International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol:13 No:03 21
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Factor Analysis of Meteorological and
Granulometrical Data of Aeolian Sands in Arid
Area as a Geo-Environmental Clue: a Case Study
From Western Bank of Lake Nasser, Egypt
Ezzat Khedr1, Kamal Abou Elmagd
1*, Mamdoh Halfawy
2
1 Geology Department, Faculty of Science, Aswan University, Egypt
(e-mail: [email protected]) 2 High Dam Authority, Aswan, Egypt
Abstract-- A monitoring program of sand accumulation
process over an arid area of about 28000 km2 is carried out at
the western side of Lake Nasser along a distance of ~ 350 km
between Aswan city and Egyptian-sudanese borders. From
geoenvironmental point of view, calculations of the flow rate of
wind blown sands from the Western Desert of Egypt and
evaluation of their encroachment hazards into Lake Nasser are
of ultimate importance. In conjurent with the local
metereological data, the granulometriacal data is evaluated. It
showed that the overall graphic mean (Mz) of these aeolian
sands ranges from 1.18 φ to 2.48 φ medium to fine grained
sand. Sorting ranges from 0.6 to 1.8 φ moderately well to
poorly sorted. Meteorologically, the mean air pressure varies
between 940 and 1001 mbar, whereas the mean air
temperature varies between 16.0 and 40.5 °C. The mean
humidity is low and ranges between 15.6% and 48.8%. The
mean wind speed in the study area ranges between 3.0 and 7.1
m/s. The prevailing wind direction is from north or north-
northwest. The interrelationships between the grain size
parameters and the climatic-regime in the present study dry
desert have been statistically modeled using factor analysis
procedure. Data are studied by factor analyses including 19
original variables are proportional to their contribution to the
factor loads, in order to learn the relative importance of each
principal variable in determining the variations among the
samples. Seven factors comprising temperature, mud, wind
speed, pressure, gravel, humidity and mean size are
recognized. These are represent the paramount controlling
factors governing the flow rate and style of blown sands in such
ideal arid region.
Index Term-- aeolian sand dunes – arid environment - factor
analysis – granulometry – meteorology – Lake Nasser
I. INTRODUCTION
Sand dune drifting is one of the surface phenomena
expresses desertification and land damage, and is generally
related with the dryness and mismanagement of water
resources throughout the world and especially in the arid
regions of Africa and the Middle East. These physical
processes involving wind erosion, dust storm, sand
transportation and deposition by wind are serious natural
hazards to human settlements, agricultural lands,
communications and water recourses. In northern and
central Africa, for example, several villages, oases, roads,
and railway lines are invaded by mobile sands. Near the
banks of the Nile in Egypt and northern Sudan, vast
quantities of wind blown sand are deposited annually into
farming areas and the river. The study area at southern
Egypt is located around the Tropic of Cancer in one of the
most arid regions in the globe. Sand dunes represent about
(16.6%) of the total surface area of Egypt and take different
shapes with different properties depending on the effect of
the various environmental conditions [1]. The Western
Desert as the largest area of sand accumulations in Egypt
includes the Greatest Sand Sea (135000 Km²), Kharga Oasis
(4000 Km²), East Farafra (7000 Km²) and other sand
accumulations extend parallel to the Nile Valley starting
from Wadi El Natrun in the north, Fayoum and Wadi El
Rayan in the west and Lake Nasser in the south [2].
The aim of the present work is providing the
necessary data base for studying the movement of the wind
blown sand as probable natural hazards affecting the volume
of the High Dam reservoir and the agricultural projects
along the western bank of Lake Nasser. Sand movement in
the western bank of Lake Nasser is a function of the various
environmental conditions such as geomorphology, lithology
of the exposed rocks, prevailing structures, air temperature,
air humidity, soil moisture and prevailing winds which often
blow from the north and north-west direction. The
lithological map of the study area and the sites of the
meteorological stations are shown in Figure 1. Several
worldwide and local studies of aeolian sand movement are
given in the classic works of [3 -16]. Sand accumulated
forms as defined by [17] are recorded in the present study
area; barchan-dunes and hanging dunes including either
inland, or coastal varieties, and the sand sheets (or zibar)
with their two types, either inland or coastal sand sheets
(Fig. 2).
Geologically, Aswan High Dam Reservoir area and
its vicinity are dominated by a sedimentary succession
ranging in age from the Post Cambrian to Holocene, with
inliers of igneous and metamorphic rocks belonging to the
Pre-Cambrian Basement Complex and Tertiary basalts [18]
and [19]. The area distribution of the stratigraphic units is
shown in (Fig. 1).
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Fig. 1. Lithological map showing the location of the study area and sites of meteorological station and sand sampling.
Fig. 2. Field photographs of sand accumulations on the western bank of Lake Nasser. (a) Coastal sand sheet
(b) Rippled inland sand sheet (c) Coastal hanging dune (d) Inland hanging dune.
Geomorphologically, the study area has been
simply classified into four regions namely, Sinn el-Kaddab
plateau (470 m high), the Nubian plain (200m high), Toshka
Depressions (135m high) and the Aswan Hills (250 m high)
which cross-cut by the recently man-made Lake Nasser
[20]. Detailed geologic setting and geomorphology of the
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western bank of Lake Nasser were previously treated by [18
- 23]. These studies refer to prevailing of the Nubia
Sandstone and basement rocks exposures in low relief or
plain region (Fig. 1).
Granulometry is a tool applied to classify the
clastic sediments and to elucidate their depositional
environments [24]. Accordingly, eleven sites representing
sand dunes and sheets from intertidal area of the western
bank of Lake Nasser are selected to establish a
granulometric model of aeolian sands deposited in intertidal
zone of the fresh water. The main characteristic
meteorological parameters responsible for deposition of the
aeolian sands of the study area were accomplished through
seven meteorological stations (Fig. 1). Reviews of the
aeolian sediment movement are given by [14], [16], [25],
and [26]. The geological and meteorological data of the
study area is manipulated by factor analysis technique to
evaluate the degree of association between different
variables and to examine the paramount controlling factors
governing the flow rate of the blown sands and their
accumulation styles on such dry area.
Scope and limitation:
The scope of the present work is to develop an
environmental sedimentological model for monitoring and
interpreting the grain size analysis data in relation with the
prevailed meteorological data in arid and hyper-arid areas. It
could be applied as a geological model to evaluate the
geological processes in similar environments. Limitations
include the mathematical formulas used in granulometric
analysis using factor analysis procedure as well as accurate
quantitative measurements of blown sand dynamics by
experimental sand traps and correlating the theoretical and
experimental results.
II. MATERIALS AND METHODS OF STUDY
Mechanical analyses were carried out for (73)
samples of drifted sands representing (11) localities in the
study area (Fig. 1). The collected samples were quartered
and about 1000 grams were screened on a one-phi set of
standard sieves with the mesh openings 2, 1, 0.5, 0.25, 0.125
and 0.063 mm covalent to –1, 0, 1, 2, 3 and 4 φ values,
respectively using an electric shaker for about 20 minutes.
The fraction retained according Wentworth scale (1922) is
weighted and the percentages and the statistical parameters
of Folk and Ward (1957) were calculated. The available
meteorological data for the period of six years (2000 to
2005) were obtained from the metrological stations of the
Aswan High Dam Authority that installed along of the west
bank of Lake Nasser. These are Gurf Hussien, Wadi El-
Arab, Afia, Toshka, Abu-Simble, Adindan and Sara stations
(Fig. 1) during a six year period extending between the year
2000 to 2005. These data include minimum, maximum and
mean air pressure (mbar), air temperature degree (0C),
relative humidity (%), wind velocity(m/s), and wind
direction. Combination of the grain size data with
meteorological data is planed herein and sediment transport
would be statistically explored to establish a
sedimentological model of the transported sand grades and
the covariant meteorological parameter at the western bank
of Lake Nasser. Detailed statistical factor analysis was
performed using a total of 19 variables including three
values of size grades (gravel, sand, and mud %) and four
values of grain size parameters calculated according to Folk
and Ward (1957) and 12 meteorological variables. Numbers
of inputted observations are 73 rows of complete cases that
treated list wise and standardized to obtain classical type of
factoring. Subsequently, the numbers of statistical factors
are extracted on the bases of the least number of
components or eigenvalues respectively.
III. RESULTS
Results of mechanical analysis are graphically plotted
as commulative weight percentage on propability scale and
the statistical size parameters according to [24] are
calculated. However, pilot correlative curves showing the
main difference beween the mean values of grain-size
ftactions are firestly aschived by plotting size fraction of
representative eleven samples from different eleven sites,
againest percent frequencies of these sizes (Fig. 3).
Percent frequencies of [27] size-grades of the analyzed
samples (Fig. 3) show that these sediments are ranging
between bimodal to polymodal types, moderate to poorly
sorted ( fine- to medium grained sand). The most frequent
distribution is represented by the polymodal type "more than
two peaks". Despite the pictorial appearance of polymodal
type in the analyzed samples, the majority of them are
compose mainly of one size grade. The modal class is
usually in the range of medium sand. The polymodal
distribution indicates that the sand grains are derived mainly
from two or more sources. Alternatively, the daily changes
in meteorological parameters including wind speed,
humidity ..etc can‟not excluded.
1. Statistical grain size parameters
The statistical grain size parameters are determined
according to the formulas given by [24]. The four
parameters :graphic mean, inclusive graphic standard
deviation, inclusive graphic skewness, graphic kurtosis were
calculated using a software programme (Sedstat)® [28].
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F
req
uen
cy %
GURF-HUSSEIN
0.0
5.0
10.0
15.0
20.0
25.0
-3.3
-2.3
0.2
1.2
2.0
2.7
4.0
Alsayal
0.0
5.0
10.0
15.0
20.0
25.0
-3.2
5
-2.2
5
0.2
3
1.2
3
2.0
0
2.7
4
3.9
9
AFIA
0.0
5.0
10.0
15.0
20.0
25.0
30.0
-3.3
-2.3
0.2
1.2
2.0
2.7
4.0
WADI ELARAB
0.0
10.0
20.0
30.0
40.0
-3.3
-2.3
0.2
1.2
2.0
2.7
4.0
TOSHKA
0.0
5.0
10.0
15.0
20.0
25.0
-3.3
-2.3
0.2
1.2
2.0
2.7
4.0
ABOSIMBLE
0.0
5.0
10.0
15.0
20.0
-3.3
-2.3
0.2
1.2
2.0
2.7
4.0
ADINDAN
0.0
10.0
20.0
30.0
-3.3
-2.3
0.2
1.2
2.0
2.7
4.0
SARA
0.0
5.0
10.0
15.0
20.0
25.0
-3.3
-2.3
0.2
1.2
2.0
2.7
4.0
Grain Size (φ)
Fig. 3. Percent frequencies of grain size of aeolian sands in the study area
a- Mean grain size (MZ)
Mean size is a function of the size range of
available materials and amount of energy imparted to the
sediments. This amount of energy depends on wind velocity,
i.e. mean size indicates the average kinetic energy of the
depositing agent [4]. Mean size is calculated from the
equation adopted by [24]. The obtained data indicate that
the graphic mean (Mz) ranges from 1.46 φ to 2.21 φ
medium to fine grained sand (Fig. 4). Both coarse and very
fine sand grades are not common in the studied sediments.
b- Sorting (I)
The inclusive graphic standard deviation (I)
measures degree of sorting which reflects the uniformity of
grain size of the sediment. Sorting of the drifted sand ranges
from 0.78 to 1.52 φ (moderately to poorly sorted) as shown
in Figure (5).
c- Skewness (SKI)
Skewness is a measure of the symmetry of the
grain size distribution of sediments and marks the position
of the mean size with respect to the median.The inclusive
graphic Skewness (SKI) values ranging between –0.24 to
0.45, indicating coarse skewed to strongly fine skewed
sediments as shown in Figure (6).
d- Kurtosis (KG)
Kurtosis measures the degree of sorting in the
extremes. The distribution compared with the sorting in the
major part of the sample, and as such, it is a sensitive and
valuable test of normality of the distribution (Folk and Ward
1957). Values of kurtosis for the dune sands of the area
under investigation are ranging between 0.74 and 1.09
indicating platykurtic to mesokurtic type of curves (Fig. 7).
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1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
K. E
l Ram
la
G. H
uss
en
W.
El A
rab
Al S
yala
Afi
a
Tosh
ka
W.
H. R
oad
Ab
o Si
mbl
e
Ad
inda
n
Sara
Tosh
ka D
ep.
me
an m
z
Fine Sand
Medium Sand
Fig. 4. Frequency distribution of the mean (Mz) value of all the study area
0.5
0.7
0.9
1.1
1.3
1.5
1.7
K. E
l Ram
la
G. H
uss
en
W. E
l Ara
b
Al S
yala
Afi
a
Tosh
ka
W. H
. Ro
ad
Ab
o S
imb
le
Ad
ind
an
Sara
Tosh
ka
Dep
.
Sort
ing
(σ
I) φ
Poorly Sorted
Moderately Sorted
Fig. 5. Frequency distribution of the Sorting (1) value of all the study area
-0.40-0.200.000.200.400.600.801.00
K. E
l Ram
la
G. H
uss
en
W. E
l Ara
b
Al S
yala
Afi
a
Tosh
ka
W. H
. Ro
ad
Ab
o S
imb
le
Ad
ind
an
Sara
Tosh
ka D
ep
.Ske
wn
ess
(S K
I) φ
Strongly Fine Skewed
Fine Skewed
Near Symnetrical Skewed
Coarse Skewed
Fig. 6. Frequency distribution of the Skewness value of all the study area
.
0.70
0.90
1.10
K. E
l Ram
la
G. H
uss
en
W. E
l Ara
b
Al S
yala
Afi
a
Tosh
ka
W. H
. Ro
ad
Ab
o S
imb
le
Ad
ind
an
Sara
Tosh
ka D
ep
.
Ku
rto
sis
(KG
) φ
Meso - kurtic
Platy - kurtic
Fig. 7. Frequency distribution of the Kurtosis value of all the study area
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2. Meteorology of the study area
The transport of sediment-grains is often governed by the
properties of the transporting agents (water, wind, gavity)
including movement velocity, temperature, humidity,
pressure, direction etc. Properties of grain size parameters of
the aeolian sand grains at the western bank of Lake Nasser
are best interpreted in the light of the available
meteorological data of the area as collected from the seven
metrological stations. Mean monthly values of the obtained
metrological data are graphically plotted (Figs 8-10). From
these figures, the following notes are concise statements on
the general meteorological characters prevailed in the seven
sites at issue:
- Mean values and maximum values of the measured air
pressure during the twelve months of the six years (2000 to
2005) in seven localities along the western bank of Lake
Nasser are illustrated in Figure (8). Mean pressure values
range between 986.6 mbar and 1028.5 mbar, whilst the
maximum values ranges between 993 mbar and 1039 mbar.
Deviation in readings records of the mean air pressure are
recorded for the months, April (in Adindan site) and in
December in Wadi El-Arab. Variation of mean values and
maximum air temperature and humidity during the twelve
months of the years (2000 to 2005) in seven localities along
the western bank of Lake Nasser Figure (9) outlines the
inverse relationship between mean temperature and mean
humidity in all the studied sites excepting for two sites
(Adindan and Sara stations) located in the southernmost part
of the study area close to the border with Sudan . The
relationships between values of mean temperature and mean
humidity in both of the two stations are positive (Fig. 9).
Annual variation in mean values of maximum wind speed
recorded during six years along the western bank of Lake
Nasser can be subdivide into three monthly periods,
dividing the study area into three regions namely, Northern,
Central, and Southern regions (Fig. 10).
General trends of meteorological conditions in the study
area
The annually and monthly distributions of the
mean air temperature, the mean air pressure, the mean
relative humidity and the mean wind speed are illustrated in
contour maps (Figs. 11-14) consequently, the following
remarks are recorded:
1) The mean air pressure ranges between 1005 mbar and
784 mbar.
2) The mean air temperature ranges between 20.56 °C and
28 °C.
3) The mean relative humidity ranges between 14% and
32%
4) The mean wind speed over the studied area ranges from
3 to 4 m/s,
5) Comparing the vector direction of the blowing winds
with the geographic North, all vector directions are
drawn from the NW to SE.
6) NW – SE orientation angels of the vector direction
measured from the north direction are gradually
increases as one moves from the High Dam southwards.
7) Small number of the annual wind directions are blowing
from the SW direction in Adindan area, whilst
noticeable number blown from SW and south directions
are recorded in Sara area near the borders with Sudan.
Detail studies on the movement of wind blown sands,
directions and quantities are described in detailed
elsewhere [16].
Fig. 8. Mean (upper) and maximum air pressure (lower) during the twelve months of the years (2000 to 2005) in seven localities along the western bank of
Lake Nasser
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Fig. 9. Variation of mean values (upper), and maximum values (lower) of air temperature and humidity during the twelve months of the year (2000 to 2005)
in seven localities along the western bank of Lake Nasser
Fig. 10. Variation in mean values of maximum wind speed recorded during six years (2000-2005) along the western bank of Lake Nasser. Notes: the study
area can be subdivided into three regions (Northern, Central and Southern)
Central
Southern
Northern
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Fig. 11. Contour map of the mean air temperatures in the study
Note: the gradual decrease in values toward Afia locality.
Fig. 12. Contour map of the mean relative humidity in the study area.
Note: Arrows indicate direction of increasing humidity
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Fig. 13 Contour map of the mean wind velocity (m\s) in the study area.
Note: Arrows indicate direction of increasing wind speed
Fig. 14. Contour map of the mean air pressure in the study area.
Note: Arrows indicate direction of increasing air pressure
3. Factor Analysis:
a. Function
The Factor Analysis procedure is designed to
extract m common factors from a set of p quantitative
variables X. In many situations, a small number of common
factors may be able to represent a large percentage of the
variability in the original variables. The ability to express
the covariance amongst the variables in terms of a small
number of meaningful factors of seven leads to important
insights about the data being analyzed. This procedure
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supports classical factor analysis. Consequently, factor
loadings may be extracted from either the sample covariance
or sample correlation matrix. The initial loadings are rotated
using Varimax, rotation method. StatPoint Technologies,
Inc. designed the Factor Analysis procedure, 2009 in a
commercial computer program named STATGRAPHICS
[29].
To study the interrelationships between the obtained
meteorological data and size-fractions of the aeolian sands
collected along the western bank of Lake Nasser, factor
analyses have been achieved for 1168 values including all
the collected and calculated “mean monthly meteorological
data” and “grain size parameters”. Every meteorological
variable (wind pressure, temperature, humidity, and wind
speed) is listed in (Table I) as three consecutive columns
designated in numbers (1, 2, 3) corresponding to mean,
maximum, and minimum values, respectively. In the same
(Table I), mean percentages of gravel, sand, and mud “silt +
clay” fractions of the monthly collected sand samples are
individually repeated for the twelve months of the years
(2000-2005) together with values of size parameters of [24],
Mz, σI, SkI, and KG. Hence, the original variables are
bringing into being 73 row and 19 column (variables) are
imputed in the Statgraphics program [29] to excuse Factor
Analyses. All the obtained data in these analyses are
standardized first to normalize the analysis on bases of the
sample correlation matrix rather than the sample covariance
matrix. This corresponds to standardizing each input
variable before calculating the covariance, by subtracting its
mean and dividing by its standard deviation. Subsequently,
the number of factors are extracted on bases of the least
number of components or eigenvalues respectively. The
original observations (rows) and variables (columns) applied
in these analyses are listed in (Table I).
b. Results of factor analysis
The factor number is decided according to the
cumulative percentage of variance and the program
permitted to use an iterative procedure to estimate
communalities by replacing the diagonal elements with
estimated values.
TABLE I
MEAN, MINIMUM AND MAXIMUM VALUES OF METEOROLOGICAL DATA AND GRAIN SIZE DATA FOR 73 AEOLIAN SAND SAMPLES COLLECTED
MONTHLY ALONG SIX YEARS, WEST OF LAKE NASSER, EGYPT
Variable Mean Minimum Maximum
Mean Press1 989.55 939.90 1001.40
Max. Press2 1009.86 987.90 1049.50
Min.Press3 990.64 915.50 1036.40
Mean Temp1 27.05 16.00 40.50
Max. Temp2 40.12 26.30 48.50
Min.Temp3 14.03 3.80 26.00
Mean Humid1 29.59 15.60 48.80
Max. Humid2 58.86 37.80 83.00
Min. Humid3 8.82 0.90 34.00
Mean Speed1 4.79 3.00 7.10
Max. Speed2 9.19 0.10 14.10
Min. Speed3 0.33 0.00 7.80
Mz 1.69 1.18 2.48
σI 1.27 0.60 1.80
KSI 0.031 -0.50 0.60
KG 0.91 0.60 1.40
Gravel % 0.55 0.00 4.20
Sand % 97.56 92.80 100.00
Mud % 1.92 0.10 5.80
Therefore, the corresponding factor values are outputted and
listed in (Table II). The method used to rotate the factor-
loading matrix after it has been extracted is the Varimax
rotation which maximizes the variance of the squared
loadings in each column. The Varimax- rotated values are
listed in (Table III). Rotated factor matrix derived by
Varimax rotation is listed in (Table IV). Values above 0.2
are considered and the result arranged in desending order.
Values can be correlated in every individual component but
different components can‟t be correlated with each other.
On this statatistical role the following paragraphs will deal
with the relationship between the positive and the negative
values in every component. Description and interpretation of
the rotated-Varimax values as they appear in (Table IV) and
(Figures 15 and 16) are delineated below.
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TABLE II
FACTOR ANALYSIS
Factor Number Eigenvalue Percent of Variance Cumulative Variable Percentage Initial Communality
1 3.95495 20.816 20.816 Press1 1.0
2 3.16429 16.654 37.470 Press2 1.0
3 2.55511 13.448 50.918 Press3 1.0
4 1.95107 10.269 61.186 Temp1 1.0
5 1.70212 8.959 70.145 Temp2 1.0
6 1.4049 7.394 77.539 Temp3 1.0
7 1.00069 5.267 82.806 Humid1 1.0
8 0.900183 4.738 87.544 Humid2 1.0
9 0.639266 3.365 90.908 Humid3 1.0
10 0.526364 2.770 93.679 Speed1 1.0
11 0.341419 1.797 95.476 Speed2 1.0
12 0.2874 1.513 96.988 Speed3 1.0
13 0.245478 1.292 98.280 Mz 1.0
14 0.123933 0.652 98.932 oI 1.0
15 0.100999 0.532 99.464 KSI 1.0
16 0.0594861 0.313 99.777 KG 1.0
17 0.0419252 0.221 99.998 Gravel % 1.0
18 0.00024963 0.001 99.999 Sand % 1.0
19 0.00016788 0.001 100.000 Mud % 1.0
TABLE III
FACTOR LOADING MATRIX BEFORE ROTATION
Column1 Factor Factor2 Factor3 Factor4 Factor5 Factor6 Factor7
1 2 3 4 5 6 7
Press1 -0.315223 0.240916 -0.0628873 0.761617 -0.183177 0.0287967 0.355755
Press2 0.485813 0.681006 0.210383 0.0800466 0.258567 -0.130967 0.0885458
Press3 0.298821 0.480696 0.338903 0.505785 -0.0384831 -0.319206 0.311824
Temp1 0.614851 -0.556204 0.437487 -0.0672386 -0.0209686 -0.18962 -0.0457
Temp2 0.511597 -0.56577 0.341412 -0.0787868 0.072655 -0.01229 0.150075
Temp3 0.434681 -0.655716 0.36917 0.114507 -0.184586 -0.164422 -0.135813
Humid1 -0.278278 0.600311 -0.178701 -0.36493 -0.0889 -0.514055 -0.0423
Humid2 -0.566728 -0.000122 -0.425403 -0.347316 -0.266523 0.0942198 0.101538
Humid3 0.248203 0.47833 0.243011 -0.310701 -0.035006 -0.620614 -0.262741
Speed1 0.546838 0.536522 0.0520451 -0.0514367 -0.005016 0.455957 -0.105015
Speed2 0.548926 0.567532 0.176365 -0.117467 -0.15696 0.502225 -0.172185
Speed3 -0.183574 -0.252296 -0.30177 0.175661 0.343261 -0.245915 0.187392
Mz -0.165175 0.0285232 0.0807722 0.583929 0.52212 0.0484284 -0.418085
oI 0.714184 0.0645445 -0.404324 0.00782181 -0.416128 -0.023749 0.218703
KSI -0.71145 -0.0505 0.348867 -0.0806539 -0.0419 0.0422541 -0.224442
KG 0.118696 0.141965 -0.16891 -0.154624 0.826502 0.0569547 0.0520675
Gravel % 0.440292 -0.185024 -0.401863 -0.380001 0.410162 0.0241403 0.29606
Sand % -0.492496 0.147091 0.773693 -0.152454 -0.0209 0.115041 0.207194
Mud % 0.336577 -0.0752 -0.686018 0.384988 -0.1963 -0.145735 -0.403464
Table (III) shows the equations which estimate the common factors before any rotation is performed. For example,
the first common factor has the equation:
(-0.315223*Press1 + 0.485813*Press2 + 0.298821*Press3 + 0.614851*Temp1 + 0.511597*Temp2 + 0.434681*Temp3 -
0.278278*Humid1 - 0.566728*Humid2 + 0.248203*Humid3 + 0.546838*Speed1 + 0.548926*Speed2 - 0.183574*Speed3 -
0.165175*Mz + 0.714184*oI - 0.71145*KSI + 0.118696*KG + 0.440292*Gravel % - 0.492496*Sand % + 0.336577*Mud
%) ……………. (1)
The values of variables in the equation (1) are standardized by subtracting their means and dividing by their standard
deviations. It also shows the estimated communalities, which can be interpreted as estimating the proportion of the
variability in each variable attributable to the extracted factors.
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TABLE IV
FACTOR LOADING MATRIX AFTER VARIMAX ROTATION
Factor Factor Factor Factor Factor Factor Factor
1 2 3 4 5 6 7
Press1 -0.3831 0.0324797 -0.193392 0.665755 -0.339687 -0.38244 0.11097
Press2 -0.01414 0.00898 0.49593 0.570383 0.323667 0.395684 0.09702
Press3 0.08081 -0.0170113 0.146294 0.900535 -0.08548 0.207717 0.044808
Temp1 0.9523 0.0393692 0.0220839 -0.01391 0.0256961 0.07881 -0.07694
Temp2 0.8134 -0.0361566 -0.00898 -0.01167 0.168607 -0.138774 -0.147197
Temp3 0.8759 0.109421 -0.100755 -0.05343 -0.229886 -0.051739 -0.00043
Humid1 -0.551 -0.0449107 -0.0885141 0.031249 -0.0091 0.726026 -0.187843
Humid2 -0.5703 -0.0538689 -0.254201 -0.413699 -0.130636 -0.085889 -0.352986
Humid3 0.07253 -0.0135335 0.174197 0.13768 -0.01305 0.91983 -0.0202998
Speed1 -0.0471 0.136142 0.860252 0.143405 0.172701 0.00397 -0.0023
Speed2 -0.0086 0.0610503 0.978378 0.0913 0.023059 0.047638 -0.051622
Speed3 -0.0703 0.130034 -0.549543 0.071769 0.278712 -0.113194 0.114931
Mz -0.0459 0.0303765 -0.0811404 0.140769 0.0479641 -0.120241 0.8827
oI 0.1658 0.6709 0.291842 0.209713 0.035932 -0.01506 -0.539505
KSI -0.2084 -0.569368 -0.207435 -0.280465 -0.370318 0.0281 0.25229
KG -0.10672 -0.0408357 0.0213517 -0.01651 0.819784 0.0531 0.295116
Gravel % 0.15316 0.265105 -0.0255873 -0.14685 0.762563 -0.0488 -0.301004
Sand % -0.02707 -0.936872 0.045197 0.102904 -0.2256 0.02459 -0.00272
Mud % -0.0494 0.950765 -0.04015 -0.0425 -0.148454 -0.0051 0.168677
Table (IV) shows the equations, which estimate the common factors after rotation has been performed. Rotation is
performed in order to simplify the explanation of the factors. The first rotated factor has the equation:
(-0.383039*Press1 - 0.0141323*Press2 + 0.0808109*Press3 + 0.952251*Temp1 + 0.813432*Temp2 + 0.875989*Temp3 -
0.550952*Humid1 - 0.570342*Humid2 + 0.072529*Humid3 - 0.0470526*Speed1 - 0.00864736*Speed2 -
0.0702393*Speed3 - 0.0458609*Mz + 0.165772*oI - 0.208318*KSI - 0.10672*KG + 0.15316*Gravel % - 0.0270733*Sand
% - 0.0493532*Mud %) ……………(2)
The values of variables in the equation (2) are standardized
by subtracting their means and dividing by their standard
deviations. It also shows the estimated communalities,
which can be interpreted as estimating the proportion of the
variability in each variable attributable to the extracted
factors.
As might be expected, the variables are highly
correlated, since most are related to climatic variation.
Recommended methods of computation using data input of
the original observations, the sample covariance matrix, or
the correlation matrix of the original data, as well as its log
(10) values of the original data; all methods are tested and
gained the same output. As the variables are in different
units, it is usually best to base the analysis on the correlation
matrix (which is the default of the presently applied
Statgraphics program).
The purpose of the analysis is to obtain a small
number of factors, which account for most of the variability
in the 19 variables. In this case, 7 factors have been
extracted, since 7 factors had eigenvalues greater than or
equal to 1.0 (Fig. 15). Together they account for 82.8059%
of the variability in the original data.
IV. INTERPRETATION OF FACTOR ANALYSIS RESULTS
Figure (15) is a plot of factor loadings of 19 meteorological
and size grade data collected monthly along six years (2000
to 2005) from the western bank of Lake Nasser. The lengths
of the 19 original variables are proportional to its
contribution to the factor loads. (Figure 16) reflects how
each variable weight the first two components. The angel
between any two variables is inversely proportional to the
correlation between them i.e. the larger the angle, the more
negatively correlation between the two variables, and vice
versa [30]. The SKI - ơI line subdivided the analyzed 19
variables variables into two clusters, these are:
- Sand and Gravel cluster: (all temperature variables,
minimum humidity and minimum pressure).
- Mud (Silt+clay) cluster: (mean and maximum pressure,
humidity and wind speed together with Mz and KG)
Variables of these two clusters are antagonized in their
behavior, implying increase of sand and gravel fractions in
prevalence of minimum humidity and minimum pressure at
all different temperatures. This increase in sand and gravel
occurs take place on expenses of the mud (silt and clay)
fraction. On the other hand, the increases of sand and gravel
fractions are positively correlated with increases of
temperature and minimum humidity. In other words, the
amount of deposited sands and gravels greater in values in
all the three-temperature variables, mean maximum and
minimum temperatures. Moreover, variability on the
weather temperature is closely related to variability in
amount of sand and gravel. Increase in these two size
fractions are a character of negative relation with (i.e.
decrease) Mz and KG values. Figure (17) is designed to
explain the interrelationship between sand size grades and
size parameters. Smaller values of Mz and KG can be
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol:13 No:03 33
137703-5959-IJCEE-IJENS © June 2013 IJENS I J E N S
interpreted as finer grained sand deposit having normality of
distribution inclined to the coarse fractions. The following
part is a trial to explain the result of factor analyses given in
Table (V) on bases of reasons of aridity given by [17].
Fig. 15. Seven factors have been extracted, since 7 factors had eigenvalues greater than or equal to 1.0.
Fig. 16. Plot of factor loadings of 19 meteorological and granulometric data
The original factor matrix (Table III) before rotation has
first been derived from classical factor analyses of
correlation matrix of log 10 values of meteorological data
and grain size data collected monthly for a consequence of
six years (2000-2005) from seven sites along the western
side of Lake Nasser. Varimax rotated factor matrix is listed
in (Table IV) after rotation. To this end, seven eigenvalues
account for more than 82 % of the total variability are
considered herein. (Table V) is an arranged list of values of
Varimax rotated factor loads, values less than 0.2 are
deleted. Accordingly, the different seven factor-loads are
named and their individual properties (for every column) are
delineated below. However, every factor includes two
groups of inversely correlated variables, implying
antagonized distribution of sand-grades or size parameters
with the different meteorological variables. The seven
factors are named as following:
- Temperature Factor: (Temp1, Temp2, and Temp3)
inversely correlated with (Humid 1, Humid2, Press1, and
skewness)
- Mud Factor: (Mud, ơ1, Gravel%, Speed1) inversely
correlated with (Sand%, SK1, Humid1, and Humid2)
- Speed Factor: (Speed2, Speed1, Press2, and ơ1) +
inversely correlated with (Speed3, Humid2, and SK1)
- Pressure Factor: (Press3, Press1, Press2, and ơ1)
inversely correlated with (Humid2, and SK1,)
- Gravel Factor: (KG, Gravel, Press2, and speed3)
inversely correlated with (SK1, Press1, Temp3, and sand
%).
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- Humidity Factor: (Humid3, Humid1, and Press2)
inversely correlated with (Press1, Temp2 and Mz)
- Mean size Factor: (Mz, KG and SKI) inversely correlated
with (ơI, Humid2, and Gravel %).
1. Temperature Factor: this factor seems to represent pure
meteorological factor emphasizing the air temperature as the
paramount controlling variable amongst the 19 analyzed
variables. This factor weights heavily on deposition of
aeolian sands at the western bank of Lake Nasser. It shows
that values recorded for air temperature in the studied seven
sites juxtaposed the lake, along six years‟ time (from the
year 2000 to 2005) are inversely correlated with variables of
mean and maximum humidity and mean pressure. Decreases
in pressure and humidity associated with increases in air
temperature can safely be attributed to the high reflectivity
(albedo) of desert surfaces [ 31]. That may cause net loss of
radiative heat, create a horizontal atmospheric temperature
gradient from the hinterlands to the coastal area of the lake,
and on to the relatively colder water body of the lake. That
induce subsidence of the land-heated -air over the Lake
water and induce air circulation in a manner similar to the
day breath occurs between the land and seas. Moreover the
increase in values of temperature factor is also associated
decrease in SkI values of the depositing sand, suggesting
deposition of (Leptokurtic) sand.
2. Mud Factor: This factor controls the amount of mud
fraction in the studied 73 aeolian sand samples. Enrichment
in mud fraction in the analyzed samples is associated with
enrichment in gravel fraction together with increase of two
other variables namely, ơ1 values and mean wind speed. All
the four variables are inversely correlated with amount of
sand fraction, skewness, mean and maximum values of
relative humidity. The peculiar association of gravel fraction
with mud fraction is definitely pointing to two subsequent
phases of sedimentation, both of them are relatively rich in
its own component. However, as every sample composes of
three fractions, it is logically to find inverse relations of the
mud and gravel fractions on one hand and the sand fraction
on the other. Moreover, the original values of mean wind
speed are the result of dividing all measured wind speeds by
their number (73 samples), then the speed1 factor includes
maximum and minimum measures. Consequently, the
increase in mud and gravel fractions taking place on
expenses of the sand fraction , implying removal of some
sands and deposition of creeping gravel grains moving from
the windward side (from the desert land to the beach zone of
the Lake Nasser). This mechanism occurs during relatively
high wind velocity capable of moving the sand fraction and
replacement of gravel fraction by creeping over the ground
surface. This process, as indicated from the inverse
correlation of wind speed with humidity, took place in
relatively dry times. As the mud and gravel fractions are
considered high in values, then (ơI) will also be in the same
side, i.e. higher ơI values. Whilst Skewness (SKI) should be
low, i.e. coarsening tail.
3. Speed Factor: Increase in maximum and mean wind
velocities concomitant with maximum pressure are character
of poorly sorted (higher ơI values) sands. This is inversely
correlated with minimum speed, maximum humidity and
lower Ski vales i.e. coarsening tail sands. The general
characters of the aeolian sands collected from western
beaches of Lake Nasser that took place in these
meteorological parameters will then be poorly sorted sands,
never been coarsening tail sands and can „not formed in
minimum speed, or maximum humidity. Maximum Wind
speed coupled with maximum pressure meteorological
parameter occurred due to movement of monsoons from the
southern part of Egypt and reaches until Qena city in the
Nile valley. The monsoons are usually bears humidity, but
the present equation denied the maximum humidity to
couple with wind speed. This can be interpreted by lose of
relative humidity during the pass of the monsoons over
Ethiopia and Sudan dry lands in summer times.
4. Pressure Factor: It contains all pressure variables
including mean, maximum and minimum pressure together
with sorting (ơ1) of the sand samples. Those variables are
inversely correlated with maximum humidity and skewness
of the sand samples. On other words, the properties of sand
samples that took place in high values of pressure and
lowest values of maximum humidity comprises high values
of (ơ1) and lowest values of SKI, poorly sorted coarsening
tail sand deposits inclining in its normal distribution to very
coarse and coarse sand where the gravel fraction is missed
herein. The meteorological high pressure in the study arid
area most probably occur in the winter time due to trade
wind conversion which force air to rise forming Hadley Cell
over the North African Sahara Belt where warm air rise and
cold air sinks. This environmental circumstance can also led
to torrential rainfall [16].
5. Gravel Factor: This factor stresses on the highest
weights of kurtoses, gravel %, maximum pressure and
minimum speed in one hand which inversely correlated with
the lowest weights of skewness, mean pressure, minimum
temperature and sand %.. Properties of the aeolian sand
samples at issue can summarized as it a character of
sediments composed mainly of sand and gravel fractions.
Enrichment of the gravel is in expenses of the sand fraction.
Mud fraction is excluded in this factor as its weights are
very low (less than 0.2 in Table V), that permitted to ignore
the mud (silt and clay) fraction. The sediment is a character
of sands its sorting inclined to finer portion of the
cumulative probability distribution curve forming
platykurtic sand including relatively highest values recorded
percentages of gravel that found in the highest recorded
maximum pressure, and minimum wind speed. The inversed
correlation with these variables can put forwards some
further properties of the sediments, where it should not low
in skewness i.e. fining tail required mean or maximum
temperature and higher pressure than the mean pressure.
This meteorological environment of high pressure occur in
the winter time due to upwelling of warm air of trade wind
forming Hadley Cell over the North African Sahara Belt
[32].
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol:13 No:03 35
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TABLE V
ARRANGED FACTOR LOADS OF VARIMAX ROTATED FACTOR (VALUES LESS THAN 0.2 ARE DELETED)
Factor
1
Factor
2
Factor
3
Factor
4
Factor
5
Factor
6
Factor
7
0.952 Temp1 0.95076 Mud % 0.978 Speed2 0.900 Press3 0.819 KG 0.92 Humid3 0.88 Mz
0.875 Temp3 0.6709 oI 0.860 Speed1 0.665 Press1 0.762 Gravel
% 0.73 Humid1 0.295 KG
0.813 Temp2 0.26510 Gravel
% 0.495 Press2 0.570 Press2 0.323 Press2 0.39 Press2 0.252 KSI
oI Speed1 0.292 oI 0.209 oI 0.278 Speed3 0.21 Press3 0.168 Mud %
Gravel
% Speed3 Humid3 Speed1 Speed1 Temp1 0.114
Speed
3
Press3 Temp3 Press3 Mz Temp2 KG 0.110 Press
1
Humid3 Speed2 Sand % Humid3 Mz Speed2 0.097 Press
2
Speed2 Temp1 Temp1 Sand % oI KSI 0.045 Press
3
Press2 Press1 KG Speed2 Temp1 Sand % -0.001 Temp
3
Sand % Mz Temp2 Speed3 Speed2 Speed1 -0.002 Speed
1
Mz Press2 Gravel
% Humid1 Humid1 Mud %
-
0.0027 Sand %
Speed1 Humid3 Mud % Temp2 Humid3 oI -0.020 Humid3
Mud % Press3 Mz Temp1 Press3 Gravel
% -0.051
Speed
2
Speed3 Temp2 Humid1 KG Humid2 Temp3 -
0.0767 Temp1
KG KG Temp3 Mud % Mud % Humid2 -
0.1472
Temp
2
-0.208 KSI Humid1 -0.193 Press1 Temp3 -0.23 Sand % Speed3 -
0.1878 Humid1
-0.383 Press1 Humid2 -0.208 KSI Gravel
% -0.23 Temp3 Mz -0.301
Gravel
%
-0.550 Humid1 -0.5693 KSI -0.254 Humid2 -0.280 KSI -0.34 Press1 Temp2 -0.353 Humid2
-0.570 Humid2 -0.936 Sand % -0.549 Speed3 -
0.4136 Humid2 -0.38 KSI -0.38 Press1 -0.54 ơ1
Fig. 17. Sketch of cumulative probability curve and nomenclature applied to describe and interpret the statistical factor analyses.
Notes: names applied according to values: fining tail= higher SKI, coarsening tail=lower SKI Finer sand= lower Mz
Coarser sand=higher Mz
Inclined to coarse, sorting=lower KG
Inclined to fine, sorting=higher KG
Well sorted=lower I
Poorly sorted=higher 1
International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol:13 No:03 36
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6. Humidity Factor: (Humid3, Humid1, and Press2)
inversely correlated with (Press1, Temp2 and Mz). This
factor provides the precise alliance of mean and minimum
humidity to maximum pressure variables and opposition of
values of these behavior with values of the mean pressure,
maximum temperature and the prevailing mean size (Mz) of
the mechanically analyzed 73 aeolian sand samples.
Properties of the sand sediments herein dose seem to
represent sands of lowest mean size (fine grained) formed
under weather condition of mean (average 29.59) and
minimum (average 8.82) humidity and maximum pressure
ranging between 987.90 and 1049.50 with an average of
1009.86 mbar. The higher the humidity and pressure the
lower the mean size of the deposited aeolian sands in the
western bank of Lake Nasser.
7. Mean size Factor: (Mz, KG and SKI ) inversely correlated
with (ơI, Humid2, and Gravel %) . This factor collect all the
sited size parameters [24]. Mz, KG and SKI as a group are
inversely correlated with Sorting (ơI), maximum humidity
and percentage of gravel fraction in the aeolian sand
samples analyzed. The increase in mean size and in values
of KG specifically “sorting inclination to finer fraction of
sand”, and increase in SK1 i.e. fining tail sediments (
inclination to silt and mud fraction), all these properties
occurs with sediments character of low values of (ơ1) i.e. ill
sorted sands include low percentage of gravel. This type of
sands cannot be formed in meteorological environment
character of maximum humidity ranging between 37.80
and 38.00 with a mean value of 83.00 %.
V. CONCLUSION
Combination of the grain size data with meteorological data
is achieved and sediment transport is statistically explored to
establish a sedimentological model of the transported sand
grades and the covariant meteorological parameter at the
western beaches of Nasser Lake. A total of 19
meteorological variables including three values of size
grades (gravel, sand, and mud %) and four values of grain
size parameters calculated according to Folk and Ward
(1957) are considered herein. Every meteorological variable
(wind pressure, temperature, humidity, and wind velocity) is
listed in three consecutive columns designated in numbers
(1, 2, 3) corresponding to mean, maximum, and minimum
values, respectively. Numbers of observation imputed are 73
rows of complete cases represent 1168 values including all
the collected and calculated mean monthly meteorological
data and grain size parameters. Data are studied by factor
analyses to learn the relative importance of each principal
variable in determining the variations among the samples,
and to examine the paramount controlling factors governing
the size distribution and the calculated size parameters of
blown sand in an ideal arid region. Seven factors comprise
temperature, mud, wind speed, pressure, gravel, humidity
and mean size are recognized. These are represent the
paramount controlling factors governing the size distribution
and the calculated size parameters of blown sand in hyper
arid and arid regions. The total annual estimated volume of
transported sand which falls down into Lake Nasser basin
are currently under calculation using artificial sand traps and
other techniques.
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