per
unit time based on storm duration.
Further methods were taken to manipulate the data to make them similarly formatted to
MEI. ENSO is represented in the MEI as bimonthly averages; MEI values from 1950 to 2013
were taken from the National Ocean and Atmospheric Administration website
(http://www.noaa.gov/). As MEI is derived from bi-monthly means, to analyze each bulk
parameter appropriately, each output was converted into bimonthly averages. This was
accomplished through the ‘BiMonthlySeasonal.m’ function (reference: Appendix I, 6.2), where
each parameter was converted into bulk bimonthly values. In this step of data manipulation, the
18. 12 | Sanchez-Lohff
problem of non-continuous data was addressed. Through calculation of bimonthly means, most
of the missing observations were averaged out. However, for some of the sites, some NaNs still
remained after this manipulation. To account for this, after bulk bimonthly values were calculated,
they were linearly interpreted. This was done by calling ‘interpNaN.m’ (Dr. Scott Marshall,
written communication, 2014; reference: Appendix I, 6.3). Through these methods, each
precipitation statistic was both continuous and analogous, and appropriately manipulated to be
compared to MEI.
Previous studies have shown that seasonal peaks of El Niño cycles correlate most
significantly with hydrologic parameters in the winter in much of the Southern US [Kurtzman and
Scanlon, 2007]. Winter is defined as DJF, characterized as an average between the bimonthly
values of December-January (DJ), January-February (JF) and February-March (FM).
Characteristically, El Niño is reflected in anomalously wet winters in the Southeastern United
States [Kurtzman and Scanlon, 2007; Seager et al., 2009]. To analyze cross-correlation between
winter months, DJF seasonal bimonthly means were calculated for each parameter. These were
produced after yearly bimonthly averages were calculated in the ‘BiMonthlySeasonal.m’ function
as well. Once all of these steps were taken, cross-correlation figures were then able to be produced.
2.4. Wavelets
Both mono- and multi- cross wavelets are used to investigate correlation in this study.
Wavelets analyze periodicity and frequency of a continuous time series [Grinsted et al., 2004]. A
wavelet is a small wave that determines signal strength at certain periods or frequencies [Holman
et al., 2010]. Transform wavelets are specific to one single time series; they are correlated to
themselves and extract signal based on the oscillation of the time series in question [Grinsted et
19. 13 | Sanchez-Lohff
al., 2004]. This single comparison is called the Continuous Wavelet Transform (CWT). Multi-
cross wavelets are also used in this study, comparing two time series together in a single transform
wavelet. The first, Cross Wavelet Transform (XWT), determines common power and common
phase of each time series [Grinsted et al., 2004]. The second, Wavelet Coherence (WTC)
identifies areas of any common power (no matter how low it may be), and compares it to noise to
determine confidence levels [Grinsted et al., 2004]. A complete description of all wavelets can
be found at Grinsted et al. [2004]. To produce all of these wavelets in an automated fashion, the
script ‘DJFautoplot.m’ (reference: Appendix I, 6.4), which defined necessary variables for each
parameter and autosaved the figures.
The application of wavelets in this data set provides important insight into significance
level of unique parameters through time. By generating cross-correlated figures, the pattern of
oscillation of both MEI and the precipitation parameter in question is analyzed, with respect to
time. Through this, we are not only able to get a visualization of where the two are significant,
but also evaluate different characteristics of the time series, including amplitude and frequency
[Gurdak and Kuss, 2014]. By analyzing these two parameters, the cross-wavelet correlation
figures identify the phase of cycles with respect to one another. The phase of the cross-analyzed
oscillations are represented on the XWT figure by arrows—arrows pointing right are completely
in phase, while left-pointing are completely out of phase. The significant areas are represented by
hotter colors (red), and significant correlative areas are outlined in black.
The analysis of CWT, XWT, and WTC gave insight into many areas of significance with
respect to each site, and also with respect to each physiographic region within the state. Although
all three of these figures were produced in this study, a main focus is placed on XWT to determine
the most significant areas to relevant parameters.
20. 14 | Sanchez-Lohff
2.5. GIS
The program arcMap, which utilizes Geographic Information Systems, was used to give a
visualization of XWT correlation figures throughout the state. By plotting them on the map, a
better idea of the difference in significance associated with the various regions is displayed more
effectively on the map. Through the produced maps, a qualitative comparison between each
parameter was evaluated. There were a number of steps taken to producing these maps.
To begin, shapefiles of the North Carolina counties and shoreline were downloaded from
the Appalachian geography drive. Then a dataset was created in order to dissolve the regions from
the county file, and also to plot all the stations used in the study; two excel files were created to
accomplish this. The first was compiled to dissolve the regions; it contained every county in
North Carolina and its associated region. This table was then joined to county shapefile and the
regions could then be dissolved out and exported as a new shapefile. A second Excel sheet was
compiled with each station and its associated longitude and latitude measurements. These
coordinates were taken from the original file that was requested from the State Climate Office of
North Carolina [http://www.nc-climate.ncsu.edu/cronos]. These were then plotted on the map to
show each of the different sites locations throughout the state.
After the base map was completed by taking the above steps, the wavelets were import and
placed in their appropriate locations. Not all of the wavelet images were placed on map to avoid
clutter; only the best sites are represented in the map. In this way, the reader is given an overall
visualization of the associated wavelets and overall trends for each parameter. There is a map
made for all of the parameters, and varying correlation between each time series can be interpreted
from each map.
21. 15 | Sanchez-Lohff
2.6. Quantification
Although the maps provide a visualization of the wavelets, there is also a quantitative
evaluation of the correlation associated throughout the state included in the study. While there are
two individual datasets produced, each is calculated in the same manner. To pinpoint the most
significant areas that are indicative of ENSO cycles, specific periods and dates were targeted.
Since ENSO oscillates at a period between 2-7 years, these are the values on the y-axis that are
targeted [Gurdak and Kuss, 2014]. Only the years 1978 to 2000 are analyzed because these are
associated with known strong ENSO cycles.
Before being able to determine the magnitude of significance within the above ENSO-
linked region, numeric values of significance for each wavelet had to be outputted. This was
accomplished through the function ‘numOscillation.m’ (reference: Appendix I, 6.5). After text
files for each wavelet were produced, the script ‘magMaxes.m’ (reference: Appendix I, 6.6)
isolated the target area noted above. The significant areas above or equal to 1.0 within the targeted
area in the previous data set are compiled. These were only done for XWT, as this figure shows
correlation for cross-correlation at the same scale. A unique scale for all analyzed sites is very
important, so a clear and accurate comparison can be executed. This is repeated for all the
parameters for every site. Through these methods, a more accurate reading of the significance of
ENSO is determined. An average of each region is also determined in this process. A significance
value of 1.0 is indicative of high correlation within the time series and falls around 2.0 in the scale
bar associated in the XWT figures. The values ≥ 1.0 are summed to find an ultimate magnitude
for each site, and the number of values ≥ 1.0 for each site are also counted. Using the two compiled
variables—magnitude of significance and number of significant variables—four figure types were
created using the curve-fitting toolbox in Matlab.
22. 16 | Sanchez-Lohff
The curve-fitting toolbox fits a surface to all the data points through cubic interpolation.
Consistent with the wavelet figures, areas with high values are plotted in hotter colors, while lower
values are plotted in cooler colors. By fitting a curve to each site’s associated numeric value, an
all-encompassing image denotes areas of high correlation on one single map of North Carolina as
opposed to one wavelet per site. The first figure-type shows the number of counted variables
plotted for each site, which is repeated for every parameter. The second figure-type shows the
magnitude of significant values plotted for each site. The third figure-type is similar to the
previous, but is depicted in contour form. The final figure-type is a 3D visualization of the
magnitude for each site.
Although all the produced plots show accurate and relevant information, only two are used
in the study: the contour plots and 3D images. The first figure-type with the counted number of
significant values plotted are very similar to the magnitude plots; therefore, they are not discussed
further in this study. The second and third figure-types are very similar as they represent the same
data. This study uses the contour plots to represent compiled magnitudes. The images are
characterized by a contour interval of 5 so that most of the extreme values are not lost. Other
adjustments were made to the scale; the scale of all parameters is forced to range from 0 to 210.
This specific range was chosen through analysis of the minimum and maximum values in the
magnitude summations of each of the parameters. During the cubic interpolation, a surface is fit
to these data, which produces some negative values. Since the scale has been forced to start at 0,
these negative values are shown as white spots on the plot. The final figure-type used in this study
is the 3D representation of the magnitudes. Although the same data as depicted in the contour
plot, the 3D images give a better visualization of the scale of magnitude and show trends in the
data that are hard to see in the 2D images. Since the utility of 3D images is greatly augmented
23. 17 | Sanchez-Lohff
with a rotational application, a video was made of each image from helpful views. To create this
automated visual, Dr. Alan Jennings’ function, ‘CaptureFigVid.m’ (reference: Appendix II), was
used. Each of these figures demonstrates the data uniquely, yet effectively.
After all of these figures were produced, a coast line was fitted on top of the contour plots.
The state border file was compiled and provided by Dr. Scott Marshall. The state border was fitted
to the contour plot using Adobe Illustrator. It is important to note that these are just an
approximation of border locations. Also, Matlab is not a mapping program, so all sites are not
located perfectly. To determine exact locations of sites in relation to state borders, please reference
Figure 1 (reference: Results, 3.1).
24. 18 | Sanchez-Lohff
3. RESULTS
3.1. Site Descriptions
To generate the results, rain observations from 46 sites were used through a time period of
64 years. A major part of this study is analyzing the difference in ENSO signal between each
physiographic region; due to this emphasis it is important to define these regions concretely. The
Blue Ridge region is the smallest and furthest west province; it is located in the Appalachian
Mountains. It is important to note that the sites in this region are at much higher elevation than
other regions; in addition, these sites are more isolated in comparison to those of other provinces.
The Piedmont region is the center region and encompasses the plateau area of North Carolina. The
Coastal Plain is the eastern most province and includes the deltaic and littoral areas within the
state. Precipitation data are used at the study sites within each province for our analysis. Figure
1 shows all of the sites with their appropriate location and name along with which region they are
located in.
3.2. Wavelet and Magnitude Analysis
When analyzing the MEI, there is more weight put on the intensity of the cycle rather than
its length [Wolter and Timlin, 1998]. For this reason, wavelet analysis is an especially effective
way of quantifying the ENSO signal, as each analysis distinguishes and places an emphasis on
highly correlative areas. Since ENSO oscillates on a 2-7 year period, all other significant areas
within the wavelet in question can be ruled out and attributed to some other climatic process
[Gurdak and Kuss, 2014]. Through examination of the MEI time series, one can compare signal
26. 20 | Sanchez-Lohff
strength in the wavelet and associate it with a strong El Niño cycle. In this way, an investigation
of ENSO correlation in relation to each storm statistic is carried out.
The following are results of examination of XWT figures representing only the winter
months (DJF). Consistently, bulk-parameter wavelets showed much poorer correlation, if any at
all; for this reason, only DJF wavelets are presented here. This cross-correlation between the two
variables, MEI and each storm statistic, allows for little room for error; it is extremely unlikely
that the areas shown as having a high correlation, are non-correlative. This is attributed to the
analysis that each cross wavelet transform figure goes through to be produced. The oscillations of
each variable with respect to time is compared and correlated to one another. A common power
as well as phase angles between standardized time series are calculated and then represented in the
figure [Grinsted et al., 2004]. To verify this, a thick black contour denotes 5% significance value,
which is associated with a 95% confidence level [Grinsted et al., 2004]. These delineated regions
are in most cases of high correlation; in this study, we have designated high significance to what
is equivalent to be greater than or equal to 2.0 on the associated scale. The resulting figures
produced from the plotted magnitudes for each site of the highly correlative areas ≥ 2.0 that fall
within the appropriate period and years, are also presented below. Although none of the
parameters yield data sets that monotonically increase or decrease in any direction, overall trends
can be visualized.
3.2.2. Storm Arrival
To reiterate, storm arrival in this study is defined as the time between the beginning of
storms in data units. It is important to note that during the evaluation of correlation, only the
27. 21 | Sanchez-Lohff
significant areas located in the middle of the wavelet, which are most likely to be linked with
ENSO, are used when determining any trends (reference: Discussion, 4.2). Arrival date proved to
be one of the highly correlative parameters. There is a strong decay in signal that can be observed
through the wavelets; this trend of increasing length between arrival dates when moving further
inland, and be visualized in Figure 2. There are a higher number of strongly correlative areas
further west than further east. The Coastal Plain region seems to have much less significance
overall than do the Piedmont or Blue Ridge regions. Consistent with most observations taken from
natural phenomenon, there are outliers in the data set. An outlier in the Coastal Plain is Kinston,
which, although relatively small, shows a positive ENSO-correlated area. In the Blue Ridge, Celo
is a larger outlier, as it has absolutely no correlation, whereas most of the neighboring sites do have
significant areas.
The quantification of correlation magnification within the targeted ENSO-linked area for arrival
date, also yields interesting results (Figure 3). This comprehensive visualization of distributed
magnitude verifies the increasing arrival date value further inland, interpreted from Figure 2. More
detail is shown in this contour plot, and with this an ENE trending line splits the area with high
significance, and low significance. Therefore, a unanimously segmented difference between each
region is not seen in arrival date; instead of increasing from east to west, arrival date more so
increases from SE to NW. This trend is also seen in a more tangible visualization in Figure 4 and
Video 1 (reference: Appendix II). This video is more effective at visualizing the contour plot, as
it allows for more observations to be made from a number of views and to give an overall all-
encompassing interpretation to be made. Although there are many individual peaks, there is an
overall much higher magnitude of significance in the NW region of the state. The outlier, Celo,
mentioned above is also pictured clearly in Figure 3. Since Celo has such a low arrival date value
28. 22 | Sanchez-Lohff
Storm Arrival Date XWT plots
Blue Ridge
Coastal Plain
Piedmont
Stations
0 50 10025 Map 2, Senior Honors Thesis
Created by: Sonia K. Sanchez Lohff
Figure 2. Map 2 gives a visualization of a number of wavelet figures in their associated regions. The physiographic
provinces are also indicated on the map. These specific wavelet figures were chosen arbitrarily in terms of
significance; they were chosen based on their location to avoid clutter and what would most the most effective
visualization to trends.
31. 25 | Sanchez-Lohff
comparatively, it is represented as a negative correlation and shows up as a white region in the
Blue Ridge region.
3.2.2. Storm Depth
Storm depth was found to have the highest correlation with ENSO in this study. As shown
in Figure 5, the significant areas in the Coastal Plain linked with ENSO are very strong and large;
this is accentuated when compared to the values in the Blue Ridge region. The figure also shows
a more unanimous variance in each region—the Coastal Plain, as a whole, seems to have a much
larger significance than either the Piedmont or Blue Ridge. Although some sites show a stronger
correlation than others in the Coastal Plain, all have some significant area. The Blue Ridge region
is not so unanimous in terms of related correlated areas. Most of the sites are fairly similar, but
there are a few sites that have a significant more amount of correlated areas. For example, the
wavelet associated with Lenoir is much more correlative in comparison to Banner Elk’s produced
wavelet. However, as is consistent with the previous observation, there is a common trend that
most discrepancies within and compared to each region are described by most significant being
east and less significant being west.
In Figure 6, the discrepancy between significance is shown well, and the maximum
magnitude is very high in comparison to the contour plots of other parameters. It is important to
note that this highly significant area is located in the SE corner of North Carolina; this area proves
to be very correlative consistently throughout out all of the parameters. The change and slope of
the contours is much more gradual and unanimous than arrival date; this can be attributed to the
presence of a higher bulk significance magnitude in the Coastal Plain. There are
32. 26 | Sanchez-Lohff
Storm Depth XWT plotsBlue Ridge
Coastal Plain
Piedmont
Stations
0 50 10025 Map 3, Senior Honors Thesis
Created by: Sonia K. Sanchez Lohff
Figure 5. Map 3 gives a visualization of a number of w avelet figures in their associated regions for Storm Depth.
The physiographic provinces are also indicated on the ma p.
35. 29 | Sanchez-Lohff
many intermediate signal strength values along with high signal strength values along the
coastline, but not many extremely low values; this is consistent with a lack of outliers in the
Coastal Plain, as discussed above. This gradual slope is exemplified well in Figure 7, as the
added dimension provides more effective visualization is magnitude discrepancies. Although the
surface fitted to these points is indeed much more planar, there is still a SE to NW trend seen in
storm depth as is similar to arrival date, which is also depicted in Figure 8 as well as Video 2
(reference: Appendix II) very well. With the rotational nature in Video 2, the maximum points
are illustrated very well in comparison to other surrounding areas, as well as the gradual
decreasing surface slope trending towards the west.
3.2.3. Storm Duration
Storm duration is one of the poorest parameters with relation to ENSO. Figure 8 shows a
spread of the storm duration wavelets, from which very few common trends or patterns are
observed. When observing correlation between Coastal Plain sites and Blue Ridge sites, there is
no particular associated significance for each of these regions; both have a mix of sites with high
significance and low significance. Curiously, Celo, which is normally an outlier within data sets,
shows relatively high significance when compared to neighboring sites. Also unlike the other
precipitation parameters, the Piedmont region is actually the one with the most wavelets showing
high correlation. This characteristic of storm duration is shown more effectively in Figure 9 and
Figure 10. Figure 10 shows the magnitude of significance as a contour plot while Figure 11 shows
these same values in 3-dimentions. All the high significance values are in the middle of the state,
many of which are located in the Piedmont. A final observation that can be made from this storm
duration is that, although not a highly correlative parameter, the reoccurring SE to NW
36. 30 | Sanchez-Lohff
Storm Duration XWT plotsBlue Ridge
Coastal Plain
Piedmont
Stations
0 50 10025 Map 4, Senior Honors Thesis
Created by: Sonia K. Sanchez Lohff
Figure 8. Map 4 gives a visualization of a number of w avelet figures for Storm Duration in their associated regions.
The physiographic provinces are also indicated on the ma p.
38. 32 | Sanchez-Lohff
Figure 10. This plot is 3D surface representation of the cont our plot for Storm Duration (Figure 9). This added
dimension gives a better visualization of magnitude wit h respect to location within the state. Video 3
(reference: Appendix), shows this plot with initiate rota tion from different angles.
39. 33 | Sanchez-Lohff
trend is somewhat apparent in Figure 9. Video 3 (reference: Appendix II) offers different views
where this trend can be visualized better. In addition, the overall lack of significance of storm
duration when compared to other parameters can be observed during the rotational views of the
plot.
3.2.4. Storm Intensity
Similar to storm duration, storm intensity wavelets and plots also returned somewhat
inconclusive results. Figure 11 shows no common trend, and investigation into each individual
region yields that each physiographic province seems to contain wavelets with similar variances
in strong and low correlation. With this individual assessment of each region, they can be observed
as a progressive unit. There is no clear progression going from the Coastal Plain to the Blue Ridge.
Much more about signal strength of storm intensity can be observed through examination
of the plotted magnitudes in Figure 12. Storm intensity shows the lowest significant values when
compared to the other precipitation parameters. We again see the SE to NW tend that is observed
in the previous contour plots. When Figure 12 is compared to the contour plot for storm depth
(Figure 6), a similarity is detected between the two; both have unique significant localized areas,
all of which whose location is depicted well in Figure 13. In summary, storm intensity did not
show very much correlation with ENSO, but yielded some interesting observations that might have
an effect on other parameters (reference: Discussion).
3.2.5. Storm Interval
As storm interval is closely associated with storm arrival, the results are fairly similar.
Although there are outliers within the data set, there is an overall increasing signal strength going
40. 34 | Sanchez-Lohff
Storm Intensity XWT plotsBlue Ridge
Coastal Plain
Piedmont
Stations
0 50 10025 Map 5, Senior Honors Thesis
Created by: Sonia K. Sanchez Lohff
Figure 11. Map 5 gives a visualization of a number of wavelet figures in their associated regions. The physiographic provinces are
also indicated on the map
43. 37 | Sanchez-Lohff
inland. Both the Blue Ridge and Piedmont regions have a much higher overall number of wavelets
that show high correlations, when compared to the Coastal Plain. Figure 14 depicts this well, as
well as some outliers that are associated with regions. In the Blue Ridge region there are two large
outliers, Banner Elk and Celo—they show low correlation, when most neighboring wavelets show
high significance when associated with ENSO. In the Piedmont, there are also a number of sites
that show higher correlation than some when compared to other wavelets in the region; for
example, Edenton shows a relatively high correlation with ENSO. Its very close neighbor,
Plymouth, shows an extremely low probable area that is associated with ENSO. With this
observation, it can be assumed that many of the outliers can be attributed to local effects or small-
scale geographical associations that cause the drastic changes.
When the contour plots of storm interval (Figure 15) and storm arrival (Figure 3) are
compared, the similarity between the two parameters is evident. It is important to note that storm
interval seems to have a wider area of correlative magnitudes, specifically in the west; however,
storm arrival have higher overall magnitudes, but is more discontinuous. In addition to this, storm
arrival also holds the weaker magnitude strength values, which are located in the east. Therefore,
storm arrival holds a greater range of magnitudes, but storm interval has more gradual changes in
magnitude. Figure 16 as well as Video 5 (reference: Appendix II), give a good visualization of
the gradual changes, yet similar geometries to storm arrival (Figure 4 & Video 1). These are just
minute differences, the two parameters yield similar development of signal strength; the ENE
trending line which splits high correlation areas to low correlation areas is present in Figure 15,
similar to storm arrival.
46. 40 | Sanchez-Lohff
Figure 16. This plot is 3D surface representation of the contour plot for Strom Interval (Figure 15). This added
dimension gives a better visualization of magnitude with respect to location within the state. Video 5
(reference: Appendix), shows this plot with initiate rotation from different angles.
47. 41 | Sanchez-Lohff
3.3. Error Analysis
There are a number of factors that must be taken into account upon interpretation of results
in this study. A principal inconsistency within the individual site records were inhomogeneities in
station rain observations, meaning that there were some daily rain observations missing. In order
to produce wavelets, the data set in question must be continuous [Grinsted et al., 2004]. The
missing data points within the data sets for each site must be linearly interpolated to produce the
required time series. There will always be error associated with any type of interpolation and
extrapolation method, as the exact values for missing points are not known. This was avoided as
much as possible by interpolating observations at each site after bi-monthly means were
calculated. By calculating bi-monthly means, some of these missing observations were eliminated
before the interpolation. Using the curve-fitting toolbox, cubic interpolation was again used to
make the surface fit of the magnitude plots. As interpolation is again used, there is error associated
with this step in the quantification process as well. Although interpolation yields some error,
extrapolation yield much more, and this method is avoided in this study.
A second problem that is hard to avoid, but must be addressed is that individual stations
may be unrepresentative of the large-scale effects, more so influenced by local effects. This is an
inevitable result in this type of study, as geography and local changes will always be present; this
can be avoided by using large data sets and interpreting an overall trend presented in the
results. Stations that are consistent outliers much be noted as well. As many stations that had the
appropriate data were used in this study. The principal way this problem can be avoided is by
including as many data points from a large data set as possible. We used as many sites are possible
in this study, however, many had to be eliminated either due to (1) lack of data spanning the
number of years used in this study, (2) too many missing rain observations when making the data
48. 42 | Sanchez-Lohff
linearly continuous, and (3) a lack of sites in areas, in particular the Outer Banks. As much of state
boundaries along the Outer Banks is covered in water (Albemarle Sound and Pamlico Sound), it
is hard to get input rain from these areas.
49. 43 | Sanchez-Lohff
4. DISCUSSION
4.1. Teleconnection within MEI Time Series
Before presenting the interpretation of our results, it is important to discuss the patterns
and trends associated with ENSO unique to itself. When observing a time series of MEI, a
visualization of extreme events of both El Niño and La Niña phases; El Niño (La Niña) being the
warm (cold) phase, typically shown in red (blue). Although there is a large emphasis placed on
ENSO in this study, the phase of the Pacific Decadal Oscillation (PDO) should also be assessed
when analyzing period of a high percentage of warm phases; is also important to acknowledge the
interannual and interdecadal connection between ENSO and PDO, as it potentially augments the
teleconnection of a parameter [Anderson and Emanuel, 2008]. Notable years of strong El Niño
cycles are 1982/83 and 1997/98 [Wolter and Timlin, 1998]. Although these are two very extreme
records of El Niño cycles, they fall within a range of years, 1978-2000, that, as a unit, are
characteristically high El Niño signals. This is due to the combination of warm ENSO cycles with
a warm PDO phase.
4.2. Wavelet Breakdown Example
Here, two wavelets are analyzed to give insight into our individual analysis of each
wavelet. Through this method, only correlation associated with ENSO was separated out and
quantified. After individual assessment at each site, regions could be evaluated as a whole and
overall trends throughout the state were determined. The two sites picked for this section are
representative of storm depth: Plymouth in the Coastal Plain, and Banner Elk in the Blue Ridge
50. 45 | Sanchez-Lohff
(Figure 18). These sites were picked as they have near continuous data, and therefore there is less
error associated with these sites. Depth was chosen as the parameter in question because it has
been proven to be very correlative with ENSO. Finally, through analysis of Banner Elk and
Plymouth, a very general trend can be determined in relation to variable signal strength.
Since ENSO oscillates at a period of 2-7 years, these were the values analyzed on the y-
axis [Gurdak and Kuss, 2014]. As explained above, there are certain years that are known to be
very intense El Niño cycles that produce strong signal strength; the combination with PDO and
ENSO will cause an even higher signal strength—these years range from 1978-2000, which are
the values targeted on the x-axis. Although there might be other highly correlative areas within
the wavelet that can be attributed to ENSO, we have used the above targeted area, as there is an
extremely low probability that contoured areas are not associated with ENSO. In addition, the
years of intense El Niño cycles fall in the middle of our data-set and cone of influence. This highly
sampled region is then even more likely to be correlative as there is no extrapolation going on.
When analyzing the sites in Figure 17, it is evident that Plymouth is much more correlative
than Banner Elk. The maximum significance level is much higher; in addition, the magnitude of
high significance as well as the area contoured is much larger than that of Banner Elk. For the
sake of this example, with the above observations taken into question, it can be inferred that there
is a much stronger ENSO signal felt in the storm depth of coastal areas of North Carolina than in
the mountains further west.
Although there is not much emphasis placed on phase of the cross-analyzed timeseries, it
is also important to note the direction the arrow is pointing within the correlative areas (Figure 17).
For example, both the ENSO-linked correlations in Banner Elk and Plymouth are nearly
52. 47 | Sanchez-Lohff
perpendicular to the x-axis pointing right. This indicates that both oscillations are in phase with
each other. However, when analyzed closer, Plymouth is a little more out of phase than Banner
Elk, therefore, it can be inferred that although there is a strong correlation between ENSO and
storm depth in Plymouth, there is a small lag between these two phenomenon.
4.3. Comparative Observations
In previous studies, winter months showed a much higher signal with ENSO than
wholescale time series. Kurtzman and Scanlon [2007] also found there to be significant (P < 0.05)
augmented (decreased) rainfall anomalies during winter seasons of El Niño cycles (La Niña
cycles). Anderson and Emanuel [2008], who approached ENSO correlation in a very similar way
to this study, saw enhanced winter discharge, which was related to minimal evapotranspiration
(maximum recharge) specific to North Carolina. Many other studies have confirmed this
tendency; however, not many studies have used wavelets as a key tool in the
investigation. Through the analysis of wavelets within each region, consistent significance was
observed with previous finding on winter-correlation early on in the study. DJF XWT results
showed much more correlation with ENSO than yearly bulk data XWT figures. In many cases,
sites that show a very high correlation in DJF cross-correlated figures, show extremely low signal,
if any in bulk-yearly data.
Another aspect of our study that proved to be consistent with previous studies was the high
correlativity of precipitation depth. As precipitation depth is the most commonly collected
parameter, many studies have shown a significant correlation with ENSO (reference: Introduction,
1.2). This study also found storm depth to be the most correlative parameter with the highest
summed power magnitude. Although not by very much, it is still important to note the strongest
53. 48 | Sanchez-Lohff
magnitude of correlation is found in the southeast region of the state. This region has proven to
be an especially correlative area in the state. Anderson and Emanuel [2008] found this area to be
highly significant in their study analyzing groundwater discharge and ENSO. Due to this highly
correlative area, instead of decaying in an east to west fashion, significance seems to decrease in
a SE to NW fashion. Although on a very broad scale, Kurtzman and Scanlon [2007] also observed
this decrease in significance going from the SE to the NW, and actually denoted the far west region
of the state of North Carolina to be almost non-significant. This is also found in other parameters,
which is explained below (reference: Discussion, 4.2).
Another important note about storm depth’s signal is the highly consistent decay of
signal. It has the least noisy and most gradual change in significance than any of the other
statistical parameters. A non-noisy data set would have a very continuous slope with a lack of
outliers. Figure 6 and 7, as well as Video 2, show this effect as a decreasing slope trending towards
the Blue Ridge region. There are lack of outliers within the data set, which gives it a more
continuous slope and gradual decay of significance. This might be attributed to its highly
significant association with ENSO.
The final hypothesis we made upon initiation of the project was that there would be a decay
in significance with distance from the Atlantic coast. This was indeed observed in storm depth, as
mentioned above. However, two parameters showed an opposite effect, with significance
increasing toward the Blue Ridge region: storm arrival and storm interval. As these two parameters
are closely related, storm arrival being the time between the beginning of a storm to the beginning
of the next and storm interval being time between the end of storms and the beginning of the next,
it makes sense that the two show similar results.
54. 49 | Sanchez-Lohff
4.2. Parameter Observations
In summary, there were three storm statistics that proved to be correlative with ENSO:
storm arrival, storm depth, and storm interval. As mentioned above, storm depth showed an
opposite decay in correlation than storm arrival and interval. Although this is not what we
expected, the two observations support themselves. Since there is a longer storm arrival and storm
interval along the Blue Ridge area, it makes sense for there to be a higher storm depth along the
Atlantic Coast. A larger magnitude of significance in the Blue Ridge for storm arrival and interval
indicates a longer time between storms. This result is consistent with augmented storm depth
along the coast, as there is a shorter time between storms.
The two other parameters, storm duration and storm intensity, did not show very conclusive
results. Although we expected intensity to be significant, its non-correlation with ENSO supports
our findings of storm depth, arrival, and interval. Since we did not find there to be any overall
trend in variability of storm duration of intensity, we can assume that these two storm statistics are
on average similar throughout the state. Therefore, it verifies that our conclusion of higher storm
depth in the Coastal Plain due to shorter interval between storms in comparison to the Blue Ridge
region.
It is important to note that a lack of variability of both storm duration and storm intensity,
however, is a very general assumption. Although at not such a significant scale as other
parameters, these two storm statistics could marginally affect other parameters. For example,
when comparing the contour plots produced for storm depth (Figure 6) and storm intensity (Figure
12), there are significant regions that overlap—the southeastern region as well as the central
northern region. The coupled significant areas between of these two parameters could be a reason
55. 50 | Sanchez-Lohff
why we see such a high magnitude of significant values in the southeastern corner of storm depth.
The central northern significant region would be due to a localized climatological effects. For this
reason, we might see a significance in the area in both storm intensity and depth.
Lastly, it is important to note the non-significant nature of the plots associated with storm
duration. This parameter is our worst in terms of significance, as well as any coupled correlation
effect with any of the other parameters. This might be due to the fact that we are forced to work
with daily data, and many storms in North Carolina last less than one day. In addition, in this
study, we classify a storm precipitation for two or more days. This also must be taken into
consideration when analyzing storm intensity and also could be something to address in future
studies.
56. 51 | Sanchez-Lohff
5. CONCLUSION
Through cross wavelet analysis done in the study, it was found that a number of storm
statistics did indeed show correlation with ENSO. Consistent with previous studies, we found
storm depth, defined as the average amount of rainfall during each storm, to be very correlative
with ENSO, decaying in significance with distance from the Atlantic Coast. Instead of decaying
uniformly between each physiographic province, however, storm depth decays in significance
from the southeastern region towards the northwestern region of the state. The other two
parameters where overall trends are observed are storm arrival and interval. Storm arrival defined
as the average amount time between the beginning of storms and storm interval defined as the
average amount of time between the storms. Both of these parameters show an opposite decay in
significance as we expected and as storm depth, with high significant areas being in the Blue Ridge
region and decaying towards the coast. These results support each other as a greater magnitude of
significance along the Blue Ridge for arrival interval indicated longer time between storms.
Assuming there is no massive variation in their storm intensity or duration, this would account for
a greater storm depth along the coast, as there is less time between storms.
The other two parameters, storm duration and intensity, did not show very conclusive
findings. Storm duration being the average time of each storm, and storm intensity being the
average depth of a storm per unit time based on storm intensity. There were no overall trends that
could be observed, and there were many extreme anomalies, most likely correlated with localized
climate effects. It is important to note that when compared to themselves, there are no conclusive
implications, but there might be a coupled effect going on with storm intensity and storm depth,
as both have significant areas that overlap. This might be due to localized augmented storm
57. 52 | Sanchez-Lohff
intensity adding to the magnitude of storm depth in those areas. Also noteworthy, storm duration
could show different results if hourly data were analyzed. Our study classified a storm as greater
than or equal to two days, and some storms in North Carolina last for less than a day. This would
be an interesting idea for a continuation of the project.
There are many other areas of further exploration for this topic of study. For example, only
XWT figures were analyzed in this study. It would be interesting to evaluate the other wavelet
figures, CWT and WTC. Both of these figures provide unique data that would add more
information to the topic in question. In addition, a more in depth analysis of the XWT figures
would be interesting further exploration. Specific to XWT figures for instance, there was not much
emphasis placed on phase of cross analyzed oscillations in this study. It would be interesting to
connect the phase of oscillations with a lag effect of associated phenomenon.
In addition to exploration of new concentrations within the topic, a broader area of study
could be evaluated. The boundaries could be extended to neighboring states like Virginia,
Tennessee, and South Carolina. Funding to produce precipitation observations for sites along the
Outer Banks would be effective as well.
Climate uncertainty is and will become an even more important reality in the future. It is
important to understand climatological processes, like ENSO, to help optimize water management
and address the impending problem of water stress. Studies like this one will help us to do so, and
could potentially help maximize the use of water in North Carolina.
58. 53 | Sanchez-Lohff
6. APPENDIX I: Associated Scripts
6.1. ‘StormStat.m’
This function identifies the individual storm within the time series in question. The
function finds arrival dates and end dates of storms and denotes a storm with “1” (non-storm
observations are classified as “0”). From these identified storms, each precipitation statistic is
calculated and returned in matrix “out”. Each column is specified below. As noted below, it was
originally created by Joshua S. Rice and was modified for this project by Dr. Bill Anderson and
Sonia K. Sanchez Lohff.
function [out, arrival_date, end_date, storm_num] = StormStat(input_rain)
% StormStat.m
% created by Joshua S. Rice (jsrice@ncsu.edu), last updated 10/16/12
% modified by William P. Anderson, Jr. (andersonwp@appstate.edu) & Sonia K.
% Sanchez Lohff, last updated 10/25/2013
% Conducts analysis of a rainfall time-series; calculating storm frequency,
% average storm intensity, and average depth of rainfall per storm
% input data should be in the format of a vector of total rainfall per day
% of observation; output units will be equal to input units
% Function outputs:
% Number of storms during record should be equal to the number of rows of
% data in the storm statistical data.
% arrival_date (:,1) = starting date of storms (in units of day number in
% the dataset)
% end_date (:,1) = ending date of storms (in units of day number in the
% dataset)
% out(:,1) = storm_arrival = arrival time of storms in data units
% (beginning of storm to beginning of storm)
% out(:,2) = storm_interval = length of time between storms in data units
% (end of storm to beginning of next storm)
% out(:,3) = storm_duration = duration of storm in data units (beginning of
% storm to end of storm)
% out(:,4) = storm_depth = depth of rainfall during each storm in data
% units
% out(:,5) = storm_intensity = average depth of storm per unit time based
% on storm duration
59. 54 | Sanchez-Lohff
rain_date = 1:length(input_rain);
rain_obs = input_rain(:,1);
% Index location of storms within the input data
%
for i = 1:length(rain_obs)
if rain_obs(i)>0
L(i,1)=1;
else
L(i,1)=0;
end
end
N=sum(L);
storm_num = N; % number of storm events in record
%
% index storm arrival rows and calculate storm arrival interval
%
aa(:,1) = find(diff(L)>0);
aa = aa+1; % add a line for fact that we start with location 2; taking row 2
- row 1 and putting in row 1
% if the first time step has precipitation it does not get counted with the 2
lines above;
% the following if loop adjusts for that
if rain_obs(1) > 0 % check if first time step is > 0
aaa = nan(N,1); % preallocate new temp variable with the length of N
aaa(2:end) = aa; % copy aa to new temp variable, starting at 2nd row
aaa(1) = 1; % set first time step to 1 (indicating rain on the first time
step)
aa = aaa; % convert back to aa
end
arrival_date = rain_date(aa);
arrival_date=arrival_date';
% Taking the diff of variable aa gives the time between the beginning of
% storms - put in variable bb
bb(:,1) = diff(aa);
bb = [NaN; bb];
storm_arrival = bb; % arrival times are for the start of one storm relative
to the start of the previous storm
out(:,1) = storm_arrival;
% index storm end rows by looking for negative diff values - put in
% variable cc
cc(:,1) = find(diff(L)<0);
cc(:,1) = cc+1; % add a day for fact that we start with location 2; taking
row 2 - row 1 and putting in row 1
end_date = rain_date(cc);
end_date=end_date';
% calculate inter-storm period (storm_interval)
% This is the time from end of one storm to beginning of the next storm
60. 55 | Sanchez-Lohff
% first row = NaN because there is no inter-storm interval for the first
% storm
for j=2:length(aa)
storm_interval(j,1) = aa(j,:) - cc(j-1,:);
end
out(:,2) = (storm_interval);
% determine length of each storm
for j=1:length(aa)-1
storm_duration(j,1) = cc(j,:) - aa(j,:);
end
storm_duration=[storm_duration; NaN;];
out(:,3) = (storm_duration);
%
% calculate depth of each storm (storm_depth)
%
for j=1:length(aa)-1
m=arrival_date(j,1);
n=end_date(j,1);
storm_depth(j,1) = sum(rain_obs(m:n));
end
storm_depth=[storm_depth; NaN;];
out(:,4) = (storm_depth);
%
% calculate intensity of each storm (storm_intensity) by dividing each
% storm depth by the duration of the storm
%
storm_intensity = storm_depth./storm_duration;
out(:,5) = (storm_intensity);
61. 56 | Sanchez-Lohff
6.2. ‘BiMonthlySeasonal.m’
As MEI, the indices for ENSO used in this study, is formulated in bimonthly averages,
this functions converts the storm precipitation statistics calculated in ‘StormStat.m’, above, into
bimonthly averages. Also in this function, winter seasonal bimonthly averages, “DJF_vec”, for
each parameter are returned. It was original created by Dr. Ryan Emanuel and was modified for
this project by Dr. Bill Anderson and Sonia K. Sanchez Lohff.
function
[MEI_vec,DJF_MEI_vec,bim_arr,DJF_arr,bim_inter,DJF_inter,bim_dur,DJF_dur,bim_
dep,DJF_dep,bim_intens,DJF_intens] = BiMonthlySeasonal(out,arrival_date)
% Calculates the correlation between MEI and DJF precip using monthly totals.
%
% BiMonthlySeasonal.m
% Version 1.0
% Created by Ryan Emanuel
% Modified by William P. Anderson and Sonia K. Sanchez Lohff
% 11/29/2007
%
%
%---------------------------MEI Bi-Monthly Values--------------------------
% Taken from R.Emanuel's ENSO script.
%
% YEAR DECJAN JANFEB FEBMAR MARAPR APRMAY MAYJUN JUNJUL JULAUG
AUGSEP SEPOCT OCTNOV NOVDEC
MEI_full=[1950 -1.022 -1.146 -1.289 -1.058 -1.419 -1.36 -1.334 -1.05
-.578 -.395 -1.151 -1.248
1951 -1.068 -1.196 -1.208 -.437 -.273 .48 .747 .858 .776
.75 .729 .466
1952 .406 .131 .086 .262 -.267 -.634 -.231 -.156 .362
.309 -.34 -.124
1953 .024 .379 .263 .712 .84 .241 .416 .253 .524
.092 .049 .314
1954 -.051 -.018 .178 -.506 -1.424 -1.594 -1.393 -1.473 -
1.156 -1.373 -1.145 -1.107
1955 -.771 -.697 -1.134 -1.557 -1.631 -2.289 -1.93 -2.04 -
1.824 -1.744 -1.826 -1.86
1956 -1.436 -1.3 -1.396 -1.156 -1.301 -1.505 -1.194 -1.136 -
1.363 -1.462 -1.036 -1.013
1957 -.948 -.35 .156 .352 .908 .773 .935 1.122 1.184
1.097 1.133 1.231
1958 1.473 1.45 1.317 1.025 .745 .904 .725 .435 .178
.208 .49 .71
1959 .574 .804 .502 .217 .017 .026 -.196 .068 .051
-.081 -.184 -.265
64. 59 | Sanchez-Lohff
% Create a winter (DJF) vector for MEI
j=1;
DJF_MEI_vec(j)=[NaN;]; %NaN because we lack D data in arr_vec
for i=12:12:762
j=j+1;
DJF_MEI_vec(j)=nanmean(MEI_vec(i:i+2));
end
DJF_MEI_vec=DJF_MEI_vec';
%-----------------------------Month Lengths--------------------------------
% Create a vector of month lengths, in days, beginning Dec 1949 and
% continuing through Dec 2013. We need these data in order to calculate
% monthly totals from the output data in storm_stat_revised.m. Once the
% monthly totals are calculated, we can determine bi-monthly averages like
% those used in the MEI.
month_length=[31
31
28
31
...
31
30
31
31
];
%-----------------------------BiMonthly Means------------------------------
% Create bimonthly mean vector of precipitation characteristics such as
% storm arrival, storm interval, storm duration, storm depth and storm
% intensity. There are 765 months of data over the course of the rainfall
% dataset.
% Start with storm arrival:
j=1; %storm number because it varies for each site
tempsum=0;
for i=1:762 %64
count=0; %number of storms in a month
while arrival_date(j)<sum(month_length(1:i))
count=count+1;
tempsum=tempsum+out(j,1);
j=j+1;
end
arr(i)=tempsum/count;
arr=arr';
count=0;
tempsum=0;
end
%
% Calculate bi-monthly storm arrival (e.g. mean of D & J goes in J)
for i=1:761 %63
bim_arr(i)=nanmean(arr(i:i+1));
end
% Send bim_arr vector to Scott Marshall's interpNaN function in order to
65. 60 | Sanchez-Lohff
% get rid of NaNs in the dataset prior to determining DJF means. This will
% have to be done for all of the five data parameters.
%
arrayNoNaN=interpNaN(bim_arr);
bim_arr=arrayNoNaN;
%
% Calculate the seasonal (e.g. DJF) bi-monthly storm arrival. This will
% allow comparison with MEI seasonal, which is derived from bi-monthly
% means.
j=1;
DJF_arr(j)=[NaN;]; %NaN because we lack D data in arr_vec
for i=12:12:760 %64
j=j+1;
DJF_arr(j)=nanmean(bim_arr(i:i+2));
end
DJF_arr=DJF_arr';
%
%
%Second is storm interval:
%
%
j=1;
tempsum=0;
for i=1:762
count=0;
while arrival_date(j)<sum(month_length(1:i))
count=count+1;
tempsum=tempsum+out(j,2);
j=j+1;
end
inter(i)=tempsum/count;
inter=inter';
count=0;
tempsum=0;
end
for i=1:761
bim_inter(i)=nanmean(inter(i:i+1));
end
%
% Send bim_inter vector to Scott Marshall's interpNaN function in order to
% get rid of NaNs in the dataset prior to determining DJF means. This will
% have to be done for all of the five data parameters.
%
arrayNoNaN=interpNaN(bim_inter);
bim_inter=arrayNoNaN;
%
% Calculate the seasonal (e.g. DJF) bi-monthly storm interval. This will
% allow comparison with MEI seasonal, which is derived from bi-monthly
% means.
j=1;
DJF_inter(j)=[NaN;]; %NaN because we lack D data in inter
66. 61 | Sanchez-Lohff
for i=12:12:760
j=j+1;
DJF_inter(j)=nanmean(bim_inter(i:i+2));
end
DJF_inter=DJF_inter';
%
%
%Third is storm duration:
%
%
j=1;
tempsum=0;
for i=1:762
count=0;
while arrival_date(j)<sum(month_length(1:i))
count=count+1;
tempsum=tempsum+out(j,3);
j=j+1;
end
dur(i)=tempsum/count;
dur=dur';
count=0;
tempsum=0;
end
for i=1:761
bim_dur(i)=nanmean(dur(i:i+1));
end
%
% Send bim_dur vector to Scott Marshall's interpNaN function in order to
% get rid of NaNs in the dataset prior to determining DJF means. This will
% have to be done for all of the five data parameters.
%
arrayNoNaN=interpNaN(bim_dur);
bim_dur=arrayNoNaN;
%
% Calculate the seasonal (e.g. DJF) bi-monthly storm duration. This will
% allow comparison with MEI seasonal, which is derived from bi-monthly
% means.
j=1;
DJF_dur(j)=[NaN;]; %NaN because we lack D data in dur
for i=12:12:760
j=j+1;
DJF_dur(j)=nanmean(bim_dur(i:i+2));
end
DJF_dur=DJF_dur';
%
%
%Fourth is storm depth:
%
j=1;
tempsum=0;
for i=1:762
67. 62 | Sanchez-Lohff
count=0;
while arrival_date(j)<sum(month_length(1:i))
count=count+1;
tempsum=tempsum+out(j,4);
j=j+1;
end
dep(i)=tempsum/count;
dep=dep';
count=0;
tempsum=0;
end;
for i=1:761
bim_dep(i)=nanmean(dep(i:i+1));
end
%
% Send bim_dep vector to Scott Marshall's interpNaN function in order to
% get rid of NaNs in the dataset prior to determining DJF means. This will
% have to be done for all of the five data parameters.
%
arrayNoNaN=interpNaN(bim_dep);
bim_dep=arrayNoNaN;
%
% Calculate the seasonal (e.g. DJF) bi-monthly storm depth. This will
% allow comparison with MEI seasonal, which is derived from bi-monthly
% means.
j=1;
DJF_dep(j)=[NaN;]; %NaN because we lack D data in dep
for i=12:12:760
j=j+1;
DJF_dep(j)=nanmean(bim_dep(i:i+2));
end
DJF_dep=DJF_dep';
%
%
%Last is storm intensity;
%
%
j=1;
tempsum=0;
for i=1:762
count=0;
while arrival_date(j)<sum(month_length(1:i))
count=count+1;
tempsum=tempsum+out(j,5);
j=j+1;
end
intens(i)=tempsum/count;
intens=intens';
count=0;
tempsum=0;
end
for i=1:761
bim_intens(i)=nanmean(intens(i:i+1));
68. 63 | Sanchez-Lohff
end
%
% Send bim_intens vector to Scott Marshall's interpNaN function in order to
% get rid of NaNs in the dataset prior to determining DJF means. This will
% have to be done for all of the five data parameters.
%
arrayNoNaN=interpNaN(bim_intens);
bim_intens=arrayNoNaN;
%
% Calculate the seasonal (e.g. DJF) bi-monthly storm intensity. This will
% allow comparison with MEI seasonal, which is derived from bi-monthly
% means.
j=1;
DJF_intens(j)=[NaN;]; %NaN because we lack D data in intens
for i=12:12:760
j=j+1;
DJF_intens(j)=nanmean(bim_intens(i:i+2));
end
DJF_intens=DJF_intens';
69. 64 | Sanchez-Lohff
6.3. ‘interpNaN.m’
This function is called in ‘BiMonthlySeasonal.m’to linearly interpolate all bimonthly
averages of each parameter vector. The interpolating is done after bimonthly averages are
produced to avoid as much interpolation as possible. The function also prints a number of things
to the screen upon successful running of the script. First, the total number of observations in
each data set. Second, the number of NaNs (‘Not a Number’) that had to be interpolated. Third,
the maximum number of consecutive number NaNs that were interpolated at one time. Lastly,
the ends of the index. All of these are returned to the user to allow for evaluation of error
associated with the station in question. The script was produced by Dr. Scott Marshall for
intentions specific to this project.
function arrayNoNaN=interpNaN(arrayNaN)
%function arrayNoNaN=interpNaN(arrayNaN)
%Written by Scott T. Marshall
%08/21/2008
%
%This function linearly interpolates a dataset with NaNs.
%In short, this function takes a vector as input and determines which values
are NaN
%and it uses linear interpolation to fill in the NaN values. Note that this
function
%does not interpolate NaNs at the beginning or ends of the input vector,
since this
%would require extrapolation and would be difficult to do reliably. So, NaN
values
%at the beginning and ends of the vector are unchanged. The returned vector
should have
%the same dimensions and number of data as the original input data.
%Some useful information about the NaN values is printed to STDOUT at the
end.
%
%Make a list of synthetic x-vals, just for interpolation purposes
x=1:length(arrayNaN);
%Figure out which elements in the vector are NaNs
nans=isnan(arrayNaN);
%Count the total NaNs
numNaN=sum(nans);
%Interpolate only the non-NaN values, but leave the same num of data as it
began with
arrayNoNaN=interp1(x(~nans),arrayNaN(~nans),x,'Linear');
70. 65 | Sanchez-Lohff
%Make Counters
count=0;
maxNaN=0;
%Figure out the max number of sequential NaNs
for i=1:length(nans)
if i==1
%For the first entry, just add it to the sum since there is no
previous entry
count=count+nans(i);
else
%For all other entries, first multiply by the previous value. This
will reset the counter to zero if it is the first NaN in a row.
count=count*nans(i-1)+nans(i);
end
%If the current count value is bigger than the max, save it along with
the index.
if count > maxNaN
maxNaN=count;
ends=i;
end
end
%Print some useful info to STDOUT
if numNaN==0
fprintf('Total Data: %dn',length(arrayNaN));
fprintf('Total NaNs: %dn',numNaN);
fprintf('No Interpolation Was Neededn');
else
fprintf('Total Data: %dn',length(arrayNaN));
fprintf('Total NaNs: %dn',numNaN);
fprintf('Max Consecutive NaNs: %dn',maxNaN);
fprintf('Ends at Index: %dn',ends);
end
return;
71. 66 | Sanchez-Lohff
6.4. ‘DJFautoplot.m’
This script calls a number of functions to produce the coherence wavelets used in this
study [Grinsted et al., 2004]. A link to the functions called from Grinsted et al. [2004] can be
found in Appendix 2. After all the statistical parameters are produced and formulated properly
with the above functions, ‘DJFautoplot.m’ specifies appropriate variables for each of the
parameters and auto-saves the figures. In this way the production of the three figures is
automated for each site. This script was written by Dr. Bill Anderson and Sonia K. Sanchez
Lohff for this project.
% Produce BiMonthly Means and Wavelet Figures
%
% DJFautoplot.m
% Written by William P. Anderson and Sonia K. Sanchez Lohff
% 22 Sept 2014
%
% This script will first take the observed rain measurements (input_rain)
% and transform it into bimonthly rainfall statistics take the filtered
% rainfall data for each site and will run CWT, XWT, and WTC from
% Grinsted et al. (2004). This will be done sequentially for rainfall
% depth, rainfall arrival, rainfall duration, rainfall interval, and
% rainfall intensity.
%--------------------------Call other functions----------------------------
% strom_stat_revised2 produces the 5 rainfall statistics in question.
[out, arrival_date, end_date, storm_num] = StormStat(input_rain);
% From this output file bimonthly values are calcuated with
% BiMonthlySeasonal and also DJF values.
[MEI_vec,DJF_MEI_vec,bim_arr,DJF_arr,bim_inter,DJF_inter,bim_dur,DJF_dur,bim_
dep,DJF_dep,bim_intens,DJF_intens] =
BiMonthlySeasonalNoNaN(out,arrival_date);
%------------------------Produce Wavelet Figures---------------------------
% After these are saved in the workspace, d1&d2 can be produced to run
% the wavelets. First, set up a variable 'd1' that will contain DJF MEI
% data. This variable will not need to be altered again. Wavelet code
% taken from Grinsted et al. (2007).
% Set MEI vecor as "d1" permanently
d1=DJF_MEI_vec(2:64);
d1(:,2)=d1(:,1);
d1(:,1)=[1951:2013];
% ***** Rainfall arrival analysis *****
% Set DJF arrival vecor as "d2"
72. 67 | Sanchez-Lohff
seriesname={'DJF MEI' 'DJF Arrival'};
d2(:,1)=DJF_arr(2:64);
d2(:,2)=d2(:,1);
d2(:,1)=[1951:2013];
% CWT
figure('color',[1 1 1])
tlim=[min(d1(1,1),d2(1,1)) max(d1(end,1),d2(end,1))];
subplot(2,1,1);
wt(d1);
title(seriesname{1});
set(gca,'xlim',tlim);
subplot(2,1,2)
wt(d2)
title(seriesname{2})
set(gca,'xlim',tlim)
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIarr_cwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIarr_cwt.jpg')
% XWT
figure('color',[1 1 1])
xwt(d1,d2)
title(['XWT: ' seriesname{1} '-' seriesname{2} ] )
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIarr_xwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIarr_xwt.jpg')
% WTC
figure('color',[1 1 1])
wtc(d1,d2)
title(['WTC: ' seriesname{1} '-' seriesname{2} ] )
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIarr_wtc.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIarr_wtc.jpg')
% ***** Rainfall depth analysis *****
% Rename "d2" to DJF depth vecor
seriesname={'DJF MEI' 'DJF Depth'};
d2(:,1)=DJF_dep(2:64);
d2(:,2)=d2(:,1);
d2(:,1)=[1951:2013];
% CWT
figure('color',[1 1 1])
tlim=[min(d1(1,1),d2(1,1)) max(d1(end,1),d2(end,1))];
subplot(2,1,1);
wt(d1);
title(seriesname{1});
set(gca,'xlim',tlim);
subplot(2,1,2)
wt(d2)
73. 68 | Sanchez-Lohff
title(seriesname{2})
set(gca,'xlim',tlim)
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIdep_cwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIdep_cwt.jpg')
% XWT
figure('color',[1 1 1])
xwt(d1,d2)
title(['XWT: ' seriesname{1} '-' seriesname{2} ] )
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIdep_xwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIdep_xwt.jpg')
% WTC
figure('color',[1 1 1])
wtc(d1,d2)
title(['WTC: ' seriesname{1} '-' seriesname{2} ] )
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIdep_wtc.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIdep_wtc.jpg')
% ***** Rainfall duration analysis *****
% Rename "d2" to DJF duration vecor
seriesname={'DJF MEI' 'DJF Duration'};
d2(:,1)=DJF_dur(2:64);
d2(:,2)=d2(:,1);
d2(:,1)=[1951:2013];
% CWT
figure('color',[1 1 1])
tlim=[min(d1(1,1),d2(1,1)) max(d1(end,1),d2(end,1))];
subplot(2,1,1);
wt(d1);
title(seriesname{1});
set(gca,'xlim',tlim);
subplot(2,1,2)
wt(d2)
title(seriesname{2})
set(gca,'xlim',tlim)
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIdur_cwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIdur_cwt.jpg')
% XWT
figure('color',[1 1 1])
74. 69 | Sanchez-Lohff
xwt(d1,d2)
title(['XWT: ' seriesname{1} '-' seriesname{2} ] )
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIdur_xwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIdur_xwt.jpg')
% WTC
figure('color',[1 1 1])
wtc(d1,d2)
title(['WTC: ' seriesname{1} '-' seriesname{2} ] )
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIdur_wtc.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIdur_wtc.jpg')
% ***** Rainfall intensity analysis *****
% Rename "d2" to DJF intesntiy vecor
seriesname={'DJF MEI' 'DJF Intensity'};
d2(:,1)=DJF_intens(2:64);
d2(:,2)=d2(:,1);
d2(:,1)=[1951:2013];
% CWT
figure('color',[1 1 1])
tlim=[min(d1(1,1),d2(1,1)) max(d1(end,1),d2(end,1))];
subplot(2,1,1);
wt(d1);
title(seriesname{1});
set(gca,'xlim',tlim);
subplot(2,1,2)
wt(d2)
title(seriesname{2})
set(gca,'xlim',tlim)
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIintens_cwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIintens_cwt.jpg')
% XWT
figure('color',[1 1 1])
xwt(d1,d2)
title(['XWT: ' seriesname{1} '-' seriesname{2} ] )
% Save figure as Matlab figure in current directory
saveas(gca,'DJF_MEIintens_xwt.fig')
% Save figure as jpeg in current directory
saveas(gca,'DJF_MEIintens_xwt.jpg')
% WTC
figure('color',[1 1 1])
