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Abstract:
A huge amount of sediment concentrates along the southern 150 km of High Dam reservoir. Systematic surveying has been carried out and developed since 1973, but never takes into consideration the whole reservoir bed surface. The reservoir’s bed varied obviously, its characteristics a few kilometers beyond the main cross sections completely different according to the geological structure of main rocks.

Hence, GIS’s spatial analyst, 3D and geostatistical analysts extensions were used to predict the reservoir bed surface, and estimate the total amount of sediment that formed since constructing High Dam directly. The results will help evaluating the reservoir capacity.

PROBLEM DESCRIPTION
The estimation of reservoir bed level based on the results of hydrographical surveying is significantly important for studying sedimentation phenomena. It could be of prime interest for modeling sediment mass, the investigation of sediment transport, etc. The data of hydrographical surveying of some cross sections always used for the analysis of sedimentation phenomena, surveying of greater part of reservoir area is required, especially in case of huge reservoirs, beside the average accuracy of the systematic method used, it is important to achieve a good accuracy for the data which highly affect the results. Two methods of modeling are appropriate for our study, RBF and Kriging. In this paper one of them was selected as more convenient for elevation modeling.

Our study area is the southern 150 km of 500 km, the total length of the reservoir, where the velocity begins to reduce that forms a huge delta within 380 km up stream High Dam body. The bed of the reservoir varied obviously, in addition, the characteristics of the sections a few kilometers beyond the main cross sections are completely different, for example, variation in bed levels at zone of cross section No. 19 are shown in Figures 1 and 2. Hence, the systematic method which considers only the cross sections taken separately along the reservoir length is not enough to represent the variation in the bed level.

CONCEPTUAL FRAMEWORK
We can estimate the complete bed surface of High Dam reservoir in different two periods, and calculate the sediment’s volume directly between these two surfaces.

Use of the available records surveyed in the current year to predict the bed levels in non-surveyed zones will result the complete bed surface in the current year, while use of 1949’s digitized records will result the complete bed surface in 1949. Then by subtracting volumes we get the quantity of sediment accumulated from 1949 to the current year as one plot.

Note: Whereas water has been storing since 1964, the measurements of bed levels taken in 1964 were added to the dataset to make the surface closed to 1964’s surface as possible.

Figure 3 shows the zones to be estimated between some of surveyed zones.


Northern profile:Mean Bed Level = 156 m.   Middle profile:Mean Bed Level = 153 m.

Southern profile:Mean Bed Level = 168 m Interpolation process will give enough data to estimate cross sections like this completely

Longitudinal section:Bed level clearly varies along the longitudinal section
Figure 1: Variation in bed levels of cross section No.19

Figure 2: Variation in bed levels of cross section No.19



SOURCE DATA
This report is devoted to the application of GIS for estimation of reservoir bed levels. The primary dataset includes 258236 digitized records that represent the reference of calculation. They were digitized from old River Nile stream map (scale 1/25000) surveyed in 1949. The map was highly damaged as shown in Figure 4. Contour lines were digitized as point’s shapefiles to be used in the interpolation process, digitizing has stopped at the expected maximum water level as shown in figure 5.




Hydrographical data surveyed in the current year’s scientific mission were also used for data processing as the current dataset. The area to be characterized spans approximately 157 km length.

EXPLORATORY DATA ANALYIS
To check the accuracy of interpolation process, a test of 27929 data sample was done, interpolation carried out four times with reducing the number of points every time. By comparing the results, the calculated volumes between a constant reference and the input surfaces are approximately the same as shown in Figures 6,7,8, 9 and table 1.







These results mean that the model used in the interpolation process and its protocol had a high accuracy. In addition, the statistical analysis will confirm this hereafter.

Two datasets include 258236 and 367659 data were used for predicting bed surfaces in 1949 and the current year respectively, as shown in Figures 10 and 11.




Statistical exploratory
Histograms and QQplots of elevation records show that the data are not normally distributed as shown in Figures 12,13,14 and 15.




Semivariograms
A variogram is a function of the distance and direction separating two locations, used to quantify autocorrelation. The goal is to fit the best model (yellow line) to the semivariogram. Semivariograms show that the points are close to the yellow line in directions 32.9? & 33.5? and are spread out in directions 74.1? & 135? for years 1949 & the current year respectively. This means that there is a directional autocorrelation in our data (anisotropy factor is not equal 1). In other words, there are many factors affect the sedimentation Phenomena. See Figures 16,17,18 and 19.




THE SELECTING OF MODELING METHOD
The following peculiarities of the problem to be solved will affect the selection of the appropriate modeling method:

• The values of elevations cannot have random distribution or be a random function realization. Thus, kriging method, most typical for geostatistical, does not seem to be appropriate in this case.
• There is a general trend affect the phenomena that help using kriging method.
• To make an informed decision as to which model provides the best predictions, the calculated statistics serve us diagnostics that indicate whether the model and/or its associated parameter values are reasonable. We compared the predicted values and the observed values, from this get useful information about the selected model. Mean prediction errors and root mean square errors (RMS) were 0.000197m & 0.2551 for RPF versus –0.00282 m & 1.277 for kriging as shown in Figures 20 and 21.

From these considerations the Radial Basis Function by spline with tension was used, while interpolation using Kriging method was disqualified.

SURFACE UNDER RBF EASTIMATION
The method selected for the spline with tension interpolation is one of the deterministic interpolation methods used in Geostatistical Analyst; a special case of RBF. The interpolated surface is forced to go through the data. The RBF is used for calculating smooth surface from a large number of data points. The functions produce good results for gently varying surfaces such as in our case. The technique is inappropriate when there are large changes in the surface values within a short horizontal distance and/or when we suspect the sample data is prone to error or uncertainly.

PREDICTION RESULTS
Accepting of the model depend on the results of geostatistical analysis. Cross-validation is the procedure where one data is removed and the rest of the data is used to predict the removed data. Full cross-validation is done by removing each data in the dataset and using the rest of data to predict it. The differences between the measured values and the predicted values are calculated, the mean value is called “mean prediction error” and it should be near zero.

We would like our prediction to be as closed to the measurement values as possible. The root-mean- square prediction errors point to this and can be used to compare different models. The smaller the root-mean-square prediction error the better.

The results of prediction process are shown in Figure 22, we have got the first complete surface for High Dam reservoir bed.

Figure 23 shows the net surfaces in 1949 and in the current year. Now we can get the total amount of sediment accumulated from 1949 to the current year by calculating volume between these two surfaces.




MODEL’S PROTOCOL
Table 2 below shows the RPF’s protocol used for modeling surfaces.

COORDINATE SYSTEM
The coordinate system was derived from the Universal Transverse Mercator (UTM), zone 36 north projection.

RESULTS DISCUSSION
To check out the accuracy of estimation process, the predicted values were reversal used as measured values to predict volume once again, the percentage of accuracy was 100%.

As shown in Figure 22, symbology tool was used to classify range of elevations. So, it will be easy to focus the places of erosion and sedimentation and calculate a particular volume.



Changes in stream from 1949 to the current year give a good idea about the river’s behavior as shown in Figure 24.




CONCLUSION
To calculate the sediment’s amount, a model of estimating the complete reservoir bed surface must be taken into consideration, because of the highly variation in bed levels as shown in Figure 25.

REFERENCES
Bob Booth, Using ArcGIS 3D Analyst, copyright (2001) ESRI.
Jill McCoy & Kevin Johnston, Using ArcGIS Spatial Analyst, copyright (2001) ESRI.
Kevin Johnston, Jay M. Ver Hoef and Neil Lucas, Using of ArcGIS Geostatistical Analyst, copyright 2001 ESRI.
Melita Kennedy and Steve Kopp, Understanding Map Projection, copyright (1994 – 2000).
Michael Zeiler, Modeling Our World.
Public Authority of High and Aswan Dams, Annual Reports of Sedimentation Study. Since (1973).