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Medio Ambiente y Desarrollo Sustentable Artículo arbitrado
Abstract
This study applied experimental design to mean annual, mean
maximum and mean minimum temperatures of Florida State, U. S. A.
Considerations are: 1. Testing various continuous probability
distributions, to identify the best one, to avoid experimental errors
using the statistics Anderson-Darling (A-D) and P-value. The results
showed the normal distribution was the best. 2. Calculations of
descriptive statistical for the mean annual, mean maximum and mean
minimum temperatures. The results showed very little experimental
errors. 3. Constructing normal probability plotting positions to
calculate return periods and probabilities of occurrence. 4. Construction
of time-series analysis and its subjectivist validation, to assess annual
tem pe ra tu re tren ds. T he re su lts s ho wed u pwa rd tren ds f or t he m ean
annual, mean maximum and mean minimum temperatures. 5.
Establishing a reliable database temperature framework for Florida
State, to be used by researchers in meteorology, environmental
engineering, hydrology, civil engineering, agriculture, etc.
Keywords: Experimental design, normal probability plotting positions
and time-series analysis.
Resumen
Este estudio aplicó diseño experimental a las temperaturas promedio
anuales, medias máximas y medias mínimas del estado de Florida, EUA.
Las consideraciones son: 1. Análisis de varias distribuciones de
probabilidad continua, para identificar la óptima, para evitar errores
experimentales usando la estadística Anderson-Darling (A-D) y valor de
p. Los resultados mostraron la distribución normal como la mejor. 2.
Cálculos de estadísticas descriptivas de la temperatura media anual, media
máxima y media mínima. Los resultados mostraron muy pocos errores
experimentales. 3. Construcción de posiciones gráficas de probabilidad
normal para calcular periodos de retorno y probabilidades de ocurrencia.
4. Estructuración de análisis de series de tiempo y su validación
subjetivista, para analizar las tendencias de temperaturas anuales. Los
resultados mostraron directrices alcistas de las temperaturas, para las
medias anuales, medias máximas y medias mínimas. 5. Establecimiento
de una infraestructura de datos de temperaturas para el estado de Florida,
EUA para ser usados por investigadores en meteorología ingeniería
ambiental, hidrología, ingeniería civil, agricultura, etc.
Palabras clave: diseño experimental, posiciones gráficas de probabilidad
normal y análisis de series de tiempo.
Modelo para el análisis de valores de temperatura: caso de
estudio serie 1895-2014 del estado de Florida, EUA
HÉCTOR QUEVEDO-URÍAS1,2, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ1, ERNESTOR ESPARZA1,
ÓSCAR IBÁÑEZ1 Y TULIO SERVIO DE LA CRUZ1
_________________________________
1 UNIVERSIDAD AUTÓNOMA DE CIUDAD JUÁREZ. Instituto de Ingeniería y Tecnología, Departamento de ingeniería Civil y Ambiental. Av. Del Charro
No. 450N, Ciudad Juárez, Chih. CP 32310.
2 Dirección electrónica del autor de correspondencia: hquevedo@uacj.mx.
Statistical model for the analysis of
temperature: case study the 1895 - 2014
serie for Florida state
Recibido: Febrero 14, 2017 Aceptado: Enero 13, 2018
• Vol. XI, Núm. 3 • Septiembre-Diciembre 2017 •156
A
Introduction
tmospheric observing systems were established in support of economically relevant
activities such a food production, transportation, hidrometeorological and weather
forecasting and lost prevention. More recently, long data-series are the base for
ten de ncy a na ly si s i n t he dete ct io n o f g lo ba l wa rm in g a nd ur ba n heat islands.
Unfortunately, certain practices that may be of
little significance in an operational environment, such
as relocating a station or shifting its observation time,
may have a profound impact on the integrity of the
historical record (Vose and Mathhew 2004). As a result,
data from most existing networks needs adjustments
to account for historical variations in observing practice
as recognized by experts and the World Meteorological
Organization (Panel on Climate Observing Systems
Status 1999; Peterson et al. 1998). Even after the
careful application of statistical adjustments, it is often
not possible to address many critical aspects of climate
variability and change (Karl et al. 1995). This situation
has lead to increasingly frequent calls for the
deployment of new observing systems and statistical
tec hn iq ues t o te st t he val i dity o s lo ng data -s eri es.
The objective of this study was the application of
statistical functions to a 118-year sample of temperature
data of the State of Florida, U.S.A., for period 1895-2014.
The study applied experimental design techniques to
identify and control background experimental errors
to assure the optimization of the results. To do so, the
study calculated descriptive statistics and cumulative and
density probabilities aimed to check for the symmetry
of the data to preclude experimental errors. Another
objective was the application of a screening process to
identify the most appropriate continuous probability
distribution, to control experimental errors aimed at
improving the results. Another directive was the
establishments of normal probability plotting positions
to calculate periods of return and probabilities of
occurrence, for any desired temperature. Another goal
was the structuring of time series statistical graphical
models to predict temperature trends for wide-state
Florida. Finally, the ultimate goal was the establishing of
a reliable database temperature framework for Florida
State, to be used by researchers in meteorology,
environmental engineering, hydrology, civil engineering,
agriculture, etc.
Insofar as the application of continuous
probability distributions, there are several revisions
done on the subject. For example, Quevedo (2012), in
his book of hydrology, applied experimental design
techniques, to identify the most appropriate
probability function, as the normal, lognormal,
gamma, Weibull, Gumbel, and so on, to minimize the
experimental error, thus, to optimize de results.
Additionally, Quevedo et al. (2014) used an analogous
procedure, in a study on precipitation values of El
Paso, Texas, aimed to minimize the background noise,
thus to enhance the results.
Another source of information on temperatures
trends is provided by the organization Remote Sensing
Systems, which discusses measurement methods for
upper air temperatures and temperature measurements
in the lower troposphere. In (Figure 1) below shows
the graph of globally averaged temperature anomaly
time series for the Lower Tropospheric Temperature
(TLT). The plot shows the warming of the troposphere
over the last 3 decades, which has been attributed to
human-caused global warming.
Figure 1. Figure showing globally averaged temperature anomaly time
series for the Lower Tropospheric Temperature (TLT). The plot
shows the warming trends of the troposphere over the last 3 decades,
which has been attributed to anthropogenic-caused global warming.
Source: Remote Sensing Systems (http://www.remss.com/
measurements/upper-air-temperature).
HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
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These concerns had been fully documented by
the IPCC as well as the relentless increment of
recognized effects of climate change in all human and
no-human vital systems (IPCC 2007). Costal
communities as those in Florida, California, Tabasco
and others are becoming more vulnerable to the rise
of sea leavel, wildfires, heat waves and droughts.
Currently, one of the mos comprehensive long-term
tem pe ra tu re a nd p re cip ita t io n da ta fo r t he c on t in en tal
US states is the one provided by NOAA´s U. S. Climate
database suitable for statistical models.
Materials and methods
The methodology consisted in the processing of
a sample data of mean annual, mean maximum and
mean minimum temperatures values for the period
of 1895 to 2014 for the State of Florida, U.S.A. To
accomplish such goal, the study applied several
statistical functions, as descriptive statistics, and
boxplot diagrams (though not shown here explicitly),
to check for the symmetry of the data and the possible
identification of outliers that could give to
experimental errors. The study also calculated
cumulative and density probabilities, to check for the
symmetry and skewness of the data. The method
attempted different probability graphs using the
tem pe ra tu re va lues to de ter min e t he be st p rob abi l ity
distribution that fits the data, thus eliminating
experimental errors. The Minitab computer program
was used to do this task, because it determines the
best continuous probability distribution based on the
value of the Anderson-Darling goodness of fit test and
the P-value, in order to control background noise.
Also, the procedure arranged normal probability
plotting positions to calculate periods of return and
probabilities of occurrence. Finally, the process
constructed time series graphical trend analyses for
the prediction of mean annual temperatures and
minimum and maximum annual temperatures.
This being so, this research used the temperature
values shown in (Table 1) below, which displays the
time, in years, from 1895 to 2014, the mean annual
temperatures, the mean annual maximum
temperatures and the mean minimum annual
tem pe ra tu re s, exp re ss ed i n deg re es Fa hr enh eit (oF).
Similarly, this research prepared a summary of
descriptive statistics that included the mean, the
median, the standard deviation, the variance, the
skewness and the maximum and minimum values.
This was done to check for the symmetry of the
data, to identify and control the possibility of
experimental errors. Tables 2, 2a and 2b beneath
show a summary of descriptive statistics using the
data of Table 1.
Table 2. Table showing the values of the mean, standard
deviation, median, minimum and maximum values, range.
Skewness and kurtosis corresponding to the mean annual
temperatures for the State of Florida.
Table 2a. Table showing the values of the mean, standard
deviation, median, minimum and maximum values, range,
skewness and kurtosis corresponding to the mean minimum
annual temperatures for the State of Florida.
Table 2b. Table showing the values of the mean, standard
deviation, median, minimum and maximum values, range,
skewness and kurtosis corresponding to the mean maximum
annual temperatures for the State of Florida.
Later on, the methodology applied several
continuous probability distributions, by going
through a trial-and-error procedure to identify the
most appropriate probability function, as the normal,
lognormal, gamma, Weibull, Gumbel, and so on. This
was done basing the criterion on the smallest values
of the Anderson-Darling (A-D) goodness-of fit test,
and on the P-value. This procedure was done to
eliminate a possible source of experimental errors
(which it did). For example: Figure 2. Below shows
the graph of the mean annual temperatures values
using the data of Table 1.
HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
• Vol. XI, Núm. 3 • Septiembre-Diciembre 2017 •158
HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
Table 1. Table showing the mean annual temperatures, the mean annual maximum temperatures and the mean minimum annual
te mp era tu re s, ex pre ss e d i n de g re es Fa hre nh ei t ( oF), for period 1895 to 2014.
Source: NOAA-National Oceanic and Atmospheric Administration.
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Figure 2. The normal probability graph of the mean annual temperatures
for Florida State, with the goodness of fit test of the Anderson-Darling
value of 0.315 and a P-Value of 0.539.
Similarly,
Figure 3. Below shows the plot of the mean maximum annual
te m p e r a tu r e s ( le ft f i g u r e ) a n d u n de r n e a th de p i cts t h e m ea n m i n i mum
annual temperatures.
Figure 4. Left: the normal probability plot for the mean maximum annual
te m p e r a tu r e s , w i t h t h e g o odn e s s o f f i t te s t o f t h e A n de r s o n - D a rling
value of 0.283 and a P-Value of 0.630. Right: the normal probability
plot for the mean minimum annual temperatures, with the goodness
of fit test of the Anderson-Darling value of 0.285 and a P-Value of 0.623.
Normal distribution. The methodology selected
the normal distribution, as the tool to process the
data. In this way, the probability density function of a
random normal variable X, with equal to 0 (where
- < < ) and standard deviation equal to 1 is:
(1)
Where the parameter is the mean of the normal
distribution and where is the standard deviation
and its variance is 2.
However, if = 0 and = 1, the distribution is
called the normal standard distribution as shown
below:
(1a)
Analogously, the cumulative normal distribution
is the integral of:
(2)
(2a)
Since it is difficult to resolve mathematically the
integral without recurring to numeric methods, it is
necessary to consult the table of the normal
distribution to make transformations, that is:
(3)
Or its statistics (3a)
HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
• Vol. XI, Núm. 3 • Septiembre-Diciembre 2017 •160
Later on, the methodology included a box plot
diagram to identify outliers. This statistical method
identifies what is called outliers or unusually large or
small observations that can cause variability of the
data, thus of experimental error or noise that can
degrade the response variable. Though not shown
here, the box plot diagrams did identify one outlier of
one mean maximum annual temperature, which
corresponded to a value of 83.6 oF that occurred in
1990 (see Table 1). Nonetheless, this extreme value
had little effect on the experimental error.
The methodology’s next step consisted in the
calculation of the mean annual, mean minimum and
mean maximum cumulative and density probabilities
(though the values not shown here, explicitly, but only
their corresponding graphs) and their graphical
analysis to estimate temperature probabilities and to
check for the symmetry (or skewness) of the
distributions of temperatures. In this instance, Figure
5 below shows this situation. Similarly, the
methodology constructed graphs for the cumulative
and density probabilities for the maximum
tem pe ra tu re s, as dis playe d i n F ig ure 6 be lo w.
Consistently, the procedures constructed the
graphs for the minimum cumulative and density
probabilities, as exposed in Figure 7.
Figure 5. Graph showing the cumulative and density probabilities for mean
annual temperatures for Florida State. The left curve shows the cumulative
probabilities and the right graph shows the density probabilities.
The next step consisted in structuring normal
probability plotting positions for the mean annual;
mean maximum and mean minimum temperatures,
for the purpose of estimating periods of return and
probabilities of occurrence, for each one of those
three categories. For example, Figure 8 shows normal
probability plotting position for the mean annual
temperatures.
Figure 6. Graph showing the cumulative and density
probabilities for mean annual maximum temperatures of
Florida State. The left curve shows the cumulative probabilities
and the right graph shows the density probabilities.
Figure 7. Graph showing the cumulative and density
probabilities for mean minimum annual temperatures for
Florida State. The left curve shows the cumulative probabilities
and the right graph shows the density probabilities.
Similarly, Figure 9 shows the normal probability
plotting position for mean minimum annual
temperatures. Correspondingly, Figure 10 beneath
shows the normal probability plotting position for
mean maximum annual temperatures. Likewise, the
methodology built a time-series graphical analysis and
its residual subjectivist validation, to assess annual
tem pera tu re tr en ds f or sta te- wi de F lo rida . F i gu re 11
below depicts this situation.
HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
161
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Further, the residual subjectivist complementary
plot validation of the time series linear trend model
of Figure 11 is shown in Figure 11a.
Figure 8. Graph showing the normal probability plotting position
of mean annual temperatures, as a function of periods of
return and their probabilities of occurrences.
Figure 9. Graph showing the normal probability plotting position
for mean minimum annual temperatures, as a function of
periods of return and their related probabilities of occurrences.
Additionally, Figure 12 underneath shows the
graph of the mean maximum linear trend model and
its accuracy criteria of MAPE, MSD and MAD. Still, the
corresponding residual subjectivist plot validation for
the mean maximum temperatures of Figure 12 is
shown in Figure 12a.
Figure 10. Graph showing the normal probability plotting position for
the mean maximum annual temperatures, as a function of periods of
return and their associated probabilities of occurrences.
Figure 11. Graph showing the linear trend model for the mean annual
te m p e r a tur e v a lu e s o f t h e S ta te o f F lo r i da . T h i s g r a p h i n c lu de s the linear
trend model and MAPE, MAD a nd MSD accura cy measures.
Figure 11a. Graph showing the residual plots for the mean annual
te m p er a tu r e s , w h ic h i n c lu des t he n o r m a l p r o ba bi l i t y p lot, t h e residual
fitted values plot, the histogram and residual observation order plot.
HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
• Vol. XI, Núm. 3 • Septiembre-Diciembre 2017 •162
Figure 12. Graph showing the linear trend model for the mean
annual maximum temperature values of the State of Florida.
This graph includes the linear trend model and the values of
MAPE, MAD and MSD accuracy measures.
Figure 12a. Graph showing the residual plots for the mean
annual maximum temperatures, which includes the normal
probability plot, the residual fitted values plot, the histogram
and residual observation order plot.
Figure 13. Graph showing the linear trend model for the mean
minimum annual temperature values of the State of Florida.
This graph includes the value of MAPE, MAD and MSD accuracy
measures.
Figure 13a. Graph showing the residual plots for the mean
minimum annual temperatures, which includes the normal
probability plot, the residual fitted values plot, the histogram
and residual observation order plot.
(oF), for the period 1895 to 2014, for the State of
Florida. The National Oceanic and Atmospheric
Administration National Centers apportioned this
information for Environmental information
(https:www.ncdc.noaa.gov/cag/).
This research chose the data of temperature
values of the State of Florida, because of its availability
and precision. By examining Table 1, there was
onlyone outlier value corresponding to the mean
annual maximum value of 83.6 oF, wh ic h o cc u rre d i n
1990. Aside from that, Tables 2, 2a and 2b show the
HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
Similarly, Figure 13 shows the graph of the mean
minimum linear trend model and its accuracy
diagnostic criteria of MAPE, MSD AND MAD. Finally,
Figure 13a below shows the residual subjective plots
of the mean minimum temperatures that complement
the results of Figure 13.
Results and discussions
Table 1 shows the mean annual temperatures
values, mean annual maximum and mean minimum
te mp era tu re s va lue s ex pr es se d i n de gre es Fa hre nh ei t
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• Vol. XI, Núm. 3 • Septiembre-Diciembre 2017 •
values of the mean, standard deviation, median,
minimum and maximum values, range, skewness and
kurtosis corresponding to the mean annual, mean
minimum and mean maximum annual temperatures.
For example, by analyzing Table 2, which depicts the
descriptive statistics for the mean annual tempera-
tures, the values of the mean and the median are almost
identical. Moreover, the relation between the mean
annual value of 70.243 and the value of standard
deviation of 0.8909 are very different. Likewise, the
values of the skewness and kurtosis are very close to
zero. These observations preclude the possibility of
experimental errors that could degrade the
trustworthiness of the pursued results. Similarly, by
analyzing the results of Table 2a, the mean maximum
value is almost the same as the median value. Too, the
skewness value is close to zero. Also the value of the
kurtosis of -0.1844 suggests a platikurtic (flat)
distribution probably attributed to the extreme value
of 83.6 oF. F o r t h e sa me r e a so n, th e res u l ts of T a b le 2 b
show more symmetric values as Table 2. From the
experimental design standpoint, all these observations
suggest a good symmetry of the distributions of the
te mp e ratu re s a nd t he a bs en c e o f se ri o us ex pe r im e nta l
errors that could compromise the predictive
capability of the statistical models of this research.
Insofar as the screening process to select the best
continuous probability distribution for the mean
annual temperatures, the results showed the normal
probability function, as the best one. This is shown in
Figure 2 with an A-D equal to 0.315 and a P value of
0.539. Likewise, Figure 3 shows the normal
probability plot corresponding to the mean annual
maximum temperatures, with an A-D value of 0.283
and a P value of 0.630. Equally, Figure 4 shows the
normal probability plot of the mean minimum annual
temperature values. In this graph the ensuing
goodness of fit test of the Anderson-Darling values of
0.285 and the P-value of 0.623 were the lowest values
recorded, after testing several continuous probability
distributions, as the lognormal, Weibull, Gamma, etc.
Besides, the usefulness of the normal probability
graphs is that these graphs are useful to calculate any
probability (by interpolation) associated with any
tem pe ra tu re , w it h a g oo d de gre e of p re cis io n.
Insofar as the results of the calculations of the
cumulative and density probabilities, Figures 5, 6 and
7 show the results. For example, Figure 5 shows the
graphs of the cumulative and density probabilities
for the mean annual temperatures. By analyzing the
density probability curve, the symmetry is almost
perfect; conditions that exclude experimental errors.
Similarly, Figure 6 shows the cumulative and density
probabilities for the mean annual maximum
temperatures. By analyzing the right-hand density
probability curve, it is a little skewed to the right due
to the extreme value of 83.6, which occurred in 1990.
Inasmuch as, Figure 7 which shows the cumulative
and density probabilities for the mean annual
minimum temperatures, it is seen that the symmetry
of these values is almost perfect barring the existence
of experimental errors that could degrade de
outcomes.
About the results related to the construction of
the probability plotting positions, these graphs are
useful to calculate periods of return and their
associated probabilities of occurrence. These
probability-plotting positions are displayed in Figures
8, 9 and 10. For example, Figure 8 shows the normal
probability plotting position for the mean annual
tem pe ra tu re s, w it h th ei r r es pe ct iv e pe ri ods o f re tu rn
and probabilities of occurrence. Likewise, Figure 9
shows the normal probability plotting position for
the mean minimum annual temperatures, with their
respective periods of return and probabilities of
occurrence. Lastly, Figure 10 shows the normal
probability plotting position for the mean maximum
annual temperatures. These graphs can be used to
calculate any desired temperature and its associated
period of return and probability of occurrence. For
example, by analyzing Figure 8, if it is desired to
calculate a period of return for a mean annual
temperature of 71 oF, its corresponding period of
return is about 5 years, with a probability of
occurrence of .2 and so on. Similarly, with Figure 9, if
it is desired to calculate a mean minimum value of 62
oF, its cor r e s p o n d i n g p er i o d o f r e tu r n i s 1 0 0 y e a r s a n d
the probability of occurrence is 0.01 and so on. Alike,
with Figure 10, if it is desired to calculate a mean
maximum annual temperature of 83 oF, i ts p er i od o f
return is 100 years and its associated probability
would be .01 and so on.
HECTOR QUEVEDO-URIAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, OSCAR IBAÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
• Vol. XI, Núm. 3 • Septiembre-Diciembre 2017 •164
Finally, about the use of the graphs of time series,
its primary goal is forecasting temperature
tendencies. In this particular scientific work, the
major objective of these analyses is to assess annual
tem pera tu re tre nds , a s ex po se d i n F ig ur es 1 1, 1 2 an d
13. As seen in all these figures, the resulting trend is
always upward for the mean annual, mean minimum
and mean maximum annual temperatures. For
example, Figure 11 displays a linear trend model for
the mean annual temperature. This figure includes the
adjusted linear trend equation of Yt = 69.55 +
0.0114(t). Here, if it is desired to calculate a mean
annual temperature for any year, just substitute the
corresponding year index in the trend equation and
that will give the forecast. Moreover, this graph
includes the statistics MAPE, MAD and MSD accuracy
measures. In this instance, the acronym MAPE stands
for Mean Absolute Percentage and measures the
precision of the adjusted values in the time series
analyses, which in this case, was equal to .9057. This
means there is about a 0.9 percent error in the
predictive capability using the adjusted linear trend
model. Likewise, the acronym MAD stands Mean
Absolute Deviation, which in this case was equal to
0.6355. This statistics measures the precision of the
adjusted time series values and helps conceptualize
the amount of error. Moreover, the resulting value of
MSD, which stands for Mean Square Deviation, was
equal to 0.6202. This statistics is used in the
measurement of precision. In general, the lower the
values of MAPE, MAD and MSD, the better off the
accuracy of the prediction being pursued. About the
subjectivist evaluation of Figure 11, Figure 11a depicts
the normal probability plots, the fits, the histograms
and the observation order plot using the residuals. All
these four residual graphs serve to evaluate the utility
of the linear trend model. The results of these graphs
suggest the linear trend models fits the data in all cases.
For example, in the normal probability plot all the
points are very close to the least square line, which
means there is little variation in the data values.
Likewise, the graph of the fitted values shows
approximately the same number of positive and
negative residual values. The histogram of the residual
values looks very symmetric and close to normality
and so on.
About the resulting structure of a time-series
graphical analyses and its subjectivist validation for
the mean annual maximum temperatures of Figure
12, the trend equation is calculated as Yt = 58.825 +
0.0114t. This equation can be used as a tool to predict
futures mean maximum annual temperatures. The
values of the statistics for the mean annual maximum
tem pe ra tu re s we re re co rde d as MA PE = 1 .3 87 , M AD
= 0.783 and MSD = 0.904. In this instance the value of
MAPE =1.387 measured the precision of the adjusted
values, as percentage. The complementary
subjectivist evaluation of Figure 12, that is, Figure
12a shows this situation. Again, by analyzing the
residual normal probability plot, the great majority
of the data points are very close to the fitted line. Also,
the graph of the fitted values show about the same
number of positive and negative values and so on.
Regarding the resulting built a time-series
graphical analyses and its subjectivist validation for
the mean minimum annual (Figure 13), the calculated
linear trend model equation is Yt = 58.771 + 0.0127t.
This equation can be used to predict future mean
minimum annual temperatures. Additionally, the
values of the statistics for the mean minimum annual
tem pe ra tu re s we re re co rde d as MA PE = 1 .3 87 , M AD
= 0.8029 and MSD = 1.004. In this instance, the value
of MAPE =1.387 measured the precision of the adjusted
values, as percentage. The subjective evaluation of
time-series graphical analyses for this temperature
category is shown in Figure 13a. The results suggest
the linear trend models fits the data in all cases. For
example, in the normal probability plot the great
majority of all the points are very close to the least
square line which means there is little variation in
the values, thus, little experimental errors. Likewise,
the graph of the fitted values shows approximately
the same number of positive and negative residual
values. Besides, the histogram of the residual values
looks pretty close to normality and so on.
Conclusions
This study is a unique instructive method, because
it applies a deep experimental design scheme, to
control experimental errors, thus, to yield more
precise temperature results in the evaluation of global
warming trends and their consequential climatic
distortions.
HECTOR QUEVEDO-URIAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, OSCAR IBAÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
165
• Vol. XI, Núm. 3 • Septiembre-Diciembre 2017 •
Further, the methodology and the results obtained
in this paper suggest that, before one attempts to
processes any temperature data, it is required to
check its symmetry by the use of descriptive statistics,
to identify the possibility of experimental errors that
can degrade the results. Besides, of utmost importance
is the identification of the best continuous probability
distribution that fits the data, to minimize background
experimental errors (by choosing the right
distribution). Too, the calculations of cumulative and
density probabilities are two-fold, because they can
be used to calculate cumulative or density
probabilities for each one of the three categories of
te mp e ra tu re s u se d. M ore ove r, t he se g ra ph s c an s er ve
to visually check the symmetry of the data.
Congruently, the use of probability plotting
positions is important to assess global warming
trends, periods of return and probabilities of
occurrence of heat waves that can affect the health
and welfare of people. Alternatively, farmers could
find useful applications of probability plotting
positions to project farming yields and future planning
and so on. Similar interrogations are derived by using
probability-plotting positions for minimum
tem pe ra tu re e ve nts. T his i s b ec aus e t he se pro ba bi l ity -
plotting positions can be used to observe historical
changes of extreme maximum or minimum values on
short and long terms. In addition, these probability-
plotting positions are of paramount importance for
planning purposes and contingency situations.
Further, the use of time series linear trend models
can be used to monitor the underway global warming
increases. Besides, time series forecasting can be used
to predict future trend temperature values based on
previously observed standards. In fact, in this research,
the results of the upward trends of the mean annual,
mean annual maximum and mean annual minimum,
demonstrate that global warming is underway, at least
in the Florida State.
On the other hand, by applying an objective and
subjective intellectualism, extreme temperature
events are going to be more and more common, due
to the undiscriminating burning of fossil fuels
(because the world economy is tied up to the oil
industry). These situations are generating artificial
greenhouse gases, which are causing the anthropo-
genic global warming and their consequential effects
on the climate, the economy, on health, on socio-
political systems and on the distortions of geographic,
regional or local temperature patterns. To challenge
these present and future adverse situations, leaders
of all world nations will have to come with more strict
environmental policies and economic and political
strategies to reduce fossil fuels consumption and to
the use of alternative sources of clean energy. This
responsibility will be crucial, so to protect the public
and the well-being of future generations.
As a final point, it is concluded that this forward-
looking method aimed to assess temperature values,
is very reliable due to the profound experimental
design statistical efforts done on its development and
to the use of trustworthy temperature data
apportioned by NOAA. In fact, it is asserted that the
main intention of this experimental design research
is to establish a dependable and precise framework
of temperature values for Florida State. That is, a
dependable database that can be used by investigators
doing research in environmental engineering,
meteorology, agriculture, civil engineering,
experimental designs and so on.
Acknowledgements
The principle author of this revision and his
associates are grateful beyond measure to the
National Oceanic and Atmospheric Administration
National Centers for Environmental Information, for
the apportionment of the cherished temperature data
used in the preparation of this study.
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HÉCTOR QUEVEDO-URÍAS, FELIPE ADRIÁN VÁZQUEZ-GÁLVEZ, ERNESTOR ESPARZA, ÓSCAR IBÁÑEZ Y TULIO SERVIO DE LA CRUZ: Statistical model for
the analysis of temperature: case study the 1895 - 2014 serie for Florida state
Este artículo es citado así:
Quevedo-Urías, H., F. A. Vázquez-Gálvez, E. Esparza, Ó. Ibáñez y T. Servio de la Cruz. 2017. Statistical model for the analysis of
temperature: case study the 1895 - 2014 serie for Florida state. TECNOCIENCIA Chihuahua 11(3):155-166.
Este artículo es citado así:
Alvarado-Raya, H. E. 2017. Peach seedling growth with mycorrhiza and vermicompost. TECNOCIENCIA Chihuahua 11(2):48-57.
Resumen curricular del autor y coautores
HÉCTOR ADOLFO QUEVEDO URÍAS. Obtuvo el doctorado en Ingeniería Ambiental por la Universidad de Oklahoma, EUA; Maestría en
Ciencias Ambientales por la Universidad de Oklahoma y licenciatura por la Universidad de Texas en El Paso. Actualmente labora
como maestro e investigador en el departamento de Ingeniería Civil y Ambiental de la Escuela de Posgrado de Ingeniería Ambiental
del Instituto de Ingeniería y Tecnología de la Universidad Autónoma de Ciudad Juárez (agosto de 1993 al presente). Es autor de 5
libros publicados en aplicaciones estadísticas en Ingeniería Ambiental e Hidrología. Ha sido ponente en múltiples conferencias en
Estados Unidos y México. Es miembro de la International Plataform Association (EUA), Greenpeace y del Consejo Consultivo para
el Mejoramiento de la Calidad del Aire en la Cuenca Atmosférica de Ciudad Juárez, El Paso, Texas y el Condado de Doña Ana, Nuevo
México.
FELIPE ADRIÁN VÁZQUEZ GÁLVEZ. Terminó su licenciatura en 1982, año en que le fue otorgado el título de Químico por el Departamento
de Química de la Universidad de Texas en El Paso (UTEP). Realizó su posgrado en la misma universidad, donde obtuvo el grado de
Maestro en Ciencias en Química en 1985 y el grado de Doctor en Filosofía también en el área de aerosoles atmosféricos por el
Instituto Mexicano de Tecnología del Agua. Desde 2014 labora en el Departamento de Ingeniería Civil y Ambiental de la Universidad
Autónoma de Ciudad Juárez y posee la categoría de Académico titular C. Su área de especialización es la química atmosférica y la
calidad del aire urbano. Se ha desempeñado como Subprocurador Federal del Ambiente, Subsecretario de Gestión en la SEMARNAT,
Director Ejecutivo de la Comisión de Cooperación Ambiental de América del Norte y Coordinador General del Servicio Meteorológico
Nacional de México.
ERNESTOR ESPARZA SÁNCHEZ. Terminó su licenciatura en 1999, año en que le fue otorgado el título de Ingeniero civil por la Universidad
Autónoma de Ciudad Juárez (UACJ). Obtuvo el grado de Maestro en Ingeniería Ambiental en 2003 por la Universidad Autónoma
de Ciudad Juárez (UACJ). Desde 2004 labora en la Universidad Autónoma de Ciudad Juárez (UACJ). Es coordinador de la Licenciatura
en Ingeniería Ambiental. Su área de especialización es la Hidrología.
SERVIO TULIO DE LA CRUZ CHÁIDEZ. Obtuvo la licenciatura en Ingeniería Civil en 1987 por el Instituto Tecnológico de Durango. Tiene el
grado de Maestría en Estructuras por la Universidad Autónoma de Chihuahua y obtuvo el grado de Máster en Ingeniería Sísmica
y Dinámica Estructural por la Universidad Politécnica de Cataluña. Obtuvo el grado de Doctorado en Ingeniería Sísmica y Dinámica
por la Universidad Politécnica de Cataluña, España en 2003. Sus líneas de investigación son Ingeniería Sísmica y Dinámica
Estructural y Ciencia y Tecnología de la Ingeniería Sísmica y la Dinámica Estructural. Es miembro de Colegio de Ingenieros Civiles
de Ciudad Juárez, A. C. Tiene publicaciones en revistas nacionales e internacionales. Actualmente es profesor investigador de
tiempo completo de la Universidad Autónoma de Ciudad Juárez.
