factor analysis of meteorological and granulometrical data...

International Journal of Civil & Environmental Engineering IJCEE-IJENS Vol:13 No:03 21

137703-5959-IJCEE-IJENS © June 2013 IJENS I J E N S

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).



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



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].



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).



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



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



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



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



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



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.



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.



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



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

%).



- 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].



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



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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