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

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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

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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.

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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

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4.3: Comparative Observations ....................................................................................47

4.4: Parameter Observations ........................................................................................49

5. CONCLUSION .......................................................................................................................51

6. APPENDIX I: Associated Scripts .........................................................................................53

6.1: ‘StormStat.m’ ........................................................................................................53

6.2: ‘BiMonthlySeasonal.m’ ........................................................................................56

6.3: ‘InterpNaN.m’.......................................................................................................64

6.4: ‘DJFautoplot.m’ ....................................................................................................66

6.5: ‘numOscillation.m’ ...............................................................................................71

6.6: ‘magMaxes.m’ ......................................................................................................75

7. APPENDIX II: Associated Hyperlinks ................................................................................81

8. REFERENCES ........................................................................................................................82

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LIST OF FIGURES

Figure Page

Figure 1. .......................................................................................................................................19

Storm Arrival:

Figure 2. ...................................................................................................................................22

Figure 3. ...................................................................................................................................23

Figure 4. ...................................................................................................................................24

Storm Depth:

Figure 5. ...................................................................................................................................26

Figure 6. ...................................................................................................................................27

Figure 7. ...................................................................................................................................28

Storm Duration:

Figure 8. ...................................................................................................................................30

Figure 9. ...................................................................................................................................31

Figure 10. .................................................................................................................................32

Storm Intensity:

Figure 11. .................................................................................................................................34

Figure 12. .................................................................................................................................35

Figure 13. .................................................................................................................................36

Storm Interval:

Figure 14. ...............................................................................................................................38

Figure 15. ................................................................................................................................39

Figure 16. ................................................................................................................................40

Figure 17. .....................................................................................................................................46

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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

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

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

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].

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

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.

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.

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

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

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

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

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

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.

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.

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.

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

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).

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

19 | Sanchez-Lohff

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

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

22 | Sanchez-Lohff

Storm Arrival Date XWT plotsBlue Ridge

Coastal Plain

Piedmont

Stations

0 50 10025Map 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.

23 | Sanchez-Lohff

24 | Sanchez-Lohff

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

26 | Sanchez-Lohff

Storm Depth XWT plotsBlue Ridge

Coastal Plain

Piedmont

Stations

0 50 10025Map 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.

27 | Sanchez-Lohff

28 | Sanchez-Lohff

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

30 | Sanchez-Lohff

Storm Duration XWT plotsBlue Ridge

Coastal Plain

Piedmont

Stations

0 50 10025Map 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.

31 | Sanchez-Lohff

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.

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

34 | Sanchez-Lohff

Storm Intensity XWT plotsBlue Ridge

Coastal Plain

Piedmont

Stations

0 50 10025Map 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

35 | Sanchez-Lohff

36 | Sanchez-Lohff

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.

38 | Sanchez-Lohff

39 | Sanchez-Lohff

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.

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

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.

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

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

46 | Sanchez-Lohff

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

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.

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

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.

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

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.

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

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

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);

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

57 | Sanchez-Lohff

1960 -.311 -.262 -.08 .019 -.325 -.237 -.358 -.251 -.474

-.365 -.339 -.432 1961 -.152 -.267 -.082 .018 -.284 -.069 -.153 -.234 -.263

-.518 -.44 -.645 1962 -1.093 -.992 -.715 -1.023 -.921 -.854 -.716 -.554 -.55

-.655 -.595 -.476 1963 -.703 -.838 -.696 -.816 -.468 -.032 .462 .63 .765

.83 .856 .749 1964 .857 .447 -.294 -.617 -1.273 -1.087 -1.4 -1.496 -

1.286 -1.206 -1.194 -.902 1965 -.525 -.323 -.249 .104 .536 .965 1.405 1.483 1.405

1.22 1.369 1.258 1966 1.311 1.191 .697 .556 -.133 -.123 -.149 .166 -.087

-.014 .026 -.182 1967 -.473 -.939 -1.079 -1.067 -.478 -.362 -.641 -.427 -.633

-.681 -.424 -.366 1968 -.595 -.7 -.613 -.973 -1.093 -.725 -.549 -.123 .234

.424 .6 .359 1969 .688 .868 .445 .617 .707 .801 .42 .14 .156 .506

.645 .38 1970 .359 .407 .215 -.055 -.134 -.745 -1.158 -1.047 -

1.245 -1.102 -1.095 -1.251 1971 -1.224 -1.521 -1.811 -1.897 -1.462 -1.508 -1.23 -1.235 -

1.461 -1.421 -1.305 -1.005 1972 -.592 -.41 -.253 -.206 .489 1.219 1.911 1.831 1.507

1.623 1.724 1.746 1973 1.707 1.481 .841 .482 -.125 -.828 -1.069 -1.377 -

1.749 -1.694 -1.524 -1.875 1974 -1.942 -1.792 -1.765 -1.684 -1.081 -.641 -.72 -.622 -.613

-1.049 -1.255 -.931 1975 -.564 -.606 -.882 -.967 -.854 -1.149 -1.473 -1.733 -

1.873 -1.999 -1.794 -1.759 1976 -1.624 -1.398 -1.255 -1.191 -.48 .348 .612 .663 1.026

.951 .482 .554 1977 .517 .254 .091 .531 .343 .503 .859 .691 .814

1.007 .972 .878 1978 .779 .897 .955 .18 -.396 -.564 -.401 -.182 -.387 -

.019 .198 .398 1979 .595 .36 -.011 .29 .397 .373 .349 .645 .766 .638

.732 1.015 1980 .695 .597 .669 .872 .917 .846 .781 .332 .279

.206 .235 .116 1981 -.245 -.162 .443 .637 .119 -.023 -.039 -.077 .181

.089 -.055 -.153 1982 -.282 -.146 .086 -.041 .407 .951 1.622 1.83 1.796

2.024 2.454 2.411 1983 2.688 2.904 3.039 2.876 2.556 2.167 1.725 1.122 .428

.002 -.176 -.177 1984 -.339 -.565 .131 .331 .121 -.142 -.149 -.184 -.084

.016 -.351 -.612 1985 -.561 -.602 -.737 -.484 -.731 -.086 -.149 -.398 -.542

-.141 -.051 -.293 1986 -.307 -.191 .033 -.169 .305 .311 .387 .818 1.168

.996 .872 1.183 1987 1.237 1.185 1.724 1.865 2.122 1.904 1.844 1.942 1.834

1.61 1.253 1.249

58 | Sanchez-Lohff

1988 1.092 .665 .456 .307 .085 -.71 -1.185 -1.396 -

1.588 -1.349 -1.469 -1.344 1989 -1.166 -1.312 -1.056 -.842 -.488 -.273 -.457 -.497 -.279

-.317 -.067 .142 1990 .234 .532 .916 .393 .593 .389 .068 .121 .373

.242 .371 .334 1991 .309 .31 .393 .444 .719 1.163 1.009 1.012 .736

1.017 1.201 1.321 1992 1.75 1.871 1.992 2.271 2.13 1.714 .931 .527 .51

.67 .602 .645 1993 .699 .999 .979 1.388 1.987 1.459 1.068 1.001 .982

1.059 .822 .559 1994 .338 .192 .159 .423 .521 .734 .81 .734 .881

1.434 1.277 1.181 1995 1.2 .961 .862 .419 .494 .454 .169 -.219 -.468 -

.486 -.496 -.561 1996 -.644 -.595 -.264 -.505 -.178 -.001 -.219 -.408 -.504

-.386 -.163 -.341 1997 -.487 -.607 -.254 .493 1.119 2.307 2.741 2.994 2.999

2.358 2.517 2.316 1998 2.483 2.777 2.748 2.673 2.169 1.129 .258 -.441 -.668

-.848 -1.171 -1.015 1999 -1.149 -1.238 -1.068 -1.022 -.681 -.42 -.474 -.796 -

1.004 -1.011 -1.08 -1.208 2000 -1.197 -1.246 -1.138 -.521 .157 -.15 -.211 -.149 -.247

-.381 -.756 -.584 2001 -.539 -.717 -.607 -.146 .185 -.076 .236 .366 -.127

-.275 -.181 -.001 2002 -.05 -.21 -.201 .339 .778 .853 .581 .917 .805

.953 1.059 1.105 2003 1.184 .927 .819 .308 .048 .026 .068 .226 .438

.51 .519 .311 2004 .308 .33 -.125 .216 .47 .17 .45 .666 .52 .468 .784

.64 2005 .301 .799 1.018 .559 .756 .487 .481 .304 .252

-.165 -.408 -.588 2006 -.471 -.455 -.591 -.688 -.036 .563 .619 .753 .793

.893 1.29 .947 2007 .974 .51 .074 -.049 .183 -.358 -.322 -.464 -1.165 -

1.141 -1.179 -1.172 2008 -1.011 -1.402 -1.635 -.942 -.355 .128 -.017 -.282 -.645

-.779 -.623 -.67 2009 -.752 -.719 -.719 -.159 .369 .96 .931 .934 .761

1.021 1.062 1.003 2010 1.153 1.52 1.386 .863 .573 -.472 -1.213 -1.846 -

2.031 -1.945 -1.604 -1.584 2011 -1.678 -1.562 -1.562 -1.492 -.325 -.2 -.113 -.491 -.766 -

.963 -.98 -.985 2012 -1.045 -.706 -.417 .058 .703 .89 1.111 .555 .268

.105 .165 .031 2013 .042 -.163 -.171 .009 .069 -.298 -.469 -.614 -.19

.094 -.093 .0312];

MEI_vec=MEI_full(:,2:13); MEI_vec=reshape(MEI_vec',[numel(MEI_vec) 1]);

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

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

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

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));

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';

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');

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: %d\n',length(arrayNaN)); fprintf('Total NaNs: %d\n',numNaN); fprintf('No Interpolation Was Needed\n'); else fprintf('Total Data: %d\n',length(arrayNaN)); fprintf('Total NaNs: %d\n',numNaN); fprintf('Max Consecutive NaNs: %d\n',maxNaN); fprintf('Ends at Index: %d\n',ends); end

return;

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"

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)

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])

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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])

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wtc(d1,d2) title(['WTC: ' seriesname{1} '-' seriesname{2} ] ) % Save figure as Matlab figure in current directory saveas(gca,'DJF_MEIintens_wtc.fig') % Save figure as jpeg in current directory saveas(gca,'DJF_MEIintens_wtc.jpg')

% ***** Rainfall interval analysis ***** % Rename "2" to DJF interval vecor seriesname={'DJF MEI' 'DJF Interval'}; d2(:,1)=DJF_inter(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_MEIinter_cwt.fig') % Save figure as jpeg in current directory saveas(gca,'DJF_MEIinter_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_MEIinter_xwt.fig') % Save figure as jpeg in current directory saveas(gca,'DJF_MEIinter_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_MEIinter_wtc.fig') % Save figure as jpeg in current directory saveas(gca,'DJF_MEIinter_wtc.jpg')

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6.5. ‘numOscillation.m’

This function auto-saves a text file of file of numerical values for each of the XWT

wavelets. The XWT figure are produced by calling Grinsted et al. [2004],as above. However,

instead of being saves as images the quantitative representation of the significance values are

exported for each statistical parameter. From these numerical values, a summation of the ENSO-

linked target area are summed. This was created by Sonia K. Sanchez Lohff and modified by Dr.

Bill Anderson for this project.

function [sumArr,sumDep,sumDur,sumIntens,sumInter]=numOscillation(fileName) % Finds numeric values of ENSO in strong correlation years % % numOscillation.m % Written by Sonia K. Sanchez Lohff % Edited by Dr. Bill Anderson % 29 October 2014 % % This function uses a user-specifed '.mat' file, which must be loaded in % order for the wavelets to run properly. This '.mat' file is output for % both functions (StormStat & BiMonthlySeasonal)that produce precipitation % parameters. Then d1 is get as winter MEI. Then each precipitation % parameter is set to d2 individually and then run through xwt to get sig95 % values, which are the numerical values used to make coherence colors in % wavelet figures. These are then returned to the user. % % NOTE: Must be in folder of site in question (found within CompletedSites) % for function to work properly. Also, when running function, each return % variable of the function must be saved correctly. An example of how to % type into command window to input data correctly is shown below: % >>[Arr,Dep,Dur,Intens,Inter]=numOscillation('CP_Edenton.mat'); % % NOTE: User must set paths to 'Code' folder and 'Grinsted' folder ('Set % Path' button found in tool menu) %

%----------------------------Input Correct Data---------------------------- % Save user-specified fileName in 'input_rain' load(fileName)

%-------------------------Set MEI as d1 perminantly------------------------ % Set winter MEI vector to column 2 d1(:,2)=DJF_MEI_vec(2:64); % Make column two range of years d1(:,1)=[1951:2013]; %----------------------------Storm Arrival Date----------------------------

% Through a number of steps, produce a single xwt value for this specific % site

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%*****Define d2***** % Set winter arrival date vector to column 2 d2(:,2)=DJF_arr(2:64); % Make column two range of years d2(:,1)=[1951:2013];

%*****Produce sig95***** % Run d1 and d2 by calling 'xwt.m' % NOTE: Wxy/period/scale/coi are not being saved, but must be called to get % the correct values saved in sig95. [Wxy, period,scale, coi, sig95]=xwt(d1,d2); % Now that we have all xwt variable for arrival write sig95 file to pwd dlmwrite('arrSig95.txt',sig95);

%*****Load Produced sig95***** % Load numeric values for arrival date load('arrSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumArr=arrSig95(6:21,25:50); % Calculate sum of all the individual columns colArr=sum(cumArr,1); % Calcualte sum of values in remaining row to get final single value sumArr=sum(colArr,2);

%--------------------------------Storm Depth------------------------------- % Through a number of steps, produce a single xwt value for this specific % site

%*****Define d2***** % Set winter arrival date vector to column 2 d2(:,2)=DJF_dep(2:64); % Make column two range of years d2(:,1)=[1951:2013];

%*****Produce sig95***** % Run d1 and d2 by calling 'xwt.m' % NOTE: Wxy/period/scale/coi are not being saved, but must be called to get % the correct values saved in sig95. [Wxy, period,scale, coi, sig95]=xwt(d1,d2); % Now that we have all xwt variable for arrival write sig95 file to pwd dlmwrite('depSig95.txt',sig95);

%*****Load Produced sig95***** % Load numeric values for storm depth load('depSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation

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% Narrow matrix down to areas of interest(above) cumDep=depSig95(6:21,25:50); % Calculate sum of all the individual columns colDep=sum(cumDep,1); % Calcualte sum of values in remaining row to get final single value sumDep=sum(colDep,2);

%------------------------------Storm Duration------------------------------ % Through a number of steps, produce a single xwt value for this specific % site

%*****Define d2***** % Set winter arrival date vector to column 2 d2(:,2)=DJF_dur(2:64); % Make column two range of years d2(:,1)=[1951:2013];

%*****Produce sig95***** % Run d1 and d2 by calling 'xwt.m' % NOTE: Wxy/period/scale/coi are not being saved, but must be called to get % the correct values saved in sig95. [Wxy, period,scale, coi, sig95]=xwt(d1,d2); % Now that we have all xwt variable for arrival write sig95 file to pwd dlmwrite('durSig95.txt',sig95);

%*****Load Produced sig95***** % Load numeric values for storm duration load('durSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumDur=durSig95(6:21,25:50); % Calculate sum of all the individual columns colDur=sum(cumDur,1); % Calcualte sum of values in remaining row to get final single value sumDur=sum(colDur,2);

%-----------------------------Storm Intensity------------------------------ % Through a number of steps, produce a single xwt value for this specific % site

%*****Define d2***** % Set winter arrival date vector to column 2 d2(:,2)=DJF_intens(2:64); % Make column two range of years d2(:,1)=[1951:2013];

%*****Produce sig95***** % Run d1 and d2 by calling 'xwt.m' % NOTE: Wxy/period/scale/coi are not being saved, but must be called to get % the correct values saved in sig95. [Wxy, period,scale, coi, sig95]=xwt(d1,d2);

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% Now that we have all xwt variable for arrival write sig95 file to pwd dlmwrite('intensSig95.txt',sig95);

%*****Load Produced sig95***** % Load numeric values for storm intensity load('intensSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumIntens=intensSig95(6:21,25:50); % Calculate sum of all the individual columns colIntens=sum(cumIntens,1); % Calcualte sum of values in remaining row to get final single value sumIntens=sum(colIntens,2);

%------------------------------Storm Interval------------------------------ % Through a number of steps, produce 1 xwt value for this specific site

%*****Define d2***** % Set winter arrival date vector to column 2 d2(:,2)=DJF_inter(2:64); % Make column two range of years d2(:,1)=[1951:2013];

%*****Produce sig95***** % Run d1 and d2 by calling 'xwt.m' % NOTE: Wxy/period/scale/coi are not being saved, but must be called to get % the correct values saved in sig95. [Wxy, period,scale, coi, sig95]=xwt(d1,d2); % Now that we have all xwt variable for arrival write sig95 file to pwd dlmwrite('interSig95.txt',sig95);

%*****Load Produced sig95***** % Load numeric values for storm interval load('interSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumInter=interSig95(6:21,25:50); % Calculate sum of all the individual columns colInter=sum(cumInter,1); % Calcualte sum of values in remaining row to get final single value sumInter=sum(colInter,2); % Through a number of steps, produce 1 xwt value for this specific site %...need to do for all, but want to fix problem first

% End Function end

6.6. ‘magMaxes.m’

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This script loads the numerical values of the XWT wavelets produced as text files in the

previous function. From this is targets the ENSO-linked area and identifies all the highly

significant values within this area. We denoted significant areas as >=2 on the wavelet scale,

which is equivalent to around >=1 in the numerical values. This script both counts the number

of significant values as well as sums all the significant values. The two produced values for each

parameters are counted values as well as magnitude of significance, all of which are auto-saved

to a new text file. This script was written by Sonia K. Sanchez Lohff and Dr. Bill Anderson.

% Sums all Significance >=1 in cumulative matrixes % % magMaxes.m % Written by Sonia K. Sanchez Lohff and Dr. Willaim Anderson % 9 November 2014 % % Load original Sig95 file. Target only significance time period and same % in new variable. From this, parse out all rows and column and save in % seperate variables. Then run a loop that saves all values >=1 in new % file. Sum both the amount of significant variables and all values saved % in the new file and store in seperate variables. Run for all parameters. % % NOTE: Every time the code is run for one site, 'magMaxes.xlsx' must be % saved to the next site folder to append correctly. MAKE SURE that if you % ran the file, the data was not saved twice. Also, run sites in order, so % you know which is which later. % % NOTE: User must set paths to 'Code' folder and 'Grinsted' folder ('Set % Path' button found in tool menu) %

%-----------------------------Clear all Existing--------------------------- % Clear workspace clear

%-------------------------------Storm Arrival------------------------------ % Load numeric values for arrival date load('arrSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumArr=arrSig95(6:21,25:50); % Seperate out rows rowArr=cumArr(:,1); % Seperate out column

76 | Sanchez-Lohff

colArr=cumArr(1,:); % Initiate Counter count=0; % Loop through all rows for i=1:length(rowArr); % For each of these rows, loop through ever column for j=1:length(colArr); % If any of these is greater than or equal to 1 if cumArr(i,j)>=1. % Incriment counter count=count+1; % Store these values in 'magArr' magArr(count)=cumArr(i,j); % End first If-Statement end % End second loop end % End first loop end

% If there are no values >=1 if count==0 %Set magArr to 0 magArr=0; % Make count empty count=0; % End second If-Statement end

%*****Sum Results***** % Save number of >=1 significance levels and save numArr=count; % Sum together all >=1 significance levels and save sumMagArr=sum(magArr);

%--------------------------------Storm Depth------------------------------- % Load numeric values for storm depth load('depSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumDep=depSig95(6:21,25:50); % Seperate out rows rowDep=cumDep(:,1); % Seperate out column colDep=cumDep(1,:);

% Initiate Counter count=0; % Loop through all rows for i=1:length(rowDep); % For each of these rows, loop through ever column for j=1:length(colDep);

77 | Sanchez-Lohff

% If any of these is greater than or equal to 1 if cumDep(i,j)>=1. % Incriment counter count=count+1; % Store these values in 'magDep' magDep(count)=cumDep(i,j); % End first If-Statement end % End second loop end % End first loop end

% If there are no values >=1 if count==0 %Set magDep to 0 magDep=0; % Make count empty count=0; % End second If-Statement end

%*****Sum Results***** % Save number of >=1 significance levels and save numDep=count; % Sum together all >=1 significance levels and save sumMagDep=sum(magDep);

%------------------------------Storm Duration------------------------------ % Load numeric values for storm duration load('durSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumDur=durSig95(6:21,25:50); % Seperate out rows rowDur=cumDur(:,1); % Seperate out column colDur=cumDur(1,:); % Initiate Counter count=0; % Loop through all rows for i=1:length(rowDur); % For each of these rows, loop through ever column for j=1:length(colDur); % If any of these is greater than or equal to 1 if cumDur(i,j)>=1. % Incriment counter count=count+1; % Store these values in 'magDep' magDur(count)=cumDur(i,j); % End first If-Statement end

78 | Sanchez-Lohff

% End second loop end % End first loop end

% If there are no values >=1 if count==0 %Set magDur to 0 magDur=0; % Make count empty count=0; % End second If-Statement end

%*****Sum Results***** % Save number of >=1 significance levels and save numDur=count; % Sum together all >=1 significance levels and save sumMagDur=sum(magDur);

%-----------------------------Storm Intensity------------------------------ % Load numeric values for storm duration load('intensSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumIntens=intensSig95(6:21,25:50); % Seperate out rows rowIntens=cumIntens(:,1); % Seperate out column colIntens=cumIntens(1,:); % Initiate Counter count=0; % Loop through all rows for i=1:length(rowIntens); % For each of these rows, loop through ever column for j=1:length(colIntens); % If any of these is greater than or equal to 1 if cumIntens(i,j)>=1. % Incriment counter count=count+1; % Store these values in 'magIntens' magIntens(count)=cumIntens(i,j); % End first If-Statement End

% End second loop end % End first loop end

% If there are no values >=1

79 | Sanchez-Lohff

if count==0 %Set magIntens to 0 magIntens=0; % Make count empty count=0; % End second If-Statement end

%*****Sum Results***** % Save number of >=1 significance levels and save numIntens=count; % Sum together all >=1 significance levels and save sumMagIntens=sum(magIntens);

%------------------------------Storm Interval------------------------------ % Load numeric values for storm duration load('interSig95.txt');

%*****Target Strong Correlation Areas***** % Y-axis (6:21) is period of ~(4-6) years % X-axis (25:50) are years of strong correlation % Narrow matrix down to areas of interest(above) cumInter=interSig95(6:21,25:50); % Seperate out rows rowInter=cumInter(:,1); % Seperate out column colInter=cumInter(1,:); % Initiate Counter count=0; % Loop through all rows for i=1:length(rowInter); % For each of these rows, loop through ever column for j=1:length(colInter); % If any of these is greater than or equal to 1 if cumInter(i,j)>=1. % Incriment counter count=count+1; % Store these values in 'magInter' magInter(count)=cumInter(i,j); % End first If-Statement end % End second loop end % End first loop end

% If there are no values >=1 if count==0

%Set magInter to 0 magInter=0; % Make count empty count=0;

80 | Sanchez-Lohff

% End second If-Statement end

%*****Sum Results***** % Save number of >=1 significance levels and save numInter=count; % Sum together all >=1 significance levels and save sumMagInter=sum(magInter);

%--------------------------Append all to one File-------------------------- % Write all outputs to one file 'data' data=[numArr,sumMagArr,numDep,sumMagDep,numDur,sumMagDur,numIntens,sumMagInte

ns,numInter,sumMagInter]; % Append 'data' to 'magMaxes.xlsx' file dlmwrite('magMaxes.txt',data,'delimiter',' ','precision','%8.2f','-

append','delimiter',' ')

%-----------------------Print Final Message to Screen---------------------- % If the file runs sucessfully, print message. fprintf('\n ''magMaxes.m'' was run successfully.\n') fprintf(' Now save ''magMaxes.txt'' to next site file and run code

again.\n\n')

81 | Sanchez-Lohff

7. APPENDIX II: Associated Hyperlinks

For copies of any of the code, figures, or videos referenced above, please contact Dr. Bill

Anderson at: andersonwp@appstate.edu.

82 | Sanchez-Lohff

8. REFERENCES

Anderson, W. P., Jr., and R. E. Emanuel (2008), Effect of interannual and interdecadal climate

oscillations on groundwater in North Carolina, Geophys.Res. Lett., 35, L23402

Anderson, W. P., and R. E. Emanuel (2010), Effect of interannual climate oscillations on rates of

submarine groundwater discharge, Water Resour. Res., 46.

Camargo, Suzana J., Kerry A Emanuel, and Adam H.Sobel (2007), Use of a Genesis Potential Index to Diagnose ENSO Effects on Tropical Cyclone Genesis. J. Climate, 20, 4819–

4834.

Dai, Aiguo, Kevin E.Trenberth, and Taotao Qian (2004), A Global Dataset of Palmer Drought

Severity Index for 1870–2002: Relationship with Soil Moisture and Effects of Surface

Warming. J. Hydrometeor, 5, 1117–1130.

Grinsted, A., J. C. Moore, and S. Jevrejeva (2004), Application of the cross wavelet transform

and wavelet coherence to geophysical time series, Nonlin. Processes Geophys., 11, 561-

566.

Holman, I. P., M. Rivas-Casado, J. P. Bloomfield, and J. J. Gurdak (2011), Identifying non-

stationary groundwater level response to North Atlantic ocean-atmosphere teleconnection

patterns using wavelet coherence,Hydrogeol. J., 19, 1269–1278

Isla, F.I. (2008), ENSO-dominated estuaries of Buenos Aires: The interannual transfer of water

from Western to Eastern South America. Global and Planetary Change, 64:69-75.

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Trenberth, Kevin E., and David P. Stepaniak (2001), Indices of El Niño Evolution. J.

Climate, 14, 1697–1701.

Kurtzman, D., and B. R. Scanlon (2007), El Niño–Southern Oscillation and Pacific Decadal

Oscillation impacts on precipitation in the southern and central United States: Evaluation

of spatial distribution and predic- tions, Water Resour. Res., 43, W10427

Lipp, Erin K., et al. (2001) Determing the effects of El Niño-Southern Oscillation events on

coastal water quality. Estuaries 24.4: 491-497.

Podesta, Guillermo, et al. (2002), Use of ENSO-related climate information in agricultural

decision making in Argentina: a pilot experience." Agricultural Systems 74.3: 371-392.

Rajagopalan, B., and U. Lall (1998), Interannual variability in western US precipitation, J.

Hydrol., 210, 51–67.

Räsänen, Timo A., and Matti Kummu, (2013), Spatiotemporal influences of ENSO on

precipitation and flood pulse in the Mekong River Basin. Journal of Hydrology476: 154-

168.

Richard Seager, Alexandrina Tzanova, and Jennifer Nakamura (2009), Drought in the

Southeastern United States: Causes, Variability over the Last Millennium, and the

Potential for Future Hydroclimate Change*. J. Climate, 22, 5021–5045.

Rodell, M., and J. S. Famiglietti (2001), An analysis of terrestrial water storage variations in

Illinois with implications for the Gravity Recovery and Climate Experiment (GRACE),

Water Resour. Res., 37(5), 1327– 1339.

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Ropelewski, C. F., and Halpert, M. S. (1986), North American Precipitation and Temperature

Patterns Associated with the El Niño/Southern Oscillation (ENSO). Mon. Wea.

Rev., 114,

2352–2362.

Roplewski, C. F., and M. S. Halpert (1987), Global and regional scale precipitation patterns

associated with the El Nin ̃o–Southern Oscillation, Mon. Weather Rev., 115, 1606–1626.

Wolter, K., and M. S. Timlin (1998), Measuring the strength of ENSO— How does 1997/98

rank?, Weather, 53, 315–324.