Bathymetric information is essential for understanding the ecosystem of a lake  . The characteristics of the lake basin morphology have an important influence on the interactions between biological, chemical and physical properties of aquatic environments  . Furthermore, ignorance of lake depth leads to quantitative errors in the evaluation of general transport processes such as sedimentation, resuspension, diffusion, mixing, burial and outflow  . Therefore, the bathymetry of the lake’s bottom directly impacts many water quality parameters such as thermal properties, internal phosphorus recycling, water clarity, suspended particulate matter and many chemical variables   . The bottom morphology of a lake can be greatly influenced by deposition of sediment carried by inflowing rivers and streams. Although this process can be modified by wave and current action  .
Despite the importance of Bathymetric surveys for lakes and reservoirs, most developing countries face obstacles in this field. The cost of surveying equipment and the location of these reservoirs within unsafe regions are the biggest obstacles. The main objective of this study was to build a 3D model for the Mosul Lake bathymetric base from digital elevation data. Remote sensing data had been used to map the Mosul Lake coastline during the period of study, March and July 2011. Furthermore, a set of ordinary kriging models were tested to select the best simulation for the bathymetric dataset. The calculated values of selected bathymetric models were compared with observed field survey data to check the accuracy and observe the developing of the lake bottom during the time of reservoir operation. A 3D TIN model of Mosul Lake was designed to support decision-makers with managing the reservoir. Furthermore, models are an effective tool to understand changes in the lake environment regarding the impact of changing seasonal water storage volume.
2. Description of Study Area
First, confirm that you have the Mosul Dam Lake is an artificial reservoir located between latitude (36˚36'N - 36˚50'N) and longitude (42˚27'E - 42˚58'E) on the Tigris River about 60 km north of Mosul City and 80 km from the borders of Syria and Turkey Figure 1. The surface area of the lake is about 385 km2; the length is about 45 km and the width ranges between 2 and 14 km at the maximum operation level (330 meters above sea level) with a maximum storage volume of 11.11 × 109 m3 and a maximum water depth of 80 m. Its drainage basin covers 4200 km2 inside Iraq    . The majority of the water entering the lake comes from Turkey. The mean annual discharge of the Tigris River was in the range from 270 to 1371 m3/s for the period from 1931 to 1997 at Mosul station  . Usually, the highest monthly discharge occurs during April and May and there is less discharge in October and September.
In the current study, remote sensing data were used to automatic waterline extraction for Mosul Dam Lake. A bathymetric model of the lake was constructed from a 30 m SRTM dataset. Field data survey and topographic maps were used
Figure 1. Location map of study area.
to verification and correction the model. The exact locations of the measurements were determined using a Garmin eTrex Legend Cx GPS.
3.1. Data Bathymetric Collection
The dataset of the Mosul Dam Lake bathymetry model analysis included 6424 geo-referenced elevation points. These points derive from, a 30 m SRTM dataset of Iraq was supplied by the U.S Army. The topographical maps were obtained from the Military Survey Office before and after the dam construction at a scale of 1:100,000 were used to check and correction the values of Mosul waterline lake. Finally, the field water depth points were measured with the Water Quality Probe (YSI 6600 V2) and standard field survey equipment used to verification the model. During field work, the elevation of the lake’s surface measured in March was 307 m.a.s.l, and in July it was almost 322 m.a.s.l. A Garmin (etrex) GPS was used to fix the geographical coordinates of field water depth points.
3.2. Coastline Extraction
A coastline is a line separating land and water mass. It is a ground feature used to obtain the orientation and shape of land and water   . Optical remote sensing data can be used to detect the shoreline using either digitization or ratio images  . In the current study, the normalized difference water index (NDWI) was used for automatic delineation of the coastline of Mosul Dam Lake from satellite images. TM5 and ETM+ images downloaded from the US Geological Survey (USGS) database (http://glovis.usgs.gov/) were used to capture the waterline of Mosul Lake. The Landsat program as an L1T product is used to catalogue the images, which are georeferenced with a level of precision exceeding 0.44 pixels (meaning 13.4 m)    . ETM+ and TM5 images were captured in March and July 2011, consequently. The images were picked up simultaneously with the operation of water quality sampling. More details on image attributes, enhancement and correction are provided by Khattab and Merkel (2014)  .
In the current study, the NDWI used for TM5 and ETM+ images was as follows   :
where ρNIR, ρSWIR, and ρGreen are the reflectance of the near-infrared band (band 4), the short-wave infrared (band 5), and the green band (band 2), respectively.
The results of waterline extraction for Mosul Dam Lake between March 5, 2011 and July 3, 2011 are shown in Figure 2. The surface area of the lake was 142 km2 during March and 285 km2 during July, and the difference in the surface area of the lake during the two periods was more than 33%.
Figure 2. Coastline of Mosul Dam Lake during March and July 2011.
3.3. Interpolation Technique
After pre-processing of the elevation and depth dataset (geographical position union and calibration between DEM and topographical map data points), these points values were merged into a database with 6424 points. The kriging or co-kriging interpolation method was used to build a digital terrain model of Mosul Lake’s bathymetry. This method is a powerful geostatistical interpolation technique based on the spatial correlation of sampled points   . The predictive values are derived by using weighted averages of known input point values   . Kriging to estimate the depth at a spatial point weight Z(u) defined as a linear regression estimator was recorded as below  .
where u and uα are spatial locations of an observation point and one of the neighboring data points, indexed by α, n(u) is the number of data points in the local neighborhood used for estimation, m(u) and m(uα) are the expected values (means) of Z(u) and Z(uα), and λα(u) is the kriging weight assigned to datum Z(uα) for estimation location u. In the current study, ordinary kriging type was selected to interpolate the bathymetry dataset, where this method gives the best statistical results.  . Ordinary kriging is a linear weighted-average technique which is unbiased with regard to the expected value of residuals  . In this context, we assume that the mean is constant in the local neighborhood of each estimation point and m(u) = m(uα) for each nearby data value and Z(uα) is used to estimate Z(u)  . Hence, the kriging estimator can be written as  .
These previous complex geospatial equations were applied in ArcGIS. The geostatistical analysis option in ArcGIS was used to interpolate the dataset of Mosul Lake’s bathymetry.
3.4. Volume Calculation
There are various techniques for 3D visualizing data on digital terrain models. The regular grid surface (grid) and TIN are among the more well-known techniques  . TIN formulas have been used successfully to visualize non-homo- geneous surfaces  . Hence, TIN models are used for the accurate control of the terrain slope, aspect, surface areas, volumetric and cut/fill analysis, and for generating contour lines   . A TIN is a vector terrain model using Delaunay triangles to join points in the three-dimensional space  . In the model, all the triangles for a set of points have a circumscribing circle without other vertices  . This method provides a set of unique vertices and allows repetition of the calculations and validation of the results separately  . This spatial distribution of triangles is the best to reflect the relief of the surface  . For the study area, triangles were created between the non-uniform bathymetric mapping data points of the lake (Figure 3).
Figure 3. Subdivision of the lake into Delaunay triangles using the TIN approach for generating a digital bathymetric model of the study area.
4. Results and Discussion
4.1. Bathymetric Mapping Analysis
The ordinary kriging (co-kriging) interpolation method was used to assign depth values to 84,838 geo-referenced points (Figure 4). Root mean square error (RMSE), mean standardized error (MSE), mean error (ME) and average standard error (ASE) were calculated to check the performance of the ordinary kriging models (Table 1). The calculated errors served for comparing the ordinary kriging interpolation models. Generally, RMSE is used to indicate how closely the values predicted by the model are to the measured values, MSE is used to estimate the uncertainty in predicting a population mean, and ASE is used to evaluate the accuracy of the prediction model’s average values. ME is used for determining the degree of bias in the estimates    . The different errors are calculated as follows:
Figure 4. Bathymetric map of Mosul Dam Lake determined using the ordinary kriging interpolation method.
Table 1. Results of root mean square error (RMSE), mean standardized error (MSE), mean error (ME) and average standard error (ASE) determined with the ordinary kriging models for the depth prediction of Mosul Lake.
Most values of the accuracy error indicated that the stable ordinary kriging model is fit to predict the depth of Mosul Lake. Generally, MSE, ASE and ME were lower for the stable model than for the other models (Table 1). Furthermore, the cross-validation scatter plot for predicted and measured depths value showed that the data prediction of this model was better correlated with the measured depth dataset (Figure 5).
After having selected the model, the interpolation process included optimizing the semivariogram model of the dataset. Semivariogram is a graphical form exemplifies calculation of semivariances for different values of distance   . A typical example of semivariogram with its component is shown in Figure 6.
Figure 5. Comparison of the cross-validation (predicted vs. measured depth) of Mosul Lake by ordinary kriging models: (a) circular, (b) exponential, (c) Gaussian, (d) spherical and (e) stable (the blue line is the fitted line and black lines represent a perfect fit 1:1).
The classical semivariogram is calculated by using the following formula   .
where γ is the calculated semivariogram of the variable v at the separation distance and direction specified by the ‘‘lag’’ vector h, the xi are the data locations and n is the number of data pairs separated by h  . Stable model is a powered exponential variogram calculated as  .
where c is the total variance or sill parameter, r is the range parameter, and p is the asymptotic power-law exponent  . For additional information on other models and semivariogram components can be found in several textbooks on geostatistic   . The statistical parameters of the semivariogram which was used for the interpolation of the lake depth values are shown in Table 2.
The relationship between modeled water depths values by ordinary kriging method and observed values for 25 locations are presented in Figure 7. The accuracy water depth showing that the predicated valued are more accurate in shallow water. Also, this figure present in general that the interpolated values at deep region are more than observed, where the heterogeneous terrain with varying slope and curvature impact on the accuracy of modeled values  . Generally, the model operates very well with R2 (0.98).
4.2. Volume Calculations
A three-dimensional TIN model was generated to represent the bottom surface of Mosul Dam Lake (Figure 8). Generally, results of interpolation are used to form the previous figure with 10 m depth intervals, a minimum depth of zero meters and a maximum depth of 80 m. The elevations of the lake bottom are calculated along the triangulation plane by determining the elevation for each triangular unit. The area and volume were estimated by simple pixels calculation
Figure 6. A theoretical example of semivariogram model showing different components  .
Table 2. Statistical parameters of the semivariogram model for which the ordinary kriging method was used to predict the depth of the lake.
*R2 is the coefficient of determination between predicted and measured depths.
Figure 7. Plots the modeled water depth values against the observed field values with field depth point’s map.
Figure 8. Plots the modeled water depth values against the observed field values with field depth point’s map.
for the TIN model. The calculation included 18,275 triangles and (10,081) nodes, and 1 m elevation tolerance with a 0.99 scale factor. The area projection of the TIN model is Transverse-Mercator with a projected coordinate system WGS-1984, UTM_Zone_38N. Value of area and volume was calculated from the TIN for the entire lake at different elevations (Table 3).
The water storage volumes of Mosul Lake which were calculated by the TIN model were compared with the storage values estimated in 1968 by an IVO operational curve, (Figure 9) for the same elevation (Table 4).
The values of elevation vs. volume were extracted from the operation curve of Mosul Lake by using the Plot Digitizer program. The differences between the
Table 3. Area/volume from triangulated irregular network model of Mosul bathymetric data collected in 2011.
Table 4. The differences in storage volume between the TIN model from 2011 and the IVO operation curve from 1968.
Figure 9. Operating curve of Mosul dam reservoir (IVO 1968)  .
storage volumes of the lake calculated by the TIN model and the IVO operation curve (Table 4) are the result of sedimentation during the lake’s operating time. Generally, the sedimentation rate is high in the elevation range of 321 to 303 m above sea level. Also, the result of the lake volume analysis showed that the change in water volume between March and July 2011 was about 3.8 × 109 m3.
The current study explored the ability and certainty of extracting bathymetric map data for the Mosul Dam Lake from a digital elevation model. The study recommended an approach for monitoring volume water storage of this reservoir using remote sensing data and GIS techniques. The methodology tested proved that the ordinary kriging interpolation method is the best model that can be applied to develop bathymetric maps of this lake. Furthermore, the verification performance of this model with observed field data values confirmed the high efficiency for the selected model. This study showed that Mosul Lake has lost about 10% of its ability to store water up to 2011. This could be a result of trap efficiency, where sediment from the Tigris River is deposited behind the dam as well as in the valleys around the lake. Also, the Mosul reservoir witnesses high seasonal variation of storage water reaching to 3.08 × 109 m3 which may lead to fluctuations in environmental conditions. Although, the calculated values of depths in the deeper regions have errors, the proposed model is still highly recommended over the more expensive traditional bathymetric data collection methods such as boat and radar in such a region of the world.
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