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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115, D14106, doi:10.1029/2009JD013398, 2010

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Changes in extreme precipitation in Texas Ashok K. Mishra1 and Vijay P. Singh1 Received 16 October 2009; revised 5 February 2010; accepted 8 March 2010; published 22 July 2010.

[1] An increase in global temperature leads to the intensification of a hydrologic cycle, which, in turn, affects spatiotemporal characteristics of precipitation. The distribution of precipitation plays an important role in water resources planning at regional and local scales. In this study, the state of Texas was used as a study area. Five kinds of annual precipitation extremes, based on the annual maximum (1, 7, and 30 days) and on the threshold level (95th and 97.5 percentiles), were analyzed. Applying the extreme value theory, a generalized extreme value distribution was fitted to these extremes, and quantiles were calculated for the preclimatic change period (1925–1964) and the postclimatic change period (1965–2005) to understand the possible changes in frequency patterns in terms of both spatial and temporal scales. Furthermore, the trend analysis of extreme precipitation was performed using the Mann‐Kendall test for preclimatic and postclimatic change periods to determine possible increasing or decreasing patterns. On the basis of the quantiles obtained for different return periods using 1 day extreme precipitation on an annual scale, mixed results were observed. The stations with higher quantiles, based on 1 day extreme events during the preclimatic period, were located mostly in the subtropical subhumid regions, whereas those during the postclimatic change period were located in most of the climatic zones. Similarly, results based on other extreme variables showed that the changes in the temporal and spatial characteristics of quantiles as well as increasing or decreasing patterns were observed at different locations during preclimatic and postclimatic change periods. Citation: Mishra, A. K., and V. P. Singh (2010), Changes in extreme precipitation in Texas, J. Geophys. Res., 115, D14106, doi:10.1029/2009JD013398.

1. Introduction [2] Precipitation has multiple effects on the environment, society, and human life. Intense rainfall increases soil erosion, chemical leaching, and the amounts of urban waste and nutrients carried from catchments into water resources and coastal aquifers. Heavy rainfall can cause flooding, and storm water can inundate streets, particularly those in urban areas. During the last century, global mean surface temperature rose by about 0.6°C [Intergovernmental Panel on Climate Change (IPCC), 2001]. Coupled global climate models, based on the Special Report on Emission Scenario, have shown that the temperature has continued to increase. The increase in global mean temperature is likely to change characteristics of extreme climate events [Meehl et al., 2000; Griffiths et al., 2005]. Climate change has different effects on geographically diverse regions. Therefore, changes in extreme events show large regional variations that are found in observations as well as in regional climate projections [Easterling et al., 2000]. 1 Departments of Biological and Agricultural Engineering and Civil and Environmental Engineering, Texas A&M University, College Station, Texas, USA.

Copyright 2010 by the American Geophysical Union. 0148‐0227/10/2009JD013398

[3] In recent decades, changes in mean precipitation of many regions throughout the world have been documented [IPCC, 2007]. A kind of amplification effect has been noted in the sense that small changes in mean values of precipitation may result in a relatively high increase in the probability of extreme precipitation [Groisman et al., 1999]. Heavy rainfall events have become more frequent since the middle of the last century, not only in the United States [Karl and Knight, 1998] but also in regions across the globe [e.g., Osborn et al., 2000; Sen Roy and Balling, 2004]. In some cases, extremes have changed despite decreases or flat trends in mean rainfall. These changes have been seen both at daily and subdaily [Palecki et al., 2005] scales. For longer‐ duration events, Brommer et al. [2007] found that in the United States, storms have become wetter, but less frequent, and collectively contribute to a smaller proportion of the total annual rainfall. Simulations by general circulation models of the coupled atmosphere‐ocean system also indicate that return periods of heavy precipitation events are expected to be shortened in a warmer climate [Burger, 2005; Palmer and Räisänen, 2002]. [4] A number of studies have found an upward trend in the frequency of heavy to extreme precipitation events in the United States. Karl et al. [1995] showed that the contribution of 1 day precipitation totals exceeding 50.8 mm to total annual precipitation increased during the 20th century. Karl

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MISHRA AND SINGH: CHANGES IN EXTREME PRECIPITATION IN TEXAS

and Knight [1998] found that the observed increase in total precipitation was due, in large part, to the increase in the intensity of heavy to extreme precipitation events. Kunkel et al. [1999] examined trends in multiday extreme precipitation events; extreme precipitation events were defined on the basis of duration and station‐specific recurrence interval thresholds. Multiday events have been found to be correlated with hydrologic flooding in some regions of the United States [Changnon and Kunkel, 1995]. Kunkel et al. [1999] found statistically significant upward trends in 1 year recurrence, 7 day duration events of ∼3% per decade and in 5 year, 7 day events of ∼4% per decade. Groisman et al. [2001] reported a 50% increase during the 20th century in the frequency of days with precipitation exceeding 101.6 mm in the upper midwestern United States. Modeling of extreme rainfall is essential in design of flood preparedness systems, therein flood protection measures, and in the design of systems for monitoring climate change [Huff and Angel, 1992]. [5] Statistics of extremes refer to the largest (or smallest) values of random variables. They have typically dealt with maximum (or minimum) values from sets of independent observations [Lambert et al. 1994]. Usually, hydrometeorologists fit the generalized extreme value (GEV) distribution to historical discharge and rainfall data to estimate magnitudes of maximum values corresponding to various return periods [Katz et al., 2002; Nguyen et al., 2002; Fowler and Kilsby, 2003]. Zwiers and Kharin [1998] performed an extreme value analysis for daily precipitation corresponding to 10, 20, and 50 year return periods using simulated outputs by a general circulation model. In particular, they espoused the application of the GEV distribution to the sample of annual extremes along with the method of L moments for the estimation of GEV parameters. [6] Kotz and Nadarajah [2000] indicated that the extreme value distributions could be traced back to the work done by Bernoulli in 1709. The first application of extreme value distributions was probably made by Fuller in 1914. Parrett [1997] studied regional analysis of annual precipitation maxima in Montana and chose the generalized extreme value as the best distribution for all durations. Several researchers have since applied the GEV to rainfall data: Karl et al. [1995], Groisman et al. [1999], Nadarajah [2005], and Khan et al. [2007] in the United States; Haylock and Nicholls [2000] in Australia; Nguyen et al. [2002] and Adamowski and Bougadis [2003] in Canada; Koutsoyiannis and Baloutsos [2000] in Greece; Crisci et al. [2002] in Italy; Withers and Nadarajah [2000] in New Zealand; Park and Jung [2002] in South Korea; Goswami et al. [2006] in India; Iwashima and Yamamoto [1993] in Japan; Carvalho et al. [2002] in southeastern South America; and Liebmann et al. [2001] in Brazil. For a review of applications of extreme value distributions to climate data, see the study by Farago and Katz [1990]. Some other frequency distributions, such as lognormal, Pearson III, log‐Pearson III, etc., are also widely used in several countries [Yue and Hashino, 2007]; EV type III [Singh, 1987], Burr III distribution [Hao and Singh, 2009], and EV‐I distribution [Mishra and Singh, 2009] have also been applied. [7] However, we are not aware of any prior investigations on spatial and temporal variability of quantiles of precipi-

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tation extremes reported so far. This study is also new for the state of Texas, and it will supplement our previous work [Mishra et al., 2009] in which we investigated uncertainties associated with annual and seasonal precipitation from water resources planning perspectives. The objective of this study, therefore, is as follows: (1) to apply the extreme value theory, a generalized extreme value distribution, to extreme precipitation indices based on annual maxima (1, 7, and 30 days) and based on the threshold levels (95th and 97.5 percentiles) for estimating their quantiles for the preclimatic change period (1925–1964) and the postclimatic period (1965–2005) to determine possible implications of climate change for frequency patterns in terms of both spatial and temporal scales, and (2) to quantify the behavior of increasing or decreasing trends of extreme precipitation during preclimatic and postclimatic periods at spatiotemporal scales.

2. Methodology [8] Section 2.1 discusses the extreme values of precipitation and their usefulness for planning purposes based on different threshold levels. This is followed by a discussion of the generalized extreme value distribution and Mann‐ Kendall (MK) test, which will be useful for understanding the spatiotemporal analysis of extreme precipitation events. 2.1. Extreme Values of Precipitation [9] For categorizing extreme events of rainy days, it is important to define threshold values. Analyses of precipitation extremes are generally based on the indices developed under the World Climate Research Programme on Climate Variability and Predictability Working Group on Climate Change Detection [Peterson et al., 2002; Peterson, 2005]. Some of these indices have been used previously in the analyses of trends in global and regional climates [e.g., Bardossy and Hundecha, 2003; Alexander et al., 2006]. In the United States, three different methods have commonly been used to identify extreme rainfall events. The first method is based on actual rainfall amounts. Over the mainland United States, a “heavy” rainfall climatology is constructed on the basis of the mean annual number of days, where 24 h accumulation exceeds 50.8 mm [Karl et al., 1996; Groisman et al., 1999]. The second method to define extreme precipitation events is to use specific thresholds, such as the 90th and 99th percentiles of precipitation days as heavy and “very heavy” events, respectively [e.g., Groisman et al., 2001]. The third method of defining extreme precipitation events is to calculate return periods of events based on the annual maximum 24 h precipitation series [e.g., Kunkel et al., 1999; Groisman et al., 2001]. [10] On the basis of the above discussion, extreme precipitation values in the present study were derived based on two methods: (1) maximum annual rainfall amounts at different time scales (1, 7, and 30 days), and (2) threshold levels (95th and 97.5 percentiles) of daily time series of annual precipitation. The rationale behind the selection of these thresholds and their usefulness are highlighted in what follows.

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2.1.1. Usefulness of Extreme Precipitation Information Based on 1 Day, 95th and 97.5 Percentiles [11] The magnitude and frequency of heavy precipitation events are two important parameters for many impact and planning sectors. Storm events bringing heavy precipitation can push many designed systems, including urban drainage, road surfaces, flood barriers, sewer works, and dam spillways, to failure. Urban planners use information on precipitation extremes for zoning development. As a consequence, for those working in engineering design and planning, it is important to understand the spatial and seasonal distribution of extreme precipitation events. Floods can damage infrastructure critical to maintaining health, such as waste treatment services and delivery of potable (drinkable) water, which can be tainted by waste and runoff from agricultural lands. Buildings and transportation infrastructure, such as roads, railways, and air services, also can be affected by extreme precipitation events and the flooding that could result in high‐risk areas. [12] The Intergovernmental Panel on Climate Change cites a 90% chance of increased frequency of heavy rainfall events in the 21st century and a potential increase in higher‐ latitude storm water runoff by as much as 10–40% [IPCC, 2007], changes that would have obvious repercussions on storm water management. Therefore, rain‐induced flood patterns in cities must be well understood to enable effective placement of flood control and other regulatory measures. Design of storm water infrastructure assumes that the probability distribution of precipitation extremes is statistically stationary. This assumption is called into question because of climate change, generating uncertainty about the future performance of systems constructed under this paradigm. It is therefore important to examine historical extremes to understand changes in the probability distributions of precipitation extremes. Possible approaches to such planning include probability‐based extreme event analysis to revisit design parameters used for design purposes. 2.1.2. Usefulness of Extreme Precipitation Information Based on 7 and 30 Day Events [13] It is often useful to study the extreme events based on longer durations. This is because the linkage between excessive precipitation and hydrologic flooding is affected by several factors, including meteorological factors (e.g., antecedent precipitation amount and the intensity, duration, and spatial pattern of precipitation events), human activities (e.g., land use change and dam construction), and basin characteristics (e.g., the size, topography, control structures, and drainage network of the basin). These factors vary from event to event, from season to season, and from region to region. The potential threat of flood occurs downstream after a certain lag time, and it depends on several factors as discussed previously. Also, the longer lag time is useful for optimal reservoir operations using information based on past inflows, current inflows, and forecasted inflows. Hence, it is interesting to look at how the longer‐duration extremes have changed over time, and it will be informative for long‐term flood management purposes, understanding groundwater, management of floods from long‐term accumulation of precipitation, and operating reservoirs. Also, there is a relationship between outbreak of water‐borne diseases and lag time of extreme precipitation. The expected percentages of outbreaks coincident with the extreme level of precipi-

tation were investigated by Curriero et al. [2001] for the United States based on the varying preceding monthly lag time and level of extreme precipitation. This suggests the usefulness of information based on extreme precipitation of longer durations. 2.2. Generalized Extreme Value Distribution [14] The generalized extreme value distribution was developed by Jenkinson [1955; see also Hosking et al., 1985, and Galambos, 1987]. The GEV family describes the distribution of maxima from sets of observations. Suppose {Xn} is a sequence of independent and identically distributed random variables and Mn is the maximum (X1, …, Xn). If there exist constants cn > 0 and dn 2 R (a real number) such that d

ðMn dn Þ=cn ! H; n ! 1;

for some nondegenerate distribution function H, then H belongs to one of the three families of extreme value distribution functions: Fr echet : F ð xÞ ¼

Weibull : Y ð xÞ ¼

8 < 0; :

x0

ex ;

8 < eðxÞ ; :

1;

x>0

> 0;

x0 x>0

> 0;

x

Gumbel : Lð xÞ ¼ ee ; x 2 R:

ð1Þ

ð2Þ

ð3Þ

Jenkinson [1955] and von Mises [1954] suggested the following one‐parameter representation of these three standard distributions, H ð xÞ ¼

8 1= < eð1þxÞ :

x

ee

if 6¼ 0

;

ð4Þ

if ¼ 0

with x such that 1 + xx > 0. This generalization, known as the generalized extreme value distribution, is obtained by setting x = a−1 for the Fréchet distribution, by setting x = −a−1 for the Weibull distribution, and by interpreting the Gumbel distribution as a limiting case for x = 0. If we introduce location and scale parameters m and s > 0, respectively, we can extend the family of distributions. We define the GEV Hx,m,s(x) to be Hx((x − m)/s), and we say that Hx,m,s is of the type Hx. [15] Considering x1, x2, …….xn as annual maxima of n years at a given location, the method of maximum likelihood is used to estimate parameters of the distribution selected to fit these data. Assuming the independence of data, the likelihood L is the product of densities for observations x1, x2, …….xn. Mathematically, L is expressed as Lð; ; Þ ¼

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1 n 1 Y ðxi Þ ðþ1Þ 1þ n i¼1 ( ) n X xi 1 1þ : exp i¼1

ð5Þ

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^ are taken to be ^ ^, and , Estimates of m, s, and x, i.e., , those values that maximize the likelihood L. In practice, we do not know the true distribution of quantiles, and as a result, we do not have any idea about the norming constants (cn and dn). Hence, we use a three‐parameter specification [Gilli and Kellezi, 2006] of the GEV, which is the limiting distribution of the unnormalized maxima: 8 > > > 1; > > > > > > < x ð1; 1Þ x 2 D; D ¼ H;; ð xÞ ¼ H > > > > > > > > > ; 1 :

where Xj and Xk are the sequential data values, n is the length of the data record, and t is the extent of any given time. The standard normal variate z is computed as 8 S1 > > pffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > > VarðS Þ > > < 0 z¼ > > > Sþ1 > > > > : pffiffiffiffiffiffiffiffiffiffiffiffiffiffi VarðS Þ

0

if

S>0

if

S ¼ 0:

if

S > > > < sgnð xÞ ¼ 0; > > > > : 1; " VarðS Þ ¼ nðn 1Þð2n þ 5Þ

if x > 0 if x ¼ 0 ;

ð10Þ

if x < 0

X t

# t ðt 1Þð2t þ 5Þ=18 ; ð11Þ

3. Study Area [18] Because of its location along the warm Gulf of Mexico, and being from the not‐so‐far‐distant Pacific Ocean, the state of Texas experiences a constant exchange of settled and unstable weather. The state’s varied physiography, from the forests in the east and the Coastal Plain in the south to the elevated plateaus and basins in the north and west, also brings a wide variety of weather on almost any day of the year. Because of its expansive and topographically diverse nature, Texas offers continental‐, marine‐, and mountain‐type climates (Handbook of Texas Online, http:// www.tshaonline.org/handbook/online/articles/WW/yzw1. html, accessed 14 May 2008). Texas’ climate is as varied as its landscape. This variability is a result of interactions between Texas’ unique geographic location and movements of seasonal air masses, such as arctic fronts, the jet stream, subtropical west winds, tropical storms, and a subtropical high‐pressure system known as the Bermuda High. The Gulf of Mexico is a dominant geographical feature, moderating temperatures along the Gulf Coast and, more importantly, providing the major source of moisture for the state [Larkin and Bomar, 1983]. The eastern Pacific Ocean and land‐recycled moisture also provide, to a lesser extent, a source for annual precipitation to the state. Texas is prone to hurricanes that find their way into the Gulf of Mexico during the hurricane season [Texas Water Development Board, 2007]. For example, Tropical Storm Amelia was a weak tropical storm that brought heavy rains and damage to Texas in July during the 1978 Atlantic hurricane season. This resulted in a 12 h total of 26 inches (660 mm) of rain at Abilene, which was an example of extreme precipitation (D. M. Roth, Tropical Storm Amelia ‐ July 30–August 5, 1978, Hydrometeorological Prediction Center, http://www.hpc. ncep.noaa.gov/tropical/rain/amelia1978.html. Retrieved 13 May 2008)., In a recent example, during Hurricane Ike (8– 15 September 2008), the maximum rainfall measured at Houston was 17.60 inches in 7 days (http://www.scribd. com/doc/14215909/Hurricane‐Ike). [19] Precipitation is not evenly distributed over the state of Texas, and variations in precipitation at any one locale from year to year are pronounced. The mean annual precipitation distribution correlates roughly with longitude and varies little from north to south across Texas. The mean annual precipitation varies from a statewide maximum of 59.20 inches at Orange in the lower Sabine River valley of east Texas to a

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Table 1. Location of Stations Used in the Study and Percentages of Missing Values at Each Sl.a Number

Station ID

Lat. (decimal deg.)

Long.b (decimal deg.)

Missing Value (%)

Serial Number

Station ID

Lat. (decimal deg.)

Long. (decimal deg.)

Missing Value (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

410120 410493 410639 410832 410902 411048 411138 412019 412121 412266 412598 412679 413183 413873 413992

32.74 31.74 28.45 30.11 29.8 30.17 31.72 32.09 33.66 29.05 32.11 28.7 29.67 29.47 33.17

−99.29 −99.99 −97.7 −98.42 −98.72 −96.41 −99 −96.47 −101.25 −96.24 −98.34 −100.49 −97.12 −96.95 −99.75

2.91 2.89 2.84 1.02 1.23 0.77 3.10 1.12 0.95 0.91 2.41 1.62 0.38 4.92 2.93

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

415018 415196 415272 415429 415618 415875 416135 417079 417336 419532 410498 410174 412906 418201 418443

31.05 30.05 30.75 29.67 32.54 35.71 34.24 34.19 34.276 32.77 30.99 30.37 28.04 32.72 32.72

−98.19 −94.8 −98.69 −97.66 −94.35 −100.64 −102.74 −101.7 −99.75 −97.82 −103.75 −103.67 −99.42 −102.67 −100.92

1.91 1.88 0.71 0.34 1.78 0.94 2.18 1.39 3.01 1.78 3.29 9.68 5.68 4.96 4.63

a

Sl., XX; Lat, latitude; Long, longitude. Longitudes are all to the west of the prime meridian and hence are given negative values.

b

minimum of 7.82 inches at El Paso at the western tip of the state. Winter is the driest time of the year in nearly all of Texas. The exception is east Texas, where precipitation typically is the least substantial in July and August. December or January is normally the driest month on High and Low Rolling Plains, as well as on Edwards Plateau. The dry season peaks somewhat later farther east in north central and south central Texas, while on the coastal plains, March is the driest month. Early spring (March and April) is normally dry in the Trans‐Pecos; in fact, in this semiarid region, rainless spells often last several weeks at a time, and 2 or even 3 months can elapse without significant rain (Handbook of Texas Online, http://www.tshaonline.org/handbook/online/articles/WW/ yzw1.html, accessed 14 May 2008). In addition, variabilities of both daily temperature and precipitation totals increase inland across the state and away from the Gulf of Mexico. The majority of precipitation in Texas occurs during storm events, when a large amount of precipitation falls over a short period of time; hence, it will be useful to analyze extreme events on different spatiotemporal scales.

4. Data [20] The United States Historical Climatology Network (USHCN) is a high‐quality source of data sets of daily and monthly records of basic meteorological variables across the 48 contiguous United States. The initial USHCN data set contained monthly data, and it has been comprehensively updated several times [e.g., Karl et al., 1990; Easterling et al., 1996]. The initial USHCN daily data set was made available through the Carbon Dioxide Information Analysis Center via the work of Hughes et al. [1992] and contained a 138‐station subset of the USHCN. This product was updated by Easterling et al. [1999] and expanded to include 1062 stations. In 2009, the daily USHCN data set was expanded to include all 1218 stations in the USHCN. A total of 30 stations having a common data period from 1925 to 2005 was chosen for investigating precipitation extremes based on return periods. The stations were selected based on two criteria, i.e., less number of missing values and maximum spatial coverage of station locations. The geographical

locations and percentages of missing values of stations are given in Table 1, and their spatial locations are shown in Figure 1. It can be observed that the maximum number of stations having missing values are less than 3%, and these can be considered as good quality data, and a few stations have missing values more than 3%. More numbers of missing values are observed in the western part of Texas, where one of the reasons is less spatial coverage of stations.

5. Results and Discussion 5.1. Precipitation Patterns in Texas [21] Six stations are chosen across Texas to understand the preliminary characteristics of precipitation patterns. These stations included 410832 and 410902, which lie in the subtropical subhumid region; 411048, 412019, and 412266, which lie in the subtropical humid region; and 412121, which lies in the continental steppe region. These stations were chosen because they have common missing values in the year 1947, which was not included in the analysis. Three variables were chosen for preliminary analyses: annual precipitation, annual rainy days at different thresholds, and interarrival time. [22] The scatterplots based on the annual precipitation are shown in Figure 2 for selected stations. It can be seen that for station 410832, the annual precipitation had a high variation with a minimum around 10 inches to a maximum of ∼60 inches. A similar pattern was also observed for station 410902, and both stations belonged to subtropical subhumid climatic regions. The linear trend for annual precipitation indicated an increasing pattern for these stations. On the basis of stations (411048, 412019, and 412266) located in the subtropical humid region, precipitation varied between 15 and ∼65 inches based on historical data. An increasing trend was also observed for these stations. In the case of station 412121, located in continental steppe, precipitation varied between 10 and ∼40 inches, and the slope of linear trend was small compared to stations located in other climatic regions. This discussion signifies large‐scale variability in annual precipitation.

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Figure 1. Spatial locations of precipitation stations used in the study.

Figure 2. Linear trends fitted to annual precipitation of stations 410832, 410902, 411048, 412019, 412121, and 412266. 6 of 29

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Table 2. Statistics of Annual Precipitation (Inches) at Stations for Three Periods: 1925–2005, 1925–1964, and 1965–2005 Mean

SD

Station ID

1925–2005a

1925–1964b

1965–2005c

1925–2005

1925–1964

1965–2005

Climatic Pattern

411048 412019 412266 413183 413873 415196 415618 410120 410493 410639 410832 410902 411138 412121 412598 413992 415018 415272 415429 417336 418443 419532 415875 416135 417079 418201 410174 410498 412679 412906

41.7 37.9 42.1 37.2 38.7 53.3 47.6 26.7 23.1 31.2 34.1 34.4 27.5 21.7 33.3 24.6 30.6 27.3 34.9 25.0 21.1 33.0 22.3 17.5 19.6 16.6 15.8 13.1 21.0 21.2

38.8 36.4 38.8 35.3 35.4 50.0 45.5 25.9 22.1 29.1 32.6 30.8 26.9 21.1 31.5 24.0 29.9 26.9 32.5 24.2 19.8 31.7 21.9 17.4 19.7 15.1 15.1 12.7 20.1 21.1

44.5 39.3 45.4 39.1 41.9 56.5 49.7 27.5 24.1 33.2 35.5 37.9 28.1 22.3 35.1 25.3 31.3 27.7 37.4 25.7 22.5 34.2 22.7 17.5 19.6 18.0 16.5 13.4 21.8 21.3

10.4 8.7 10.9 10.7 11.1 12.2 9.7 7.8 6.8 8.4 9.7 11.2 6.5 6.5 8.1 6.5 8.1 6.8 9.5 7.2 6.6 8.4 5.9 5.5 5.7 6.2 4.8 5.3 7.1 6.3

10.1 9.5 11.3 10.8 11.1 10.8 9.0 8.2 7.7 8.5 10.2 10.0 7.4 6.7 7.6 7.2 8.6 8.1 8.1 7.7 6.8 8.9 7.0 6.0 6.1 6.4 5.0 5.4 7.3 6.2

10.0 7.6 9.6 10.3 10.3 12.8 10.0 7.3 5.8 7.8 9.1 11.3 5.6 6.4 8.2 5.8 7.5 5.4 10.2 6.8 6.2 7.9 4.7 4.9 5.5 5.7 4.5 5.2 6.9 6.5

Subtropic humid Subtropic humid Subtropic humid Subtropic humid Subtropic humid Subtropic humid Subtropic humid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Subtropic subhumid Continental steppe Continental steppe Continental steppe Continental steppe Arid Arid Subtropical steppe Subtropical steppe

a

Entire data set (1925–2005). Preclimatic change data (1925–1964). c Postclimatic change data (1965–2005). b

[23] Statistical properties (mean and standard deviation) of annual precipitation based on three time periods (i.e., the entire data set (1925–2005), preclimatic change data (1925– 1964), and postclimatic change data (1965–2005)) are shown in Table 2. It can be seen that the mean annual precipitation of the postclimatic change data is higher than the preclimatic change data as well as the entire data set, except at station 417079. The top five stations where the difference in the mean values of annual precipitation between two climatic periods was found to be higher were 410902, 411048, 412266, 413873, and 415196. Interestingly, all five stations form a distinct pattern and are located in the southeastern part of Texas. All these stations have small differences in their latitudinal locations. Similarly, the stations where the difference in mean annual precipitation was lesser between two subperiods included 415875, 416135, 417079, 410498, and 412906. All these stations are located in the far northern, western, and southwestern parts of Texas. When the standard deviations between two subperiods were compared, it was observed that most of the stations had higher values during the preclimatic change period except stations 410902, 412598, 415196, 415429, 415618, and 412906. All these stations are located in the central and eastern parts of the Texas. The standard deviation of annual precipitations decreased at most of the stations during the second subseries compared to the first subseries. [24] To understand the patterns in annual rainy days, three threshold levels (0.5, 1, and 2 inches) were chosen for

analysis, as shown in Figure 3. In the case of stations located in subtropical subhumid regions, the maximum number of annual rainy days varied between 5 and 35, based on the 0.5 inch threshold. When the threshold increased to 1 inch, the number of annual rainy days varied between 2 and 20, and in the case of the 2 inch threshold level, it varied between 0 and 8. An increasing trend of annual number of rainy days was observed with varying slope. In the case of station 410832, the slope of increasing trend was higher for a higher threshold (2 inches) compared to a lower threshold (0.5 inch). When the subtropical humid region was considered, the annual number of rainy days varied between 10 and ∼40 days based on the 0.5 inch threshold, and this number decreased to 2–25 and 0–10 days based on 1 and 2 inch threshold levels, respectively. An increasing trend was observed for stations 411048 and 412266 for all threshold levels, whereas no trend was observed for station 412019. Interestingly, stations with increasing trends are located to the south of stations with no trend. This shows the changes in the annual rainy day pattern within the same climatic zone. Contrasting observations were made for station 412121 located in the continental steppe region in terms of the following: (1) less number of rainy days for all threshold levels, and (2) no trend was observed at the 0.5 and 2 inch threshold levels. [25] Scatterplots of interarrival time for selected stations are shown in Figure 4. For stations located in the subtropical subhumid region, the maximum time span without rain was found to be around 60 days, and in the case of the sub-

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Figure 3. Linear trends fitted to annual rainy days at different thresholds for precipitation at same stations as in Figure 2. 8 of 29

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Figure 4. Linear trends fitted to the interarrival time for precipitation of same stations as in Figure 2.

tropical humid region, it was approximately 45 days. When the plot of station 412266, which is located in southeast Texas, was analyzed, it can be seen that interarrival time increased during the recent time in contrast to the other two stations located in the same climatic zone. For station 412121, which is located in the continental steppe climatic region, the maximum interarrival time of precipitation was higher (∼68 days) than for other stations located in other climatic zones. No clear trend was observed for interarrival time for stations. The discussion here signifies the behavior of precipitation in climatic zones, which gives a brief idea before the discussion was focused on extreme precipitation in Texas. 5.2. Suitability of GEV Distribution for Extreme Precipitation [26] In this study, different goodness‐of‐fit tests were used to examine whether the GEV distribution fitted the empirical distributions of annual extremes. These tests included the probability plot (PP plot) and the quantile plot (QQ plot), which allowed a visual comparison between theoretical and empirical distributions of annual extremes. Furthermore, we applied a standard Kolmogorov–Smirnov (KS) goodness‐of‐fit test that measures the overall differ-

ence between two cumulative distribution functions. The KS statistic D is defined as the maximum absolute difference between two distribution functions (D = max ∣F[x] − G[x]∣), where F[x] is the fitted distribution function (GEV) and G[x] is the empirical distribution function estimated from a sample of N observations as the proportion of data values less than or equal to x. The null hypothesis that the annual extremes are drawn from a GEV distribution is rejected when the value of D is greater than a critical value. [27] To test the applicability of the GEV distribution, PP and QQ plots for the GEV distribution were fitted to the series of annual extremes based on the longest duration of 30 day events. From PP plots (Figure 5, station 415196), there is a close agreement with the theoretical distribution; no strong deviation of the PP plot from the main diagonal in the unit square indicated the fitted distribution seemed to be a good choice. From QQ plots (Figure 6), the line closely approximated the plot, although one can see relatively few random deviations at larger values. This good linear approximation justifies the conclusion that these extremes follow the GEV distribution. To apply the KS test to station 415196, the KS statistic (D) was found to be 0.044 (1 day extreme), 0.055 (7 day extreme), 0.057 (30 day extreme), 0.050 (95th percentile), and 0.095 (97.5 percentile), and

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Figure 5. PP plots for the GEV distribution fitted to the 30 day annual precipitation extremes at station 415196 (1925–1965). these values are less than the critical value at the 95% confidence level. Graphically, the KS statistic calculation was demonstrated by plotting the cumulative distribution function based on the 30 day maximum annual precipitation using empirical and theoretical GEV distributions for station 415196 (Figure 7). It can be observed that both curves matched well and the maximum difference was not significant. Hence, in the present study, the GEV distribution was used for calculating quantiles of annual precipitation extremes, which are discussed in section 5.3.

based on 50 and 100 year return periods (Table 3). It can be observed from the plot (Figure 8) that there is an increase in precipitation quantiles based on postclimatic data when 1 day maximum annual precipitation was considered. From the quantiles obtained for different return periods using 1 day extreme precipitation on an annual scale, mixed results were observed. Of seven stations considered in the study, five stations (411048, 412019, 413873, 415196, and 415618) demonstrated higher quantiles for postclimatic data, whereas two stations (412266 and 413183) demonstrated higher

5.3. Quantiles of Extreme Precipitation Based on Annual Maximum and Threshold Levels [28] Here the annual maximum was based on 1, 7, and 30 day precipitation amounts. The quantiles drawn from the GEV distribution as a function of return periods for the stations were based on five variables (1, 7, and 30 day annual maximum and 95th and 97.5 threshold events) for three subperiods that included the entire data set (1925– 2005), preclimatic change data (1925–1964), and postclimatic change data (1965–2005). Representative stations were analyzed based on different climatic zones, and characteristics of other stations with reference to representative stations are discussed below. 5.3.1. Subtropical Humid Zone [29] The subtropical humid climate located in the eastern part of Texas is mostly noted for hot summers [Larkin and Bomar, 1983]. At most of the stations, quantiles varied for two subperiods and were different from those obtained for the complete period. This implies that the behavior of quantiles had changed over time. To graphically demonstrate, station 411048 was selected; quantiles were plotted based on 1, 7, and 30 day extreme annual precipitation events (Figures 8–10), and the corresponding values were

Figure 6. QQ plots for the GEV distribution fitted to the 30 day annual precipitation extremes at station 415196 (1925–1965).

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Figure 7. Cumulative density function based on the GEV distribution for 30 day maximum annual precipitation for station 415196 (1925–2005). quantiles during the preclimatic change period. These two stations with increasing quantiles for preclimatic data were located in the southern part of the subtropical humid climatic zone. When maximum values of extremes were compared for station 412266, they were 19.29 inches during the preclimatic change period and 9.3 inches during the postclimatic change period, which is the primary reason for large differences in return periods for the station. Similar observations were also made for 7 day annual extreme events as demonstrated for station 411048 (Figure 9). The margin of difference between quantiles for two climatic periods is less for station 412019. Interestingly, some changes were observed for stations 412019 and 413873, when the length of extreme scale was increased to 30 days. These two stations did not show much deviation in their quantiles during two climatic periods, and besides this, other stations followed a similar pattern as for 1 and 7 day extreme events. [30] The extremes based on the 95th and 97.5 percentiles were plotted for station 411048 as shown in Figures 11 and 12, and the corresponding values are shown in Table 3. The differences in quantiles are observed at decimal places. On the basis of the 95th percentile, quantiles were observed to be higher during the postclimatic period. When all other stations located in the subtropical humid climatic zone were considered, five stations showed an increase in quantiles during the postclimatic change period, although a marginal increase was observed for two stations (413183 and 415196), whereas one station (412019) marked higher quantiles during the preclimatic period. Interestingly, the quantiles based on the 97.5 percentile for representative station 411048 differed from the 95th percentile, as the values were higher during the preclimatic change period and also for higher return periods. All other stations based on the 97.5 percentile behaved similar to the 95th percentile, except for stations 411048 and 415618. 5.3.2. Subtropical Subhumid Zone [31] Subtropical subhumid climates are mostly located in the central part of Texas, extending from south to north, and

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are characterized by hot summers and wet winters. Fifteen precipitation stations were chosen for the quantile estimation based on different return periods. To demonstrate graphically, two stations (410639 and 410493) located far apart were selected; quantiles were plotted based on 1, 7, and 30 day extreme annual precipitation events as shown in Figures 8–10, and the corresponding values are shown in Table 3. Contrasting results were observed based on 1 day extreme events for these two stations, i.e., the quantiles were higher during postclimatic data for station 410639 (Figure 8), whereas in the case of 410493, higher quantiles were observed for preclimatic change data. This difference occurs because of their geographical locations, as station 410493 is located in the southern part of Texas and station 410639 is located in the central part of Texas. Of 15 stations used in the study for the subtropical subhumid climate, 8 stations indicated more quantiles based on the postclimatic change period, and the remaining stations indicated more quantiles during the preclimatic period. The difference in quantiles for both subperiods was found to be higher for stations 410832 and 415272 because of higher values in extremes that occurred from 1925 to 1964. For example, when the mean of precipitation extremes was compared for both subperiods for station 410832, it was found to be 3.89 inches during the first subperiod and 3.318 inches during the second subperiod. Although the difference in mean was less, when maximum values of extremes were compared, they were 17.47 inches during the first subperiod and 6.75 inches during the second subperiod, which is the primary reason for large differences in return periods for station 410832. Similarly, for station 415272, values were 12.53 inches during the preclimatic change period compared to 6.5 inches during the postclimatic period. The nature of extreme precipitation based on 7 and 30 day duration for selected stations 410639 and 410493 looks similar to 1 day events (Figures 9 and 10). Most of the stations follow a similar pattern based on 1, 7, and 30 day events. However, stations such as 413992 and 415429 differ in their 1 and 7 day patterns, and the quantiles vary for stations 418443 and 419532 based on the 7 and 30 day events. This discussion indicates changes occur for some stations with a higher duration of extreme events. [32] The quantile plots based on 95th and 97.5 percentiles for representative stations 410639 and 410493 are shown in Figures 11 and 12, and these two stations located in the same climatic zone behaved differently based on their quantiles. For station 410639, quantiles were higher during the postclimatic change period for both 95th and 97.5 percentile events, although the difference between quantiles was higher for the 97.5 percentile events, whereas for station 410493, quantiles were higher during the preclimatic change period considering both the 95th and 97.5 percentile threshold levels. Most of the stations (including 410120, 410639, 410832, 412121, 412598, 413992, 415018, and 418443) did not show any changes in quantiles based on the 95th percentile except minor deviations. On the basis of the 97.5 percentile, most stations (including 410120, 410639, 410902, 411138, 412598, 415429, 418433, and 419532) showed higher quantiles during the postclimatic change period, and the difference varied in decimal places. 5.3.3. Continental Steppe Zone [33] Continental steppe is located in the extreme northwestern part of Texas. A continental steppe climate is

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Figure 8. Quantiles based on return periods for 1 day extreme precipitation events at stations 411048, 410639, 410493, 415875, 410174, and 412906.

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Figure 9. Quantiles based on return periods for 7 day extreme precipitation events at same stations as in Figure 8. 13 of 29

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Figure 10. Quantiles based on return periods for 30 day extreme precipitation events at same stations as in Figure 8.

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Table 3. Quantiles Based on 50‐ and 100‐Year Return Periods for Selected Stations Based on Preclimatic and Postclimatic Periodsa 1 Day

7 Day

30 Day

95th Percentile

97.5 Percentile

Stations

Climatic Periods

50 yr

100 yr

50 yr

100 yr

50 yr

100 yr

50 yr

100 yr

50 yr

100 yr

411048

Preclm. Postclm. Preclm. Postclm. Preclm. Postclm. Preclm. Postclm. Preclm. Postclm. Preclm. Postclm.

7.40 9.80 7.42 9.62 9.30 5.83 4.73 4.88 2.86 3.15 7.07 5.03

8.48 11.52 8.43 11.73 12.44 6.56 5.42 5.51 3.04 3.33 8.38 5.33

11.33 13.78 12.47 21.24 12.23 8.34 7.87 6.71 5.25 6.93 9.43 9.29

12.28 16.08 15.08 27.79 15.12 9.10 9.11 7.34 5.64 7.72 11.04 10.28

16.51 24.11 15.19 23.35 15.76 13.36 12.48 12.24 9.98 11.15 13.60 18.57

17.84 28.12 16.97 27.44 18.37 14.94 13.79 13.45 11.44 12.03 15.32 23.21

0.97 1.19 0.84 0.89 0.87 0.71 0.65 0.58 0.63 0.50 0.66 0.77

0.99 1.24 0.88 0.94 0.99 0.74 0.68 0.60 0.77 0.53 0.73 0.83

1.93 1.88 1.40 1.60 1.36 1.16 1.43 1.13 0.96 0.83 1.20 1.54

2.03 1.94 1.44 1.66 1.48 1.20 1.60 1.18 1.05 0.87 1.30 1.69

410639 410493 415875 410174 412906 a

Preclm., preclimatic; Postclm., postclimatic.

prevalent in the Texas High Plains. This climate type is typical in the interior of continents and is characterized by large variations in the magnitude of ranges of daily temperature extremes, low relative humidity, and irregularly spaced rainfall of moderate amounts. The main feature of this climate in Texas is semiarid with mild winters. Four stations, which are scattered across the region, were chosen for analysis. For demonstration purposes, station 415875 was chosen, and plots of quantiles based on 1, 7, and 30 day extreme precipitation events (Figures 8–10) and the corresponding values at 50 and 100 year return periods (Table 3) are shown. For 1 day extreme precipitation, it was observed in Figures 8–10 that there was not much change in quantiles during preclimatic and postclimatic periods, although higher marginal quantiles were observed during the postclimatic period. A similar variation of quantiles was also observed for other stations, which included 416135, 417079, and 418201. Interestingly, based on the 7 day extreme events, the characteristics changed with higher return quantiles during the preclimatic change period, and the difference in quantile values between preclimatic and postclimatic change periods seemed to be much higher than for 1 day events (Figure 9). While two stations, 415875 and 417079, showed higher quantiles during the preclimatic change period, the other station, 416135, showed higher quantiles during the postclimatic change period, whereas station 418201 showed mixed patterns. When looking at the plot of 30 day annual extreme events for station 415875 (Figure 10), the quantiles did not change in either of the climatic periods although there were little deviations at higher return periods. But for all other stations (416135, 417079, and 418201), quantiles were higher during preclimatic periods. [34] On the basis of 95th and 97.5 percentiles, station 415875 was chosen as a representative station, and quantiles were plotted in Figures 11 and 12. It was seen that quantiles were higher during the preclimatic change period for both thresholds based on the representative station, and a similar trend was also observed for station 416135. However, for stations 417079 and 418201, quantiles looked similar, except for minor deviations at both threshold levels.

5.3.4. Arid Zone [35] The basin and plateau region of the Trans‐Pecos features a subtropical arid climate that is marked by summertime precipitation anomalies of the mountain relief, and it is located in the extreme eastern part of Texas. On the basis of long‐term data as well as missing values, only two stations (410174 and 410498) were chosen for analysis. For demonstration purposes, station 410174 was chosen, and plots of quantiles based on 1, 7, and 30 day extreme precipitation events (Figures 8–10) and the corresponding values (Table 3) are shown. On the basis of 1 day extreme precipitation, it was observed that the quantiles based on different return periods were higher during the postclimatic change period for station 410174. Interestingly, the difference between preclimatic and postclimatic period quantiles increased from 1 day to 7 day annual maximum extremes; however, it again decreased for 30 day maximum extremes. The other station, 410498, located in the arid region, also behaved in a similar way, with higher quantiles during the postclimatic period. [36] For the arid climatic region, station 410174 was considered as the representative station. Higher quantiles were observed during the preclimatic change period based on 95th and 97.5 percentile threshold levels (Figures 11 and 12), whereas changes in quantiles for other stations in the same arid region with a different geographic location differed from the representative station with higher quantiles during the postclimatic change period for both threshold levels. 5.3.5. Subtropical Steppe Zone [37] The broad swath of Texas from the mid‐Rio Grande Valley to the Pecos Valley has a subtropical steppe climate and is typified by semiarid to arid conditions. Two stations, 412679 and 412906, were found to be suitable for analysis. To evaluate possible changes in quantiles for 1, 7, and 30 day extremes, station 412906 was chosen for analysis as shown in Figures 8–10, and the corresponding values are shown in Table 3. An interesting observation was made as quantiles changed with the increase in the duration of extreme events. On the basis of 1 day annual extremes, quantiles were higher during preclimatic periods, and no significant changes in quantiles were observed based on 7 day extremes, with little

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Figure 11. Quantiles based on return periods for 95th percentile extreme precipitation events at same stations as in Figure 8.

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Figure 12. Quantiles based on return periods for 97.5 percentile extreme precipitation events at same stations as in Figure 8. 17 of 29

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Figure 13. Spatial location of stations with increasing return values based on postclimatic change data compared with those based on preclimatic change data. Plus symbol, return values are higher for all return periods; diamond, return values are higher after the 50 year return period. deviations for station 412906. However, in contrast, based on 30 day extremes, quantiles were higher during the postclimatic change period compared to the preclimatic change period based on 1 day extremes. For station 412679, quantiles were higher during the preclimatic change period for both 1 and 7 day extremes, and no changes were observed based on 30 day extremes with little deviations. On the basis of 95th and 97.5 percentile threshold levels, station 412906 was chosen as a representative station (Figures 11 and 12), and for both threshold levels, the quantiles looked to be

higher during the postclimatic period. A similar observation was made for the other station, 412679, located in the subtropical steppe. [38] It was noted that at most of the stations, quantiles varied during preclimatic and postclimatic periods. This implies that the behavior of quantiles had changed over time. On the basis of the quantiles obtained for different return periods using 1 day extreme precipitation on an annual scale, mixed results were observed. The stations where quantiles were higher based on 1 day extreme events

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Figure 14. Return values of 1 day extreme events for different return periods (10, 50, and 100 years) for (a, c, e) 1925–1964 and (b, d, f) 1965–2005.

during preclimatic periods were located in the subtropical subhumid regions that are characterized by hot summers and dry winters. Also, a few stations were located in the subtropical steppe region. Spatially, these stations stretched from southwest to northeast, although a few stations were located elsewhere. The stations where quantiles were higher during the postclimatic change period were located in most of the climatic zones, including subtropical humid, subtropical subhumid, continental steppe, and subtropical arid zones. Interestingly, these stations extended from southeast to northwest in contrast to stations where the return period was higher during the first subperiod (extending from southwest to northeast). Quantiles based on the 7 day maximum precipitation on an annual basis looked similar to 1 day precipitation at most of the stations in terms of similar increasing or decreasing patterns for both preclimatic and postclimatic periods. The stations do not follow similar patterns of 1 day extreme precipitation located in the northern part of Texas, where the behavior changes with the increase in the window

length of extreme precipitation. The stations, based on 30 day extremes that followed an opposite pattern for preclimatic and postclimatic periods compared to 1 and 7 day extreme precipitations, were located west of continental steppe, north of subtropical subhumid, south of subtropical steppe, and in the eastern part of the subtropical humid climate. This demonstrates that when the extreme precipitation window length increased to 30 days, its behavior changed at the far locations of climatic zones compared to a lower window length. Several stations based on the 95th percentile where the changes in quantiles were not observed included 412598, 418201, and 418433, and interestingly, all these stations lie in the same latitude, although they vary in their longitudinal location. The higher values of quantiles based on the 97.5 percentile as a threshold level during the preclimatic period were located in central north Texas. Most of the stations followed a similar pattern based on the 95th and 97.5 percentiles in terms of the trend in their quantiles (increasing or decreasing pattern based on two periods).

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Figure 15. Return values of 7 day extreme events for different return periods (10, 50, and 100 years) for (a, c, e) 1925–1964 and (b, d, f) 1965–2005.

5.4. Higher Quantiles of Extremes During Recent Period (1965–2005) [39] After observing quantiles of stations during preclimatic and postclimatic periods, it is worth highlighting the regions where higher extremes occurred during the postclimatic period, as shown in Figure 13. Stations with increasing trends based on the 1 day extreme included stations in the central northern, western, and southeastern parts of Texas, which fall in subtropical subhumid, subtropical humid, and subtropical arid regions (Figure 13a). These patterns changed slightly in the case of 7 day extreme events with stations more scattered, but the patterns in the subtropical arid region remained the same as in the western part of Texas (Figure 13b). These changes in short‐term (1 and 7 day) extreme precipitation are likely to alter flash flooding, which generally occurs when the ground becomes saturated with water that has fallen too quickly to be absorbed. The runoff is collected in low‐lying areas and rapidly flows downhill. Flash floods most often occur in normally dry

areas that have recently received precipitation, but they may be seen anywhere downstream from the source of precipitation. Changes observed in the 30 day windows of maximum precipitation compared to 1 and 7 day precipitation with a distinct cluster of stations were in central north Texas, which falls in subtropical subhumid zones (Figure 13c). [40] On the basis of the extremes calculated using the threshold (95th and 97.5 percentiles), the stations with increasing patterns observed from 1965 to 2005 differed from the extremes calculated based on annual maximum extremes. There is a distinct pattern observed based on the 95th percentile, where the quantiles of extremes were concentrated in the central southern part of Texas (Figure 13d), which is at the intersection between subtropical humid and subtropical subhumid climatic zones. On the basis of the 97.5 percentile, however, two distinct patterns were observed, one lying in the central southern and the other in the central northern part of Texas and both of them lying in the subtropical subhumid regions (Figure 13e).

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Figure 16. Return values of 30 day extreme events for different return periods (10, 50, and 100 years) for (a, c, e) 1925–1964 and (b, d, f) 1965–2005. 5.5. Spatial Analysis of Quantiles Based on Annual Maximum [41] A spatial map based on quantiles of extreme events was constructed using the kriging interpolation method, which is basically a geostatistical technique to interpolate the value of a random field (e.g., elevation, z, of the landscape as a function of geographic location) at an unobserved location from observations of its value at nearby locations. The spatial map of Texas, based on the 1 day extreme event with return periods 10, 50, and 100 years during two subperiods (preclimatic and postclimatic), is shown in Figure 14. On the basis of the 10 year return period, it was observed that the maximum 1 day precipitation was expected to be more than 2 inches in any part of Texas based on the two climatic periods. The spatial pattern of maximum precipitation for these two periods based on the 10 year return period was observed in the extreme eastern part of Texas (Figures 14a and 14b), which then extended toward the central part of Texas, except that there were a few pockets where the spatial pattern differed. The spatial pat-

tern became more distinct when the 50 year return period was considered (Figures 14c and 14d). During the preclimatic period, the maximum 50 year return period precipitation was observed in pockets located in southeast and central Texas, whereas during the postclimatic period, the pockets were observed in east, southeast, and central north Texas. Similar observations were also made for the 100 year return period, with the magnitude of extremes higher in a few pockets during preclimatic periods. [42] On the basis of the 7 day maximum precipitation, the spatial distribution of quantiles was plotted as in Figure 15. It was observed that during the preclimatic period based on the 10 year return period, the extreme values were observed in southeast Texas, and these were in the subtropical humid zone. The minimum quantile of 7 day maximum rainfall with a 10 year return period likely to fall in every part of Texas would be 4 inches. During the postclimatic period, a pattern similar to that of the preclimatic period was observed, except that there was a slight increase in the spatial extent from the southeast to the lower central part of Texas. When the return period increased to 50 years, a

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Figure 17. Return values of 95th percentile extreme events for different return periods (10, 50, and 100 years) for 1925–1964 and (b, d, f) 1965–2005. distinct patch of maximum extreme was concentrated in southeast Texas. Spatial changes were observed during the postclimatic compared to preclimatic period: (1) the magnitudes of quantiles were lower in the second half than in the first half; (2) there was a change in the spatial distribution in the extreme north, which is in the continental steppe climate zone; and (3) there was an increase in the spatial distribution of maximum extreme in the south central part of Texas and a lesser extent of extreme in the north central part of Texas, and these two spatial locations are from subtropical subhumid zones. Similar spatial distributions were also observed for the 100 year return period with maximum extremes occurring in the southeastern and central parts of Texas extending from south to north in subtropical subhumid climatic zones. [43] On the basis of the maximum precipitation using consecutive 30 days, the spatial location of quantiles is shown in Figure 16. Unlike 7 day extreme, the maximum quantiles for 30 day extremes based on the 10 year return period seemed to be higher during the postclimatic than preclimatic period. Also, changes in the spatial distribution

were observed in the extreme north in continental steppe climatic zones. Maximum extreme precipitation values were observed in the eastern part of Texas, which was also slightly spread toward the northeastern part during the preclimatic period based on the 10 year return period, whereas during the postclimatic period, the spatial extents were more toward southern and central parts of Texas. Interesting results were observed for the 50 year return period. The spatial location of maximum extreme precipitation during the preclimatic period formed a diagonal extending from the southeastern to the central part of Texas. When the postclimatic change period was compared, the maximum extreme precipitation seemed to be higher at locations adjacent to the formed diagonal observed during the first half. Changes were also observed in the extreme northern part of Texas and in the southeastern and lower central parts of Texas. When the 100 year return period was considered, the spatial distribution of extremes looked similar to the 50 year extreme with higher magnitudes of quantiles. [44] A spatial map of extreme precipitation based on two (95th and 97.5) threshold levels was also constructed, as

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Figure 18. Return values of 97.5 percentile extreme events for different return periods (10, 50, and 100 years) for (a, c, e) 1925–1964 and (b, d, f) 1965–2005. shown in Figures 17 and 18. The spatial distribution, based on the 10 year return period, was observed to follow the same pattern for both preclimatic and postclimatic periods. Extremes were observed to be maximum in the eastern part of Texas and minimum in the western part of Texas. This transition occurred from subtropical humid to subtropical subhumid to subtropical steppe and subtropical arid zones. On the basis of the 50 year return period, changes were observed in the extreme northern and extreme western parts of Texas. Similar changes were also observed in spatial patterns based on a 100 year return period. On the basis of the 97.5 percentile (Figure 18), the spatial pattern of the 10‐ year return period looked similar to the decreasing pattern from east to west Texas, with the changes in the spatial pattern observed in the extreme western part of Texas when two periods were compared. During preclimatic periods, based on the 50 year return period, there was a uniform decrease in the 97.5 percentile extremes from eastern to western parts of Texas, whereas during postclimatic periods, pockets of extremes were observed, and the pattern of

decrease of extremes was not so uniform. When 100 year extremes were observed, the spatial pattern was similar to 50 year extremes with more extremes concentrating in far east Texas. 5.6. Trend Analysis of Extreme Precipitation [45] For trend analysis, the Mann‐Kendall nonparametric test was performed for extreme events based on 1, 7, and 30 day annual maximum precipitation as well as the 95th and 97.5 percentiles of daily precipitation data for two time periods, i.e., preclimatic and postclimatic periods. When the MK statistic was positive, it indicated an increasing trend, and when it was negative, it indicated a decreasing trend. Also, a value of 0.05 was chosen as the local significance level for a two‐sided test. On the basis of this significance level, values larger than 1.96 or lower than −1.96 indicated, respectively, a significant positive or negative trend. To demonstrate the trend graphically, plots of precipitation using the 97.5 threshold for station 415196 based on preclimatic and postclimatic data are shown in Figure 19. The

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Figure 19. Linear trend for the 97.5 threshold level for station 415196 during the (a) 1925–1964 and (b) 1965–2004 periods. linear slope from 1925 to 1964 was −0.004 (MK statistic of −1.21), whereas from 1965 to 2005 it was +0.006 (MK statistic of 1.38), indicating negative and positive trends, respectively. The Mann‐Kendall test statistics for all extreme time series based on two time periods are shown in Figure 20. It was observed that for the same station, there was a difference in the MK statistics during two periods, and this difference became more distinct for extremes calculated based on the threshold level as shown in Figure 20. [46] On the basis of 1 day extreme events, 11 stations showed an increasing trend and 16 stations showed a decreasing trend based on preclimatic change data, whereas based on the postclimatic change data, increasing and decreasing numbers of stations were found to be 13 and 17, respectively. Also, during the postclimatic change period, station 415196 exhibited a significantly increasing trend, and station 410498 exhibited a significantly decreasing trend. During the preclimatic change period, stations with increasing patterns were mostly located in central north Texas, and in the case of postclimatic change data, the stations with increasing patterns were scattered more in central north and extreme north Texas (Figure 21a). Interestingly, in far east Texas no trend was observed during the preclimatic change period, whereas during the postclimatic change period, increasing patterns were observed. Also, during the postclimatic change period, the stations with a significant increasing trend were located in the extreme east, whereas the stations with a significant decreasing trend were located in western Texas. [47] On the basis of the 7 day scale, 11 stations had increasing trends and 18 stations showed decreasing trends during the preclimatic change period, whereas during the postclimatic change period, 13 stations showed increasing trends and 16 stations had decreasing trends. Among these stations, stations 415196 and 412019 showed significant increasing and decreasing trends, respectively, at the 5%

significance level. Stations with increasing patterns were located in central north Texas as well as scattered stations observed in other parts of Texas (Figure 21b). An interesting pattern was noticed for the postclimatic change period with all increasing stations located within the eastern part as well as the southeastern part of Texas. Also, stations in the southeastern part of Texas, which demonstrated decreasing trends based on the 1 day extreme, showed increasing trends based on 7 day maximum precipitation. Stations located in far east Texas behaved in a similar manner for both 1 and 7 day extremes during the postclimatic change period (Figure 21b). [48] On the basis of a 30 day scale, 6 stations had increasing trends and 23 stations had decreasing trends during the preclimatic change period, whereas 14 stations had increasing trends and 16 stations had decreasing trends based on postclimatic change data, with one station (419532) showing a significant increasing trend. The nature of trend based on the 30 day maximum precipitation differed from that of both 1 and 7 day precipitation. First, the number of stations with increasing trends was higher during the postclimatic change period than in the preclimatic change period. Second, the stations with increasing trends during the preclimatic change period did not follow any clusters, whereas during the postclimatic change period, the clusters of stations with increasing patterns were distinctly visible in the southeastern part of Texas (Figure 21c). [49] On the basis of the 95th percentile, 8 and 22 stations showed increasing and decreasing trends, respectively, during the preclimatic change period, with 2 stations (410498 and 410493) showing significant decreasing trends. When the postclimatic change period was considered based on the 95th percentile threshold level, 18 stations showed increasing trends and 11 stations showed decreasing trends, with 1 station (412906) indicating a significant decreasing trend. There was a marked increase in the number of stations

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Figure 20. Mann‐Kendall statistics for stations, based on annual extremes of 1 day maximum annual precipitation for 1925–1964 and 1965–2005. 25 of 29

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Figure 21. Spatial distribution of trends for the annual extremes for two different time periods. Solid circle, increasing trend; open circle, decreasing trend; triangle, significantly increasing trend; inverted triangle, significantly decreasing trend; plus, no trend. 26 of 29

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showing increasing trends during the postclimatic change period. Both increasing and decreasing patterns in the 95th percentile were observed in the eastern part of Texas during the preclimatic change period, whereas during the postclimatic change period, more stations with increasing trends were observed diagonally extending from the southeast to the northwest of Texas (Figure 21d). Similarly, based on the 97.5 percentile threshold, 11 and 19 stations showed increasing and decreasing trends, respectively, during the preclimatic change period, whereas during the postclimatic change period, 21 stations indicated increasing trends and 9 stations showed decreasing trends. The number of stations with increasing trends seemed to be high during the recent period based on the 97.5 percentile. Most of the increasing trend stations were located in the southeastern part of Texas during the preclimatic change period, whereas during the postclimatic change period, the stations were located in the upward side extending diagonally from southeast to northwest Texas (Figures 21e and 21f).

6. Conclusions [50] Extreme precipitation exercises multiple effects on environment, society, and human life. This study was performed to estimate the quantiles of extreme precipitation by fitting a GEV distribution and to determine the changes in trend during recent periods. Five annual precipitation extremes based on annual maximum (1, 7, and 30 days) and on the threshold level (95th and 97.5 percentiles) were performed. The changes in precipitation characteristics were observed and are highlighted with the following conclusions. [51] 1. On the basis of the quantiles obtained for different return periods using 1 day extreme precipitation on an annual scale, mixed results are observed. The stations where quantiles are higher based on 1 day extreme events during preclimatic periods are mostly located in subtropical subhumid regions. The stations where quantiles are higher during the postclimatic change period are located in most of the climatic zones, which include subtropical humid, subtropical subhumid, continental steppe, and subtropical arid zones. Interestingly, these stations extend from southeast to northwest in contrast to stations where the return period is higher during the preclimatic change period. [52] 2. Quantiles, based on the 7 day maximum precipitation on an annual basis, look similar to 1 day precipitation at most of the stations in terms of similar increasing or decreasing patterns for both preclimatic and postclimatic periods. The stations do not follow similar patterns of 1 day extreme precipitation located in the northern part of Texas, where the behavior changes with the increase in the window length of extreme precipitation. [53] 3. Changes observed during the postclimatic period in the 30 day windows of maximum precipitation compared to 1 and 7 day precipitation with a distinct cluster of stations are in central north Texas, which falls in subtropical subhumid zones. [54] 4. Higher values of quantiles based on the 97.5 percentile as a threshold level during the preclimatic period are located in central north Texas. Most of the stations follow a similar pattern based on the 95th and 97.5 percentiles in

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terms of trend in their quantiles (increasing or decreasing pattern based on two periods). [55] 5. During the preclimatic change period, stations based on the 1 day extremes with increasing patterns are mostly located in the central northern part of Texas, and in the case of postclimatic change data, the stations with increasing patterns are scattered more in the central northern and extreme northern parts of Texas. [56] 6. On the basis of 7 day extremes, stations with increasing patterns are located in the central northern part of Texas, and scattered stations are observed in other parts of Texas. An interesting pattern is noticed for the postclimatic change period with all increasing stations located within the eastern part as well as southeastern part of Texas. [57] 7. It is observed that for similar stations, there is a difference in the Mann‐Kendall statistics for two periods. For example, when the temporal scale of extreme precipitation increases from 1 to 7 days, the changes in quantiles are observed for nearly 35% of stations based on varying return periods. The nature of trend based on 30 day maximum precipitation differs from both 1 and 7 day precipitation in terms of more numbers of stations with increasing trends during the postclimatic change period than in the preclimatic change period. Also, during the postclimatic period, the clusters of stations with increasing patterns are distinctly visible in the southeastern part of Texas. [58] 8. The differences in the Mann‐Kendall statistics between preclimatic and postclimatic change periods are more prominent when extremes based on the 95th and 97.5 percentile threshold levels are considered. There is also a marked increase in the number of stations showing increasing trends during the postclimatic change period. [59] Acknowledgments. This work was financially supported by the United States Geological Survey (project 2009TX334G) and the Texas Water Resources Institute through the project “Hydrological Drought Characterization for Texas Under Climate Change, with Implications for Water Resources Planning and Management.” We are thankful to the reviewers for their insightful comments, which helped improve the quality of this manuscript.

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